Semiconductor devices are a fascinating yet challenging physical system to model. In gallium nitride (GaN) high electron mobility transistors (HEMTs), there are complex interactions in the electrical, thermal, and mechanical domains owing to the strong polar nature of wurtzite GaN and the high voltages, current densities, and power densities applied to GaN HEMTs. To capture the key physics of electron transport in these devices, I utilize the Silvaco ATLAS/BLAZE semiconductor device simulation software and couple the results to COMSOL Multiphysics and/or MATLAB. The following sections showcase some of my device simulation research towards understanding self-heating and inverse piezoelectric stress and strain in GaN HEMTs under bias.

Although thermal issues in GaN-based electronics have been widely investigated with modeling tools, certain issues remain unclear in the thermal analysis of GaN HEMTs needed for the design of advanced thermal management strategies. For instance, the length of the heat source in a GaN HEMT under bias and the dependence of the heat source length on gate and drain bias is not clear. We have been working to develop high-fidelity electro-thermal models in Silvaco ATLAS of GaN HEMTs fabricated by our collaborators in Prof. Tomas' Palacios' group (EECS, MIT). Our preliminary results indicate that the heat source extends over a region much longer than the gate length and depends strongly on the gate bias at constant power. This information is helpful in developing accurate device-level thermal models.

Due to the high critical electric field of wurtzite GaN, AlN, and AlGaN, GaN HEMTs can sustain very high voltage bias conditions. However, strong electric fields in GaN HEMTs under bias lead to inverse piezoelectric stress and strain, which may induce structural damage to critical areas of the device. I am using electro-mechanical modeling to predict the dominant stress and strain components for comparison to micro-Raman spectroscopy.

In many reports of thermal analysis of GaN HEMTs in industry and academia, numerical methods such as the finite element or finite difference methods are used to compute the temperature distribution. While the finite element method is flexible and robust for solving the steady-state heat equation, small heat sources in thin epitaxial layers in GaN HEMT structures may require a large number of elements and long computation times. As an alternative to numerical models, we have been developing analytical solutions based on Fourier-series techniques for thermal spreading in multi-layer structures. These models are much more computationally-efficient than 3D finite element methods and can account for the complexities of thermal interfacial resistance and convection at the boundaries. These analytical solutions are particularly helpful in parametric studies, such as the optimization of diamond substrate thickness in GaN-on-diamond epitaxy.

One important feature of thermal analysis of GaN-based HEMTs is that the thermal conductivity of GaN,
SiC, Si, AlN, and other semiconductor materials depends strongly on temperature. In particular, the thermal
conductivity decreases with increasing temperature, leading to higher junction temperatures than predicted
with constant thermal conductivity evaluated at room temperature. Under certain conditions, the Kirchhoff
transform can be used to self-consistently account for temperature-dependent thermal conductivity with a
simple algebra step. In a paper in *IEEE Trans. CPMT*, we demonstrate how to apply the Kirchhoff
transform to GaN epitaxial structures with a finite thermal conductance at the bottom of the substrate and
obtain an accurate solution with minimal computation time.

In addition to advanced simulation, experimental characterization of temperature rise in GaN HEMTs with high spatial resolution is critical in assessing the reliability and performance of these devices. I have primarly used visible micro-Raman spectroscopy to measure the temperature in GaN HEMTs with 1 micron spatial resolution. To accomplish this, I rebuilt and customized a free space micro-Raman spectroscopy system in the MIT Spectroscopy Laboratory with 532 nm and 633 nm laser lines, polarization control, time-resolved capability, and automated control software coupled with electronic test instruments. With these capabilities, we can measure temperature, stress, strain, and electric field components in GaN HEMTs and a variety of other semiconductor devices.

Micro-Raman spectroscopy is one of the most common techniques for characterizing the composition, crystal quality, and residual stress in III-nitride materials. Over the last fifteen years, micro-Raman specroscopy has also become one of the most popular techniques for measuring temperature in GaN HEMTs owing to its high spatial resolution of ~1 micron, time-resolved capability, and relative ease of calibration and instrumentation. However, the III-nitride community has also learned that accurate temperature measurements require careful decoupling of the thermoelastic stress from the temperature rise in interpreting the Raman spectrum of GaN. Recently, we have developed a technique for decoupling the inverse piezoelectric stress and vertical electric field from the thermoelastic stress and temperature rise. Our current understanding of how stress, strain, temperature rise, and electric field all contribute to the shift in the Raman peak positions allows us to measure these quantities independently in GaN HEMTs under bias.

Although most studies of self-heating and thermal characterization of GaN HEMTs have focused on the steady-state temperature rise associated with constant power dissipation, the transient temperature rise of GaN HEMTs under pulsed power dissipation is critical in many applications. We have added time-resolved capability to the micro-Raman spectroscopy system by moduling a high power diode pumped solid-state laser with an acousto-optic modulator (AOM). Owing to the fast response of the AOM, we can achieve a time resolution as low as ~20 ns. With this technique, we are investigating the transient thermal behavior and thermal time constant spectra of GaN HEMTs.

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