Semiconductor device simulation method and calculation program

Abstract

Provided is a method for calculating the mobility of an oxide semiconductor capable of more accurately calculating the mobility of various oxide semiconductor materials. The method for calculating the mobility of an oxide semiconductor by using a computer includes a step for causing the computer to execute a step for calculating the mobility using two or more terms, which are calculated using a free carrier concentration in the oxide semiconductor, wherein the two or more terms are calculated using a scattering model derived in consideration of generation on the basis of the free carrier concentration in the oxide semiconductor, or a regression model generated on the basis of actual measurement values ​​of the mobility and the free carrier concentration.

Description

Semiconductor device simulation method and calculation program

[0001] The present invention broadly relates to semiconductor device simulation methods and calculation programs, and for example, to methods for calculating the mobility of oxide semiconductors, device simulation methods, methods for manufacturing semiconductor devices, semiconductor devices, information processing devices, and device simulation systems.

[0002] Thin-film transistors using amorphous silicon (a-Si) or low-temperature polysilicon (LTPS) have been used conventionally, for example, in display manufacturing. Device simulation technology has already been established to calculate the mobility of a-Si semiconductors and design devices based on the results obtained.

[0003] In recent years, thin-film transistors using amorphous oxide semiconductors (IGZOs) have come into use in display manufacturing and other applications. However, in the case of amorphous oxide semiconductors (IGZOs), when the above-mentioned mobility calculation method (a-Si model) is used, there is a discrepancy between the calculated mobility and the measured value, indicating that the a-Si model cannot be applied. Therefore, a method for accurately calculating the mobility of amorphous oxide semiconductors (IGZOs) has been developed, and amorphous oxide semiconductor (IGZO) device simulation technology (Tokyo Model) has been established (see Non-Patent Document 1, etc.).

[0004] On the other hand, in recent years, development has progressed on polycrystalline oxide semiconductors, mainly composed of in, which have higher mobility than amorphous oxide semiconductors (see Non-Patent Document 2, etc.).

[0005] "Temperature Properties of Amorphous In-Ga-Zn-O Thin-Film Transistors with a new Mobility Model", The Simulation Standard, October 1, 2017 (https: / / silvaco.com / dynamicweb / jsp / downloads / DownloadDocStepsAction.do?req=download&nm=simstd_Q4_2017_a3.pdf)Kazuaki Ebata, "High-Mobility Thin-Film Transistors with Polycrystalline In-Ga-O Channel Fabricated by DC Magnetron Sputtering", The Japan Society of Applied Physics Applied Physics Express, 6 January 2012, Volume 5, Number 1, page.011102John Y. W. Seto, J. Appl. Phys. 46 5247 (1975)C. H. Seager, T. G. Castner J Appl Phys 49, 3879 (1978)H. Frohlich, Advances in Physics 3 325 (1954)J. J. Wang et. al., Phys. Lett. A 374 2286 (2010)M. Stokey. et. al., J. Appl. Phys. 129 225102 (2021)J. Ederth et. al., Phys. Rev. B 68 155410 (2003)A. Bikowski, K. Ellmer, J. Appl. Phys. 116 143704 (2014)E. Conwell, V.F.Weisskopf, Phys. Rev. 69 258 (1946)E. Conwell, V.F.Weisskopf, Phys. Rev. 77 388 (1946)H. Brooks, Phys. Rev. 83 879 (1951)H. Brooks, Adv. Electron.Phys. 7 85 (1955)D. Chattopadhyay, H. Queisser J. Rev. Mod. Phys. 53 745 (1981)T. Pisarkiewicz, et. al., Thin Solid Films 174 217 (1989)C. Erginsoy, Phys. Rev. 79 1013 (1950)T. Quisse, Physica B 270 262 (1999)C. Kittel, H. Kroemer, "Thermal Physics" Freeman, New York, 2nd ed. (1980) Chap.13 pp.367R.B. Dingle, Philos. Mag. 46 831 (1955).

[0006] However, it has become clear that applying the mobility calculation method (Tokyo Model) used for amorphous oxide semiconductors to calculate the mobility of, for example, polycrystalline oxide semiconductors with higher mobility may not yield accurate results.

[0007] The object of the present invention is to provide a method for calculating the mobility of oxide semiconductors, a device simulation method, a method for manufacturing semiconductor devices, a semiconductor device, an information processing device, and a device simulation system that can more accurately calculate the mobility of various oxide semiconductor materials.

[0008] The inventors investigated various physical properties to develop a method for accurately calculating the mobility of various oxide semiconductor materials, such as polycrystalline oxide semiconductors and amorphous oxide semiconductors. As a result, they found that the mobility of various oxide semiconductor materials can be accurately calculated by using two or more terms calculated using the free carrier concentration in the oxide semiconductor, thus completing the present invention. The inventors furthered their investigation and created a mobility model by physically modeling each physical property parameter that is a scattering factor of polycrystalline oxide semiconductors. When calculations were performed using this mobility model, the measured mobility-carrier concentration line was reproduced well, confirming that the mobility model is functioning correctly. Furthermore, when this mobility model was incorporated into device simulation software and device simulation of a thin-film transistor was performed, the measured current-voltage characteristics were reproduced well. This confirmed that the mobility model can be applied to device simulation of thin-film transistors.

[0009] According to the present invention, the following are provided: a method for calculating the mobility of an oxide semiconductor, a device simulation method, a method for manufacturing a semiconductor device, a semiconductor device, an information processing device, and a device simulation system.

[0010] In other words, the present invention includes the following embodiments: [1] A method for calculating the mobility of an oxide semiconductor using a computer, comprising the step of causing the computer to perform a step of calculating the mobility using two or more terms calculated using the free carrier concentration in the oxide semiconductor, wherein the two or more terms are calculated by a scattering model derived considering the free carrier concentration in the oxide semiconductor, or by a regression model generated based on measured values ​​of the mobility and the free carrier concentration. [2] The two or more terms are calculated by the scattering model, and the step of calculating the mobility is to calculate the mobility μ within the crystal grains of the oxide semiconductor using the two or more terms calculated by the scattering model. ｉｎ－ｇｒａｉｎ The scattering model includes the step of calculating the neutral impurity concentration NＮＩ A neutral impurity scattering model including a variable, and the ionization impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ An ionization impurity scattering model in the non-degenerate region including a variable, and the ionization impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ An ionization impurity scattering model in the degenerate region including a variable, and the optical phonon frequency ω ｏｐ The method according to [1] above, selected from the group consisting of an optical phonon scattering model including a variable. [3] The ionization impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ , and the ionization impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ where at least one of them is calculated using the free carrier concentration, the method according to [2] above. [4] The computer uses the scattering model at the grain boundaries of the oxide semiconductor to calculate the mobility μ in the grains of the oxide semiconductor ｉｎ－ｇｒａｉｎ from the macro mobility μ of the oxide semiconductor, further comprising the step of causing the computer to execute the step. The method according to [2] or [3] above. [5] The computer uses the scattering model at the grain boundaries of the oxide semiconductor to calculate the Fermi energy difference δ between the grain boundaries and the grains ＥＦ using the Fermi energy difference δ between the grain boundaries and the grains to calculate the height V of the grain boundary barrier between the grain boundaries and the grains Ｂ The method according to [4] above, further comprising the step of causing the computer to execute the step. [6] The computer uses the scattering model at the grain boundaries of the oxide semiconductor to calculate the effective state density N in the grains based on the free carrier concentration and the grains ｃ０ and calculating the Fermi energy difference δ based on the Fermi energy difference δ between the grain boundaries and the grains ＥＦ The method according to [5] above, further comprising the step of causing the computer to execute the step. [7] The two or more terms are calculated by the regression model, and the mobility is calculated from the logarithm of the sum of two or more terms of an exponential function having the free carrier concentration as a variable by the regression model. The method according to [1] above. [8] The step of calculating the mobility includes the step of calculating the macro mobility μ of the oxide semiconductor by the regression model, and the regression model has the following formula: [In Equation (1), a１ a ２ , b １ , b ２

[11] The method according to [7] above, expressed as follows:

[11] The density of states of defects includes an acceptor-like exponential function distribution, and the acceptor-like exponential function density of states g ＴＡ This is the energy E at the lower end of the conduction band. ｃ Density of states N of acceptor-like defects in ＴＡ 10 １０ ~10 ２２ cm －３ / eV, the reciprocal of the slope of the acceptor-like defect density of states W ＴＡ The device simulation method according to

[10] above, wherein the mobility μ is in the range of 0.001 to 0.5 eV.

[12] The device simulation method according to any one of [9] to

[11] above, wherein the step of performing the device simulation includes the step of calculating the heat generation effect due to the current flowing through the oxide semiconductor and the heat dissipation effect due to the thermal conductivity and boundary conditions of the oxide semiconductor.

[13] The mobility μ ｉｎ－ｇｒａｉｎ The step of calculating the ionized impurity concentration N in the non-degenerate region using the free carrier concentration in the oxide semiconductor is performed. ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿ＤｅｇA step of calculating the ionized impurity concentration N in the non-degenerate region. ＩＩ＿ｎｏｎＤｅｇ The mobility μ calculated using ＩＩ （ｎｏｎＤｅｇ） And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The mobility μ calculated using ＩＩ （Ｄｅｇ） Using the above, the mobility μ ｉｎ－ｇｒａｉｎ The method according to any one of the above [2] to [6], comprising the step of calculating N.

[14] The ionized impurity concentration N in the non-degenerate region. ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ However, the ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The boundary is when the sum of is constant and the free carrier concentration is the same as or approximately the same as the critical density of the Mott transition, and the ionized impurity concentration N in the non-degenerate region is defined as such. ＩＩ＿ｎｏｎＤｅｇ And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The method according to

[13] above, wherein the relationship between the magnitudes of the two is expressed in such a way that it switches continuously.

[15] The ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The method described in

[14] above, which is calculated by formulas (2) and (3) below, respectively. (N ＩＩ (where is the ionized impurity concentration and f is a sigmoid function with the free carrier concentration as a variable.)

[16] The mobility μ ｉｎ－ｇｒａｉｎ However, the method described in any one of the above items [2] to [6] and

[13] to

[15] , calculated according to (A1-1) below. [In formula (A1-1), μ ＯＰ μ is the mobility calculated by the optical phonon scattering model. ＮＩ μ is the mobility calculated by the neutral impurity scattering model. ＩＩ （Ｄｅｇ） μ is the mobility calculated by the ionized impurity scattering model in the degenerate region.ＩＩ （ｎｏｎＤｅｇ） This is the mobility calculated by the ionized impurity scattering model in the non-degenerate region, and Z ＯＰ Z ＮＩ Z ＩＩ＿Ｄｅｇ , and Z ＩＩ＿ｎｏｎＤｅｇ is 0 or 1, Z ＯＰ Z ＮＩ Z ＩＩ＿Ｄｅｇ , and Z ＩＩ＿ｎｏｎＤｅｇ At least two selected from the group consisting of are 1.

[17] The method according to [4] above, wherein the mobility μ is calculated by the following formula (A10). [In equation (A10), q is the elementary charge [C], and V Ｂ k is the height [eV] of the grain boundary barrier between the grain boundary and the inside of the grain, and k Ｂ is the Boltzmann constant [eV / K], T is the temperature [K], and μ ｉｎ－ｇｒａｉｎ The mobility μ ｉｎ－ｇｒａｉｎ [cm ２ [Vs] is the Fermi energy difference δ.

[18] ＥＦ However, the method described in [6] above is calculated by the following formula (4). [In formula (4), δ ＥＦ０ This is the Fermi energy difference δ at absolute zero or when the free carrier concentration is equal to the effective density of states. ＥＦ And n is the free carrier concentration [cm³]. －３ ] and N ｃ０ The effective density of states [cm³] －３ ] and Z δＥＦＴｎ

[19] The acceptor-like exponential distribution g ＴＡ The device simulation method described in

[11] above, wherein (E) is calculated by the following formula (5). [In formula (5), N ＴＡ This is the energy E at the lower end of the conduction band. ｃ Density of states of acceptor-like defects in [cm²] －３ / eV] and W ＴＡE is the reciprocal of the slope of the acceptor-like defect's density of states [eV], where E is the energy of the acceptor-like defect [eV], and E ｃ

[20] A method for manufacturing a semiconductor device, comprising the steps of: performing a device simulation including the device simulation method described in any one of the above items [9] to

[12] and

[19] ; ​​and performing a device design based on the device simulation results obtained in the step of performing the device simulation.

[21] The method for manufacturing a semiconductor device according to

[20] , wherein the oxide semiconductor is an oxide mainly composed of In.

[22] The method for manufacturing a semiconductor device according to

[20] or

[21] , wherein the oxide semiconductor is a polycrystalline oxide semiconductor.

[23] A semiconductor device manufactured by the method for manufacturing a semiconductor device according to any one of the above items

[20] to

[22] .

[24] An information processing device for calculating the mobility of an oxide semiconductor, comprising the steps of: performing a step of calculating the mobility using two or more terms calculated using the free carrier concentration in the oxide semiconductor; wherein the two or more terms are calculated by a scattering model derived considering the free carrier concentration in the oxide semiconductor, or by a regression model generated based on measured values ​​of the mobility and the free carrier concentration.

[25] A device simulation system comprising the steps of: calculating the mobility of an oxide semiconductor using two or more terms calculated by a computer using the free carrier concentration in the oxide semiconductor; and causing the computer to perform a device simulation to simulate a device including the oxide semiconductor, which is the subject of the simulation, wherein the two or more terms are calculated by a scattering model derived considering the free carrier concentration in the oxide semiconductor, or by a regression model generated based on measured values ​​of the mobility and the free carrier concentration.

[0011] According to the present invention, it is possible to provide a method for calculating the mobility of an oxide semiconductor that can more accurately calculate the mobilities of various oxide semiconductor materials, a device simulation method, a method for manufacturing a semiconductor device, a semiconductor device, an information processing apparatus, and a device simulation system.

[0012] It is a graph showing the mobility-carrier concentration characteristics at room temperature of each measurement sample. It is a graph in which each scattering parameter extracted by parameter fitting for each measurement sample is plotted. It is a graph showing the carrier concentration dependence of each scattering parameter common to each measurement sample. Q / πa of the Quisse model ０ ２ −ka ０ In the double-logarithmic graph, each q ｓ a ０ at which Q / πa ０ ２ −ka ０ In the Quisse model where the curve is regarded as the upper base and the hypotenuse of a right trapezoid, Q / πa ０ ２ is a conceptual diagram when formulating an approximation formula. Each q shown in FIG. 4 ｓ a ０ of ka ０ =0 of Q / πa ０ ２ value (Q ０ @k ‘ =0) is obtained from the Quisse model, and each q in FIG. 4 ｓ a ０It is a graph in which the value of the upper base is approximated. It is a graph showing the results of inputting the approximate analytical formula of the neutral impurity scattering Quisse model and the parameters of the ionized impurity scattering (degenerate, introducing a sigmoid function in addition to the self-formed donor in the Dingle model). It is a functional block diagram of the information processing apparatus 100 according to the present embodiment. It is a flowchart showing an example of the process of the method for calculating the mobility of the oxide semiconductor according to the present embodiment. It is a functional block diagram of the device simulation system 200 according to the present embodiment. It is a diagram showing an example of the hardware configuration of the information processing apparatus 100 according to the present embodiment. It is a flowchart showing an example of the process of device simulation according to the present embodiment. (a) shows a cross-sectional view of the device structure, and (b) shows Ids-Vgs characteristics and μ ＦＥ is shown. (a) shows the low-frequency (low-f) Cg(s + d)-Vg(s + d) characteristics, and (b) shows the trap density. (a) shows the relationship between Id and the extraction carrier concentration per unit area (n ａ ) extracted during trap extraction, (b) and (c) are diagrams explaining the modeling procedure, (d) shows μ and the fitting line, and (e) shows the measured Ids and the simulated Ids. Ids-Vgs characteristics are shown. The μ-n dependence depending on T is shown. It is a diagram for explaining the self-heating effect. (a) shows the measured value μ ｏｂｓ． of the mobility of Specimen 1 with respect to the carrier concentration n, and the calculated value μ ｃａｌｃ of the macro DC mobility obtained in Example 1. It is a graph plotting the relationship, and (b) shows the measured value μ ｏｂｓ． of the mobility of Specimen 1 on the horizontal axis and the calculated value μ ｃａｌｃ of the macro DC mobility obtained in Example 1 on the vertical axis. It is a graph plotting. (a) shows the measured value μ ｏｂｓ． of the mobility of Specimen 2 with respect to the carrier concentration n, and the calculated value μ ｃａｌｃ of the macro DC mobility obtained in Example 2. It is a graph plotting the relationship, and (b) shows the measured value μ ｏｂｓ． of the mobility of Specimen 2 on the horizontal axis and the calculated value μ ｃａｌｃ of the macro DC mobility obtained in Example 2 on the vertical axis. It is a graph plotting. (a) shows the measured value μ of the mobility of Specimen 1 with respect to the carrier concentration nｏｂｓ． And the calculated macroscopic DC mobility μ obtained in Comparative Example 1. ｃａｌｃ This graph plots the relationship between (b) and (c), with the measured value μ of the mobility of sample 1 on the horizontal axis. ｏｂｓ． The vertical axis shows the calculated macroscopic DC mobility μ obtained in Comparative Example 1. ｃａｌｃ This is a graph plotting the following: (a) is the measured value μ of the mobility of sample 2 relative to the carrier concentration n. ｏｂｓ． And the calculated macroscopic DC mobility μ obtained in Comparative Example 2. ｃａｌｃ This graph plots the relationship between (b) and (c), with the measured value μ of the mobility of sample 2 on the horizontal axis. ｏｂｓ． The vertical axis shows the calculated macroscopic DC mobility μ obtained in Comparative Example 2. ｃａｌｃ This is a graph plotting the following. This graph shows the mobility-carrier concentration line (μ-n line) obtained by the method for calculating macroscopic DC mobility μ(T) using the physical model in the present invention, along with the plot of measured values. Measured value μ of mobility relative to carrier concentration n for the sample used for measurement. ｏｂｓ． This is a graph plotting the relationship between the calculated mobility value and the calculated value. This is a graph plotting the carrier concentration of each measured sample on the horizontal axis and the scattering rate of each scattering parameter on the vertical axis. This is a graph showing the mobility-carrier concentration line (μ-n line) obtained by the method for calculating mobility μ using the scattering model of the present invention in Example A, along with the plot of the measured value. This is a graph showing the mobility-carrier concentration line (μ-n line) obtained by the method for calculating mobility μ using the scattering model of the present invention in Example B, along with the plot of the measured value. This is a graph showing the relationship between the measured and calculated values ​​of current values ​​obtained by the device simulation method of the present invention in Example A and Example B.

[0013] The embodiments of this disclosure will be described below with reference to the drawings as appropriate. 1. Method for Calculating the Mobility of an Oxide Semiconductor First, the method for calculating the mobility of an oxide semiconductor will be described. The method for calculating the mobility of an oxide semiconductor according to the embodiments of this disclosure is a method for calculating the mobility of an oxide semiconductor using a computer, and includes the step of causing the computer to perform a step of calculating the mobility using two or more terms calculated using the free carrier concentration in the oxide semiconductor, wherein the two or more terms are calculated by a scattering model derived considering the free carrier concentration in the oxide semiconductor, or by a regression model generated based on measured values ​​of mobility and free carrier concentration. In the method for calculating the mobility of an oxide semiconductor according to the embodiments of this disclosure, the scattering model may be derived, for example, by using the free carrier concentration as one of the parameters, as described later.

[0014] In this embodiment, the free carrier concentration is defined as the free electron density [cm³] in an n-type semiconductor. －３ ] is equal to the hole density [cm²] in p-type semiconductors. －３ In this specification, using an n-type semiconductor as an example, the free carrier concentration is equal to the free electron density [cm²]. －３ The following describes the case where the free carrier concentration is the hole density [cm³]. －３ It can also be applied to p-type semiconductors, which are [...].

[0015] In this embodiment, the mobility of the oxide semiconductor is a physical quantity influenced by the semiconductor material's inherent effective mass, crystal structure, crystal transitions, crystal grains, and defect amount, and is a physical quantity that varies with temperature, free carrier concentration, scattering parameters, and potential barriers at crystal grain boundaries.

[0016] In this embodiment, the mobility of the oxide semiconductor is calculated using two or more terms derived from the free carrier concentration, thereby enabling more accurate calculation of the mobility of various oxide semiconductor materials.

[0017] In this embodiment, the mobility may be calculated using the scattering model described below as "2. Method for calculating the mobility of an oxide semiconductor using a scattering model," or the mobility may be calculated using the regression model described below as "3. Method for calculating the mobility of an oxide semiconductor using a regression model." Furthermore, when calculating the mobility using the scattering model, the matters described in the calculation of mobility using the regression model may be appropriately applied, and vice versa.

[0018] Furthermore, "performing the step of calculating mobility using two or more terms calculated using free carrier concentrations" means calculating mobility using two or more terms calculated using free carrier concentrations, and is not limited to calculating mobility by linearly combining those two or more terms. For example, mobility may be calculated by combining two or more terms, or it may be calculated using the exponential or logarithmic form of a linear combination of two or more terms.

[0019] (Types of semiconductor materials) The mobility calculation method according to this embodiment can be applied to various oxide semiconductor materials such as crystalline oxide semiconductors and amorphous oxide semiconductors. In one embodiment, the semiconductor is a polycrystalline semiconductor. In one embodiment, the semiconductor is a single-crystal semiconductor. In one embodiment, the polycrystalline semiconductor is an oxide semiconductor mainly composed of In. In one embodiment, the single-crystal semiconductor is an oxide semiconductor mainly composed of In.

[0020] "Mainly composed of In" means that the ratio of In content to all metal elements in the oxide semiconductor ([In] / ([In] + [All other metal elements]) × 100) (atomic %) is greater than the respective content ratios of the other metal elements. In one embodiment, the In content ratio among all metal elements in the oxide semiconductor is 33 atomic % or more, preferably 50 atomic % or more, and more preferably 70 atomic % or more. A higher In content ratio is more likely to yield more accurate calculation results.

[0021] In one embodiment, the oxide semiconductor is in the form of an oxide thin film. In semiconductor devices, such as thin-film transistors, the semiconductor is used in the form of a thin film. The mobility calculation method according to this embodiment is suitable when the semiconductor is a thin film.

[0022] In one embodiment, the crystalline oxide semiconductor includes a Bixbyte structure. Having a Bixbyte structure in the crystalline oxide semiconductor is likely to yield more accurate calculation results. The presence of a Bixbyte structure in the crystalline oxide semiconductor can be confirmed by the following method.

[0023] (Method for evaluating whether or not a semiconductor has a Bixbite structure) Whether or not a semiconductor has a Bixbite structure can be determined, for example, by obtaining a diffraction pattern by electron diffraction and comparing it with an electron diffraction pattern that can be calculated from the crystal structure data of Bixbite structures in ICSD (Inorganic Crystal Structure Database: Japan Chemical Information Association).

[0024] 2. Method for Calculating the Mobility of an Oxide Semiconductor Using a Scattering Model As described above, in the method for calculating the mobility of an oxide semiconductor according to the embodiment of this disclosure, two or more terms calculated using the free carrier concentration in the oxide semiconductor may be calculated using a scattering model derived considering the free carrier concentration in the oxide semiconductor.

[0025] In other words, in one embodiment, the mobility of the oxide semiconductor is calculated based on a scattering model. In this case, first the mobility μ within the crystal grains of the oxide semiconductor is calculated. ｉｎ－ｇｒａｉｎ [cm ２ By calculating [Vs] and using it to calculate the macroscopic mobility μ of the oxide semiconductor, the influence of scattering within the crystal grains and the influence of scattering due to the potential barrier at the crystal grain boundaries can be separated and the mobility can be calculated. However, if the oxide semiconductor is a single crystal or the potential barrier at the grain boundary is extremely small, the mobility μ within the crystal grains can be used. ｉｎ－ｇｒａｉｎ [cm ２The value of [ / Vs] can be used directly as the macroscopic mobility μ. In other words, in this embodiment, the step of calculating the macroscopic mobility μ can be omitted.

[0026] 2.1. Intragranular mobility μ of semiconductors ｉｎ－ｇｒａｉｎ Method for calculating the intragranular mobility μ of a semiconductor according to one aspect of this embodiment. ｉｎ－ｇｒａｉｎ In the calculation method (hereinafter sometimes abbreviated as "method for calculating intragranular mobility"), the step of calculating mobility is to use two or more terms calculated by the scattering model to determine the intragranular mobility μ of the oxide semiconductor crystal grain. ｉｎ－ｇｒａｉｎ The step may include calculating the neutral impurity concentration N. ＮＩ A neutral impurity scattering model with N as a variable, and the ionized impurity concentration in the non-degenerate region. ＩＩ＿ｎｏｎＤｅｇ Ionized impurity scattering model in the non-degenerate region, with N as a variable, and ionized impurity concentration in the degenerate region. ＩＩ＿Ｄｅｇ Ionized impurity scattering model in the degenerate region, which includes the variable ω, and optical phonon frequency ω ｏｐ The optical phonon scattering models that include as a variable may be selected from the group. In this embodiment, for example, the ionized impurity concentration N in the non-degenerate region is ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the above-mentioned degenerate region ＩＩ＿Ｄｅｇ At least one of these may be calculated using the free carrier concentration described above.

[0027] Here, "the mobility μ within the crystal grains of an oxide semiconductor" ｉｎ－ｇｒａｉｎ "(T)" represents the mobility within a single crystal grain. By determining this, it is possible to determine not only the mobility within the crystal grain, but also the macroscopic DC mobility in the case of a single crystal state and the macroscopic DC mobility when the potential barrier at the grain boundary is extremely small. In the following description, the calculation of DC mobility will be explained as an example, but this embodiment may also be applied to the calculation of AC mobility. Therefore, in the following description of the embodiment, the term "DC mobility" may be appropriately replaced with the term "AC mobility".

[0028] A "non-degenerate semiconductor" is a semiconductor with a low carrier concentration and no Fermi energy in the conduction band or valence band. The statistical average number of electrons occupying energy level E can be expressed, for example, by the Boltzmann approximation.

[0029] (1) Physical Modeling of Various Scattering Parameters In order to specifically perform physical modeling of various scattering parameters, the following studies were conducted. In the following explanation, "scattering factor" refers to the scattering ability for conduction electrons or holes that are factors that reduce mobility present in semiconductors, and "scattering parameter" refers to the numerical representation of the mobility reduction index possessed by each "scattering factor". For fitting, a Combined model, which has a proven track record in the analysis of polycrystalline oxide semiconductors, was adopted, and the scattering parameter (here, the grain boundary scattering barrier height V) was used to explain the temperature dependence of mobility. Ｂ Optical phonon scattering a ＯＰ , neutral impurity scattering a ＮＩ , ionized impurity scattering a ＩＩ The ) was optimized using automatic fitting.

[0030] The regression equation using the combined model is as follows: [In equation (A10), q is the elementary charge [C], V Ｂ The grain boundary scattering barrier height [eV], k Ｂ This is the Boltzmann constant (8.617 × 10⁻¹⁰). -５ [eV / K]), T is temperature [K], μ ｉｎ－ｇｒａｉｎ This is the mobility within the crystal grains of an oxide semiconductor [cm²]. ２ / Vs], and in equation (A101), μ ｉｎ－ｇｒａｉｎ This is the mobility within the crystal grains of an oxide semiconductor [cm²]. ２ / Vs], T is temperature [K], a ＯＰ a ＮＩ , and a ＩＩ The above fitting parameter, k Ｂ This is the Boltzmann constant.

[0031] Furthermore, in this specification, This is the energy [eV] of the optical phonon, which varies depending on the carrier concentration. This is the Dirac constant (6.58212 × 10⁻¹⁰). －１６ [eV・s]) The following explanations will be omitted if they are redundant.

[0032] (2) Measured data and its acquisition method The scattering parameter is the grain boundary scattering barrier height V Ｂ Optical phonon scattering a ＯＰ , ionized impurity scattering in the non-degenerate region (hereinafter also referred to as "ionized impurity scattering (non-degenerate)") a ＩＩ＿ｎｏｎＤｅｇ , ionized impurity scattering in the degenerate region (hereinafter also referred to as "ionized impurity scattering (degenerate)") a ＩＩ＿Ｄｅｇ Neutral impurity scattering a ＮＩ The following was used. Scattering parameters can be obtained by performing temperature-dependent Hall effect measurements for each carrier concentration on samples under the same deposition conditions.

[0033] The samples analyzed (hereinafter sometimes referred to as "samples") are, for example, the six types of oxide semiconductor thin films (film thickness 30 nm, annealed at 400°C for 1 hour in air) shown in Tables 4-1 to 4-3 of the examples described later. The mobility-carrier concentration characteristics (hereinafter sometimes referred to as μ-n characteristics or μ-n lines) of each sample at room temperature are shown in Figure 1. Although IO, IGO(L.G.), IGO(Ref), and IGO(111) (samples 3 to 6 shown in Tables 4-1 and 4-2) differ in crystal orientation and grain size, it can be seen that there is no significant difference in terms of the μ-n line compared to IGO(Amo.) and IGO(L.Q.) (samples 7 and 8 shown in Table 4-3). Therefore, IO, IGO(L.G.), IGO(Ref), and IGO(111) were adopted as model samples when creating a mobility model for polycrystalline oxide semiconductors.

[0034] Next, Figures 2(a) to 2(d) summarize the scattering parameters extracted by parameter fitting. In the initial stages of the analysis, T －３／２ Assuming that the coefficient is due to ionized impurity scattering, a ＩＩ However, after consideration, a ＩＩ Ionized impurity scattering (non-degenerate) a ＩＩ＿ｎｏｎＤｅｇ and ionized impurity scattering (degeneracy) a ＩＩ＿ＤｅｇIt became clear that it is necessary to discuss them separately. Therefore, T －３／２ The coefficient of a ＩＩ＿ｎｏｎＤｅｇ And similarly, T ０ Assuming that the coefficient is due to neutral impurities, a ＮＩ However, in conclusion, T ０ It became clear that the coefficient is greatly influenced by neutral impurity scattering and ionized impurity scattering (degeneracy). The scattering parameter considering the effects of neutral impurity scattering and ionized impurity scattering (degeneracy) is shown below as a ０ It was expressed as (n).

[0035] (3) Investigation of the carrier concentration dependence of scattering parameters in polycrystalline oxide semiconductors In order to physically model the μ-n line of polycrystalline oxide semiconductors, we first determined the scattering parameter-carrier concentration dependence (hereinafter sometimes referred to as the a-n line) of each scattering parameter. The carrier concentration dependence of each scattering parameter common to the above model samples is shown in Figures 3(a) to 3(d). The dashed line in each graph represents V Ｂ - This corresponds to the -n line or a-n line.

[0036] (4) Examination of grain boundary scattering models: Grain boundary barrier-carrier concentration dependence (V) in Figure 3(a) Ｂ To explain the -n line, we first examined the Seto model [John YW Seto, J. Appl. Phys. 46 5247 (1975)], which is commonly used in discussions of grain boundary barriers in polycrystalline semiconductors. However, in the Seto model, V Ｂ The carrier concentration dependence is "V Ｂ The graph of -n exhibits a downward convex behavior, as shown in Figure 3(a) V Ｂ - It was found that there was a large deviation from the n line. Here, after diligently researching the literature, it was found that by using the Seager model [CH Seager, TG Castner J Appl Phys 49, 3879 (1978)], V Ｂ - A behavior that accurately reflects the behavior of the n line, "V ＢIt was found that a curve with an upwardly convex "-n" graph can be obtained. The Seto model has a drawback that there is no concept of energy levels for traps (it changes automatically), but in the Seager model that overcomes this drawback, the energy levels of traps and the trap amount are used as independent variables, and the equation for V Ｂ (n) has been derived, so it is considered to be in agreement with the experimental behavior. The V Ｂ -n line in Fig. 3(a) is the result of setting the Fermi level difference between grain boundaries and grains to 25 meV and the trap density at grain boundaries to 7.5×10 １３ cm －２ eV －１ in the Seager model. As described above, the Seager model that well represents the behavior of V Ｂ (n) was adopted, and the following equation (A11) was obtained. <00,00898> [In equation (A11), V Ｂ is the grain boundary barrier height [eV], and α is as follows: (In the equation, ε ０ is the permittivity of vacuum [F / cm], ε ｒ is the relative permittivity (static), n is the free carrier concentration [cm －３ , e is the elementary charge [C], N Ｔ is the trap density at grain boundaries [cm －２ eV －１ .), δ ＥＦ is the Fermi energy difference between grain boundaries and grains (E Ｆ ＧＢ -E Ｆ Ｂ ) [eV], provided that V Ｂ ≥0. ]

[0037] (5) Examination of the optical phonon scattering model: Regarding optical phonon scattering, a plurality of models based on temperature dependencies have been proposed. However, a ＯＰ extracted from parameter fitting is Since the temperature dependence was shown, a model with this temperature-dependent term was explored. As a result, regarding optical phonon scattering, the following equation (A2-2) [J. J. Wang et. al., Phys. Lett. A 374 2286 (2010)] based on the Frohlich model [H. Frohlich, Advances in Physics 3 325 (1954)] was adopted.

[0038] [In Equation (A2-2), μ ＯＰ is the optical phonon scattering mobility [cm 2 / Vs], ε ０ is the permittivity of vacuum [F / cm], k Ｂ is the Boltzmann constant [eV / K], T is the temperature [K], e is the elementary charge [C], m ＊ is the effective mass normalized by the speed of light [eV / c ２ (c is the speed of light [cm / s], 1 [eV / c ２ ≈ 1.782662×10 ―３６ [kg]), ε ｏｐｔ is the relative permittivity (optical), ε ｒ is the relative permittivity (static).]

[0039] Actually, when ω ｏｐ ?= 360 cm [[ID=, should there be a unit here?]] －１ 、ε ｏｐｔ = 4、ε ｒ = 14 are substituted into the above Equation (A2-2), the a ＯＰ (n) line shown in Fig. 3(b) was obtained. These substitution values show good agreement with the vibration frequency 363.4 cm －１ [M. Stokey. et. al., J. Appl. Phys. 129 225102 (2021)] of the TO phonon, which is the most dominant vibration mode of indium oxide, the optical permittivity 4 [J. Ederth et. al., Phys. Rev. B 68 155410 (2003)] of the ITO thin film, and the relative permittivity value 11.85 extracted from impedance measurement. From the fact that these substitution values are consistent with past reports and the reproducibility of a ＯＰ , the selected Frohlich model was judged to be reasonable.

[0040] There seems to be an unclear part in the original text around line . Please check and clarify if possible for a more accurate translation.Furthermore, the low carrier concentration region (<5 × 10) in Figure 3(b) １８ cm －３ ) then, a ＯＰ The influence is very small, and from the experimental point a ＯＰ Although we could not determine this, in the low carrier concentration region, the temperature dependence term of grain boundary scattering < exp(-qV) Ｂ / k Ｂ The contribution of other terms such as T)> is large, and the above a ＯＰ This is because it becomes difficult to extract the temperature-dependent term. In fact, it has been reported that the mobility equation for optical phonon scattering is almost maintained even when the carrier concentration changes from the degenerate region to the non-degenerate region [A. Bikowski, K. Ellmer, J. Appl. Phys. 116 143704 (2014)]. Based on the above, we assumed that the above equation (A2-2) based on the Frohlich model holds true for the entire carrier concentration range as an optical phonon scattering model.

[0041] Therefore, in one embodiment, the mobility μ determined by the optical phonon scattering model is ＯＰ [cm ２ / Vs] is expressed by the above formula (A2-2).

[0042] (6) Ionized Impurity Scattering (Non-Degenerate) Models As mobility models for ionized impurity scattering (non-degenerate), the Conwell-Weisskopf model (commonly known as the CW model) [E. Conwell, VFWeisskopf, Phys. Rev. 69 258 (1946), and E. Conwell, VFWeisskopf, Phys. Rev. 77 388 (1946)] and the Brooks-Herring model (commonly known as the BH model) [H. Brooks, Phys. Rev. 83 879 (1951), and H. Brooks, Adv. Electron. Phys. 7 85 (1955)] are well known. Comparing the CW model and the BH model, the long-range component term of the clone potential (the shielding function F in ionized impurity scattering in equation (A3-2) described later) ＩＩRegarding the terms (corresponding to), there is a difference in whether they are truncated or shielded, but otherwise the equation is the same. Also, the truncation term in the CW model uses the distance between ionized impurities as an indicator, so the ionized impurity concentration N ＩＩ It becomes a function of [D. Chattopadhyay, H. Queisser J. Rev. Mod. Phys. 53 745 (1981)]. On the other hand, in the BH model, ionized impurities are shielded by the influence of the surrounding electron concentration, so F ＩＩ is N ＩＩ It is a function of the free carrier concentration n, not of [D. Chattopadhyay, H. Queisser J. Rev. Mod. Phys. 53 745 (1981)]. In a typical single-crystal semiconductor, the ionization impurity concentration N ＩＩ Therefore, the free carrier concentration n is approximately equal to N ＩＩ The relationship ~n often holds true, and since many studies do not strictly distinguish between them, care must be taken when selecting a formula.

[0043] The dashed line in Figure 3(c) is a ＩＩ＿ｎｏｎＤｅｇ -n line, and the dashed line in the low carrier concentration region of Figure 3(c) is the result of applying the following equation (A5-CW), which is a CW model. As is clear from the definition of the CW model, the scattering parameter a ＩＩ＿ｎｏｎＤｅｇ It does not show carrier concentration dependence. On the other hand, when the BH model is applied, F ＩＩ The influence of the free carrier concentration n within the term was significant, and the scattering parameter increased monotonically toward the low carrier concentration range, failing to reproduce the experimental results. Therefore, in consideration of the continuity with the ionized impurity scattering (degenerate) model described later, F in the CW model ＩＩ Regarding this, the shielding parameters of the Pisarkiewicz type [T. Pisarkiewicz, et. al., Thin Solid Films 174 217 (1989)] were applied. As a result, in the following equations (A5-BH) and (F), the scattering parameter a was similar to that of the truncated type (the following equation (A5-CW)). ＩＩ＿ｎｏｎＤｅｇ It was found that the desired properties could be obtained. Here, the non-degenerate region and the degenerate region are defined as the critical density N of the Mott transition. ｃAlthough it is possible to divide the region using a boundary, the mobility function becomes discontinuous, so we chose a continuous change using the sigmoid function.

[0044] In one embodiment, the mobility μ is determined by the ionized impurity scattering (non-degenerate) model. ＩＩ （ｎｏｎＤｅｇ） [cm ２ The [Vs] can be expressed using a mobility formula of the Conwell-Weisskopf model type or the Brooks-Herring model type.

[0045] In one embodiment, the mobility μ is determined by the ionized impurity scattering (non-degenerate) model. ＩＩ （ｎｏｎＤｅｇ） [cm ２ The coefficient [Vs] can be expressed by the following mobility formula (A5-CW) of the Conwell-Weisskopf model type.

[0046] [In formula (A5-CW), ε ０ ε is the permittivity of vacuum [F / cm]. ｒ This is the relative permittivity (static), k Ｂ is the Boltzmann constant [eV / K], T is the temperature [K], m ＊ This is the effective mass normalized at the speed of light [eV / c ２ ] (where c is the speed of light [cm / s]), e is the elementary charge [C], Z is the ionic charge of the ionized impurity, N ＩＩ This is the ionized impurity concentration [cm³] －３ ], N ＩＩ＿ｎｏｎＤｅｇ This is the ionized impurity concentration [cm³] －３ ] is. ]

[0047] In one embodiment, the mobility μ is determined by the ionized impurity scattering (non-degenerate) model. ＩＩ （ｎｏｎＤｅｇ） [cm ２ The coefficient of Vs can be expressed by the following mobility formula (A5-BH) of the Brooks-Herring model type. [In formula (A5-BH), F ＩＩ ε is the shielding function in ionized impurity scattering, ０ ε is the permittivity of vacuum [F / cm]. ｒThis is the relative permittivity (static), k Ｂ is the Boltzmann constant [eV / K], T is the temperature [K], m ＊ This is the effective mass normalized at the speed of light [eV / c ２ ] (where c is the speed of light [cm / s]), e is the elementary charge [C], Z is the ionic charge of the ionized impurity, N ＩＩ＿ｎｏｎＤｅｇ This is the ionized impurity concentration [cm³] －３ ] is. ]

[0048] In equation (A5 - BH), the shielding function F ＩＩ This can be expressed by the following formula (F). In this case, the F ＩＩ The shielding function F in Pisarkiewicz-type ionized impurity scattering is ＩＩ That is the case. [In formula (F), ξ ｄ The formula is as follows: (In the formula, n is the free carrier concentration [cm³) －３ ], ε ０ ε is the permittivity of vacuum [F / cm]. ｒ This is the relative permittivity (static), m ＊ This is the effective mass normalized at the speed of light [eV / c ２ F is expressed as (where c is the speed of light [cm / s], and e is the elementary charge [C]). ＩＩ The reduction shielding parameter in this case is ξ ｎｐ The formula is as follows: (In the formula, m ０ ＊ m is the minimum effective mass of free carriers at the lower end of the conduction band or the upper end of the valence band. ＊ This is the effective mass of a free carrier normalized at the speed of light [eV / c ２ F is represented by ] (where c is the speed of light [cm / s]). ＩＩ This is an additional shielding parameter to accommodate the change in effective mass in [the specified region].

[0049] In one embodiment, the mobility determined by the ionized impurity scattering (non-degenerate) model, which can be expressed by the Conwell-Weisskopf model or Brooks-Herring model mobility equation, is μ ＩＩ＿ＣＷ－ＢＨ （ｎｏｎＤｅｇ） [cm ２When [Vs] is used, the mobility μ is determined by the ionized impurity scattering (non-degenerate) model. ＩＩ （ｎｏｎＤｅｇ） [cm ２ The expression [Vs] can be expressed as a sigmoid function (A5-S) with respect to the carrier concentration n.

[0050] [In formula (A5-S), N Ｃ The critical density for the Mott transition is [cm²]. －３ ], n is the free carrier concentration [cm³] －３ ], where a is a parameter that represents the rate of change of the sigmoid function.

[0051] (7) Scattering parameter a ０ (n) Discussion and Modeling Of the scattering parameter behaviors to be clarified in Figures 3(a) to (d), a shown in Figure 3(d) ０ (n) is a case where the mobility does not show temperature dependence (μ(T)∝T ０ ) This refers to the scattering parameter. Here, a ０ (n) is complex because it is the dominant factor (the most important scattering parameter) of the mobility characteristics during TFT operation, involves two types of scattering (neutral impurity scattering and ionized impurity scattering (degenerate)), and conventional models cannot be applied to neutral impurity scattering. Therefore, we will discuss it in separate parts as follows.

[0052] (7-1) Neutral Impurity Scattering Erginsoy Model Neutral impurity scattering, in the narrow sense, assumes a hydrogen-like atom as the neutral impurity scatter, and the cross-sectional area (Bohr radius a) of the hydrogen-like atom ０The mechanism involves scattering conduction carriers, with the total scattering cross-section being approximately the square of (3 × 10⁻²). Furthermore, this scattering assumes elastic scattering and quantum scattering due to the potential of hydrogen-like atoms, and it is common to treat the total scattering cross-section as a phase shift in wavenumber space. In addition, the Erginsoy model [C. Erginsoy, Phys. Rev. 79 1013 (1950)] has been widely adopted as a model for neutral impurity scattering. This is thought to be due to the use of bold approximations when calculating the total scattering cross-section, resulting in simple mathematical formulas. On the other hand, because it uses a linear approximation for the scattering cross-section, there is a tendency to overestimate scattering in the high-energy region, and there is a problem of underestimating mobility even at low scattering concentrations. In fact, when the Erginsoy model is applied to Figure 3(d), the low carrier concentration region (<3 × 10⁻²) １７ cm －３ While it shows good agreement with the measured values ​​for the plateau component in the high carrier concentration region, it exhibits nonlinear behavior in the high carrier concentration region. ０ (n) The difference from the measured value becomes significant for changes. ０ Since no factors other than neutral impurity scattering exhibited a dependence, except for ionized impurity scattering (degeneracy), which will be discussed later, further investigations were conducted on the neutral impurity scattering model and ionized impurity scattering (degeneracy).

[0053] In one embodiment, the mobility μ determined by the neutral impurity scattering model is ＮＩ [cm ２ The function [Vs] can be expressed using either an Erginsoy-type mobility model or a Quisse-type mobility approximation formula.

[0054] In one embodiment, the mobility μ is determined by the Erginsoy-type mobility model. ＮＩ [cm ２ The expression [Vs] is represented by the following formula (A3E).

[0055] [In formula (A3E), m ＊ This is the effective mass normalized at the speed of light [eV / c ２ ] (where c is the speed of light [cm / s]), e is the elementary charge [C], ε ０ε is the permittivity of vacuum [F / cm]. ｒ This is relative permittivity (static), N ＮＩ This is the neutral impurity scattering concentration [cm²]. －３ ] is. ]

[0056] (7-2) Neutral Impurity Scattering Quisse Model A literature search on neutral impurity scattering models revealed that the total scattering cross-section Q is dependent on the carrier concentration, i.e., a ０ We found the Quisse model [T. Quisse, Physica B 270 262 (1999)], which may be able to explain the carrier concentration changes in (n). The Quisse model incorporates the concept of an effective Bohr radius that takes into account the Debye shielding length due to carrier concentration changes, and by combining numerous analytical formulas in the trial wave function, it is possible to calculate the total scattering cross-section and mobility for hydrogen-like atoms without approximations.

[0057] First, to determine whether the Quisse model could be applied to our system, we replicated the Quisse paper [T. Quisse, Physica B 270 262 (1999)]. The results of the replication showed that Q / πa was the same as in the Quisse paper. ０ ２ -ka ０ A graph can be drawn, and the scattering parameter a ＮＩ The change in a is also shown in Figure 3(d) ０ It was confirmed that this is consistent with the behavior of (n). Furthermore, when comparing the Erginsoy model and the Quisse model, it became clear that the former does not have a temperature dependence or carrier concentration dependence on mobility, while the latter is affected by both temperature and carrier concentration.

[0058] In one embodiment, the mobility μ is determined by the Quisse-type mobility model. ＮＩ [cm ２ The expression [Vs] is expressed by the following equations (Q-1) to (Q-26).

[0059]

[0060]

[0061]

[0062] Next, the Debye shielding parameter q used in the Quisse paper. ｓ Since the formula was found to be difficult to apply to the high carrier concentration region, the Debye shielding parameter q is expressed by the following formulas (Qq-1) to (Qq-5), which can be applied to the degenerate semiconductor region with high carrier concentrations. ｓ This was modified as follows [C. Kittel, H. Kroemer, "Thermal Physics" Freeman, New York, 2nd ed. (1980) Chap.13 pp.367].

[0063] In other words, in one embodiment, the Debye shielding parameter q ｓ However, it is selected from the group consisting of the following formulas (Qq-1) to (Qq-5). In one embodiment, q represented by the following formula (Qq-2) ｓ Use this. [In equations (Qq-1) to (Qq-5), q is the elementary charge [C], ε ０ ε is the permittivity of vacuum [F / cm]. ｒ This is the relative permittivity (static), k Ｂ is the Boltzmann constant [eV / K], T is the temperature [K], and n is the free carrier concentration [cm³]. －３ ], N Ｃ The critical density for the Mott transition is [cm²]. －３ ] is. ]

[0064] The Debye shielding parameter q has been modified as described above. ｓ By applying this, the Quisse model in polycrystalline oxide semiconductors is 1 × 10⁻⁶ ２０ cm －３ We confirmed that it can be extended to a certain range of carrier concentrations. Also, a obtained from the Quisse model ＮＩ The carrier concentration dependence and temperature dependence were examined, and in the carrier concentration region corresponding to the plateau region in Figure 3(d), the scattering parameter a ＮＩ (corresponding to the reciprocal of mobility n) is T －３／２ When plotted, it was found that the extrapolated values ​​converged to a single point. This means that T ０ a that has a dependency ＮＩmeans the presence of components. It was confirmed that the experimental results were supported by the Quisse model.

[0065] In addition, in the high carrier concentration region of 1×10 １８ cm －３ or more, it was confirmed that a ＮＩ decreases. Although this result does not directly explain the change of a ０ (n) in Fig. 3(d) in the high carrier concentration region, it is not a deviation like the Erginsoy model, suggesting that it can be explained by a combination with other scattering factors.

[0066] (7-3) Approximate analytical formula of neutral impurity scattering Quisse model So far, the verification results of the Quisse paper have been described. Considering the expansion of the model formula to the simulator, in the Quisse model, a total of 24 analytical formulas need to be combined to calculate the total scattering cross section Q, and further numerical calculations are required when calculating the mobility, which may cause restrictions on the program loaded with the model formula. Therefore, an attempt was made to obtain an analytical formula for mobility by using an approximate formula that can be integrated for the behavior of the total scattering cross section Q in the Quisse model. Specifically, regarding the double logarithmic graph of Q / πa ０ ２ - ka ０ as a right trapezoid with a fixed hypotenuse, as shown in Fig. 4, the height D of the upper base is q ｓ a ０ a function of (n, T) was used and incorporated into the integral calculation during mobility calculation.

[0067] By expanding the formula, a Quisse-type approximate analytical formula represented by the following formula (A3Q-app) was obtained. Therefore, in one embodiment, the mobility μ ＮＩ [cm ２ / Vs] can be expressed by the following approximate formula (A3Q-app).

[0068] [In formula (A3Q-app), e is the elementary charge of electricity [C], and μ ＮＩ s is the mobility [cm ２ calculated by the neutral impurity scattering model determined by the Quisse-type approximate analytical formula. / Vs] and a ０ is the Bohr radius [cm], and is given by the following formula: (In the formula, ε ０ ε is the permittivity of vacuum [F / cm]. ｒ This is the relative permittivity (static), m ＊ This is the effective mass normalized at the speed of light [eV / c ２ It is expressed as follows: (where c is the speed of light [cm / s], and e is the elementary charge [C]), and C is given by the following formula: (In the formula, a ０ , and m ＊ As stated above, k Ｂ ) is the Boltzmann constant [eV / K], and T is the temperature [K]. ) where D is the empirical Q / πa in the Quisse model k=0. ０ ２ value (q ｓ a ０ (function of cm) ２ ], k' １ This is the Quisse model Q / πa shown in Figure 4. ０ ２ -ka ０ Equation in the graph: Q / πa ０ ２ = D (upper base of the right trapezoid) and equation: Q / πa ０ ２ = 4 (ka ０ ) －３ The horizontal axis value (ka) of the intersection of the hypotenuses of the right trapezoid ０ Value), N ＮＩ This is the neutral impurity scattering concentration [cm²]. －３ ] is. ]

[0069] In one embodiment, the parameters D and k' in formula (A3Q-app) are １ However, each can be expressed by the following formulas. [In the formula, D is the empirical Q / πa at k=0 in the Quisse model.] ０ ２ value, a ０ q is the Bohr radius [cm], and is defined in the same way as in the above formula (A3Q - app), and q ｓ This is the modified Debye occlusion parameter [cm] described above. －１] and is expressed by the above formula (Qq-2). [In the formula, k' １ This is the Q / πa of the Quisse model, as shown in Figure 4. ０ ２ -ka ０ Q / πa in the graph ０ ２ = D (upper base of the right trapezoid) and Q / πa ０ ２ = 4 (ka ０ ) －３ ka at the intersection of the hypotenuses of the right trapezoid ０ The value D is the empirical Q / πa in the Quisse model k=0. ０ ２ value (q ｓ a ０ (function of cm) ２ ] is. ]

[0070] Furthermore, the approximate formula for D and the Quisse model Q / πa ０ ２ -ka ０ The formula for representing the hypotenuse of a right-angled trapezoid in a graph is not limited to the formula described above; an approximation formula may be adjusted depending on the purpose.

[0071] Figure 5 shows each of the q shown in Figure 4. ｓ a ０ no ka ０ Q / πa at = 0 ０ ２ Value (Q) ０ @k ’ The values ​​(=0) are obtained from the Quisse model, and each q in Figure 4 ｓ a ０ This is a graph that approximates the upper base value D in the equation. In fact, it was confirmed that the results of the Quisse model and the above approximate analysis formula (A3Q-app) show good agreement. From the above, the neutral impurity scattering parameter a ＮＩ It became possible to express (n) using a Quisse-type approximate analytical formula.

[0072] (7-4) Ionized Impurity Scattering (Degenerate) Model As described above, we were able to model the scattering of neutral impurities, but the scattering parameter a ０ (n) of which, carrier concentration (3 × 10 １７ cm－３ The above behaviors are difficult to explain solely by neutral impurity scattering. ０ Since (n) is the dominant factor in TFT mobility, it is preferable to investigate scattering models other than those mentioned above and elucidate the behavior in all carrier concentration ranges. After thorough investigation, it was found that ionized impurity scattering (degeneracy) is μ(T)∝T ０ It was found that this relationship exists and has been reported as a scattering mechanism for transparent conductive films.

[0073] Here, the Dingle model [RB Dingle, Philos. Mag. 46 831 (1955)] was commonly used as the mobility model for ionized impurity scattering (degeneracy), so we examined it in detail. Furthermore, the shielding parameter F ＩＩ Regarding this, after careful selection, it was found that the Pisarkiewicz type [T. Pisarkiewicz, et. al., Thin Solid Films 174 217 (1989)] is optimal, similar to the ionized impurity scattering (non-degenerate) method mentioned above.

[0074] In one embodiment, the mobility μ is determined by the ionized impurity scattering (degeneracy) model. ＩＩ （Ｄｅｇ） [cm ２ / Vs] can be represented by a Dingle-type mobility model. In one embodiment, the Dingle-type mobility model can be represented by the following mobility formula (A4D).

[0075] [In formula (A4D), ε ０ ε is the permittivity of vacuum [F / cm]. ｒ is the relative permittivity (static), Z is the ionic charge of the ionized impurity, m ＊ This is the effective mass normalized at the speed of light [eV / c ２ ] (c is the speed of light [cm / s]), F ＩＩ is the shielding function in ionized impurity scattering, and n is the free carrier concentration [cm³]. －３ ], N ＩＩ＿Ｄｅｇ This is the ionized impurity concentration (degeneracy) [cm²] －３ ] is. ]

[0076] On the other hand, there is a concern that ionized impurities will neutralize as the carrier concentration increases, so when confirming the scattering effect, it is necessary to consider the influence of the energy position and shape of the donor level, using the ionized impurities as donors. Also, the polycrystalline oxide semiconductor sample in this case is N ２ Since the carrier concentration is increased by the annealing process, or in other words, the number of electrons increases along with the oxygen vacancy, the donor self-formation process must also be considered. On the other hand, in the non-degenerate region, there are many ionized donors, and the number of self-formed donors is also smaller than that of the initial donors, so these effects can be considered negligible.

[0077] When calculations are performed that incorporate the neutralization of donor levels and the contribution of self-forming donors, it is found that even if the donor level is Gaussian or a donor with no energy level width (hereinafter referred to as a simple donor), by positioning the donor level at least 30 meV closer to the vacuum level than the CBM (lower end of the conduction band) and setting an appropriate impurity concentration, a high carrier concentration region (1 × 10⁻¹⁰) can be achieved. １９ cm －３ a in the above region) ０ (n) It was found that the behavior could be reproduced. In conclusion, a model was adopted in which a simpler donor level exists at a sufficiently high energy level relative to the CBM and does not undergo neutralization, and the following equation (A4-1) was obtained.

[0078] In one embodiment, the mobility μ is determined by the ionized impurity scattering (degeneracy) model. ＩＩ （Ｄｅｇ） [cm ２ The [Vs] is of the Dingle type and can be expressed by the following mobility formula (A4-1), which also takes into account the donor's autogenetic process. [In formula (A4-1), ε ０ ε is the permittivity of vacuum [F / cm]. ｒ This is the relative permittivity (static), m ＊ This is the effective mass normalized at the speed of light [eV / c ２ ] (where c is the speed of light [cm / s]), e is the elementary charge [C], F ＩＩ is the shielding function in ionized impurity scattering, Z is the ionic charge of the ionized impurity, and NＩＩ＿Ｄｅｇ This is the ionized impurity concentration (degeneracy) [cm²] －３ ], n is the free carrier concentration [cm³] －３ ] is. ]

[0079] In one embodiment, the shielding function F in the Dingle-type mobility formula (A4D) or (A4-1) ＩＩ However, the shielding function F in Pisarkiewicz-type ionized impurity scattering, represented by the above equation (F), is ＩＩ That is the case.

[0080] (7-5) T ０ Verification of the scattering model with dependency Next, T ０ Regarding the scattering model with dependency, the approximate analytical formula of the neutral impurity scattering Quisse model obtained so far, and the ionized impurity scattering (degenerate) Dingle model adapted to the polycrystalline oxide semiconductor system, are used to obtain the scattering parameter a in Figure 3(d). ０ We checked whether the behavior of (n) could be explained. Specifically, Figure 6 shows the results of inputting parameters into the following equation (A4-S), which is obtained by introducing a sigmoid function to the above equation (A3Q-app) (approximate analysis formula for the neutral impurity scattering Quisse model) and the above equation (A4-1) (ionized impurity scattering (degenerate) Dingle model).

[0081] As shown in Figure 6, the following equation (A4-S), which incorporates the above equation (A3Q-app) and the above equation (A4-1), reproduced the experimental results well. It should be noted that a slight temperature dependence is observed for the above equation (A3Q-app). Furthermore, the critical density N for the Mott transition is given by the following equation (A4-S). Ｃ (In this system, 2 x 10 １８ cm －３ A sigmoid function is introduced to represent the transition from degeneracy to non-degeneracy with the boundary at (Figure 6 shows the sigmoid a parameter set to 2). In any case, by adjusting the parameter from Figure 6, a ０ The behavior of (n) can be explained, and it has been verified that the following equation (A4-S), which incorporates the above equation (A3Q-app) and the above equation (A4-1), is actually usable.

[0082] Therefore, in one embodiment, the Dingle-type mobility formula represented by formula (A4D) or formula (A4-1) is μ ＩＩ＿Ｄｉｎｇｌｅ （Ｄｅｇ） [cm ２ When [Vs] is used, the mobility μ is determined by the ionized impurity scattering (degenerate) model. ＩＩ （Ｄｅｇ） [cm ２ The expression [Vs] can be expressed as a sigmoid function (A4-S) with respect to the free carrier concentration n. [In formula (A4-S), N Ｃ The critical density for the Mott transition is [cm²]. －３ ], n is the free carrier concentration [cm³] －３ ], where a is a parameter that represents the rate of change of the sigmoid function.

[0083] (8) Intragranular mobility μ ｉｎ－ｇｒａｉｎ Modeling (T) By using the model equation obtained from the physical modeling of the various scattering parameters described above, the intragranular mobility μ ｉｎ－ｇｒａｉｎ A model can be constructed to calculate this.

[0084] In one embodiment, the mobility calculated by the neutral impurity scattering model is expressed by the equations (Q-1) to (Q-26) above, which are determined by the Quisse-type mobility model.

[0085] In one embodiment, in formulas (Q-1) to (Q-26), the Debye shielding parameter q ｓ However, it is represented by an equation selected from the group consisting of the above equations (Qq-1) to (Qq-5), and preferably by the above equation (Qq-2).

[0086] In one embodiment, the mobility calculated by the neutral impurity scattering model is expressed by the approximate formula (A3Q-app) determined by the Quisse-type mobility model.

[0087] In one embodiment, the effective mass m ＊ However, it can be expressed by either of the following equations (M-1) or (M-2). [In formulas (M-1) and (M-2), m ＊ This is the effective mass normalized at the speed of light [eV / c２ ] (where c is the speed of light [cm / s]), m ０ ＊ This is the minimum effective mass at the lower end of the conduction band or the upper end of the valence band [eV / c ２ ] (where c is the speed of light [cm / s]), α' is the nonparabolic coefficient relating to the band curvature of the conduction band or valence electrons (where α'≧0 and α'=0 the E-k band in wavenumber k space is parabolic, and as α' increases it becomes nonparabolic and the band broadens), E is the energy [eV], n is the free carrier concentration [cm －３ ] is. ]

[0088] In one embodiment, the parameters D and k' in formula (A3Q-app) are １ However, these can be expressed by the aforementioned formulas (D-1) and (D-2), respectively.

[0089] In one embodiment, the mobility μ is as shown below. ｉｎ－ｇｒａｉｎ The step of calculating (intragranular mobility) is to use the free carrier concentration in the oxide semiconductor to determine the ionized impurity concentration N in the non-degenerate region. ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The steps include calculating the ionized impurity concentration N in the non-degenerate region. ＩＩ＿ｎｏｎＤｅｇ Mobility μ calculated using ＩＩ （ｎｏｎＤｅｇ） And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ Mobility μ calculated using ＩＩ （Ｄｅｇ） Using and , mobility μ ｉｎ－ｇｒａｉｎ The step of calculating the ionized impurity concentration N in the non-degenerate region may also be included. In this embodiment, for example, the ionized impurity concentration N in the non-degenerate region may be included. ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The ionized impurity concentration N in the non-degenerate region is calculated using the formula described below. ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ By substituting this into the ionized impurity scattering model described above, the mobility μ ｉｎ－ｇｒａｉｎ You may calculate this.

[0090] Furthermore, in one embodiment, the ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ However, the ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The boundary is when the sum of is constant and the free carrier concentration is the same as or approximately the same as the critical density of the Mott transition, and the ionized impurity concentration N in the non-degenerate region is defined as such. ＩＩ＿ｎｏｎＤｅｇ And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The relationship between the magnitudes of the values ​​may be expressed in a way that switches continuously. A value equivalent to the critical density of the Mott transition may mean a value that falls within a range of, for example, ±10%, ±8%, ±5%, ±3%, ±1%, ±0.5%, or ±0.1% centered on the density corresponding to the critical density of the Mott transition.

[0091] At this time, the ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ However, they may also be calculated using the following formulas (2) and (3). (N ＩＩ (where is the ionized impurity concentration and f is a sigmoid function with the free carrier concentration as a variable.) Thus, in this embodiment, the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ And the ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ This can be calculated based on a sigmoid function with free carrier concentration as a variable.

[0092] The sigmoid function f is calculated using the following formula (A130): (n is the free carrier concentration, N ｃ is the critical density for the Mott transition (the density corresponding to the critical density for the Mott transition), and a ２ (where is the width of the sigmoid function.)

[0093] In one embodiment, the intragranular mobility μ of the semiconductor is ｉｎ－ｇｒａｉｎ However, it is calculated using the following formula (A1-1). [In formula (A1-1), μ ＯＰμ is the mobility calculated by the optical phonon scattering model, and may be calculated by the above formula (A2) or (A2-2), ＮＩ μ is the mobility calculated by the neutral impurity scattering model, and may be calculated by the Quisse-type mobility model using the above formula (A3E), the above formulas (Q-1) to (Q-26), or the above formula (A3Q-app), μ ＩＩ （Ｄｅｇ） μ is the mobility calculated by the ionized impurity scattering model of the degenerate region, and may be calculated by the above formulas (A4), (A4-1), or (A4-S), ＩＩ （ｎｏｎＤｅｇ） This is the mobility calculated by the ionized impurity scattering model in the non-degenerate region, and may be calculated by the above formulas (A5-CW), (A5-BH), or (A5-S), Z ＯＰ Z ＮＩ Z ＩＩ＿Ｄｅｇ Z ＩＩ＿ｎｏｎＤｅｇ is 0 or 1, Z ＯＰ Z ＮＩ Z ＩＩ＿Ｄｅｇ , and Z ＩＩ＿ｎｏｎＤｅｇ At least two selected from the group consisting of are 1, preferably at least Z ＩＩ＿Ｄｅｇ , and Z ＩＩ＿ｎｏｎＤｅｇ is 1, and far Z ＯＰ Z ＮＩ Z ＩＩ＿Ｄｅｇ , and Z ＩＩ＿ｎｏｎＤｅｇ All of them are 1.

[0094] In one embodiment, the mobility μ is determined by the ionized impurity scattering (degenerate) model represented by formula (A4D) or (A4-1). ＩＩ （Ｄｅｇ） And, and mobility μ determined by the ionized impurity scattering (non-degenerate) model represented by the formula (A5-CW) or (A5-BH) above. ＩＩ （ｎｏｎＤｅｇ） However, the critical density N for the Mott transition is relative to the carrier concentration n. Ｃ They are linearly combined by sigmoid functions with respect to the boundary, and each has a shielding function F ＩＩ However, the Pisarkiewicz type F represented by the above formula (F) ＩＩ That is the case.

[0095] The embodiments described above may be combined as appropriate. For example, in one embodiment, the ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The above equations (2) and (3) are used to calculate the intragranular mobility μ of the semiconductor. ｉｎ－ｇｒａｉｎ This can be calculated using the above formula (A1-1).

[0096] 2.2. Method for Calculating Macroscopic DC Mobility μ(T) of Semiconductors A method for calculating the macroscopic mobility μ(T) of a semiconductor according to one aspect of the present invention (hereinafter sometimes abbreviated as "macroscopic mobility calculation method") uses a computer to calculate the mobility μ within the crystal grains of an oxide semiconductor using a scattering model at the crystal grain boundaries of the oxide semiconductor. ｉｎ－ｇｒａｉｎ The procedure may include the step of performing a step to calculate the macroscopic mobility μ of the oxide semiconductor.

[0097] The macroscopic mobility μ of a semiconductor obtained by the calculation method of this embodiment is the calculated mobility value used in actual device simulations. Here, "macroscopic mobility of a semiconductor" refers to the mobility of the carriers responsible for electrical conduction, calculated from the resistance value, which is the real part of the complex impedance obtained when a voltage is applied to the entire semiconductor material formed as a thin film and the current is measured.

[0098] The intragranular mobility μ of the semiconductor obtained by the above formula (A101), the following formula (1-1), the above formula (A1-1), or the following formula (A1-2) ｉｎ－ｇｒａｉｎ By using this method, the macroscopic DC mobility μ(T) of a semiconductor, represented by the following formula (A10), can also be calculated.

[0099] In one embodiment, the intragranular mobility μ of the semiconductor is as shown in the following formula (1-1). ｉｎ－ｇｒａｉｎ As the reciprocal of (T), 1 / (exp(β / T)-1), T ０ , T －３／２ , T １／２ and T ３／２ Two or more terms selected from the group consisting of, and 1 / μ such that the temperature dependence is a function of the carrier concentration n. ＮＩ The (T, n) term may also be used.

[0100] [In formula (1-1), μ ｉｎ－ｇｒａｉｎ This is the intragranular mobility of a semiconductor [cm²]. ２ / Vs], T is temperature [K], β[K], a １ [cm －２ Vs], a ２ [cm －２ Vs], a ３ [cm －２ Vs. K ３／２ ], a ４ [cm －２ Vs. K －１／２ ], and a ５ [cm －２ Vs. K -３／２ ] represents the coefficients, respectively. However, in the above formula (1-1), the above 1 / (exp(β / T)-1), T ０ , T －３／２ , T １／２ and T ３／２ The coefficient a of the unselected term １ ~a ５ Let it be 0.

[0101] Furthermore, in one embodiment, the above formula (1-1) can be expressed by the following formula (A1-2). [In formula (A1-2), μ ＯＰ μ is defined as shown in formula (A2) below, or formula (A2-2) above, ＩＩ （Ｄｅｇ） μ is defined as in the above formulas (A4D), (A4-1), or (A4-S), ＩＩ （ｎｏｎＤｅｇ） μ is defined as in the above formulas (A5-CW), (A5-BH), or (A5-S), ＮＩ (T, n) is defined as a Quisse-type mobility model using equations (Q-1) to (Q-26) above, or as defined by equation (A3Q-app).

[0102] Here, in one embodiment, the coefficient of the 1 / (exp(β / T)-1) term in formula (A101) is a １ [cm －２ Vs is the mobility μ determined by the optical phonon scattering model. ＯＰIt can be expressed as the mobility μ determined by the optical phonon scattering model. ＯＰ [cm ２ The reciprocal of [Vs] is expressed by the following formula (A2). [In equation (A2), T is the temperature [K], and β [K] is the coefficient.]

[0103] That is, 1 / μ represented by the above formula (A2) ＯＰ This is the term in formula (A101) above. It corresponds to.

[0104] In one embodiment, the macroscopic DC mobility μ(T) of a semiconductor can be calculated using the following formula (A10). [In equation (A10), q is the elementary charge [C], V Ｂ The grain boundary barrier height [eV], k Ｂ is the Boltzmann constant [eV / K], where T is the temperature [K], μ ｉｎ－ｇｒａｉｎ (T) is the intragranular mobility μ of the semiconductor. ｉｎ－ｇｒａｉｎ The intragranular mobility of the semiconductor obtained by the calculation method of (T) [cm ２ [Vs] is the case.

[0105] In one embodiment, V in formula (A10) Ｂ This is expressed by the following formula (A11). [In formula (A11), α is the following formula] (In the formula, ε ０ ε is the permittivity of vacuum [F / cm]. ｒ n is the relative permittivity (static), and n is the free carrier concentration [cm³]. －３ ] (In oxide semiconductors dealt with in this specification, the free electron density [cm －３ ] is equal to), e is the elementary charge [C], N Ｔ The grain boundary trap density [cm³] －２ eV －１ ] is expressed as ) and δ ＥＦ V is the Fermi energy difference [eV] between the grain boundary and within the grain. Ｂ It is ≥ 0.

[0106] In one embodiment, δ ＥＦ The formula is as follows: (In the formula, E Ｆ ＧＢ E is the Fermi energy [eV] at the grain boundary. Ｆ Ｇ This is the Fermi energy [eV] within the grain. It may be calculated as follows:

[0107] Thus, in the method for calculating the mobility of an oxide semiconductor according to this embodiment, a computer uses a scattering model at the grain boundaries of the oxide semiconductor to calculate the Fermi energy difference δ between the grain boundaries and within the grains. ＥＦ Using the height V of the grain boundary barrier between the grain boundary and the inside of the grain, Ｂ The process may further include a step of performing a step to calculate [the result].

[0108] In the method for calculating the mobility of the oxide semiconductor according to this embodiment, a computer is used with a scattering model at the grain boundaries of the oxide semiconductor to calculate the free carrier concentration and the effective density of states N within the crystal grains. ｃ０ The Fermi energy difference δ is used with ＥＦ The process may further include a step of performing a step to calculate [the result].

[0109] At this time, the Fermi energy difference δ ＥＦ This may be calculated, for example, using the following formula (4). [In formula (4), δ ＥＦ０ This is the Fermi energy difference δ at absolute zero or when the free carrier concentration is equal to the effective density of states. ＥＦ And n is the free carrier concentration [cm³]. －３ ] and N ｃ０ The effective density of states [cm³] －３ ] and Z δＥＦＴｎ is a coefficient. ] Here, Z δＥＦＴｎ The Fermi energy difference is δ ＥＦ This is a coefficient that adjusts the dependence of temperature and free carrier concentration in the system, and is an appropriate value (for example, -10 to 10, -5 to 5, -2 to 2, -1 to 1, 0 to 1, or 0 or 1).

[0110] In one embodiment, the mobility μ in formula (A10) is shown. ｉｎ－ｇｒａｉｎThe reciprocal of (T) can be expressed by any of the above equations (1-1), (A1-1), and (A1-2).

[0111] Furthermore, in this specification, q (elementary charge 1.602 x 10) －１９ [C]) is the same as e (elementary charge [C]) above.

[0112] The intragranular mobility μ of the semiconductor is calculated by the above formula (A-1). ｉｎ－ｇｒａｉｎ Furthermore, the macroscopic mobility μ of the semiconductor calculated by the above formula (A10) will be shown to be in good agreement with the measured value of the measurement sample, as will be demonstrated in the examples described later.

[0113] 3. Method for Calculating the Mobility of an Oxide Semiconductor Using a Regression Model In the method for calculating the mobility of an oxide semiconductor according to this embodiment, as described above, two or more terms calculated by a computer using the free carrier concentration in the oxide semiconductor may be calculated by a regression model generated based on measured values ​​of mobility and free carrier concentration. In this case, in the method for calculating the mobility of an oxide semiconductor according to this embodiment, the mobility may be calculated by the regression model from the logarithm of the sum of two or more terms of an exponential function with free carrier concentration as a variable.

[0114] Furthermore, the step of calculating the mobility described above includes the step of calculating the macroscopic mobility μ of the oxide semiconductor using the regression model described above, and the regression model is given by the following equation: [In formula (1), a １ a ２ , b １ , b ２ , and c are constants of a regression equation set based on the measured values, μ is the macroscopic mobility of the oxide semiconductor, and n is the free carrier concentration. This may be expressed as follows:

[0115] As described above, in the method for calculating the mobility of an oxide semiconductor according to this embodiment, the two or more terms calculated by the computer using the free carrier concentration in the oxide semiconductor may be, for example, two or more terms in the argument part of the logarithm, as shown in formula (1) above.

[0116] 4. Device Simulation Method A device simulation method for determining the macroscopic DC mobility μ(T) of a semiconductor according to one aspect of the present invention involves performing a device simulation that simulates a device containing an oxide semiconductor, using the semiconductor mobility μ.

[0117] By using the device simulation method of this embodiment, it is possible to design a device with high reliability before actually fabricating a semiconductor device.

[0118] The device simulation method according to the embodiments of this disclosure may include, for example, the step of having a computer perform a device simulation to simulate a device containing the oxide semiconductor in question, using the mobility of the oxide semiconductor calculated by the method described above.

[0119] In this case, the step of performing the above device simulation may include the steps of calculating the carrier density in the oxide semiconductor using the density of states of defects in the oxide semiconductor contained in the device, and calculating the current flowing through the device using the mobility μ and the carrier density.

[0120] Here, the density of states of the above defects includes an acceptor-like exponential distribution, and the acceptor-like exponential density of states g ＴＡ This is the energy E at the lower end of the conduction band. ｃ Density of states N of acceptor-like defects in ＴＡ 10 １０ ~10 ２２ cm －３ / eV, the reciprocal of the slope of the acceptor-like defect density of states W ＴＡ The value may be in the range of 0.001 to 0.5 eV.

[0121] The above acceptor-like exponential distribution g ＴＡ (E) may also be calculated by the following formula (5). [In formula (5), N ＴＡ This is the energy E at the lower end of the conduction band. ｃ Density of states of acceptor-like defects in [cm²] －３ / eV] and WＴＡ E is the reciprocal of the slope of the acceptor-like defect's density of states [eV], where E is the energy of the acceptor-like defect [eV], and E ｃ This is the energy at the lower end of the conduction band [eV]. Furthermore, the step of performing a device simulation may include the step of calculating the heat generation effect due to the current flowing through the oxide semiconductor and the heat dissipation effect due to the thermal conductivity and boundary conditions of the oxide semiconductor.

[0122] In this embodiment, the density of states of the semiconductor may include, for example, at least one of the following: an acceptor-like exponential function distribution, an acceptor-like Gaussian function distribution, a donor-like exponential function distribution, or a donor-like Gaussian function distribution.

[0123] Furthermore, in this embodiment, the macroscopic DC mobility at room temperature of 25°C is 10 １５ ~10 ２０ cm －３ In the carrier density range of 1 to 200 cm ２ / Vs is also acceptable.

[0124] Furthermore, in this embodiment, the maximum value of the semiconductor density of states is 10 １０ ~10 ２２ cm －３ / eV is also acceptable.

[0125] Furthermore, in the device simulation method according to this embodiment, for example, the drain current of a transistor such as a thin-film transistor may be simulated. In this case, for example, the carrier density distribution accumulated in the channel during transistor operation may be calculated using the applied voltage and density of states, and the drain current may be calculated by combining this carrier density distribution with the macroscopic mobility μ.

[0126] (Simulation Service) By using the device simulation method of this embodiment, it is possible to provide a simulation service that accepts input of necessary physical properties from the customer and presents the simulation results to the customer.

[0127] 5. Method for Manufacturing Semiconductor Devices A method for manufacturing semiconductor devices according to one aspect of the present invention comprises the steps of: performing a device simulation including the device simulation method described above; and performing a device design based on the device simulation results obtained in the step of performing the device simulation.

[0128] In one embodiment, the semiconductor device to be manufactured may be a thin-film transistor, or a device including a thin-film transistor. The thin-film transistor has electrodes, an oxide semiconductor film, and an insulating film. Examples of electrodes include a source electrode, a drain electrode, and a gate electrode, and examples of insulating films include a gate insulating film and a protective film. As for the configuration of the thin-film transistor, for example, a conventionally known configuration can be adopted.

[0129] In one embodiment, a semiconductor device may be manufactured based on the device design carried out as described above. The manufacturing process for the semiconductor device after the device design can employ, for example, a conventionally known configuration. For example, the oxide semiconductor contained in the semiconductor device can be manufactured by sputtering or atomic layer deposition (ALD).

[0130] By using the semiconductor mobility calculation method or device simulation method according to one aspect of the present invention described above, semiconductor devices with desired performance can be manufactured efficiently.

[0131] As described above, in the method for manufacturing a semiconductor device according to this embodiment, the oxide semiconductor may be an oxide mainly composed of In.

[0132] Furthermore, in the method for manufacturing a semiconductor device according to this embodiment, the oxide semiconductor may be a polycrystalline oxide semiconductor.

[0133] Examples of semiconductor devices include oxide semiconductor films, thin-film transistors, and various integrated circuits such as logic circuits, memory circuits, and differential amplifier circuits. Oxide semiconductor films can be applied, for example, as a layer in a solar cell, and as a layer in a display device such as a liquid crystal element, an organic electroluminescent element, an inorganic electroluminescent element, a micro-organic EL display, a micro-LED (Light Emitting Diode) display, a mini-LED display, and electronic paper. Furthermore, oxide semiconductor films can be applied as a layer in a solid-state image sensor, an X-ray sensor, a power semiconductor element, a touch panel, an LSI (Large Scale Integrated Circuits), a resistive random-access memory, a DRAM (Dynamic Random Access Memory), a ferroelectric memory, a BEOL (Back End of Line), and a microprocessor. Furthermore, oxide semiconductor films can be used as semiconductor layers in field-effect transistors, electrostatic-induced transistors, quantum tunneling field-effect transistors, Schottky barrier transistors, Schottky diodes, PN diodes, and resistive elements, as well as as parts of these layers.

[0134] 6. Electronic Devices Semiconductor devices according to the embodiments of this disclosure may be manufactured by the semiconductor device manufacturing method described above. Semiconductor devices may be mounted in electronic devices. Examples of electronic devices include solar cells, liquid crystal elements, organic electroluminescent elements, inorganic electroluminescent elements, micro-organic EL displays, micro-LED (Light Emitting Diode) displays, mini-LED displays, electronic paper, solid-state image sensors, X-ray sensors, power semiconductor elements, touch panels, LSIs (Large Scale Integrated circuits), resistive random-access memory, DRAM (Dynamic Random Access Memory), ferroelectric memory, BEOL (Back End of Line), microprocessors, and the like.

[0135] An electronic device according to one aspect of the present invention may include a semiconductor device manufactured using the semiconductor device manufacturing method according to the above-described aspect of the present invention.

[0136] 7. Information Processing Apparatus An information processing apparatus according to the embodiment of the present disclosure is an information processing apparatus for calculating the mobility of an oxide semiconductor, which performs a step of calculating the mobility using two or more terms calculated using the free carrier concentration in the oxide semiconductor, wherein the two or more terms may be calculated by a scattering model derived considering the free carrier concentration in the oxide semiconductor, or by a regression model generated based on measured values ​​of mobility and free carrier concentration.

[0137] The information processing device 100 according to this embodiment will be described with reference to Figure 7. Figure 7 is an example of a functional block diagram of the information processing device 100 according to this embodiment. The information processing device 100 includes an input unit 110, a registration unit 120, an acquisition unit 130, a mobility calculation unit 140, an output unit 150, and a storage unit 160.

[0138] For example, more specifically, the information processing device 100 according to this embodiment may include an input unit 110 configured to receive input of information about an oxide semiconductor that is the target of calculating mobility and / or information about a mathematical formula used to calculate mobility; a registration unit 120 configured to register the information about the oxide semiconductor and / or information about a mathematical formula used to calculate mobility received by the input unit in a storage unit 160; a mobility calculation unit 140 that calculates the mobility of the oxide semiconductor based on the registered information about the oxide semiconductor and / or information about a mathematical formula used to calculate mobility; and an output unit 150 configured to output the calculated mobility.

[0139] Furthermore, the information processing device 100 according to this embodiment may include, for example, an input unit 110 configured to receive input of information relating to an oxide semiconductor that is the target of calculating mobility and / or information relating to a mathematical formula used to calculate mobility; an acquisition unit 130 configured to acquire information relating to an oxide semiconductor and / or information relating to a mathematical formula used to calculate mobility based on the information relating to an oxide semiconductor and / or information relating to a mathematical formula used to calculate mobility received by the input unit; a mobility calculation unit 140 that calculates the mobility of an oxide semiconductor based on the acquired information relating to an oxide semiconductor and / or information relating to a mathematical formula used to calculate mobility; and an output unit 150 configured to output the calculated mobility. In this case, the input unit 110 may be configured to receive input of identification information of an oxide semiconductor that is the target of calculating mobility and / or identification information of a mathematical formula used to calculate mobility, and the acquisition unit 130 may be configured to acquire information relating to an oxide semiconductor and / or information relating to a mathematical formula from a storage unit 160 based on the identification information of an oxide semiconductor and / or identification information of a mathematical formula.

[0140] Furthermore, the information processing device 100 according to this embodiment may include, for example, an input unit 110 configured to receive input of information relating to an oxide semiconductor that is the target of calculating mobility and / or information relating to a mathematical formula used to calculate mobility; a registration unit 120 configured to register the information relating to the oxide semiconductor and / or information relating to a mathematical formula used to calculate mobility received by the input unit in a storage unit 160; an acquisition unit 130 configured to acquire the registered information relating to the oxide semiconductor and / or information relating to a mathematical formula used to calculate mobility from the storage unit 160; a mobility calculation unit 140 that calculates the mobility of the oxide semiconductor based on the acquired information relating to the oxide semiconductor and / or information relating to a mathematical formula used to calculate mobility; and an output unit 150 configured to output the calculated mobility.

[0141] The input unit 110 receives information entered by the user, for example, which is used to calculate mobility. For example, the user inputs information about the oxide semiconductor for which mobility is to be calculated to the input unit 110. For example, if information about one or more oxide semiconductors for which mobility is to be calculated is stored in advance in the memory unit 160 or the like, the user may input identification information of the oxide semiconductor for which mobility is to be calculated (such as the name or identification number of the oxide semiconductor) to indicate which oxide semiconductor is to be calculated. Also, for example, if information about the oxide semiconductor for which mobility is to be calculated is not registered, the user may input information about the oxide semiconductor (such as its composition).

[0142] Furthermore, the user may input information such as a formula used to calculate mobility into the input unit 110. For example, if one or more formulas used to calculate mobility are pre-stored in the memory unit 160, the user may input identification information related to the formula (such as the name or identification number of the numerical model corresponding to the formula) to indicate which formula to use to calculate mobility. Also, for example, if no formula for calculating mobility is registered, the user may input a formula. In this case, the user may also input program code or the like corresponding to the formula.

[0143] The registration unit 120 may be configured to register, for example, information about the oxide semiconductor to be used for calculating mobility, which is received by the input unit 110, and information about the mathematical formula used for calculating mobility. The registration unit 120 may be configured to store, for example, the information about the oxide semiconductor to be used for calculating mobility and the information about the mathematical formula used for calculating mobility in the storage unit 160.

[0144] The acquisition unit 130 may be configured to acquire information from the storage unit 160 regarding oxide semiconductors corresponding to the input identification information when the input unit 110 receives identification information or the like regarding oxide semiconductors to be used for calculating mobility. Alternatively, the acquisition unit 130 may be configured to acquire information from the storage unit 160 regarding mathematical formulas corresponding to the input identification information when the input unit 110 receives identification information or the like regarding mathematical formulas used for calculating mobility.

[0145] Furthermore, the acquisition unit 130 may be configured to acquire data used for calculating mobility stored in the storage unit 160, for example. For example, the storage unit 160 stores information regarding the free carrier concentration of an oxide semiconductor to be used for calculating mobility, and the acquisition unit 130 may acquire information regarding the free carrier concentration from the storage unit 160. Also, for example, the storage unit 160 may store at least one of a scattering model derived considering the free carrier concentration in the oxide semiconductor, and a regression model generated based on measured values ​​of mobility and free carrier concentration, and the acquisition unit 130 may acquire at least one of the scattering model and the regression model from the storage unit 160.

[0146] The mobility calculation unit 140 is configured to calculate the mobility of an oxide semiconductor. The mobility calculation unit 140 may be configured to calculate the mobility of an oxide semiconductor, which is the target of the mobility calculation, using a mathematical formula or numerical model specified by the user input, for example, based on information input by the user to the input unit 110.

[0147] The output unit 150 may be configured to output the mobility calculated by the mobility calculation unit 140 to a display device or the like.

[0148] The storage unit 160 may store, for example, information about the oxide semiconductor for which mobility is to be calculated, as received by the input unit 110, as described above, and information about the mathematical formula used to calculate mobility. The storage unit 160 may also store information about the free carrier concentration of the oxide semiconductor for which mobility is to be calculated, and at least one of a scattering model derived considering the free carrier concentration in the oxide semiconductor and a regression model generated based on measured values ​​of mobility and free carrier concentration. The storage unit 160 may further store, for example, a program executed by the information processing device 100. The storage unit 160 may also store the mobility calculated by the mobility calculation unit 140.

[0149] 8. Program for Calculating the Mobility of Oxide Semiconductors A program for calculating the mobility of an oxide semiconductor according to one aspect of the present invention (hereinafter sometimes abbreviated as "mobility calculation program") is characterized in that a computer functions as: means for receiving input of measured values ​​of the mobility of the oxide semiconductor; means for setting initial conditions of a mobility model used for calculating the mobility; and means for calculating the mobility based on the initial conditions.

[0150] Here, the means for calculating the mobility is to calculate the mobility of the oxide semiconductor using at least one of the calculation methods detailed in "1. Method for calculating the mobility of an oxide semiconductor" to "3. Method for calculating the mobility of an oxide semiconductor using a regression model". Preferably, the mobility is calculated using two or more terms calculated using the free carrier concentration in the oxide semiconductor.

[0151] Furthermore, the mobility calculation program may further include means for accepting the selection of a mobility model to be used for calculating mobility. This means may allow the user to select a mobility model from among the mobility models detailed in "1. Method for Calculating Mobility of Oxide Semiconductors" to "3. Method for Calculating Mobility of Oxide Semiconductors Using a Regression Model". This means may allow the user to select a mobility model from the scattering model using equations (A10) and (A1-1), and the regression model using equation (1). If the scattering model using equations (A10) and (A1-1) is selected, the μ of equation (A1-1) ＯＰ , μ ＮＩ , ＩＩ （Ｄｅｇ） , and μ ＩＩ （ｎｏｎＤｅｇ） Regarding this, the user may be allowed to select the model equation to use from among the multiple model equations described above.

[0152] Referring to Figure 8, a process executed by a computer, for example, based on a mobility calculation program in one embodiment will be described. Figure 8 is a diagram showing an overview of the mobility calculation method executed by the program for calculating the mobility of an oxide semiconductor according to this embodiment.

[0153] In the operation procedure of the mobility calculation program, first, in step S802, the measured value of mobility is input to the computer. The measured value of mobility may be input by the user to the input unit 110, or it may be input by reading the measured value data registered in the registration unit 120. Note that acquiring the measured value may be performed separately from the mobility calculation flow, before the mobility calculation, or in parallel with the mobility calculation. In step S802, for example, measured data related to the material for which mobility is calculated is acquired. As measured data, for example, not only mobility but also current-voltage characteristics may be acquired.

[0154] Next, in step S804, the mobility model to be used is selected. At this point, the type of semiconductor material may also be selected. The mobility model and semiconductor material type entered here may be selected from, for example, a database registered in the registration unit 120. The database used here is built up by accumulating data as measured values ​​corresponding to the mobility model and semiconductor material type are entered and calculations are performed.

[0155] The mobility model may be selected from among the mobility models detailed in sections 1. Method for Calculating the Mobility of Oxide Semiconductors to 3. Method for Calculating the Mobility of Oxide Semiconductors Using a Regression Model, for example, from the scattering model using equations (A10) and (A1-1), and the regression model using equation (1). In this case, it is also possible to set which coefficients in the calculation formula of the mobility model are constants and which are variables. The type of material to be selected includes the composition of the semiconductor, the crystalline state (amorphous, single crystal, polycrystalline, etc.), the crystalline structure (space group, lattice constant, and atomic coordinates), etc.

[0156] In step S806, it is determined whether the initial conditions for the mobility model can be selected from the database. Specifically, it is queried whether the initial conditions for the mobility model selected in step S804 are registered in the database of the registration unit 120. If the initial conditions are registered in the database, the user is asked whether they want to use the registered initial conditions, and if the user chooses to use them, it is determined that the initial conditions for the mobility model can be selected from the database (YES in S806). If the initial conditions are not registered in the database, or if the user decides not to use the registered initial conditions, it is determined that the initial conditions for the mobility model cannot be selected from the database (NO in S806).

[0157] Initial conditions for a mobility model include the initial values ​​of the coefficients in the calculation formula used in the mobility model, the range of values ​​the coefficients can take, and the range of values ​​the calculated values ​​can take.

[0158] If it is determined that initial conditions for the mobility model can be selected from the database (YES in S806), the user is prompted to select initial conditions for the mobility model via the input unit 110 (S808). If there is only one selectable initial condition, confirmation of the selection to the user may be omitted. If there are multiple selectable initial conditions, the mobility calculation program may appropriately select the most suitable initial condition.

[0159] If it is determined that the initial conditions for the mobility model cannot be selected from the database (NO in S806), the user is prompted to input the initial conditions for the mobility model via the input unit 110 (S810). In this case, the user may be assisted in inputting the initial conditions by displaying the initial conditions for similar or related mobility models. Alternatively, instead of prompting the user to input the initial conditions, the mobility calculation program may set random values ​​as the initial conditions.

[0160] In step S812, the mobility of the oxide semiconductor is calculated using the mobility model selected in step S804, based on the initial conditions entered in step S808 or S810.

[0161] In step S814, the calculation result (calculated value) is compared with the measured data (measured value). For example, the calculated value and measured value of mobility are compared. Alternatively, the current-voltage characteristics of the calculation result may be compared with the current-voltage characteristics of the measured data.

[0162] If it is determined that the calculation result (calculated value) and the measured data (measured value) match (for example, that a predetermined evaluation index is within a predetermined tolerance range) (YES in S816), the process is terminated.

[0163] If it is determined that the calculation result (calculated value) and the measured data (measured value) do not match (for example, a predetermined evaluation index is outside a predetermined tolerance range) (NO in S816), the parameters set as initial conditions are changed (S818), and steps S812 to S816 described above are executed again. Steps S812 to S816 are repeated, for example, until the agreement between the measured value and the calculation result reaches a predetermined tolerance range (i.e., a certain error range). The "predetermined tolerance range" may be, for example, a range of 10% or less of the mobility when determined using the maximum absolute error MAE.

[0164] The processing procedure described with reference to Figure 8 is illustrative, and the operation procedure of the mobility calculation program according to this embodiment is not limited thereto. For example, the steps described above do not have to be executed in this order and may be changed as appropriate. For example, in step S816, instead of determining whether the calculation result (calculated value) and the measured data (measured value) match, it may be determined whether the execution of the movement calculation (S812) and the condition change (S818) have been repeated a predetermined number of times, and the process may be terminated if they have been repeated a predetermined number of times.

[0165] The obtained calculation results may be displayed on a display device or stored in the database of the registration unit 120.

[0166] 9. Device Simulation System The device simulation system 200 according to this embodiment will be described with reference to Figure 9. Figure 9 is an example of a functional block diagram of the device simulation system 200, which is an information processing device that performs device simulation according to this embodiment.

[0167] The device simulation system 200 includes an input unit 210, a registration unit 120, an acquisition unit 230, a simulation execution unit 240, a measured data comparison unit 250, a condition change unit 260, an output unit 270, and a storage unit 280. The device simulation system 200 according to this embodiment may include, for example, an input unit 210 configured to receive information input by a user regarding the conditions used to execute a device simulation; a registration unit 220 configured to register the information used to execute the device simulation received by the input unit in a storage unit 280; a simulation execution unit 240 configured to execute a device simulation based on the registered information used to execute the device simulation; a measured data comparison unit 250 configured to compare the simulation results executed by the simulation execution unit 240 with measured data; a condition change unit 260 configured to change conditions such as boundary conditions for executing the simulation based on the comparison results between the simulation results and measured data by the measured data comparison unit 250; and an output unit 270 configured to output the simulation results executed by the simulation execution unit 240 and / or the comparison results between the simulation results and measured data by the measured data comparison unit 250.

[0168] Furthermore, the device simulation system 200 according to this embodiment may also include, for example, an input unit 210 configured to receive information input by a user regarding the conditions used to execute the device simulation; an acquisition unit 230 configured to acquire information regarding the conditions used to execute the device simulation from a storage unit 280 based on the information used to execute the device simulation received by the input unit; a simulation execution unit 240 configured to execute the device simulation based on the acquired information regarding the conditions used to execute the device simulation; a measured data comparison unit 250 configured to compare the simulation results executed by the simulation execution unit 240 with measured data; a condition change unit 260 configured to change conditions such as boundary conditions for executing the simulation based on the comparison results between the simulation results and measured data by the measured data comparison unit 250; and an output unit 270 configured to output the simulation results executed by the simulation execution unit 240 and / or the comparison results between the simulation results and measured data by the measured data comparison unit 250. In this case, the input unit 210 may be configured to accept, for example, identification information relating to the conditions used to execute the device simulation, and the acquisition unit 230 may be configured to acquire information relating to the conditions used to execute the device simulation from the storage unit 280 based on the identification information relating to the conditions used to execute the device simulation.

[0169] Furthermore, the device simulation system 200 according to this embodiment may also include, for example, an input unit 210 configured to receive information input by a user regarding the conditions used to execute a device simulation; a registration unit 220 configured to register the information used to execute the device simulation received by the input unit 210 in a storage unit 280; an acquisition unit 230 configured to acquire the registered information used to execute the device simulation from the storage unit 280; a simulation execution unit 240 configured to execute a device simulation based on the acquired information used to execute the device simulation; a measured data comparison unit 250 configured to compare the simulation results executed by the simulation execution unit 240 with measured data; a condition change unit 260 configured to change conditions such as boundary conditions for executing the simulation based on the comparison results between the simulation results and measured data by the measured data comparison unit 250; and an output unit 270 configured to output the simulation results executed by the simulation execution unit 240 and / or the comparison results between the simulation results and measured data by the measured data comparison unit 250.

[0170] The input unit 210 may be configured to accept information input by the user, for example, regarding conditions used for running device simulations. The input unit 210 may be configured to accept information input by the user, for example, regarding the structure and materials of the device, information regarding boundary conditions such as voltage, temperature, and heat generation calculations, information regarding the density of states of the oxide semiconductor, and information regarding the mobility model of the oxide semiconductor used for device simulations.

[0171] In the device simulation system 200 according to this embodiment, for example, the storage unit 280 may have a device information database 280a, a boundary condition information database 280b, a density of states information database 280c, and a mobility model information database 280d, and the above-mentioned information regarding devices, boundary conditions, density of states, and mobility models may be stored in the device information database 280a, boundary condition information database 280b, density of states information database 280c, and mobility model information database 280d, respectively. In this case, the input unit 210 may be configured to receive, for example, information identifying the information regarding devices, boundary conditions, density of states, and mobility models stored in the storage unit 280. Furthermore, if information not stored in the storage unit 280 is to be used, the user may input new information regarding devices, boundary conditions, density of states, and mobility models to the input unit 210.

[0172] Furthermore, in this embodiment, the storage unit 280 may also have a measured value database 280e, and information regarding the measured data used in the comparison process between the simulation results and the measured data described later may be input to the input unit 210 by the user.

[0173] As described above, the registration unit 220 may be configured to register newly input information in the storage unit 280 when, for example, information not stored in the storage unit 280 is used, new information such as information about a new device, information about boundary conditions, information about the density of states, information about the mobility model, or measured data is input to the input unit 210.

[0174] The acquisition unit 230 may, for example, acquire device information such as the structure and materials of a device corresponding to the input identification information when identification information related to device information is input to the input unit 210, from the device information database 280a of the storage unit 280. Similarly, the acquisition unit 230 may be configured to acquire information such as boundary conditions, density of states, mobility model, and measured data corresponding to the input identification information when information such as boundary conditions, density of states, mobility model, and measured data is input to the input unit 210.

[0175] The simulation execution unit 240 is configured to perform device simulations. The simulation execution unit 240 may be configured to perform device simulations using a mobility model specified by the user, based on device information, boundary condition information, state density information, etc., which are specified based on information input by the user to the input unit 210.

[0176] The measured data comparison unit 250 may be configured to compare the simulation results executed by the simulation execution unit 240 with measured data (for example, measured data input or specified by the user in the input unit 210). As measured data, for example, data relating to the current-voltage characteristics of the device being measured may be compared with the current-voltage characteristics of the simulation results.

[0177] The condition modification unit 260 may be configured to change conditions such as boundary conditions for running the simulation. For example, the measured data comparison unit 250 may calculate the accuracy of the simulation's reproduction of the measured data based on the comparison result between the simulation results and the measured data. Based on the calculated accuracy, if the accuracy falls below a predetermined threshold, the condition modification unit 260 may change the simulation conditions such as boundary conditions, and the simulation execution unit 240 may run the device simulation again based on the changed conditions.

[0178] The simulation results, executed again by the simulation execution unit 240, are compared with the measured data by the measured data comparison unit 250. Based on the reproduction accuracy of the re-executed device simulation, the boundary conditions and other parameters may be further modified by the condition modification unit 260, and the device simulation may be executed again by the simulation execution unit 240. In this way, the simulation conditions may be modified and the execution of the device simulation may be repeated until the reproduction accuracy of the simulation exceeds a predetermined threshold.

[0179] The output unit 270 may be configured to output, for example, the simulation results executed by the simulation execution unit 240, or the comparison results between the simulation results and actual measured data performed by the actual measured data comparison unit 250, to a display device or the like.

[0180] The storage unit 280 may, for example, have a device information database 280a, a boundary condition information database 280b, a density of states information database 280c, a mobility model information database 280d, and a measured value database 280e, as described above, and may be configured to store the above-mentioned device information, boundary condition information, density of states information, mobility model information, and measured data. The storage unit 280 may also store, for example, a program executed by the device simulation system 200. Furthermore, the storage unit 280 may store simulation results executed by the simulation execution unit 240, and comparison results between simulation results and measured data by the measured data comparison unit 250.

[0181] 10. Hardware Configuration of the Information Processing Device Next, an example of the hardware configuration of the information processing device 100 will be described with reference to Figure 10. Figure 10 is a diagram showing an example of the hardware configuration of the information processing device 100.

[0182] The information processing device 100 according to this embodiment includes, as described later, a memory for storing information (e.g., programs and various data) and a processor that operates based on the information stored in the memory. The processor may, for example, have the functions of each part implemented by individual hardware, or the functions of each part may be implemented by integrated hardware. The processor may be, for example, a CPU. However, the processor is not limited to a CPU, and various types of processors such as a GPU (Graphics Processing Unit) or a DSP (Digital Signal Processor) can be used. The processor may also be a hardware circuit using an ASIC. The memory may be a semiconductor memory such as an SRAM (Static Random Access Memory) or DRAM (Dynamic Random Access Memory), a register, a magnetic storage device such as a hard disk drive, or an optical storage device such as an optical disk drive. For example, the memory stores instructions that can be read by a computer, and the functions of each part of the information processing device may be realized by the execution of these instructions by the processor. The instructions here may be instructions from an instruction set that constitutes a program, or instructions that instruct the hardware circuit of the processor to operate.

[0183] As shown in Figure 10, the information processing device 100 includes, for example, a processor 100a, a memory 100b, a storage device 100c, an input I / F unit 100d, a data I / F unit 100e, a communication I / F unit 100f, and a display device 100g.

[0184] The information processing device 100 may be, for example, a server computer, a personal computer (e.g., a desktop, laptop, tablet, etc.), a media computer platform (e.g., a cable, satellite set-top box, digital video recorder, etc.), a handheld computer device (e.g., a PDA, email client, etc.), or another type of computer or communication platform.

[0185] The processor 100a is a control unit that controls various processes in the information processing device 100 by executing a program stored in the memory 100b.

[0186] Memory 100b is a storage medium such as RAM (Random Access Memory). Memory 100b temporarily stores the program code of the program executed by the processor 100a, as well as data required during program execution.

[0187] The storage device 100c is a non-volatile storage medium such as a hard disk drive (HDD) or flash memory. The storage device 100c stores the operating system and various programs for realizing the above configurations.

[0188] The input interface unit 100d is a device for receiving input from the user. The input interface unit 100d may be, for example, a keyboard, mouse, touch panel, various sensors, or a wearable device. The input interface unit 100d may be connected to the information processing device 100 via an interface such as USB (Universal Serial Bus).

[0189] The data I / F unit 100e is a device for inputting data from outside the information processing device 100. The data I / F unit 100e is, for example, a drive device for reading data stored on various storage media. The data I / F unit 100e may be provided outside the information processing device 100. If the data I / F unit 100e is provided outside the information processing device 100, it is connected to the information processing device 100 via an interface such as USB.

[0190] The communication interface unit 100f is a device for performing data communication with an external device of the information processing device 100 via a network such as the Internet, either by wire or wireless connection. The communication interface unit 100f may be located outside the information processing device 100. If the communication interface unit 100f is located outside the information processing device 100, it is connected to the information processing device 100 via an interface such as USB.

[0191] The display device 100g is a device for displaying various types of information. The display device 100g is, for example, a liquid crystal display, an organic EL (Electro-Luminescence) display, or a display for a wearable device. The display device 100g may be provided outside the information processing device 100. If the display device 100g is provided outside the information processing device 100, it is connected to the information processing device 100, for example, via a display cable. Also, if a touch panel is used as the input I / F unit 100d, the display device 100g may be configured to be integrated with the input I / F unit 100d.

[0192] The program or a part thereof for calculating the mobility of the oxide semiconductor according to this embodiment may be stored and provided on a computer-readable storage medium such as the storage device 100c. The storage medium storing the program may be a non-transitory computer-readable medium. The non-transitory storage medium is not particularly limited, but may be a storage medium such as a USB memory or CD-ROM.

[0193] Alternatively, the program for calculating the mobility of the oxide semiconductor according to this embodiment may be provided from outside the information processing device 100 via a communication network to which the information processing device 100 is connected. In the information processing device 100, for example, the processor 100a executes the program for calculating the mobility of the oxide semiconductor according to this embodiment, thereby realizing various operations described later with reference to Figure 11, etc.

[0194] In this embodiment, for example, the storage unit 160 of the information processing device 100 described above can be realized using the storage device 100c provided by the information processing device 100. Furthermore, the input unit 110, registration unit 120, acquisition unit 130, mobility calculation unit 140, and output unit 150 can be realized by the processor 100a of the information processing device 100 executing a program stored in the storage device 100c.

[0195] These physical configurations are illustrative examples and do not necessarily have to be independent. For example, the information processing device 100 according to this embodiment may include a Large-Scale Integration (LSI) in which the processor 100a and the storage device 100c are integrated.

[0196] Furthermore, the information processing device 100 is not limited to the configuration described above. For example, some or all of the functions of the information processing device 100 may be performed by other information processing devices. Alternatively, some or all of the functions of the information processing device 100 may be performed by other information processing devices or servers, or the information processing device 100 may be configured using a cloud server.

[0197] For example, the information processing device 100 according to this embodiment is not limited to the configuration described above with reference to Figure 8, and among the processes executed in the information processing device 100, the acquisition of information used for calculating mobility and the calculation of mobility may be performed by an external computer such as a cloud server. In this case, for example, all or part of the acquisition unit 130, the mobility calculation unit 140, and the storage unit 160 of the information processing device 100 may be implemented by an external computer. For example, in cases where mobility is calculated by a user's terminal accessing the server of a service provider for mobility calculation processing, this embodiment can be applied even if the user transmits information about oxide semiconductors that are the subject of mobility calculation and information about mathematical formulas used for mobility calculation to the service provider's server using the information processing device 100. In this case, for example, a new mathematical formula that has not been previously provided by the service provider may be transmitted by the user as the mathematical formula used for mobility calculation, and the new mathematical formula may be configured to be registered in a storage device used by the service provider's server.

[0198] In this embodiment, the device simulation system 200 may have the same hardware configuration as the information processing device 100 described with reference to Figure 10. Furthermore, the information processing device 100 and the device simulation system 200 may consist of one or more physical computers or servers as needed, or they may be configured using virtual servers operating on a hypervisor.

[0199] Furthermore, the device simulation system 200 according to this embodiment is not limited to the configuration described above with reference to Figure 9. The acquisition of information used for executing the device simulation and the execution of the device simulation, among the processes performed in the device simulation system 200, may be performed by an external computer, such as a cloud server. In this case, for example, all or part of the acquisition unit 230, the simulation execution unit 240, and the storage unit 280 of the device simulation system 200 may be implemented by an external computer. For example, this embodiment can be applied even when a user's terminal accesses a service provider's server to execute a device simulation, and the user transmits information regarding boundary conditions and numerical models used for executing the device simulation to the service provider's server via a terminal (such as the information processing device 100). In this case, for example, a new numerical model not previously provided by the service provider may be transmitted by the user as the numerical model used for executing the device simulation, and the new numerical model may be configured to be registered in a storage device used by the service provider's server.

[0200] 11. Device Simulation Processing Procedure The overview of the device simulation processing according to this embodiment will be described with reference to Figure 11. Figure 11 is a diagram showing an overview of the device simulation performed by the device simulation system 200 according to this embodiment.

[0201] First, information regarding the structure and materials of the device to be simulated is input (S1102). As described above, this information may be input by the user to the input unit 110. In step S1102, other calculation conditions for the device simulation, other than the information regarding the device structure and materials, may be set. By inputting the information regarding the device structure, the calculation boundary conditions are set. The information regarding the device structure may be obtained by referring to the device information DB 280a.

[0202] Next, information regarding the density of states of defects in the semiconductor is input (S1104). This information includes the function used, the initial values ​​of the coefficients in the function, and the numerical range that the density of states of defects and / or the initial values ​​can take. This information may be obtained from the density of states information DB280c or input by the user to the input unit 110.

[0203] Next, information regarding the semiconductor mobility model is input (S1106). This information includes the mobility model to be used and the values ​​of the coefficients in the mobility model. This information may be obtained from the mobility model information DB280d or input by the user to the input unit 110.

[0204] Next, boundary conditions for running the simulation are input (S1108). These boundary conditions may include, for example, voltage, temperature, and information related to heat generation calculations.

[0205] The order of steps S1102, S1104, S1106, and S1108 described above does not matter, and they may be performed in parallel.

[0206] Next, a device simulation is performed based on the input information (S1110).

[0207] Next, measured data is acquired (S1112). Note that acquiring measured data may be performed separately from the device simulation flow, either before the device simulation or in parallel with the device simulation. In step S1112, for example, measured data related to the device targeted for simulation is acquired. As measured data, for example, current-voltage characteristics may be acquired.

[0208] Next, the calculation results (simulation results) are compared with the measured data (S1114). For example, the current-voltage characteristics of the simulation results are compared with the current-voltage characteristics of the measured data.

[0209] Next, it is determined whether the simulation results match the measured data (S1116). For example, whether the measured data and the simulation results match may be determined using predetermined evaluation metrics. Examples of evaluation metrics for determining whether the measured values ​​and simulation results match include the Maximum Absolute Error (MAE), the Mean Squared Error (MSE), and the coefficient of determination R. ２ The following may also be used.

[0210] If it is determined that the calculation result (simulation result) and the measured data match (for example, that a predetermined evaluation index is within a predetermined tolerance range) (YES in S1116), the process is terminated.

[0211] If it is determined that the calculation result (simulation result) and the measured data do not match (for example, a predetermined evaluation index is outside a predetermined tolerance range) (NO in S1116), the simulation conditions, such as boundary conditions or the initial values ​​of the set parameters, are changed (S1118), and steps S1110 to S1116 described above are executed again. Steps S1110 to S1116 are repeated, for example, until the agreement between the measured value and the calculation result reaches a predetermined tolerance range (i.e., a certain error range). The "predetermined tolerance range" may be, for example, a range of 10% or less of the mobility when determined using the maximum absolute error MAE.

[0212] The processing procedure described with reference to Figure 11 is illustrative, and the device simulation processing according to this embodiment is not limited thereto. For example, the steps described above do not have to be performed in this order and may be changed as appropriate. For example, the input of the device structure and materials (S1102), the input of the semiconductor density of states (S1104), the input of the semiconductor mobility model (S1106), and the input of boundary conditions (S1108) do not have to be performed in this order, and some or all of these steps may be performed simultaneously. Furthermore, in step S1116, instead of determining whether the simulation results match the measured data, it may be determined whether the execution of the device simulation (S1110) and the modification of the conditions (S1118) have been repeated a predetermined number of times, and the process may be terminated if the predetermined number of repetitions have occurred.

[0213] The obtained simulation results may be displayed on a display device or stored in a simulation results database.

[0214] The present invention will be described in detail below based on examples, but the present invention is not limited in any way by these examples.

[0215] 1. Verification of the scattering model (A-1) Preparation of semiconductor thin film samples for actual measurement Sample 1 Using an oxide target having the metal composition ratio shown in Table 1, an oxide layer was deposited on a glass substrate with a target thickness of 30 nm by sputtering under the deposition conditions shown in Table 1. The oxide target and metal composition ratio (at%) were determined by the following formula: [In] / ([In] + [M]) * 100 (In the formula, [In] represents the number of moles of In in the oxide target, and [M] represents the number of moles of metal elements other than In in the oxide target.) Next, the first heat treatment (1st annealing) was performed under the conditions shown in Table 1 to prepare Sample 1. The crystallinity of the obtained Sample 1 was evaluated by XRD measurement. The results are shown in Table 1. Subsequently, the second heat treatment (2nd annealing) was performed under the conditions 1 to 5 shown in Table 1 to produce Samples 1-1 to 1-5.

[0216] Sample 2 was prepared in the same manner as Sample 1, except that the composition of the oxide target, the film formation conditions, and the conditions for the first annealing were changed, and its crystallinity was evaluated. Subsequently, a second heat treatment (second annealing) was performed in the same manner as for Sample 1, resulting in Samples 2-1 to 2-5.

[0217]

[0218] (A-2) Measurement of physical properties of semiconductor thin films for actual measurement The following physical properties were measured for each sample obtained.

[0219] (Carrier solution [cm] －３ ], and mobility μ ｏｂｓ． [cm ２ [Vs]) Carrier concentration of semiconductor thin film (cm －３ ), and mobility μ ｏｂｓ． [cm ２ For the evaluation of the electrical properties, resistivity measurement using the van der Pauw method and Hall effect measurement (AC Hall effect measurement) were used. For the measurements, thin film samples cut into 1 cm squares were used, with Ti electrodes formed at the four corners. Furthermore, AC Hall measurements were performed on each sample at 50 K intervals within the temperature range of 20 to 300 K. The measurement conditions are as follows: • Measurement device: Retest 8400, manufactured by Toyo Technica • Maximum applied voltage: 20 V • Applied magnetic field: 0.4 T

[0220] <Examples 1 and 2> For samples 1 and 2 obtained above, the macroscopic DC mobility μ(T) according to one embodiment of the present invention was calculated.

[0221] (B) Intragranular mobility μ ｉｎ－ｇｒａｉｎ Calculation of (T) Using the above formulas (A101-1) and (A102), the intragranular mobility μ for each temperature T and carrier concentration n is calculated. ｉｎ－ｇｒａｉｎ (T) was calculated. Here, each A for each carrier concentration ｎｅｕｔｒａｌ、 A ｏｐ、 The weak localization constant and acoustic phonon scattering constant were calculated using the values ​​shown in Table 2 below and the values ​​of n (300K) using equations (A103), (A104), and (A105). Intragranular mobility μ ｉｎ－ｇｒａｉｎThe values ​​of each parameter used to calculate (T) are shown in Table 2 below.

[0222]

[0223] [In the formula, μ ｉｎ－ｇｒａｉｎ This is the intragranular mobility of a semiconductor [cm²]. ２ / Vs], T is temperature [K], β[K], a １ [cm －２ Vs], a ２ [cm －２ Vs], a ３ [cm －２ Vs. K ３／２ ], a ４ [cm －２ Vs. K －１／２ ], and a ５ [cm －２ Vs. K -３／２ ] represents the coefficients. Also, hω ｏｐ / 2π is the energy of the optical phonon [eV] which varies depending on the carrier concentration, k Ｂ This is the Boltzmann constant (8.617 × 10⁻¹⁰). －５ [eV / K]), where h is Planck's constant (4.1357 × 10⁻¹⁰). －１５ [eVs] represents the free carrier concentration [cm³]. －３ ] A １ [cm －２ Vs], B １ , and C １ [cm －２ Vs] are coefficients, N ０１ a １ This is the carrier concentration corresponding to the inflection point in equation (A103) represented by (n). Also, A ２ [cm －２ Vs], B ２ , and C ２ [cm －２ Vs] are coefficients, N ０２ a ２ This is the carrier concentration corresponding to the inflection point in equation (A104) represented by (n). Also, A ３ [cm －８ Vs. K ３／２ ] and B ３ , C ３ [cm－２ Vs. K ３／２ ] 、 D ３ [cm ３ ] and F ３ [cm －２ Vs. K ３／２ ] are coefficients, N ０３ a ３ The maximum carrier concentration [cm³] in equation (A105) represented by (n) －３ ] is. ]

[0224] (C) Calculation of macroscopic DC mobility μ(T) For each temperature T and carrier concentration n, the intragranular mobility μ calculated above ｉｎ－ｇｒａｉｎ (T), calculated using the following equations (A1010) and (A1012). Potential barrier V Ｂ For this, the values ​​shown in Table 2 and those calculated using the following formula (A1013) were used.

[0225] [In the formula, μ is the mobility of the semiconductor [cm] ２ / Vs], T is temperature [K], γ[K] and θ[K ２ ] is a coefficient and is a positive number including 0. Also, q is the elementary charge 1.602 x 10 －１９ [C], V Ｂ The potential barrier value is [eV], k Ｂ This is the Boltzmann constant (8.617 × 10⁻¹⁰). －５ [eV / K] represents the free carrier concentration. －３ ] A ６ [eV], B ６ , C ６ [eV] and D ６ These are coefficients, N ０６ [eV] is V Ｂ This is the carrier concentration corresponding to the inflection point in equation (A1013) represented by (n).

[0226] Here is the measured value μ ｏｂｓ．If the macroscopic DC mobility μ(T) did not agree well, regression was performed using the nonlinear least squares method. Convergence was confirmed by repeating the fitting multiple times and ensuring that the result remained unchanged, and the parameters were then used as experimental results. The values ​​of each parameter used to calculate the macroscopic DC mobility μ(T) are shown in Table 2 below.

[0227] <Comparative Examples 1 and 2> For the above samples 1 and 2, mobility μ was measured using the conventional Tokyo Model. ｄ The calculation was performed.

[0228] (D) Mobility μ by Tokyo Model ｄ The calculation of mobility μ according to the Tokyo Model for each temperature T and carrier concentration n. ｄ [cm ２ The calculation of [ / Vs] was performed using the following formulas (I) and (II). Here, n is the free carrier concentration [cm³] －３ ], T is the temperature [K], μ ｄ０ [cm ２ / Vs], n ｃｒ [cm －３ ], T γ [K], γ ０ This is a coefficient.

[0229] Measured value μ ｏｂｓ． and mobility μ by Tokyo Model ｄ In cases where the agreement was poor, regression was performed using the nonlinear least squares method, and convergence was confirmed by confirming that the values ​​did not change even after repeating the fitting multiple times, thereby using the parameters as experimental results. Mobility μ by Tokyo Model ｄ The values ​​of each parameter used in the calculation are shown in Table 3 below.

[0230] (E) Evaluation of calculation results (R ２ Coefficient of determination) Measured value μ of mobility obtained in (A-2) above ｏｂｓ． The coefficient of determination R between the macroscopic DC mobility μ(T) calculated in (C) above, or the mobility μ calculated in (D) Tokyo Model above. ２ The coefficient of determination R was calculated using the following formula (X). ２ The values ​​are shown in Tables 2 and 3 below.

[0231] Here, y ｉ This is the measured value of the i-th mobility. This is the calculation result for the i-th mobility. This is the average value of the measured mobility.

[0232] The horizontal axis represents the measured macroscopic DC mobility μ. ｏｂｓ． The vertical axis shows the macroscopic DC mobility μ calculated using each model. ｃａｌｃ When plotted, the coefficient of determination R ２ The closer the value is to 1, the more appropriate the model used is. In the table, "E" is in exponential notation, and the integer after "E" represents the power of 10 applied to that number. For example, "4.60E-2" is 4.60 × 10 －２ It represents.

[0233]

[0234]

[0235] Furthermore, the measured value μ of the mobility of each sample relative to the carrier concentration n. ｏｂｓ． Figures 18(a) to 21(a) show graphs plotting the relationship between the calculated mobility values ​​obtained in the examples and comparative examples and the actual measured mobility value μ for each sample on the horizontal axis. ｏｂｓ． The vertical axis represents the calculated value of mobility μ. ｃａｌｃ Graphs plotting these values ​​are shown in Figures 18(b) to 21(b), respectively. From Figures 18 to 21, it can be seen that while the calculated mobility values ​​by Tokyo Model (Comparative Examples 1 and 2) showed a discrepancy with the measured values, the calculated values ​​by the macroscopic DC mobility μ(T) calculation method of the present invention (Examples 1 and 2) showed good agreement for both crystalline oxide semiconductors and amorphous oxide semiconductors, indicating high reproducibility.

[0236] <Verification of the mobility model> (F-1) Semiconductor thin film samples 3-8 for actual measurement Thin films were prepared in the same manner as sample 1, except that the oxide target composition, film deposition conditions, and 1st annealing conditions were changed, as shown in Tables 4-1 to 4-3 below, and the crystallinity was evaluated. Then, a second heat treatment (2nd annealing) was performed in the same manner as sample 1 to obtain samples 3-8.

[0237]

[0238]

[0239]

[0240] Figure 1 above shows a graph plotting the mobility-carrier concentration of each obtained sample.

[0241] (F-2) Measurement of physical properties of semiconductor thin films for actual measurement The following physical properties were measured for each sample obtained.

[0242] (Carrier solution [cm] －３ ], and mobility μ ｏｂｓ． [cm ２ [Vs] Carrier concentration of semiconductor thin film [cm³] －３ ], and mobility μ ｏｂｓ． [cm ２ For the evaluation of the electrical properties, resistivity measurement using the van der Pauw method and Hall effect measurement (AC Hall effect measurement) were used. For the measurements, thin film samples cut into 1 cm squares were used, with Ti electrodes formed at the four corners. Furthermore, AC Hall measurements were performed on each sample at 50 K intervals within the temperature range of 20 to 300 K. The measurement conditions are as follows: • Measurement device: Retest 8400, manufactured by Toyo Technica • Maximum applied voltage: 20 V • Applied magnetic field: 0.4 T

[0243] (G) Calculation of macroscopic DC mobility μ(T) <Examples 3-8> Using the group of equations (mobility model equations) shown in Tables 5-1 and 5-2 below, as described in the detailed explanation, and inputting the fitting parameters shown in Table 6 below, the mobility-carrier concentration lines (μ-n lines) for each scattering parameter at temperatures of 200.0 K, 250.0 K, and 300.0 K are shown in Figure 22 along with plots of the measured values ​​for each of the samples 3-8.

[0244]

[0245]

[0246]

[0247] Figures 22(a) to (f) show that the calculated values ​​of macroscopic DC mobility μ(T) using the physical model in the present invention agree well with those of amorphous oxide semiconductors, demonstrating high reproducibility.

[0248] Figure 23, like Figure 22, is the mobility-carrier concentration line at 300K, obtained by inputting the parameters from Table 7 below into the formula list in Table 5 above. It accurately reproduces the upper limits of each plot of mobility-carrier concentration for the polycrystalline oxide semiconductor material. Figure 24 shows the μ and μ at each carrier concentration obtained in Figure 23. ＯＰ , μ ＮＩ , μ ＩＩ （Ｄｅｇ） , and μ ＩＩ （ｎｏｎＤｅｇ） By utilizing the fact that [a certain value] can be obtained, the scattering rate of each scattering parameter was calculated. Note that the scattering rate S of each scattering parameter is μ / μ ｘ Defined as follows: Here, μ ｘ μ ＯＰ , μ ＮＩ , μ ＩＩ （Ｄｅｇ） , μ ＩＩ （ｎｏｎＤｅｇ） and μ ＧＢ It is one of the following. Here, the mobility μ at the grain boundary (GB) ＧＢ V is derived from the macroscopic DC mobility μ. Ｂ As the reduction in mobility due to this, μ is calculated to satisfy the Mathiesen rule below. ＧＢ This was defined.

[0249]

[0250] (H) Calculation of scattering rate Figure 24 shows graphs plotting the carrier concentration of each sample on the horizontal axis and the scattering rate of each scattering parameter on the vertical axis. In this way, with the mobility model revealed, it became possible to visualize the scattering rate, which is the degree of influence of each scattering factor at each carrier concentration.

[0251] 2. Mobility Modeling and Device Simulation using a Scattering Model (Mobility Modeling using a Scattering Model) Mobility modeling using the scattering model of this embodiment was performed on the physical property measurement results of sample 5 obtained in Example 5 above. Specifically, the group of equations (mobility model equations) shown in Tables 5-1 and 5-2 above were used, and the ionized impurity concentration N in the non-degenerate region, which was treated as a constant in Table 6 above, was further examined. ＩＩ＿ｎｏｎＤｅｇ And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ A model equation was used to calculate the following using equations (2), (3), and (A130). In addition, the Fermi energy difference δ, which was treated as a constant in Table 6 above, was also used. ＥＦ A model equation was used to calculate the following using equation (4). However, in the equation, n is the free carrier concentration, and N ｃ is the critical density for the Mott transition, and a ２ is the width of the sigmoid function. Also, δ ＥＦ０ This is the Fermi energy difference δ at absolute zero or when the free carrier concentration is equal to the effective density of states. ＥＦ And N ｃ０ The effective density of states [cm³] －３ ] and Z δＥＦＴｎ This is a coefficient.

[0252]

[0253] Figure 25 shows the mobility-carrier concentration lines (μ-n lines; calculated values) at temperatures of 200.0 K, 250.0 K, and 300.0 K, obtained by inputting the fitting parameters described in Table 8 as Example A, along with plots of the measured values ​​for each of the samples of sample 5. Table 9 below shows the root mean square logarithmic error (RMSLE) between the calculated mobility values ​​and the measured values ​​based on the scattering model. Figure 25 shows that the plots of the measured values ​​and the lines based on the calculated values ​​of the mobility model are in good agreement.

[0254] Figure 25 shows a carrier concentration of 10 １８ cm －３Since a locally convex region was observed nearby, the temperature-carrier density dependence of the effective density of states was adjusted to obtain a smooth curve in this region. The result of recalculation using the fitting parameters described as Example B in Table 8 is shown in Figure 26. As shown in Figure 26, by adjusting the coefficients of various scattering models, a suitable smooth μ-n line can be obtained in device simulations.

[0255]

[0256]

[0257] (Poly-IGO TFT) Next, device simulation was performed using mobility modeling based on the scattering model described above. The device structure of the poly-IGO TFT used in this embodiment is shown in Figure 12(a). Figure 12(a) is a cross-sectional view of the device structure of the poly-IGO TFT. For the oxide semiconductor channel layer in Figure 12(a), an oxide semiconductor manufactured under the same conditions as for sample 5 was used. The manufacturing of the poly-IGO TFT device was performed in the same manner as described in "3. Mobility Modeling and Self-Heating Simulation using Regression Model" below.

[0258] (Device Simulation of Scattering Model) The μ-n lines obtained from the mobility modeling using the scattering model described above were incorporated into the mobility model of the device simulator to simulate the current Ids-voltage Vgs characteristics of the TFT. The device simulation method was the same as described in "3. Mobility Modeling and Self-Heating Simulation using Regression Model" below. The parameters used in the device simulation are shown in Table 10 below. In the device simulation, the distribution of exponential acceptor-like defects was expressed by equation (5) below, and the distribution of Gaussian acceptor-like defects was expressed by equation (6) below. For more information on the device simulation, please refer to the Atlas User's Manual (SILVACO Inc., Atlas User's Manual DEVICE SIMULATION SOFTWARE, April 10, 2018).

[0259]

[0260] [In formula (5), N ＴＡ This is the energy E at the lower end of the conduction band. ｃ Density of states of acceptor-like defects in [cm²] －３ / eV] and W ＴＡ E is the reciprocal of the slope of the acceptor-like defect's density of states [eV], where E is the energy of the acceptor-like defect [eV], and E ｃ is the energy at the lower end of the conduction band [eV]. ] [In equation (6), N ＧＡ The maximum density of states for acceptor-like defects [cm²] －３ / eV] and W ＧＡ E is the standard deviation [eV] of the energy of the acceptor-like defect, and E is the energy [eV] of the acceptor-like defect. ＧＡ This is the central energy [eV] from the lower edge of the conduction band.

[0261] Figures 27(A) and (B) show the device simulation results obtained using the μ-n lines calculated in Examples A and B described above. In both simulation results, the calculated values ​​agree well with the measured values, indicating that accurate calculation results can be obtained. In Example B, where the mobility model was adjusted to result in a more continuous change, the error between the calculated and measured values ​​is improved compared to Example A. This confirms that by adjusting the mobility model, accurate device simulations corresponding to actual TFTs can be performed. The root mean square logarithmic error (RMSLE) between the calculated and measured current values ​​obtained from the device simulation is shown in Table 11 below.

[0262]

[0263]

[0264] 3. Mobility modeling using regression models and self-heating simulation examples: 40 cm ２ Field effect mobility of Vs or greater (μ ＦＥA polycrystalline In-Ga-O (poly-IGO) thin-film transistor with the field-effect mobility (μ) was analyzed using a mobility model and self-heating simulation. ＦＥ ) is highest among metal oxide semiconductor TFTs using common semiconductor materials and mature manufacturing processes. As shown below, first, the intrinsic carrier mobility (μ) is positively dependent on the carrier concentration (n), and the field-effect mobility (μ) ＦＥ It was revealed through mobility modeling that this increases the field-effect mobility (μ). Furthermore, self-heating simulations showed that μ (inherent carrier mobility (μ)) has a slight positive dependence on T (temperature (T)), and this increases the field-effect mobility (μ). ＦＥ It was revealed that the properties of poly-IGO TFTs can be enhanced. Due to these characteristics, it is expected that poly-IGO TFTs can be replaced by amorphous IGZO TFTs (In-Ga-Zn-O(α-IGZO)TFTs) in the near future.

[0265] (Poly-IGO TFT) Figure 12(a) shows the device structure of the poly-IGO TFT according to this embodiment. Figure 12(a) is a cross-sectional view of the device structure of the poly-IGO TFT.

[0266] First, the glass substrate and SiO ２ IGO was deposited onto a buffer layer as a 30 nm thick oxide channel layer by DC magnetron sputtering, patterned, and then crystallized by heat treatment at 400°C in air, the highest temperature in the manufacturing process. As a result, a poly-IGO TFT was fabricated on a glass substrate during the back-end of line (BEOL) wiring process.

[0267] Next, as the gate insulating layer, SiO ２ A 100 nm layer was deposited, and molybdenum was deposited as a gate electrode layer and then patterned.

[0268] Subsequently, SiO is used as the interlayer insulating layer. ２ By depositing it again, a low-resistance region with a sheet resistance of 418 Ω / □ is automatically formed in the oxide channel layer.

[0269] Finally, molybdenum is deposited again on the low-resistance region as source and drain electrode layers.

[0270] Ids-Vgs characteristics and μ ＦＥ This is shown in Figure 12(b). Here, μ ＦＥ This is obtained from the equation for Ids in the linear region for Vds = 0.1V and the equation for Ids in the saturation region for Vds = 10V and 20V. μ ＦＥ The maximum value is 40.1 cm for Vds = 0.1 V. ２ / Vs, and for Vds = 20V, it is 44.7 cm. ２ It was found to be / Vs. Furthermore, as mentioned above, μ ＦＥ This is the highest performance among metal-oxide semiconductor (OS) thin-film transistors (TFTs) using common materials and mature manufacturing processes.

[0271] (Mobility Modeling) A. Trap Extraction Trap extraction will be explained with reference to Figure 13. Figure 13(a) shows the low-frequency (low-f) Cg(s+d)-Vg(s+d) characteristics. Figure 13(b) shows the trap density.

[0272] Here, the trap density is extracted using the low-frequency (f) Cg(s+d)-Vg(s+d) characteristic (see M. Kimura, T. Nakanishi, K. Nomura, T. Kamiya, and H. Hosono, "Trap densities in amorphous-InGaZnO4 thin-film transistors," Appl. Phys. Lett., vol. 92, 133512, Apr. 2008). This extraction method has the excellent advantage that the trap density can be extracted only by the low-frequency (low-f) Cg(s+d)-Vg(s+d) characteristic, which does not have the Ids-Vgs characteristic that enables mobility modeling later. As shown in Figure 13(a), the low-frequency (low-f) Cg(s+d)-Vg(s+d) characteristic shows that the characteristic plot does not shift further even when the frequency (f) decreases to below 1 Hz. This indicates that quasi-static conditions can be obtained at 1 Hz. The density of states N of acceptor-like defects obtained by applying equation (5) to the extracted trap density shown in Figure 13(b) ＴＡ is 7.2 x 10 １７ cm －３ / eV, the reciprocal of the slope of the acceptor-like defect density of states W ＴＡ The voltage was 0.14 eV.

[0273] B. Mobility Modeling Mobility modeling will be explained with reference to Figure 14. Figure 14(a) shows Id and the extracted carrier concentration (n) per unit area extracted during trap extraction. ａ This shows the relationship with ).

[0274] n ａ The plot of is linear, while the plot of Ids is concave, suggesting that μ (inherent carrier mobility (μ)) depends on n.

[0275] The modeling procedure will be explained with reference to Figures 14(b) and 14(c). In short, Ids is reproduced by obtaining one intrinsic carrier mobility (μ) for each carrier concentration n (see M. Kimura, T. Kamiya, T. Nakanishi, K. Nomura, and H. Hosono, "Intrinsic carrier mobility in amorphous In-Ga-Zn-O thin-film transistors determined by combined field-effect technique," Appl. Phys. Lett., vol. 96, 262105, June 2010).

[0276] Figures 14(b) and 14(c) show the calculation procedure using the field-effect method. First, the carrier density is defined as n(z) as a function of the channel layer depth z from the gate insulating film interface, and the intrinsic carrier mobility is defined as μ{n(z)} as a function of the carrier density. As a result, Ids is calculated by integrating the product of μ{n(z)} and n(z) over the entire channel layer from the gate insulating film interface to the back surface interface. This is approximated as the sum of slice sheets with a thickness Δz parallel to the film surface, where n(z) and μ{n(z)} are within a certain range and can be considered constant. The thickness of the slice sheets changes according to Vgs, and for the region with the minimum n(z) in Figure 14(b), the same region in Figure 14(c) is the calculated result of Ids at the minimum Vgs. When Vgs is changed by a small amount, Ids in Figure 14(c) increases in the region where n(z) increases in Figure 14(b). Finally, by sequentially integrating Ids in response to the change in Vgs, the value of Ids corresponding to Vgs is calculated. Ids is composed of the sum of the currents for each carrier concentration n and corresponding μ along the channel layer depth and is expressed by the following formula (A131). (A131) Here, i is the order in which each Vgs is applied, and κ is expressed by the following formula (A132). (A132) z is the axis along the channel layer depth. Therefore, μi can be obtained inductively such that the calculated Ids is equal to the measured Ids by the following equation (A133). (A133)

[0277] The μ-n dependence is shown in Figure 14(d). Here, the obtained μ and the calculated value fitted with the regression model of equation (1) are shown. n = 10 １７ cm －３ Below this value, μ is low and constant, but above this value, it was found to increase linearly. This is thought to be due to the behavior at the potential boundary in the grain boundaries (see M. Kimura, S. Inoue, T. Shimoda, and T. Sameshima, “Device simulation of carrier transport through grain boundaries in lightly doped polysilicon films and dependence on dopant density,” Jpn. J. Appl. Phys. pt. 1, vol. 40, pp. 5237-5243, 2001).

[0278] In other words, μ is positively dependent on n, and thus μ ＦＥ This is strengthened because as n increases, Ids is pushed up more significantly. The μ-n dependence can be a universal curve. This curve is well known for conventional silicon but has not been reported for poly-OS semiconductors and is thought to be applicable to the design of future devices and circuits. Furthermore, whole mobility (μ Ｈａｌｌ ) is also superimposed on Figure 14(d). As can be seen from Figure 14(d), the general shape is similar. That is, below a certain n, μ Ｈａｌｌ μ is low and constant, but increases linearly as n becomes higher than a certain value, but μ with respect to n Ｈａｌｌ The value of is different from μ. ＨａｌｌThe reason it falls below this level is thought to be because the device fabrication process differs from that of a single thin film, resulting in reduced mobility. In poly-OS, mobility changes significantly depending on the TFT fabrication process (M. Tsubuku, H. Watakabe, T. Sasaki, T. Tamaru, R. Onodera, M. Mochizuki, H. Kimura, E. Kawashima, D. Sasaki and Y. Tsuruma, "High mobility poly-crystalline oxide TFT achieving mobility over 50 cm"). 2 / Vs and high level of uniformity on the large size substrates," SID 2023 Digest, pp. 78-81, May 2023.)

[0279] These findings demonstrate the importance of actually fabricating TFTs and modeling mobility using this method. Figure 14(d) shows the intrinsic carrier mobility (μ) of α-IGZO. α－ＩＧＺＯ ) is also shown superimposed. It was confirmed that the shapes and values ​​are significantly different, and from this, it was confirmed that α-OS, which includes α-IGZO and α-IGO, has no grain boundaries and no large impurity scattering, thus guaranteeing that the μ-n dependence is due to the behavior of potential barriers at grain boundaries and intra-grain scattering such as neutral impurity scattering and ionized impurity scattering (see Y. Tsuruma, H. Nagatomi, N. Iwase, K. Yamaguchi, D. Sasaki, E. Kawashima, A. Kaijo and K. Inoue, "Poly-OS IGO for high mobility TFT applications," MRM 2023 / IUMRS-ICA 2023 Digest, S2-O202-02, Dec. 2023).

[0280] Figure 14(e) shows a comparison between the measured Ids and the simulated Ids, which are simulated by employing a device simulator and implementing μ-n dependence. It was confirmed that the measured Ids and the simulated Ids completely overlap, which guarantees the validity of the mobility modeling using the regression model.

[0281] (Self-heating simulation) A μ that depends on T (T-dependent μ) Figure 15 shows the Ids-Vgs characteristics that show the dependence on temperature T. In Figure 15, the dependence on T for the Ids-Vgs characteristics is not clear, but g ｍ -The characteristics of Vgs are relatively clear. That is, when Vgs is lower than 10V, the higher T is, the greater g ｍ As it increases, and Vgs is higher than 10V, the inverse relationship occurs, that is, the higher T is, g ｍ It was found that it becomes smaller. Here, the transconductance g ｍ The mobility μ is expressed by the following formula, C ｏｘ This represents the capacity of the gate oxide film. It can be understood that the mobility μ also depends on T in a similar manner.

[0282] The T-dependent μ-n dependence is shown in Figures 16(a) and 16(b).

[0283] Here, the modeling procedure is the same as described above: fitting lines for the regression model are obtained for each T, and these are smoothly interpolated and extrapolated as functions of n and T. Furthermore, the μ-n dependence, which depends on T, also exhibits a universal curve and may become indispensable for future device and circuit design.

[0284] B. Self-heating simulation. The self-heating effect is shown in Figure 17. Figure 17(a) shows the experimental results. Here, the planar T distribution is measured using an infrared microscope. It was found that T increases rapidly up to approximately 90°C on the oxide channel layer.

[0285] Figure 17(b) shows the simulation results. Here, the cross-sectional T distribution was simulated using device simulation with a thermal analysis module. T is approximately the same on the channel and across the surface, which confirms that the planar T distribution of the experimental results shown in Figure 17(a) reflects the T distribution within the channel layer. Furthermore, comparing T between the experiment and the simulation can be said to confirm the validity of the simulation. In addition, the Ids-Vgs characteristics for μ-n dependence that is dependent on T and that is not dependent on T are also shown. As shown in Figure 17(b), g ｍ It was found that the μ-n dependence, which depends on T, becomes larger. That is, μ has a slight positive dependence on T, and as a result, Ids is pushed up more and more as T increases due to the self-heating effect, μ ＦＥ This will increase the value.

[0286] As described above, 40 cm ２ μ greater than or equal to / Vs ＦＥ A poly-IGO TFT with μ was analyzed using a regression-based mobility model and a self-heating simulation. ＦＥ This is the highest among OS-TFTs using common materials and mature manufacturing processes. Furthermore, mobility modeling shows that μ is positively dependent on n, and as a result, μ ＦＥ It became clear that this increases. Furthermore, self-heating simulations showed that μ also depends positively on T, and as a result, μ ＦＥ It was revealed that this is increased. The μ-n dependence, which is dependent on T, exhibits a universal curve, which can be an essential characteristic for device and circuit design. Due to these characteristics, it is expected that poly-IGO TFTs can replace amorphous IGZO TFTs in the near future.

[0287] A macroscopic DC mobility calculation method and calculation program according to one aspect of the present invention are useful as simulation means in the device design of semiconductor devices using crystalline oxide thin films mainly composed of In.

[0288] Although several embodiments and / or examples of the present invention have been described in detail above, those skilled in the art will find it easy to make many modifications to these exemplary embodiments and / or examples without substantially departing from the novel teachings and effects of the present invention. Accordingly, many of these modifications fall within the scope of the present invention.

[0289] 100 Information Processing Device 110 Input Unit 120 Registration Unit 130 Acquisition Unit 140 Mobility Calculation Unit 150 Output Unit 160 Storage Unit 200 Device Simulation System 210 Input Unit 220 Registration Unit 230 Acquisition Unit 240 Simulation Execution Unit 250 Actual Measured Data Comparison Unit 260 Condition Change Unit 270 Output Unit 280 Storage Unit

Claims

A method for calculating the mobility of an oxide semiconductor using a computer, The step of causing the computer to perform the step of calculating the mobility using two or more terms calculated using the free carrier concentration in the oxide semiconductor, The two or more terms mentioned above are calculated by a scattering model derived considering the free carrier concentration in the oxide semiconductor, or by a regression model generated based on measured values ​​of the mobility and the free carrier concentration. method. 　 The two or more terms mentioned above are calculated by the scattering model, The step of calculating the mobility involves using the two or more terms calculated by the scattering model to determine the mobility μ within the crystal grains of the oxide semiconductor. ｉｎ－ｇｒａｉｎ The step includes calculating, The aforementioned scattering model is based on the neutral impurity concentration N ＮＩ A neutral impurity scattering model with N as a variable, and the ionized impurity concentration in the non-degenerate region. ＩＩ＿ｎｏｎＤｅｇ Ionized impurity scattering model in the non-degenerate region, with N as a variable, and ionized impurity concentration in the degenerate region. ＩＩ＿Ｄｅｇ Ionized impurity scattering model in the degenerate region, which includes the variable ω, and optical phonon frequency ω ｏｐ Selected from the group of optical phonon scattering models that include as a variable, The method according to claim 1. 　 The ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ At least one of the following is calculated using the free carrier concentration: The method according to claim 2. 　 To the aforementioned computer, Using the scattering model at the grain boundaries of the oxide semiconductor, the mobility μ within the grains of the oxide semiconductor is calculated. ｉｎ－ｇｒａｉｎ The further step includes performing the step of calculating the macroscopic mobility μ of the oxide semiconductor from the above, The method according to claim 2 or 3. 　 To the aforementioned computer, Using the scattering model at the grain boundaries of the oxide semiconductor, the Fermi energy difference δ between the grain boundaries and the grain interior ＥＦ Using this, the height V of the grain boundary barrier between the grain boundaries and the grain interior Ｂ Further including a step of causing a step of calculating to be executed The method according to claim 4. 　 To the aforementioned computer, Using the scattering model at the grain boundaries of the oxide semiconductor, the free carrier concentration and the effective density of states N within the crystal grains are used. ｃ０ Based on the above, the Fermi energy difference δ ＥＦ The further step includes causing the calculation step to be performed, The method according to claim 5. 　 The two or more terms mentioned above are calculated by the regression model, According to the regression model, the mobility is calculated from the logarithm of the sum of two or more terms of an exponential function with the free carrier concentration as the variable. The method according to claim 1. 　 The step of calculating the mobility includes the step of calculating the macroscopic mobility μ of the oxide semiconductor using the regression model, The regression model is given by the following equation: [In formula (1), a １ a ２ , b １ , b ２ , and c are constants of the regression equation set based on the measured values, μ is the macroscopic mobility of the oxide semiconductor, n is the free carrier concentration. Represented by, The method according to claim 7. 　 A step of causing the computer to perform a device simulation to simulate a device including the oxide semiconductor, using the mobility of the oxide semiconductor calculated by any one of claims 1 to 8. A device simulation method that includes this. 　 The step of performing the aforementioned device simulation is: A step of calculating the carrier density in the oxide semiconductor using the density of states of defects in the oxide semiconductor contained in the device, A step of calculating the current flowing through the device using the mobility μ and the carrier density, including, The device simulation method according to claim 9. 　 The density of states of the aforementioned defects includes an acceptor-like exponential distribution, The acceptor-like exponential density of states g ＴＡ This is the energy E at the lower end of the conduction band. ｃ Density of states N of acceptor-like defects in ＴＡ 10 １０ ~10 ２２ cm －３ / eV, the reciprocal of the slope of the acceptor-like defect density of states W ＴＡ The range is 0.001 to 0.5 eV. A device simulation method according to claim 10. 　 The step of performing the device simulation includes calculating the heat generation effect due to the current flowing through the oxide semiconductor and the heat dissipation effect due to the thermal conductivity and boundary conditions of the oxide semiconductor. A device simulation method according to any one of claims 9 to 11. 　 The mobility μ ｉｎ－ｇｒａｉｎ The calculation step is, The ionized impurity concentration N in the non-degenerate region is obtained by using the free carrier concentration in the oxide semiconductor. ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The steps to calculate, At least the ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ The mobility μ calculated using ＩＩ （ｎｏｎＤｅｇ） And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The mobility μ calculated using ＩＩ （Ｄｅｇ） Using the above, the mobility μ ｉｎ－ｇｒａｉｎ The steps to calculate, including, The method according to any one of claims 2 to 6. 　 The ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ However, the ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The boundary is when the sum of is constant and the free carrier concentration is the same as or approximately the same as the critical density of the Mott transition, and the ionized impurity concentration N in the non-degenerate region is defined as such. ＩＩ＿ｎｏｎＤｅｇ And the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ The relationship between magnitudes is expressed in a way that it switches continuously. The method according to claim 13. 　 The ionized impurity concentration N in the non-degenerate region ＩＩ＿ｎｏｎＤｅｇ , and the ionized impurity concentration N in the degenerate region ＩＩ＿Ｄｅｇ However, these are calculated by the following formulas (2) and (3): The method according to claim 14. (N ＩＩ (where f is the ionized impurity concentration, and f is the sigmoid function with the free carrier concentration as a variable.) 　 The mobility μ ｉｎ－ｇｒａｉｎ However, it is calculated as follows (A1-1): The method according to any one of claims 2 to 6 and 13 to 15. [In formula (A1-1), μ ＯＰ This is the mobility calculated by the optical phonon scattering model, μ ＮＩ This is the mobility calculated by the neutral impurity scattering model, μ ＩＩ （Ｄｅｇ） This is the mobility calculated by the ionized impurity scattering model in the degenerate region. μ ＩＩ （ｎｏｎＤｅｇ） This is the mobility calculated by the ionized impurity scattering model in the non-degenerate region. Z ＯＰ Z ＮＩ Z ＩＩ＿Ｄｅｇ , and Z ＩＩ＿ｎｏｎＤｅｇ is 0 or 1, Z ＯＰ Z ＮＩ Z ＩＩ＿Ｄｅｇ , and Z ＩＩ＿ｎｏｎＤｅｇ At least two of the group consisting of these elements are 1. 　 The mobility μ is calculated by the following formula (A10): The method according to claim 4. [In formula (A10), q is the elementary charge [C], V Ｂ This is the height [eV] of the grain boundary barrier between the grain boundary and the inside of the grain, k Ｂ This is the Boltzmann constant [eV / K], T is the temperature [K], μ ｉｎ－ｇｒａｉｎ The mobility μ ｉｎ－ｇｒａｉｎ [cm ２ [Vs] is the case. The Fermi energy difference δ ＥＦ However, it is calculated by the following formula (4): The method according to claim 6. [In formula (4), δ ＥＦ０ This is the Fermi energy difference δ at absolute zero or when the free carrier concentration is equal to the effective density of states. ＥＦ And, n is the free carrier concentration [cm³] －３ ] and N ｃ０ The effective density of states [cm³] －３ ] and Z δＥＦＴｎ This is a coefficient. The acceptor-like exponential distribution g ＴＡ (E) is calculated by the following formula (5): The device simulation method according to claim 11. [In formula (5), N ＴＡ This is the energy E at the lower end of the conduction band. ｃ Density of states of acceptor-like defects in [cm²] －３ / eV] and W ＴＡ This is the reciprocal [eV] of the slope of the acceptor-like defect's state density, E is the energy [eV] of the acceptor-like defect, E ｃ This is the energy [eV] at the lower end of the conduction band. 　 A step of performing a device simulation including the device simulation method described in any one of claims 9 to 12 and 19, The step of performing a device simulation is followed by a step of performing a device design based on the results of the device simulation, A method for manufacturing semiconductor devices, including [the specified element]. 　 The aforementioned oxide semiconductor is an oxide mainly composed of In. The manufacturing method according to claim 20. 　 The oxide semiconductor is a polycrystalline oxide semiconductor. The manufacturing method according to claim 20 or 21. 　 A semiconductor device manufactured by the manufacturing method described in any one of claims 20 to 22. 　 An information processing device for calculating the mobility of an oxide semiconductor, The step of calculating the mobility is performed using two or more terms calculated using the free carrier concentration in the oxide semiconductor, The two or more terms mentioned above are calculated by a scattering model derived considering the free carrier concentration in the oxide semiconductor, or by a regression model generated based on measured values ​​of the mobility and the free carrier concentration. Information processing device. 　 A device simulation system, A step of calculating the mobility of the oxide semiconductor using two or more terms calculated by a computer using the free carrier concentration in the oxide semiconductor, The steps include: having the computer perform a device simulation to simulate a device containing the oxide semiconductor, using the mobility of the oxide semiconductor; Execute, A device simulation system in which the two or more terms are calculated by a scattering model derived considering the free carrier concentration in the oxide semiconductor, or by a regression model generated based on measured values ​​of the mobility and the free carrier concentration.

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