Simulation and Design of Enhanced p-GaN HEMT Devices Using Nuwa TCAD Software

GMPT, October 2024

The third-generation semiconductor material GaN offers advantages such as a wide bandgap, high electron saturation velocity, and excellent thermal conductivity. GaN high electron mobility transistors (HEMT) exhibit high electric field strength, high mobility, and good thermal stability, making them particularly advantageous in high-frequency, high-power applications. However, most AlGaN/GaN HEMTs are normally-on, which is not entirely safe for practical high-power switching applications. Therefore, the market urgently requires AlGaN/GaN HEMTs that achieve normally-off operation while maintaining low on-resistance. To meet these needs, this work introduces a p-type GaN insertion layer structure that uses hole injection from the p-type gate to the two-dimensional electron gas (2DEG) to modulate conductivity, effectively reducing the 2DEG density in the channel under the gate. This study uses Nuwa TCAD software for the simulation and design of p-GaN HEMTs and presents the software's simulation results.

1. Device Structure

Fig. 1. Structure of AlGaN/GaN p-GaN HEMT device

In this study, the AlGaN/GaN HEMT device structure on a silicon (Si) heterostructure substrate is shown in Fig. 1. The p-GaN gate thickness is 50 nm with a doping concentration of $5\times 10^{19}{cm}^{-3}5\backslash times\; 10^\{19\}\; \{cm\}^\{-3\}$; the AlGaN barrier layer thickness is 13 nm with an Al composition of 0.26; the GaN channel layer thickness is 25 nm; the AlGaN back barrier layer thickness is 60 nm with an Al composition of 0.05; the GaN buffer layer thickness is 3 $\mu \backslash mu$m; and the AlN nucleation layer thickness is 0.2 $\mu \backslash mu$m. Additionally, the drain, gate, and source are all Ohmic contacts with a width of 1 $\mu \backslash mu$m. The gate-source spacing (L_GS) and gate-drain spacing (L_GD) are 0.8 $\mu \backslash mu$m and 12 $\mu \backslash mu$m, respectively.

2. Physical Model Settings

2.1 Thermionic Emission Model

2.2 Continuity Equation

$$\begin{array}{c}{\displaystyle \mathrm{\nabla }\cdot J_n-\sum _j{R}_n^{tj}-R_{sp}-R_{st}-R_{au}+G_{opt}(t)=\frac{\mathrm{\partial }n}{\mathrm{\partial }t}+N_D\frac{\mathrm{\partial }{f}_D}{\mathrm{\partial }t}}\end{array}\backslash begin\{aligned\}\; \backslash nabla\; \backslash cdot\; J\_n-\backslash sum\_j\; R\_n^\{t\; j\}-R\_\{s\; p\}-R\_\{s\; t\}-R\_\{a\; u\}+G\_\{o\; p\; t\}(t)=\backslash frac\{\backslash partial\; n\}\{\backslash partial\; t\}+N\_D\; \backslash frac\{\backslash partial\; f\_D\}\{\backslash partial\; t\}\; \backslash end\{aligned\}$$ $$\begin{array}{c}{\displaystyle \mathrm{\nabla }\cdot J_p+\sum _j{R}_p^{tj}+R_{sp}+R_{st}+R_{au}-G_{opt}(t)=-\frac{\mathrm{\partial }p}{\mathrm{\partial }t}+N_A\frac{\mathrm{\partial }{f}_A}{\mathrm{\partial }t}}\end{array}\backslash begin\{aligned\}\; \backslash nabla\; \backslash cdot\; J\_p+\backslash sum\_j\; R\_p^\{t\; j\}+R\_\{s\; p\}+R\_\{s\; t\}+R\_\{a\; u\}-G\_\{o\; p\; t\}(t)=-\backslash frac\{\backslash partial\; p\}\{\backslash partial\; t\}+N\_A\; \backslash frac\{\backslash partial\; f\_A\}\{\backslash partial\; t\}\; \backslash end\{aligned\}$$

2.3 Poisson’s Equation

$$-\mathrm{\nabla }\cdot \left(\frac{{ϵ}_0{ϵ}_{dc}}{q}\mathrm{\nabla }V\right)=-n+p+N_D(1-f_D)-N_A{f}_A+\sum _j{N}_{tj}({\delta }_j-f_{tj})-\backslash nabla\; \backslash cdot\backslash left(\backslash frac\{\backslash epsilon\_0\; \backslash epsilon\_\{d\; c\}\}\{q\}\; \backslash nabla\; V\backslash right)=-n+p+N\_D\backslash left(1-f\_D\backslash right)-N\_A\; f\_A+\backslash sum\_j\; N\_\{t\; j\}\backslash left(\backslash delta\_j-f\_\{t\; j\}\backslash right)$$

2.4 Low-Field and High-Field Mobility Model

• Low-Field Mobility Model

• High-Field Mobility Model (Canali Model)

2.5 Source and Drain Heavily Doped Ohmic Contact Formation

• Tunneling Model

2.6 Interface Defect Model

• Exponential Tail Model

  $$\mathrm{DOS}(E)=\frac{N_{trap}}{E_{tail}}{e}^{[-\frac{(E-E_0)}{E_{tail}}]}\backslash operatorname\{DOS\}(E)=\backslash frac\{N\_\{\; \{trap\; \}\}\}\{E\_\{\; \{tail\; \}\}\}\; e^\{\backslash left[-\backslash frac\{\backslash left(E-E\_0\backslash right)\}\{E\_\{\{tail\; \}\}\}\backslash right]\}$$

• Gaussian Model

  $$\mathrm{DOS}(E)=\frac{N_{trap}}{\sqrt{2\pi }\sigma }{e}^{[-\frac{{(E-E_0)}^2}{2{\sigma }^2}]}\backslash operatorname\{DOS\}(E)=\backslash frac\{N\_\{\; \{trap\; \}\}\}\{\backslash sqrt\{2\; \backslash pi\}\; \backslash sigma\}\; e^\{\backslash left[-\backslash frac\{\backslash left(E-E\_0\backslash right)^2\}\{2\; \backslash sigma^2\}\backslash right]\}$$

2.7 Bulk Defect Model

• Shockley-Read-Hall Model

$$\begin{array}{c}{\displaystyle R_n^{tj}=c_{nj}n{N}_{tj}(1-f_{tj})-c_{nj}{n}_{1j}{N}_{tj}{f}_{tj}}\end{array}\backslash begin\{aligned\}R\_n^\{t\; j\}=c\_\{n\; j\}\; n\; N\_\{t\; j\}\backslash left(1-f\_\{t\; j\}\backslash right)-c\_\{n\; j\}\; n\_\{1\; j\}\; N\_\{t\; j\}\; f\_\{t\; j\}\backslash end\{aligned\}$$ $$\begin{array}{c}{\displaystyle R_p^{tj}=c_{pj}p{N}_{tj}{f}_{tj}-c_{pj}{p}_{1j}{N}_{tj}(1-f_{tj})}\end{array}\backslash begin\{aligned\}R\_p^\{t\; j\}=c\_\{p\; j\}\; p\; N\_\{t\; j\}\; f\_\{t\; j\}-c\_\{p\; j\}\; p\_\{1\; j\}\; N\_\{t\; j\}\backslash left(1-f\_\{t\; j\}\backslash right)\backslash end\{aligned\}$$ $$\begin{array}{c}{\displaystyle N_{tj}\frac{\mathrm{\partial }{f}_{tj}}{\mathrm{\partial }t}=R_n^{tj}-R_p^{tj}}\end{array}\backslash begin\{aligned\}N\_\{t\; j\}\; \backslash frac\{\backslash partial\; f\_\{t\; j\}\}\{\backslash partial\; t\}=R\_n^\{t\; j\}-R\_p^\{t\; j\}\backslash end\{aligned\}$$ $$\begin{array}{c}{\displaystyle c_{nj}={\sigma }_{nj}{v}_n={\sigma }_{nj}\sqrt{\frac{8kT}{\pi m_n}};c_{pj}={\sigma }_{pj}{v}_p={\sigma }_{pj}\sqrt{\frac{8kT}{\pi m_p}}}\end{array}\backslash begin\{aligned\}c\_\{n\; j\}=\backslash sigma\_\{n\; j\}\; v\_n=\backslash sigma\_\{n\; j\}\; \backslash sqrt\{\backslash frac\{8\; k\; T\}\{\backslash pi\; m\_n\}\}\; ;\; \backslash quad\; c\_\{p\; j\}=\backslash sigma\_\{p\; j\}\; v\_p=\backslash sigma\_\{p\; j\}\; \backslash sqrt\{\backslash frac\{8\; k\; T\}\{\backslash pi\; m\_p\}\}\backslash end\{aligned\}$$ $$\begin{array}{c}{\displaystyle \frac{1}{{\tau }_{nj}}=c_{nj}{N}_{tj};\frac{1}{{\tau }_{nj}}=c_{nj}{N}_{tj}}\end{array}\backslash begin\{aligned\}\backslash frac\{1\}\{\backslash tau\_\{n\; j\}\}=c\_\{n\; j\}\; N\_\{t\; j\};\; \backslash quad\; \backslash frac\{1\}\{\backslash tau\_\{n\; j\}\}=c\_\{n\; j\}\; N\_\{t\; j\}\backslash end\{aligned\}$$

• Gaussian Model$$\mathrm{DOS}(E)=\frac{N_{trap}}{\sqrt{2\pi }\sigma }{e}^{[-\frac{{(E-E_0)}^2}{2{\sigma }^2}]}\backslash operatorname\{DOS\}(E)=\backslash frac\{N\_\{\; \{trap\; \}\}\}\{\backslash sqrt\{2\; \backslash pi\}\; \backslash sigma\}\; e^\{\backslash left[-\backslash frac\{\backslash left(E-E\_0\backslash right)^2\}\{2\; \backslash sigma^2\}\backslash right]\}$$

2.8 Polarization Model

$$P_{sp}=-0.090x-0.034(1-x)+0.019x(1-x)\text{ for }A{l}_{x}G{a}_{1-x}NP\_\{s\; p\}=-0.090\; x-0.034(1-x)+0.019\; x(1-x)\backslash quad\; \backslash text\; \{\; for\; \}\; A\; l\_x\; G\; a\_\{1-x\}\; N$$ $$\epsilon (x)=\frac{a_{subs}-a(x)}{a(x)}\backslash varepsilon(x)=\backslash frac\{a\_\{\{subs\; \}\}-a(x)\}\{a(x)\}$$ $$\begin{array}{c}{\displaystyle a(x)=0.31986-0.00981x\text{ for }A{l}_{x}G{a}_{1-x}N}\end{array}\backslash begin\{aligned\}\; a(x)=0.31986-0.00981\; x\; \backslash quad\; \backslash text\; \{\; for\; \}\; A\; l\_x\; G\; a\_\{1-x\}\; N\; \backslash end\{aligned\}$$ $$P_{pz\mathrm{\_}GaN}=-0.918\epsilon (x)+9.541\epsilon (x{)}^{2}x=0P\_\{pz\backslash \_GaN\}=-0.918\; \backslash varepsilon(x)+9.541\; \backslash varepsilon(x)^2\; \backslash quad\; x=0$$ $$P_{pz}=x{P}_{pz\mathrm{\_}AlN}[\epsilon (x)]+(1-x)P_{p{z}_{-}GaN}[\epsilon (x)]P\_\{p\; z\}=x\; P\_\{pz\backslash \_AlN\}[\backslash varepsilon(x)]+(1-x)\; P\_\{p\; z\_\{-\}\; G\; a\; N\}[\backslash varepsilon(x)]$$ $$P_{total}=P_{sp}+P_{pz}P\_\{total\; \}=P\_\{s\; p\}+P\_\{p\; z\}$$ $$P=screening\times P_{total}P=\; screening\; \backslash times\; P\_\{total\; \}$$

2.9 Impact Ionization Model

• Chynoweth Model

$$\begin{array}{c}{\displaystyle {\alpha }_n={\alpha }_n^{\mathrm{\infty }}{e}^{-{\left(\frac{F_{cn}}{F}\right)}^{{\kappa }_n}}}\end{array}\backslash begin\{aligned\}\; \backslash alpha\_n=\backslash alpha\_n^\{\backslash infty\}\; e^\{-\backslash left(\backslash frac\{F\_\{c\; n\}\}\{F\}\backslash right)^\{\backslash kappa\_n\}\}\; \backslash end\{aligned\}$$ $$\begin{array}{c}{\displaystyle {\alpha }_p={\alpha }_p^{\mathrm{\infty }}{e}^{-{\left(\frac{{}_{cp}}{F}\right)}^{{\kappa }_p}}}\end{array}\backslash begin\{aligned\}\; \backslash alpha\_p=\backslash alpha\_p^\{\backslash infty\}\; e^\{-\backslash left(\backslash frac\{\{\; \}\_\{c\; p\}\}\{F\}\backslash right)^\{\backslash kappa\_p\}\}\; \backslash end\{aligned\}$$

Impact Ionization Parameters

	${\alpha }^{\mathrm{\infty }}(1\mathrm{/}m)\backslash alpha^\{\backslash infty\}(1\; /\; m)$	$F_{\mathrm{c}}(V\mathrm{/}m)F\_\{\backslash mathrm\{c\}\}(V\; /\; m)$	$\kappa \backslash kappa$	Field Range $(\mathrm{V}\mathrm{/}\mathrm{m})(\backslash mathrm\{V\}\; /\; \backslash mathrm\{m\})$
Electron	$2\times 10^{8}2\; \backslash times\; 10^\{8\}$	$3\times 10^{9}3\; \backslash times\; 10^\{9\}$	1	$3.2\times 10^{8}3.2\; \backslash times\; 10^\{8\}$
	$1\times 10^{7}1\; \backslash times\; 10^\{7\}$	$2.2\times 10^{9}2.2\; \backslash times\; 10^\{9\}$	1	$\mathrm{\infty }\backslash infty$
Hole	$1.34\times 10^{10}1.34\; \backslash times\; 10^\{10\}$	$2.03\times 10^{9}2.03\; \backslash times\; 10^\{9\}$	1	$\mathrm{\infty }\backslash infty$

3. Results and Discussion

3.1 Band Structure Diagram

Fig. 2. (a) Band structure distribution at p-GaN/Al_0.26GaN/GaN channel interface, (b) Band structure distribution at SiN/Al_0.26GaN/GaN channel interface

In this simulation, the polarization effects of the AlGaN barrier and back barrier layers, as well as the GaN channel layer, are taken into account. Polarization charges at both interfaces generate a triangular barrier well, confining electrons within the channel layer. Fig. 2(a) shows the vertical band distribution and electron wave function distribution at the p-GaN/Al_0.26GaN/GaN channel interface. Due to the introduction of the p-GaN gate, the potential in the channel region is elevated, and the two-dimensional electron gas (2DEG) beneath the gate is depleted, enabling normally-off operation, making this an enhancement-mode device. At locations beyond the gate, as shown in Fig. 2(b), the Al_0.26GaN/GaN interface generates 2DEG.

3.2 Forward Conduction Characteristics

Fig. 3. (a) Output characteristic curve (V_GS=3.5 V), (b) Transfer characteristic curve (V_DS=5 V)

Fig. 3(a) and Fig. 3(b) show the output and transfer characteristic curves of the p-GaN HEMT during forward conduction. In Fig. 3(a), at V_GS=3.5 V, the channel is already open, and the drain voltage is swept from 0 to 8 V, displaying robust conduction performance. At V_GS=3.5 V and V_DS=8 V, the output current of the device reaches 253 A/m. The transfer characteristic curve in Fig. 3(b) illustrates the device’s excellent enhancement mode characteristics, with a threshold voltage above 0 V, reaching 2.1 V (defined as the gate voltage at which the drain current reaches 1 mA). Therefore, the p-GaN gate structure is an effective design for achieving normally-off GaN HEMTs.

Fig. 5. Off-state breakdown curve (V_GS=0 V)

3.3 Off-State Characteristics

Fig. 5. Off-state breakdown curve (V_GS=0 V)

For power devices, both forward conduction and off-state breakdown characteristics require balanced consideration. While achieving enhanced conduction characteristics, a high breakdown voltage in the off-state is also a necessary requirement. Fig. 5 demonstrates that the device maintains strong off-state performance up to a drain voltage of 158 V at V_GS=0 V.

Fig. 6. 2D electric field distribution in the off-state for (a) V_DS=50 V and (b) V_DS=100 V

Fig. 7. 2D potential distribution in the off-state for (a) V_DS=50 V and (b) V_DS=100 V

Fig. 8. 2D impact ionization distribution in the off-state for (a) V_DS=50 V and (b) V_DS=100 V

Figures 6 and 7 illustrate the electric field and potential distributions under varying drain bias voltages in the off-state. As the drain bias voltage increases, the depletion region expands from the drain towards the gate-source side, with the strongest electric field appearing near the edge of the gate close to the drain contact. Additionally, Fig. 8 shows the 2D impact ionization rate distribution for drain bias voltages of 50 V and 100 V. This figure effectively reveals that, for HEMT devices, the strongest impact ionization in the off-state occurs at the gate edge near the drain side, corresponding to the strongest electric field distribution position in Fig. 7. This behavior aligns well with the Chynoweth model used in the simulation. Therefore, designing an effective edge termination to mitigate the strong electric field at the gate edge is key to enhancing the voltage endurance of current GaN HEMT devices.

3.4 Capacitance-Frequency Characteristics

Fig. 9. (a) C_GS-V characteristic curve, (b) C_GD-V characteristic curve, (c) Equivalent circuit model with C1 as C_GD and C2 as C_GS, (d) 2D electron concentration distribution when the channel is fully depleted

In CMOS device models, the Meyer capacitance model is commonly used to describe the non-uniform charge distribution and the C_GS/C_GD ratio under the gate when V_DS is non-zero. The p-GaN HEMT, with its edge capacitance resulting from the depletion region extending along the gate edge at high V_DS, along with the series resistance from gate-to-source and gate-to-drain, exhibits excellent C_GD-V_DS characteristics^[1]. The gate capacitance C_G can be modeled by the following formula:

$$\left[\begin{array}{c}{C}_{\mathrm{G}\mathrm{D}}(v_{\mathrm{D}\mathrm{S}},v_{\mathrm{G}\mathrm{S}})\\ \\ C_{\mathrm{G}\mathrm{S}}(v_{\mathrm{D}\mathrm{S}},v_{\mathrm{G}\mathrm{S}})\end{array}\right]=\left[\begin{array}{c}{C}_{\mathrm{G}\mathrm{D}0}\\ \\ C_{\mathrm{G}\mathrm{S}0}\end{array}\right]+\left[\begin{array}{c}{k}_1\left(v_{\mathrm{D}\mathrm{S}}\right)\cdot C_{\mathrm{G}-\mathrm{c}\mathrm{h}}(v_{\mathrm{G}\mathrm{S}},v_{\mathrm{G}\mathrm{D}})\\ \\ k_2\left(v_{\mathrm{D}\mathrm{S}}\right)\cdot C_{\mathrm{G}-\mathrm{c}\mathrm{h}}(v_{\mathrm{G}\mathrm{S}},v_{\mathrm{G}\mathrm{D}})\end{array}\right]\backslash left[\backslash begin\{array\}\{l\}C\_\{\backslash mathrm\{GD\}\}\backslash left(v\_\{\backslash mathrm\{DS\}\},\; v\_\{\backslash mathrm\{GS\}\}\backslash right)\; \backslash \backslash \backslash \backslash \; C\_\{\backslash mathrm\{GS\}\}\backslash left(v\_\{\backslash mathrm\{DS\}\},\; v\_\{\backslash mathrm\{GS\}\}\backslash right)\backslash end\{array\}\backslash right]=\backslash left[\backslash begin\{array\}\{l\}C\_\{\backslash mathrm\{GD\}\; 0\}\; \backslash \backslash \backslash \backslash \; C\_\{\backslash mathrm\{GS\}\; 0\}\backslash end\{array\}\backslash right]+\backslash left[\backslash begin\{array\}\{l\}k\_1\backslash left(v\_\{\backslash mathrm\{DS\}\}\backslash right)\; \backslash cdot\; C\_\{\backslash mathrm\{G\}-\backslash mathrm\{ch\}\}\backslash left(v\_\{\backslash mathrm\{GS\}\},\; v\_\{\backslash mathrm\{GD\}\}\backslash right)\; \backslash \backslash \backslash \backslash \; k\_2\backslash left(v\_\{\backslash mathrm\{DS\}\}\backslash right)\; \backslash cdot\; C\_\{\backslash mathrm\{G\}-\backslash mathrm\{ch\}\}\backslash left(v\_\{\backslash mathrm\{GS\}\},\; v\_\{\backslash mathrm\{GD\}\}\backslash right)\backslash end\{array\}\backslash right]$$

In this study, the C_GS-V and C_GD-V characteristic curves were calculated at a gate voltage of 0 V under the channel off-state, as shown in Fig. 9(a) and Fig. 9(b). These results show that as the drain bias gradually increases, the carrier concentration in the channel depletes, causing capacitance to decrease with increasing drain voltage. When the drain bias exceeds 80 V, the channel becomes fully depleted, as shown in Fig. 9(d). As a result, the capacitance remains nearly constant as the drain bias increases further.

3.5 Current Collapse Characteristics

Fig. 10. Output characteristic curves before and after the Stress process (V_GS=3 V, V_DS=0-3 V)

Due to the presence of defects, when the device operates in high-frequency scenarios, as in continuous high-speed switching, defects in the GaN buffer layer and nearby interfaces (such as in the AlGaN layer or at the AlGaN/passivation insulator interface) may trap hot electrons from the channel. This trapping reduces the electron concentration in the channel and subsequently decreases the output current density, resulting in current collapse, as shown in Fig. 10. Methods have been developed to mitigate this, such as introducing a field plate that generates a vertical electric field in the opposite direction, repelling hot electrons trapped at the surface^[2].

4. Summary

This study presents the simulation and design of an enhancement-mode p-GaN HEMT device, introducing the formulas for the physical models used in the simulation and displaying the device simulation results, including band structure, output characteristics, transfer characteristics, off-state characteristics, capacitance-frequency characteristics, and current collapse characteristics. The simulation results obtained via Nuwa TCAD software further analyze the internal mechanisms of the device, including band distribution, carrier transport, polarization effects, impact ionization, depletion region expansion, and defect electron trapping, providing insights into p-GaN HEMT device structure analysis and performance enhancement.

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References

1. C. Sun, Z. Niu and S. Yang, "Dynamic Gate Capacitance Model for Switching Transient Analysis in P-GaN Gate HEMTs," 2023 35th International Symposium on Power Semiconductor Devices and ICs (ISPSD), Hong Kong, 2023, pp. 135-138.

2. I. Hwang et al., "Impact of Channel Hot Electrons on Current Collapse in AlGaN/GaN HEMTs," in IEEE Electron Device Letters, vol. 34, no. 12, pp. 1494-1496.