A Noise Characterization Method for Trap Distribution in the Gate Oxide of MOSFETs

Abstract

The present invention relates to a method for characterizing traps in the gate oxide layer of MOSFETs, and the steps are as follows: 1) Measure the transfer characteristics to extract the threshold voltage, and test the noise power spectral density S of the device in the linear region id ; 2) Draw a double y-axis graph according to the measurement data to judge the noise fluctuation mechanism; 3) Calculate the trap energy position distribution in the gate oxide layer at a certain gate voltage V g ; 4) Repeat step 3 for all gate voltages to draw the energy position distribution diagram of the oxide layer traps. This method breaks through the limitation of only using uniform distribution or exponential distribution to characterize the trap distribution with position, and at the same time takes into account the non-uniformity of trap position and energy distribution, and by drawing a three-dimensional image, the distribution of oxide layer traps with energy position can be clearly observed.

Description

Technical Field

[0001] The present invention belongs to the technical field of semiconductor device characterization, and relates to a method for characterizing the trap energy position distribution of the gate oxide layer of MOSFETs by measuring the 1 / f noise of MOSFETs. Background Art

[0002] The 1 / f noise of MOSFETs is significantly affected by the traps in the gate oxide layer. Therefore, the 1 / f noise can be used to reflect the trap characteristics of the gate oxide layer of MOSFETs. Currently, the characterization technology of the gate oxide layer traps of MOSFETs based on 1 / f noise is mainly qualitative analysis. The power spectrum of 1 / f noise is always approximated as S~1 / f r , where r is generally between 0.8 and 1.2, which results in the traps in the oxide layer changing with z (perpendicular to the channel direction) only in the form of an exponential distribution N t =N t0 ·exp(β·z) or a uniform distribution (the uniform distribution can be regarded as a special case of the exponential distribution, i.e., β = 0) [1-3]. In this way, although it is convenient to qualitatively compare the levels of traps and extract the changes of traps with energy, it cannot reflect the change of the trap density in the oxide layer with position.

[0003] References:

[0004] 【1】Hua Chen, Liang He. The spatial and energy distribution of oxide trap responsible for 1 / f noise in 4H-SiC MOSFETs. J. Phys. Commun. 5(2021)035002.

[0005] 【2】Martin von Haartman, Mikael Low Frequency Noise In Advanced Mos Devices. Springer, 2007.

[0006] 【3】Zhuang Yiqi, Sun Qing. Noise in Semiconductor Devices and Its Low-Noise Technology. National Defense Industry Press, 1993. Summary of the Invention

[0007] To solve the deficiencies of the above-mentioned prior art, the object of the present invention is a noise characterization method for the trap distribution of the MOSFETs gate oxide layer. This method relates low-frequency noise to the energy position distribution of oxide traps through a device physical model and a discrete form of the 1 / f noise model, and proposes a series of steps to determine the energy position distribution of traps in the sample.

[0008] The technical solution of the present invention is as follows: A noise characterization method for the trap distribution of the MOSFETs gate oxide layer, and the steps are as follows:

[0009] 1) Measure the transfer characteristic curve (I d -V g ) of the MOSFETs sample and extract the threshold voltage V t . Set the drain voltage and gate voltage to make the sample in the linear region, and measure the noise S d of the drain current I id (f) of the sample at different gate voltages in the linear region;

[0010] 2) Judge the noise fluctuation mechanism. First, use the measured data to draw a double y-axis graph. In the double y-axis graph, the x-axis is the drain current |I d |, and the two y-axes are respectively Among them, represents the transconductance. Then compare the two curves. If the trends of the two curves are the same, the number fluctuation is the main noise mechanism, and proceed to step 3. (This patent is applicable to the noise mechanism dominated by number fluctuations)

[0011] 3) Determine the trap energy position distribution of the gate oxide layer under a certain gate voltage V g . First, calculate the distance ΔE of the trap energy from the band edge corresponding to a certain gate voltage V g : Numerically solve the transcendental equation Solve to get Among them, C ox is the gate oxide capacitance, V g is the gate voltage, k is the Boltzmann constant, T is the absolute temperature, q is the electron charge, is the ionized doping impurity concentration. In n-type MOSFETs is the acceptor ionization concentration In p-type MOSFETs is the donor ionization concentration ε s is the semiconductor dielectric constant, R represents the ratio of the equilibrium minority carrier concentration to the majority carrier concentration of the substrate. In n-type MOSFETs, R is the ratio of the substrate electron concentration to the hole concentration In p-type MOSFETs, R is the ratio of the substrate hole concentration to the electron concentration Use Calculate the distance ΔE of the trap energy from the band edge, using E c -E t to represent the distance ΔE of the energy of n-type MOSFETs from the band edge. Substitute into to obtain E c -E f . Let E c -E t =E c -E f , where E g represents the bandgap width, is the substrate Fermi potential. Use E t -E v to represent the distance ΔE of the energy of p-type MOSFETs from the band edge. Substitute into to obtain E f -E v . Let E t -E v =E f -E v . Then calculate the distribution of the oxide trap density with position N t (z) at this gate voltage: Numerically solve the equation to obtain N t (z), where W and L represent the width and length of the channel respectively, τ = τ0exp(γ·z), the typical value of τ0 is 10 -10 , f is the frequency, and Δz i is the unit oxide thickness. Finally, obtain the trap density N t (ΔE, z) of the gate oxide layer at this gate voltage.

[0012] 4) Plot the energy-position distribution diagram of the oxide traps at different gate voltages. Repeat step 3) for all gate voltages to obtain N t (ΔE, z) at different gate voltages. Use the oxide trap position as the x-axis, the distance ΔE of the trap energy from the band edge as the y-axis, and the oxide trap density N t as the z-axis. Plot the distribution diagram of the oxide trap density varying with energy and position at different gate voltages.

[0013] Compared with the prior art, the beneficial effect of the present invention is that it breaks through the limitation of only using uniform distribution or exponential distribution to characterize the trap density distribution with position, and at the same time considers the non-uniformity of energy and position distributions, extracting more detailed information about the trap density distribution with position. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is the flowchart of the embodiment of the present invention;

[0015] Figure 2 is the noise power spectral density S id as a curve showing the variation with frequency f;

[0016] Figure 3 is and comparison;

[0017] Figure 4 is the distribution map of the trap energy positions in the oxide layer of the n-type MOSFETs sample;

[0018] Figure 5 is the distribution map of the trap energy positions in the oxide layer of the p-type MOSFETs sample. Specific embodiments

[0019] To make the present invention easier to understand, the present invention will be further described below in conjunction with the accompanying drawings.

[0020] As Figure 1 shown, a noise characterization method for the trap distribution in the gate oxide layer of MOSFETs, taking an n-type MOSFETs sample as an example, the specific steps are as follows:

[0021] 1) Measure the transfer characteristic curve (I d -V g ) of the sample and extract the threshold voltage V t , set the drain voltage V d and the gate voltage V g to make the sample in the linear region, and measure the drain current I d of the sample at different gate voltages in the linear region and the noise S id (f);

[0022] The step 1) described above includes:

[0023] (1) When measuring the transfer characteristic curve, the gate voltage V g is swept from 0V to 6V. To ensure that the MOSFETs sample operates in the linear mode during low-frequency noise measurement, a relatively small drain voltage V d = 0.1V is selected as the noise test condition;

[0024] (2) Draw the transfer characteristic curve according to the measurement data, with the gate voltage V g on the horizontal axis and the drain current I d on the vertical axis, and then take the partial derivative of I d with respect to V g to obtain the transconductance curve (g m -V g ), draw a vertical line of the horizontal axis V g at the highest point of the transconductance curve, and at the intersection position of the vertical line and the I d -V g curve make Id -V g The tangent of the curve, and the intersection of the tangent with the horizontal axis minus V d Divided by 2 is the threshold voltage V t , V t = 2.9V;

[0025] (3) As shown Figure 2 Set the drain voltage V d = 0.1V, and select the gate-source voltages V g = 3.0V, 3.2V, 3.4V, 3.6V, 3.8V, etc., measure the noise power spectral density S id , and record the drain current I d .

[0026] 2) Judge the noise fluctuation mechanism. First, use the measured data to draw a double y-axis graph, as shown Figure 3 in the figure, the x-axis is the drain current I d , and the two y-axes are respectively Among them, represents the transconductance; then compare the two curves. If the trends of the two curves are the same, the number fluctuation is the main noise mechanism, and proceed to step 3).

[0027] 3) Determine the energy position distribution N g of the traps in the gate oxide layer under a certain gate voltage V t (ΔE, z).

[0028] The said step 3) includes:

[0029] (1) Calculate the distance ΔE of the trap energy from the band edge corresponding to the gate voltage V g . Select the gate voltage V g = 3.0V, the drain voltage V d = 0.1V, and substitute the material parameters and the device structure parameters into (where C ox is the gate oxide capacitance, k is the Boltzmann constant, T is the absolute temperature,[[]] q is the electron charge,[[]] is the ionized doping impurity concentration, and in n-type MOSFETs is the acceptor ionization concentration ε s is the semiconductor dielectric constant, R represents the ratio of the equilibrium minority carrier concentration to the majority carrier concentration in the substrate, and in n-type MOSFETs it is the ratio of the substrate electron concentration to the hole concentration Solve to get Substitute into to get E c - E f , let ΔE = E c - Et = E c -E f , where E g represents the bandgap width, is the substrate Fermi potential.

[0030] (2) Calculate the variation of the trap energy in the oxide layer with position N g (z) under the gate voltage V t . Select the gate voltage V g = 3.0 V and the drain voltage V d = 0.1 V; construct an m-row and two-column matrix [S id , f] from the measured noise power spectral density S id and the frequency f. Divide the oxide layer into n parts in the thickness direction and set n variables N t (z1), N t (z2),... N t (z n ). Each set of [S id , f] satisfies (where W and L represent the width and length of the channel respectively, τ = τ0exp(γ·z), the typical value of τ0 is 10 -10 , f is the frequency, and Δz i is the divided unit oxide layer thickness), forming a system of linear equations with n unknowns and m equations. Solve this system of linear equations by non-negative least squares method to obtain N t (z i ).

[0031] (3) Relate the distance ΔE of the trap energy corresponding to the gate voltage V g from the band edge and the variation of the trap density with position N t (z), and finally obtain the energy position distribution N t (ΔE, z) of the gate oxide layer under this gate voltage.

[0032] (4) Plot the energy position distribution diagram of the oxide layer traps. Repeat step 3) for all gate voltages to obtain N t (ΔE, z) under different gate voltages. Take the oxide layer trap position as the x-axis, the energy E c -E t as the y-axis, and the oxide layer trap density N t as the z-axis to plot the density distribution diagram of the oxide layer traps varying with energy and position under different gate voltages. As shown in Figure 4 .

[0033] In the embodiment of the present invention, an n-type MOSFETs is used as the characterization object to extract the energy position distribution of its oxide layer traps. This method is also applicable to the trap characterization of p-type MOSFETs. The characterization result of a p-type MOSFETs is as shown inFigure 5 as shown

Claims

1. A noise characterization method for the trap distribution in the gate oxide layer of MOSFETs, characterized in that: Including the following steps: 1) Measure the transfer characteristic curve of the sample ( ) and extract the threshold voltage , set the drain voltage and the gate voltage to make the sample in the linear region, and measure the drain current noise of the sample at different gate voltages in the linear region ; 2) Determine the noise fluctuation mechanism; use the measured data to first plot a dual y-axis graph, where the x-axis in the dual y-axis graph is the leakage current , and the two y-axes are respectively , , where represents the transconductance; then compare the dual y-axis curves. If the trends of the two curves are the same, the number fluctuation is the main noise mechanism, and proceed to step 3); 3) Use the noise data to determine the trap energy position distribution of the lower gate oxide layer at a certain gate voltage ; 4) Plot the energy position distribution diagrams of oxide traps under all gate voltages; Repeat step 3) for all gate voltages to obtain , with the position of the oxide traps as the x-axis, the distance of the trap energy from the band edge as the y-axis, and the oxide trap density as the z-axis, and plot the distribution diagrams of oxide traps varying with energy and position under different gate voltages; Step 1), including the following steps: 1.1) Measuring the transfer characteristic curve; 1.2) Draw the transfer characteristic curve according to the measurement data, with the gate voltage on the horizontal axis , and the drain current on the vertical axis . Then take the partial derivative with respect to to obtain the transconductance curve . Draw a vertical line on the horizontal axis at the highest point of the transconductance curve. At the intersection of the vertical line and the curve, draw a tangent line to the curve. The intersection of this tangent line and the horizontal axis is the threshold voltage ; 1.3) Set the drain voltage and the gate voltage to keep the MOSFETs in the linear region, fix the drain voltage , and respectively select different gate voltages , measure the noise power spectral density , and record the drain current at this time ; Step 3) includes the following steps: Using the noise data to determine the trap energy position distribution of the lower gate oxide layer at a certain gate voltage , including: 3.1) Calculate the gate voltage The distance of the corresponding trap energy from the band edge ; 3.2) Calculate the gate voltage Variation of the lower oxide trap density with position ; 3.3) Obtain the gate voltage Energy position distribution of the bottom gate oxide layer ; 3. A noise characterization method for the trap distribution of the gate oxide layer of MOSFETs according to claim 1, characterized in that: The described step 3.1) calculates the gate voltage The distance of the corresponding trap energy from the band edge , including the following steps: 3.1.1) Numerical solution of transcendental equations , the solution is , where is the gate oxide capacitance, is the Boltzmann constant, is the absolute temperature, is the semiconductor dielectric constant, , is the electronic charge, is the ionized doped impurity concentration. In n-type MOSFETs is the acceptor ionization concentration . In p-type MOSFETs is the donor ionization concentration , represents the ratio of the minority carrier concentration to the majority carrier concentration in the substrate equilibrium state. In n-type MOSFETs is the ratio of the substrate electron concentration to the hole concentration . In p-type MOSFETs is the ratio of the substrate hole concentration to the electron concentration ; 3.1.2) Utilize Calculate the distance of the trap energy from the band edge ; Use To represent the distance of the energy of n-type MOSFETs from the band edge ; Substitute Into We can obtain , Let , where Is the surface potential, Represents the bandgap width, Is the conduction band, Is the valence band, Is the Fermi level, Is the trap energy, Is the substrate Fermi potential; Use To represent the distance of the energy of p-type MOSFETs from the band edge , Substitute Into We can obtain , Let .

4. A noise characterization method for the trap distribution of the gate oxide layer of MOSFETs according to claim 1, characterized in that: The step 3.2) calculates the gate voltage The variation of the lower oxide layer trap density with position , numerically solves the equation , and obtains , where and respectively represent the width and length of the channel , The typical value of -10 is is the frequency is the divided oxide layer thickness is the tunneling coefficient 4. A method for noise characterization of the trap distribution in the gate oxide layer of MOSFETs according to claim 2, characterized in that: The method for solving the equation in step 3.1.1) is to use the non - negative least - squares method.

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