使用Nuwa TCAD软件仿真超结VDMOS器件

GMPT, 2024/05/27

摘要： 垂直双扩散金属氧化物半导体场效应晶体管(Vertical Double-Diffused Metal Oxide Semiconductor Field Effect Transistor, VDMOS)，是一种单极型功率开关器件，具有开关速度快、静态输入阻抗高的优点，被广泛应用于电机调速、雷达、开关电源、汽车电子、逆变器、移动通信等领域。超结VDMOS在传统 VDMOS结构的基础上引入了超结结构，代替了原漂移区的轻掺杂结构，使得器件处于反偏状态时，在横向电场的作用下N型半导体与P型半导体的电荷相互补偿耗尽，超结区域形成横向耐压层，从而提升器件的反向击穿电压。

   本文将基于Nuwa TCAD软件对超结VDMOS器件进行仿真，并展示软件仿真结果。

一、器件结构

图1. 超结VDMOS器件结构示意图

   在此项工作中，超结VDMOS器件结构如图1所示。其中，P柱高度设置为36$\mu \backslash mu$m，元胞宽度设置为12$\mu \backslash mu$m，柱区掺杂浓度设置为$2\times 10^{15}{cm}^{-3}2\backslash times\; 10^\{15\}\; \{cm\}^\{-3\}$，Pbase区掺杂浓度设置为$5\times 10^{16}{cm}^{-3}5\backslash times\; 10^\{16\}\; \{cm\}^\{-3\}$，漏极区掺杂浓度设置为$5\times 10^{19}{cm}^{-3}5\backslash times\; 10^\{19\}\; \{cm\}^\{-3\}$，源区掺杂浓度设置为$1\times 10^{18}{cm}^{-3}1\backslash times\; 10^\{18\}\; \{cm\}^\{-3\}$，栅氧厚度设置为0.1$\mu \backslash mu$m。(本文部分仿真数据来源于参考文献[1])

二、物理模型设置

2.1 连续性方程

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

2.2 泊松方程

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

2.3 低场和高场迁移率模型

低场迁移率模型(Masetti Model) $${\mu }_0={\mu }_{\min 1}{e}^{-\frac{P_c}{N_i}}+\frac{{\mu }_{\max }{\left(\frac{T_L}{T_0}\right)}^{-\zeta }-{\mu }_{\min 2}}{1+{\left(\frac{N_i}{C_r}\right)}^{\alpha }}-\frac{{\mu }_1}{1+{\left(\frac{C_s}{N_i}\right)}^{\beta }}\backslash mu\_\{0\}=\backslash mu\_\{\backslash min\; 1\}\; e^\{-\backslash frac\{P\_\{c\}\}\{N\_\{i\}\}\}+\backslash frac\{\backslash mu\_\{\backslash max\; \}\backslash left(\backslash frac\{T\_L\}\{T\_\{0\}\}\backslash right)^\{-\backslash zeta\}-\backslash mu\_\{\backslash min\; 2\}\}\{1+\backslash left(\backslash frac\{N\_\{i\}\}\{C\_\{r\}\}\backslash right)^\{\backslash alpha\}\}-\backslash frac\{\backslash mu\_\{1\}\}\{1+\backslash left(\backslash frac\{C\_\{s\}\}\{N\_\{i\}\}\backslash right)^\{\backslash beta\}\}$$

高场迁移率模型(Canali Model)

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

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

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

2.6 碰撞电离模型 Okuto Model $$\begin{array}{c}{\displaystyle \alpha \left(F_{\text{ava }}\right)=a\cdot (1+c(T-T_0))F_{\text{ava }}^{\gamma }\exp [-{\left(\frac{b[1+d(T-T_0)]}{F_{\text{ava }}}\right)}^{\delta }]}\end{array}\backslash begin\{aligned\}\backslash alpha\backslash left(F\_\{\backslash text\; \{ava\; \}\}\backslash right)=a\; \backslash cdot\backslash left(1+c\backslash left(T-T\_\{0\}\backslash right)\backslash right)\; F\_\{\backslash text\; \{ava\; \}\}^\{\backslash gamma\}\; \backslash exp\; \backslash left[-\backslash left(\backslash frac\{b\backslash left[1+d\backslash left(T-T\_\{0\}\backslash right)\backslash right]\}\{F\_\{\backslash text\; \{ava\; \}\}\}\backslash right)^\{\backslash delta\}\backslash right]\backslash end\{aligned\}$$

三、结果与讨论

3.1 反向加压电势分布

图2. 超结VDMOS器件在 (a)平衡态 (b)反向加压300V (c)反向加压600V (d)反向击穿 时的电势分布

上图展示了超结VDMOS器件从平衡态开始加反向电压直到反向击穿的电势分布情况。

3.2 反向击穿特性

图3. 超结VDMOS器件的反向击穿曲线

如图可知，反向击穿之前漏电流约为$5\times 10^{-6}A/m$，在击穿电压附近漏电流急剧增大，发生雪崩击穿，反向击穿电压约为790V。

3.3 阈值电压

图4. 超结VDMOS器件的阈值电压

如图可知，超结VDMOS器件的阈值电压约为2.8V。

3.4 转移特性

图5. 超结VDMOS器件在不同栅压下的转移特性

   图5展示了超结VDMOS器件在栅压分别为2.5V，3V, 3.5V和4V下的转移特性。已知器件的阈值电压为2.8V，所以栅压为2.5V时器件沟道未打开，器件此时没有正向输出。当栅压大于阈值电压后，器件沟道打开并开始正向输出，随着栅压增大器件的输出也随之增强，漏电流也在漏极电压增大之后趋于饱和。

四、总结

   本文对超结VDMOS器件进行了仿真，介绍了仿真中引用的物理模型，并展示了器件的仿真结果，包括反向加压电势分布、反向击穿特性、阈值电压和不同栅压下的转移特性。

参考文献 [1] 李吕强，超结器件工艺窗口改善与可靠性提升，电子科技大学硕士学位论文