Modeling method of surface potential model for gallium arsenide high electron mobility transistor device considering dislocation scattering

Abstract

The application discloses a modeling method of a surface potential model of a gallium arsenide HEMT device considering dislocation scattering, and comprises the following steps: S1, based on the quasi-ballistic transport mechanism of the gallium arsenide HEMT device, using flux to calculate the charge density at the virtual source; S2, establishing a mobility model from the dislocation scattering introduced by the heterojunction of the gallium arsenide HEMT device; S3, further calculating the mean free path and the transmission coefficient from the mobility model; S4, analytically calculating the Fermi level E f by using the charge density formula considering the E0 and E1 energy levels; in order to improve the accuracy near the threshold value, the E f is recalculated by using the Householder method; and S5, verifying by using numerical solution. The application solves the problem that the channel length of the gallium arsenide HEMT device is continuously reduced, and solves the problem that the previous model does not consider the dislocation scattering introduced by the heterojunction.

Description

Technical Field

[0001] This invention relates to microelectronic device modeling technology, and more particularly to a modeling method for a surface potential model of a gallium arsenide HEMT device that considers dislocation scattering. Background Technology

[0002] As the size of gallium arsenide (GaAs) HEMT devices continues to shrink, when the channel length of the transistor is comparable to or less than λ (mean free path of charge carriers), GaAs HEMT devices will be in a fully ballistic (no carrier scattering) or quasi-ballistic (carrier scattering) state. However, most current GaAs HEMT device models are only applicable to devices with long channel lengths and in a drift-diffusion operating state, such as the Advanced SPICE (Simulation Program with Integrated Circuit Emphasis) model (ASM) based on surface potentials. Models applicable to quasi-ballistic transport are mainly for silicon devices. Although the virtual source (VS) model from MIT and its extended versions are applicable to quasi-ballistic GaAs HEMT devices, these models, as well as the ASM model, do not consider dislocation scattering. In addition to ionization impurity scattering and lattice scattering, GaAs HEMT devices also exhibit dislocation scattering due to the presence of heterojunctions. Furthermore, the MIT VS model and its extended versions are based on charge models, which are semi-empirical models. They lack descriptions of physical effects and have insufficient guidance for process fabrication. Physically based surface potential models can address these shortcomings, establishing a clear connection between the model and the actual physical effects in the device. Gallium arsenide HEMT devices with channel lengths close to or less than λ are becoming increasingly complex in structure, with higher power, higher frequencies, and constantly evolving circuit design requirements. These developments present new problems and challenges for the accurate development of device models and parameter extraction. The development of surface potential-based models for gallium arsenide HEMT devices considering dislocation scattering has become a recognized challenge in both industry and academia. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of gallium arsenide (GaAs) HEMT device modeling technology by providing a modeling method for the surface potential of GaAs HEMT devices that considers dislocation scattering. This method aims to solve the problems that most models are only applicable to long-channel GaAs HEMT devices operating under drift diffusion, and models applicable to quasi-ballistic transport are mainly for silicon devices. Existing quasi-ballistic transport models applicable to GaAs HEMT devices do not consider dislocation scattering and have insufficient process guidance capabilities. The invention aims to establish an accurate surface potential model applicable to GaAs HEMT devices with channel lengths close to or less than λ.

[0004] This invention proposes a modeling method for the surface potential model of gallium arsenide HEMT devices considering dislocation scattering, comprising the following steps:

[0005] S1. For the quasi-ballistic transport characteristics of gallium arsenide HEMT devices, the charge density at the virtual source considering the two energy levels E0 and E1 is calculated by flux and transport coefficient, and then the 2DEG charge density along the channel is calculated to obtain the 2DEG charge density formula of the quasi-ballistic model of gallium arsenide HEMT devices considering dislocation scattering.

[0006] S2. Based on the physical structure of the heterojunction of gallium arsenide HEMT device, a mobility model with dislocation scattering as the main scattering mechanism is established.

[0007] S3. Calculate the mean free path from the mobility model in step S2, and then calculate the transmission coefficient;

[0008] S4. Substitute the transport coefficient obtained in step S3 into the formula for the 2DEG charge density obtained in step S1, and combine it with the Poisson equation and the charge density formula obtained by charge conservation to form a set of equations that can solve the surface potential.

[0009] To accurately and analytically solve for the surface potential, the Fermi level E is... f The first energy level E0 and the second energy level E1 are divided into three regions depending on the gate voltage. The surface potentials of the three regions are calculated separately and then combined into a unified E. f Expression; The Householder method is used to improve the accuracy near the threshold voltage, and the reference ballistic model of the surface potential of gallium arsenide HEMT device considering dislocation scattering is established;

[0010] S5, Surface Potential Reference Ballistic Model Verification

[0011] Numerical solution is performed on the system of equations formed in step S4, and E is obtained. f The analytical solution is compared with its numerical solution, and the accuracy of the established surface potential model is verified by the degree of fit.

[0012] Preferably, step S1 specifically includes the following steps:

[0013] When the channel length of a gallium arsenide (GaAs) HEMT device is close to or less than the mean free path, ballistic transport becomes non-negligible. In such devices, a portion of the charge carriers injected from the source are transported unscattered in a ballistic manner, while another portion is scattered back to the source. The probability of the other portion of charge carriers being transported in a ballistic manner is t. s ,like Figure 2 As shown, the flux a at the virtual source (top of the barrier) x0 (1);

[0014] a x0 =a s t s (1)

[0015] Wherein the source injection flux as (2);

[0016]

[0017] Where the thermal velocity of the charge carrier is v T =(2k B T / πm * ) 1 / 2 The effective density of states is D 2D =k B TS 2D The density of states is m * The effective mass of the charge carriers, To reduce Planck's constant, the thermoelectric potential V th =k B T / q, k B It is Boltzmann's constant, T is Kelvin, ambient temperature, and E is... f It is the Fermi level, with E0 and E1 being the first and second levels, respectively;

[0018] From flux a x0 Infer the charge density n at the virtual source x0 (3);

[0019]

[0020] 2DEG charge density n along the channel s See formula (4);

[0021]

[0022] Where y max It is the depth of 2DEG;

[0023] Preferably, step S2 specifically includes the following steps:

[0024] Considering the scattering mechanism of gallium arsenide HEMT devices, the low-field effective mobility μ 0,eff It can be defined as formula (5):

[0025]

[0026] Where, μ dsl μ ii μ latt The effects of dislocation scattering, ionized impurity scattering, and lattice scattering on carrier mobility are represented, respectively. For dislocation densities of 10... 10 cm -2 At the order of magnitude 1, dislocation scattering is the main scattering mechanism for reduced mobility, and at this point, the effective mobility μ at low field is... 0,eff for

[0027]

[0028] Where ε is the relative permittivity, d l N is the distance along the dislocation line from the acceptor center. dis Here, q is the dislocation density, f is the elementary unit charge, f is the occupancy rate of the acceptor center, and λ is the Debye shielding length. db =[εk B T / (q 2 n s )] 1 / 2 ;

[0029] Preferably, step S3 specifically includes the following steps:

[0030] The mean free path λ can be characterized as

[0031]

[0032] Transmission coefficient t s With respect to the mean free path λ and the critical length L of the low-field region at the virtual source eff Related, defined as:

[0033]

[0034] For ease of modeling, let λ+L eff =κL g κ is a semi-empirical factor, L g It is the grid length; formula (8) becomes:

[0035]

[0036] Preferably, step S4 specifically includes the following steps:

[0037] Substituting formulas (6), (7), and (9) into formula (4) yields:

[0038]

[0039] in,

[0040]

[0041]

[0042]

[0043] γ0 and γ1 are constants obtained from experiments, and are 2.26 × 10⁻⁶ respectively. 10 4.0×10 10 ;

[0044] Combining the Poisson equation and the charge conservation equation to obtain the charge density calculation formula (14):

[0045]

[0046] where d ox is the gate oxide thickness, V g is the gate voltage, V off is the threshold voltage, C ox is the gate capacitance,

[0047] V g0 =V g -V off ;

[0048] Solving the equations (10)-(14) for the Fermi potential E f is a formidable task, as these equations are transcendental equations. The variations of E f , E0, and E1 with the gate voltage are obtained through numerical iterative solution. From the perspective of compact modeling, analytical solutions are desirable, because numerical calculation will drastically reduce the speed of circuit simulation. By dividing the variations of E f , E0, and E1 with the gate voltage into three regions, as shown in Figure 3 , analytical solutions are found in each of the regions respectively, and finally the respective regions are combined into a single unified expression that is very accurate in all regions.

[0049] First region: cut-off region (V g <V off ), the surface potential of this region is:

[0050]

[0051] Second region: moderate inversion region (V g >V off , E f >E0, E f <E1), the surface potential of this region is:

[0052]

[0053]

[0054] Third region: strong inversion region (V g >V off , E f <E0 / E1), the surface potential of this region is:

[0055]

[0056]

[0057] In V g >V off Under these conditions, combining the intermediate-trans region and the strong-trans region yields:

[0058] E II-III =V g0 (1-F(V g0 (20)

[0059]

[0060]

[0061]

[0062] V g <V off subthreshold region E f,sub-voff Equation (15) and V g >V off Region E f,above Combining the results, we get:

[0063]

[0064] N p2d =(4β) c N 2-D ) 2 V th (25)

[0065] To improve the model in V off The accuracy at that point was re-evaluated using the Householder numerical calculation method iteratively. f .

[0066]

[0067] The calculations of p, z, and δ are as follows:

[0068]

[0069] V gf =V g -V off -E f,all (28)

[0070]

[0071]

[0072]

[0073]

[0074] surface potential V can be obtained separately x =V s The surface potential at the source end and V x =V d The surface potential at the drain end, V s It is the voltage at the source, V d It is the voltage at the drain terminal;

[0075] Beneficial effects of the present invention

[0076] This invention provides a modeling method for the surface potential base model of gallium arsenide (GaAs) HEMT devices that considers dislocation scattering. This method breaks through the existing GaAs HEMT device modeling techniques and solves the problems that most current GaAs HEMT device models are only applicable to devices with long channel lengths and in a drift-diffusion operating state, that existing quasi-ballistic transport models mainly deal with silicon devices, and that models applicable to quasi-ballistic GaAs HEMT devices lack process guidance capabilities and do not consider dislocation scattering introduced by heterojunctions. The newly derived surface potential formula can more accurately describe the physical transport characteristics of GaAs HEMT devices with channel lengths close to or less than λ. Attached Figure Description

[0077] Figure 1 The derivation process of the model of this invention is as follows;

[0078] Figure 2 Schematic diagram of the quasi-ballistic transport model;

[0079] Figure 3 Ef, E0, E1 of a 30nm InGaAs HEMT device as a function of gate voltage V g The changing numerical simulation results and the division of the three regions;

[0080] Figure 4 For 30nm InGaAs HEMT devices E f Comparison and error between analytical and numerical solutions; Detailed Implementation

[0081] The present invention will be further verified and analyzed below with reference to the accompanying drawings and specific embodiments.

[0082] 30nm InGaAs HEMT devices operate under quasi-ballistic transport. This invention establishes a surface potential reference ballistic model and solves and verifies the surface potential for an InGaAs HEMT device with a 30nm gate length and a 24nm gate oxide thickness. Figure 1 As shown, the modeling method for the InGaAs HEMT surface potential reference ballistic model includes the following steps;

[0083] Step 1. Establish a baseline ballistic model of the InGaAs HEMT surface potential considering dislocation scattering:

[0084] For the quasi-ballistic transport characteristics of 30nm InGaAs HEMT devices, the charge density of the two energy levels E0 and E1 at the virtual source is calculated by flux and transport coefficient, and then the 2DEG charge density along the channel is calculated.

[0085] Step 2. Establish a mobility model characterizing dislocation scattering:

[0086] Based on the physical structure of the heterojunction of InGaAs HEMT device, a mobility model with dislocation scattering as the main scattering mechanism is established.

[0087] Step 3. Calculate the mean free path from the mobility model in Step 2, and then calculate the transmission coefficient;

[0088] Step 4. Substitute the transport coefficient obtained in Step 3 into the formula for the 2DEG charge density in Step 1, and combine it with the charge density formula obtained from the Poisson equation and charge conservation to form a set of equations that can solve the surface potential.

[0089] To accurately solve the surface potential analytically, such as Figure 3 As shown, E f E0 and E1 are subdivided into three regions. The surface potentials of the three regions are calculated separately and then combined into a unified E. f Expression; The Householder method is used to improve the accuracy near the threshold voltage, and the reference ballistic model of the InGaAs HEMT surface potential considering dislocation scattering is established;

[0090] Step 5. Verification of the surface potential reference ballistic model:

[0091] Numerical solutions are performed on the system of equations formed in step four, such as... Figure 4 30nm InGaAs HEMT E is given f A comparison of analytical and numerical solutions. Figure 4 The error values ​​in the illustrations verify the accuracy of the established surface potential basis model.

Claims

1. A modeling method for the surface potential model of gallium arsenide HEMT devices considering dislocation scattering, characterized in that... The method includes the following steps: S1. For the quasi-ballistic transport characteristics of gallium arsenide HEMT devices, the charge density at the virtual source considering the two energy levels E0 and E1 is calculated by flux and transport coefficient, and then the 2DEG charge density along the channel is calculated to obtain the 2DEG charge density formula of the quasi-ballistic model of gallium arsenide HEMT devices considering dislocation scattering. S2. Based on the physical structure of the heterojunction of gallium arsenide HEMT device, a mobility model with dislocation scattering as the main scattering mechanism is established. S3. Calculate the mean free path from the mobility model in step S2, and then calculate the transmission coefficient; S4. Substitute the transport coefficient obtained in step S3 into the formula for the 2DEG charge density obtained in step S1, and combine it with the Poisson equation and the charge density formula obtained by charge conservation to form a set of equations that can solve the surface potential. Fermi level E f The first energy level E0 and the second energy level E1 are divided into three regions depending on the gate voltage. The surface potentials of the three regions are calculated separately and then combined into a unified E. f Expression; The Householder method is used to improve the accuracy near the threshold voltage, and the surface potential model of gallium arsenide HEMT device considering dislocation scattering is established; S5. Surface potential model verification: Numerical solution is performed on the system of equations formed in step S4, and E is obtained. f The analytical solution is compared with its numerical solution, and the accuracy of the established surface potential model is verified by the degree of fit.

2. The modeling method for the surface potential model of gallium arsenide HEMT devices considering dislocation scattering as described in claim 1, characterized in that, The specific steps of S1 are as follows: When the channel length of a gallium arsenide HEMT device is close to or less than the mean free path, a portion of the carriers injected from the source propagate unscattered in a ballistic manner, while another portion is scattered and returns to the source. The probability of the other portion of carriers propagating in a ballistic manner is t. s Then the flux a at the virtual source x0 for; （1） Wherein the source injection flux a s for; （2） Where the thermal velocity of the charge carrier is v T =(2k B T / πm * ) 1 / 2 The effective density of states is D 2D =k B TS 2D The density of states is S 2D =2m * / (πħ 2 ), m * Let V be the effective carrier mass of the InGaAs layer, ħ be the reduced Planck constant, and V be the thermoelectric potential. th = k B T / q, k B It is Boltzmann's constant, T is Kelvin, ambient temperature, and E f It is the Fermi level, with E0 and E1 being the first and second levels, respectively; From flux a x0 Infer the charge density n at the virtual source x0 for; （3） 2DEG charge density n along the channel s for: （4） Where y max It is the depth of 2DEG.

3. The modeling method for the surface potential model of gallium arsenide HEMT devices considering dislocation scattering as described in claim 1, characterized in that, Step S2 is as follows: Considering the scattering mechanism of gallium arsenide HEMT devices, the low-field effective mobility is defined as: （5） Where, μ dsl μ ii μ latt These represent the effects of dislocation scattering, ionized impurity scattering, and lattice scattering on carrier mobility, respectively; for dislocation densities of 10... 10 cm -2 At the order of magnitude 1, dislocation scattering is the main scattering mechanism for reduced mobility, and at this point, the effective mobility μ at low field is... 0,eff for: （6） Where ε is the relative permittivity of the gallium arsenide HEMT device, and d l N is the distance along the dislocation line from the acceptor center. dis Here, q is the dislocation density, f is the elementary unit charge, f is the occupancy rate of the acceptor center, and λ is the Debye shielding length. db =[εk B T / (q 2 n s )] 1 / 2 .

4. The modeling method for the surface potential model of gallium arsenide HEMT devices considering dislocation scattering as described in claim 1, characterized in that, Step S3 is as follows: The mean free path λ is characterized as: （7） Transmission coefficient t s With respect to the mean free path λ and the critical length L of the low-field region at the virtual source eff Related, defined as: （8） Let λ+L eff =κL g κ is a semi-empirical factor, L g It is the gate length; the transmission coefficient t s The definition is transformed into: （9）。 5. The modeling method for the surface potential model of gallium arsenide HEMT devices considering dislocation scattering as described in claim 1, characterized in that, Step S4 is as follows: The low-field effective mobility μ in step S3 0,eff Formula (6), the mean free path λ formula (7) in step S4, and the transmission coefficient t s Substituting the definition (9) into the 2DEG charge density formula (4) in step S2, we obtain the following expression: （10） in, （11） （12） （13） γ0 and γ1 are 2.26 × 10⁻⁶ respectively. 10 and 4.0×10 10 ; Combining Poisson's equation and charge conservation, we obtain the expression for charge density: （14） Where d ox It is the gate oxide layer thickness, V g It's the gate voltage, V off It is the threshold voltage, C ox It is the gate capacitance, V g0 =V g -V off ; E is obtained through numerical iteration. f E0, E1 vary with gate voltage; by... f E0 and E1 are divided into three regions depending on the gate voltage. Analytical solutions are found in each region, and finally, these regions are combined into a single unified expression: First region: Cutoff region V g <V off The surface potential of this region is: （15） Second region: moderate inversion region V g >V off , E f >E0, E f <E1, the surface potential of this region is: （16） （17） Third region: strong inversion region V g >V off , E f <E0 / E1, the surface potential of this region is: （18） （19） In V g >V off Under these conditions, combining the intermediate-trans region and the strong-trans region yields: （20） （21） （22） （23） V g <V off subthreshold region E I Equation (15) and V g >V off Region E II-III Combining the results, we get: （24） （25） V was iteratively re-evaluated using the Householder numerical calculation method. f : （26） Where p, z, and δ are calculated as follows: （27） （28） （29） （30） （31） （32）。

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