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1. A Domain Specific Language Applied to Phonon Boltzmann Transport for Heat Conduction

   https://doi.org/10.1115/IMECE2022-95034  

   Heisler, Eric; Saurav, Siddharth; Deshmukh, Aadesh; Mazumder, Sandip; Sadayappan, Ponnuswamy; Sundar, Hari (October 2022, ASME International Mechanical Engineering Congress and Exposition)

   The phonon Boltzmann transport equation is a good model for heat transfer in nanometer scale structures such as semiconductor devices. Computational complexity is one of the main challenges in numerically solving this set of potentially thousands of nonlinearly coupled equations. Writing efficient code will involve careful optimization and choosing an effective parallelization strategy, requiring expertise in high performance computing, mathematical methods, and thermal physics. To address this challenge, we present the domain specific language and code generation software Finch. This language allows a domain scientist to enter the equations in a simple format, provide only basic mathematical functions used in the model, and generate efficient parallel code. Even very complex systems of equations such as phonon Boltzmann transport can be entered in a very simple, intuitive way. A feature of the framework is flexibility in numerical methods, computing environments, parallel strategies, and other aspects of the generated code. We demonstrate Finch on this problem using a variety of parallel strategies and model configurations to demonstrate the flexibility and ease of use. 

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2. A practical theoretical model for Ge-like epitaxial diodes. II. Matching the experimental optical responsivity in pin devices

   https://doi.org/10.1063/5.0235516  

   Mircovich, Matthew_A; Kouvetakis, John; Menéndez, José (March 2025, Journal of Applied Physics)

   A theoretical model that can be used to simultaneously fit the I–V characteristics and spectral optical responsivity of Ge-like pin diodes is described in detail and validated experimentally using specially fabricated Ge- and Ge1−ySny devices. The model combines a numerical solution of the basic semiconductor transport equations with a rigorous calculation of the optical generation rate that accounts for multiple reflections in the device structure multilayers. The results can be used to quantify the reduction of photocurrent associated with recombination centers for full optimization of the device structure. 

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3. Nonlinear effects in modeling thin-film graded-bandgap solar cells

   https://doi.org/10.1117/12.2632264  

   Ahmad, Faiz; Civiletti, Benjamin; Lakhtakia, Akhlesh; Monk, Peter B. (October 2022, Proc. SPIE 12196, Active Photonic Platforms 2022)

   Subramania, Ganapathi S.; Foteinopoulou, Stavroula (Ed.)

   We model the e ect of concentrated sunlight on CIGS thin- lm graded-bandgap solar cells using an optoelectronic numerical model. For this purpose it is necessary  first to solve the time-harmonic Maxwell equations to compute the electric  eld in the device due to sunlight and so obtain the electron-hole-pair generation rate. The generation rate is then used as input to a drift-diffusion model governing the flow of electrons and holes in the semiconductor components that predicts the current generated. The optical submodel is linear; however, the electrical submodel is nonlinear. Because the Shockley{Read{Hall contribution to the electron-hole recombination rate increases almost linearly at high electron/hole densities, the effciency of the solar cell can improve with sunlight concentration. This is illustrated via a numerical study. 

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4. Black phosphorus photoconductive terahertz antenna: 3D modeling and experimental reference comparison

   https://doi.org/10.1364/JOSAB.419996  

   Batista, Jose_Santos; Churchill, Hugh_O_H; El-Shenawee, Magda (March 2021, Journal of the Optical Society of America B)

   This paper presents a 3D model of a terahertz photoconductive antenna (PCA) using black phosphorus, an emerging 2D anisotropic material, as the semiconductor layer. This work aims at understanding the potential of black phosphorus (BP) to advance the signal generation and bandwidth of conventional terahertz (THz) PCAs. The COMSOL Multiphysics package, based on the finite element method, is utilized to model the 3D BP PCA emitter using four modules: the frequency domain RF module to solve Maxwell’s equations, the semiconductor module to calculate the photocurrent, the heat transfer in solids module to calculate the temperature variations, and the transient RF module to calculate the THz radiated electric field pulse. The proposed 3D model is computationally intensive where the PCA device includes thin layers of thicknesses ranging from nano- to microscale. The symmetry of the configuration was exploited by applying the perfect electric and magnetic boundary conditions to reduce the computational domain to only one quarter of the device in the RF module. The results showed that the temperature variation due to the conduction of current induced by the bias voltage increased by only 0.162 K. In addition, the electromagnetic power dissipation in the semiconductor due to the femtosecond laser source showed an increase in temperature by 0.441 K. The results show that the temperature variations caused the peak of the photocurrent to increase by $\sim <\#comment/>3.4\mathrm{\%<\#comment/>}$and $\sim <\#comment/>10\mathrm{\%<\#comment/>}$, respectively, under a maximum bias voltage of 1 V and average laser power of 1 mW. While simulating the active area of the antenna provided accurate results for the optical and semiconductor responses, simulating the thermal effect on the photocurrent requires a larger computational domain to avoid false rise in temperature. Finally, the simulated THz signal generation electric field pulse exhibits a trend in increasing the bandwidth of the proposed BP PCA compared with the measured pulse of a reference commercial LT-GaAs PCA. Enhancing signal generation and bandwidth will improve THz imaging and spectroscopy for biomedical and material characterization applications. 

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5. Automating GPU Scalability for Complex Scientific Models: Phonon Boltzmann Transport Equation

   https://doi.org/10.1109/IPDPS57955.2024.00045  

   Heisler, Eric; Saurav, Siddharth; Deshmukh, Aadesh; Mazumder, Sandip; Sundar, Hari (May 2024, IEEE)

   Heterogeneous computing environments combining CPU and GPU resources provide a great boost to large-scale scientific computing applications. Code generation utilities that partition the work into CPU and GPU tasks while considering data movement costs allow researchers to develop high-performance solutions more quickly and easily, and make these resources accessible to a larger user base.We present developments for a domain-specific language (DSL) and code generation framework for solving partial differential equations (PDEs). These enhancements facilitate GPU-accelerated solution of the Boltzmann transport equation (BTE) for phonons, which is the governing equation for simulating thermal transport in semiconductor materials at sub-micron scales. The solution of the BTE involves thousands of coupled PDEs as well as complicated boundary conditions and solving a nonlinear equation that couples all of the degrees of freedom at each time step. These developments enable the DSL to generate configurable hybrid GPU/CPU code that couples accelerated kernels with user-defined code. We observed performance improvements of around 18X compared to a CPU-only version produced by this same DSL with minimal additional programming effort. 

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