16.2.4 Multiphysics: Electrical, Thermal, Mechanical

necessitates an electrothermomechanical (ETM) simulation due to their propensity for self-heating at normal operating temperatures and the piezoelectric nature of AlGaN and GaN.

Various commercial tools handle aspects of ETM modeling. COMSOL, Silvaco Atlas, and Sentaurus SDevice have fully coupled electrothermal solvers; however, they have limitations with mechanical simulation. In COMSOL, mechanical strain due to thermal expansion is a one-way couple. Atlas does not support mechanical simulations. SDevice does not support the inverse piezoelectric strain or temperature dependence on Young’s modulus.

To date, researchers who need all three domains and a rigorous treatment of electronic properties in semiconductors use a combination of commercial software or write their own code. Venkatachalam et al. used a combination of Sentaurus for the electrical simulation and COMSOL for the thermal-mechanical simulation to model GaN-based HFETS [13]. Gao et al. used Silvaco Atlas and in-house software to simulate ETM effects on a GaN HEMT [14]. In both cases, the mechanics were one-way coupled to the electrical part. Thus, any strain-induced change on electrical performance could not be captured. One fully coupled finite element-based simulation couples electronic properties, strain, and transport in nanostructured devices [15]. However, thermal effects are not considered.

Recent work has shown that a mechanical-to-electrical couple is needed for the reliability assessment of AlGaN/GaN HEMTs. Horton et al. show that mechanical strain in the device enhances impurity diffusion on the drain side of the gate in the off state, which will ultimately affect I–V characteristics [16].

2-D simulation results from FLOORS are provided on examples of a MEMS thermal actuator and an AlGaN/GaN HEMT in the subsequent text. Equations 16.1, 16.2, 16.3, and 16.4 are implemented within the simulations. Mechanical strain caused by a mismatch of the thermal coefficient of expansion between two materials is simulated in both examples by a definition for initial stress given in Eq. 16.10:

where amismatch is the difference in the coefficients of thermal expansion. Strain due to the inverse piezoelectric effect in the HEMT example is modeled by Eq. 16.11:

where dpz is the matrix of inverse piezoelectric coefficients.

Figure 16.5 shows the mechanical deformation caused by a 3-V bias on the resistive heating element inside a bimorph beam. Dirichlet boundary conditions for the displacement and temperature were assigned to the bottom of the structure (bulk Si). Figures 16.6 and 16.7 compare the displacement and temperature results from FLOORS and COMSOL along the top of the beam. At most, there is a 2% difference in the simulation results. This demonstrates that the basic piezoelectric behavior is captured in FLOORS and that this can be used in more complex structures and devices with confidence.

Fig. 16.5 FLOORS electrothermomechanical simulation of a 2-D MEMS thermal actuator showing the resulting beam deformation with 3-V bias across the polysilicon heater

Fig. 16.6 Electrothermomechanical simulation validation on a 2-D MEMS thermal actuator showing the temperature at the top of the beam. The FLOORS results show at most a difference of 2% to COMSOL results

Using the same device as shown in Fig. 16.2, the influence of the inverse piezoelectric effect and self-heating can be seen in the plot of vertical strain shown in Fig. 16.8. The compressive strain peaks at the drain edge of the gate and is in good qualitative agreement with simulation results from Gao et al. [14]. For the HEMT simulation, the Young’s modulus was made dependent on temperature. Thus at elevated lattice temperatures, the decreased Young’s modulus and addition of tensile strain due to the thermal expansion mismatch act to decrease the