Numerical Simulation of Semiconductor Devices and Circuits for THz Applications
Final Report Abstract
In this project we set out to develop a general solver framework based on the extended drift-diffusion model to investigate plasma instabilities as a means of efficient generation of THz waves and the general impact of plasma oscillations on the performance of THz circuits. Due to fundamental problems not forseen at the beginning of the project the development of the device simulator was much delayed. The numerical stabilization of the transport model was much more challenging than expected, and the existing Scharfetter-Gummel scheme could not be adapted to include the additional terms in a stable way. It also turned out that the extended drift-diffusion model does not have a smooth stationary solution in the transsonic case which fundamentally limits it to rather low bias voltages for which it remains subsonic, especially when high mobilities are considered. The first successfully developed scheme was too complex to apply to hydrodynamic models or a 2D real space. Nevertheless, we were able to develop a second simpler scheme which we used to simulate a passive mixer circuit for THz wave detection based on a silicon double-gate MOSFET in which the electron transport remained subsonic. Next, we tried multiple schemes for the 2D case, which failed for various reasons. Only near the end of the project a new scheme was developed that might work in the 2D case, but still has to be tested. Parallel to the development of the stabilization scheme for the drift-diffusion model we investigated plasma waves by the Boltzmann equation and higher-order transport models derived from it. The unexpected results of this extensive investigation were firstly that even the Boltzmann equation discretized by the usual even/odd splitting fails under the quasi-ballistic conditions necessary for the Dyakonov-Shur instability. We were able to reuse the first method that we had developed for the extended drift-diffusion model to discretize the Boltzmann equation directly in the phase space similar to Godunov’s approach. This new scheme has many advantages. It is stable even in the ballistic case, works with realistic boundary conditions, is CPU and memory efficient and makes it possible to easily integrate more complex band structures and scattering models. At the end of the project we obtained the first transient large-signal results for a nanowire transistor by this new method. We are currently exploring this scheme in another DFG funded project in the case of III-V HBTs. The stabilization scheme for the 2D drift-diffusion model currently under development will also be tried in the case of the Boltzmann equation. Secondly, it turned out that the Dyakonov-Shur plasma instability seems to be an artifact of the transport and contact modeling. If the more fundamental Boltzmann equation is solved together with realistic boundary conditions, the Dyakonov-Shur instability vanishes. The impact of plasma resonances on the behavior of THz devices is much weaker than previously thought. The simple drift-diffusion model without the convective derivative and the second time derivative and stabilized by the Scharfetter-Gummel scheme yields only positive solutions for the densities. This should be a fundamental property of all transport models, since densities must be positive by definition. In order to better understand this property, we re-investigated the simple drift-diffusion model and were able to confirm this even in the transient case. First results for the newly discretized Boltzmann equation suggest that it also has this property which usually results in improved numerical robustness.
Publications
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“Investigation of moments-based transport models applied to plasma waves and the Dyakonov–Shur instability,” Semiconductor Science and Technology, vol. 34, no. 1, p. 014002, 2018
T. Linn, Z. Kargar, and C. Jungemann
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“Investigation of the Dyakonov–Shur instability for THz wave generation based on the Boltzmann transport equation,” Semiconductor Science and Technology, vol. 33, no. 10, p. 104001, 2018
Z. Kargar, T. Linn, and C. Jungemann,
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“On the simulation of plasma waves in HEMTs and the Dyakonov-Shur instability,” in Proc. SISPAD, pp. 331–334, Sept 2019
C. Jungemann, T. Linn, and Z. Kargar
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“Simulation of Plasma Waves in III-V Devices Based on the Boltzmann Equation,” Dissertation RWTH Aachen, 2019
Z. Kargar
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“A numerical approach to quasi-ballistic transport and plasma oscillations in junctionless nanowire transistors,” Journal of Computational Electronics, vol. 19, pp. 975–986, 2020
M. Noei, T. Linn, and C. Jungemann
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“Deterministic Simulation of Junctionless Nanowire FETs,” Dissertation RWTH Aachen, 2020
M. Noei
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“Simulation of THz oscillations in semiconductor devices based on balance equations,” J. Sci. Comput., vol. 85, 2020
T. Linn, K. Bittner, H. G. Brachtendorf, and C. Jungemann
