AN EQUILIBRIUM-MODEL OF THE SEMICONDUCTOR HETEROJUNCTION DIODE BASED ON KINETIC-THEORY

A mathematical model for a semiconductor heterojunction diode at equilibrium based on kinetic theory of inhomogeneous systems is presented. A generalized Boltzmann equation for variable effective mass is obtained from Marshak and van Vliet's extended Wannier-Slater Hamiltonian [Solid-State Elec...

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Bibliographic Details
Published in:Journal of applied physics 1992-08, Vol.72 (3), p.971-975
Main Authors: LECOZ, YL, TIERSTEN, HF
Format: Article
Language:English
Subjects:
Applied sciences
Diodes
Electronics
Exact sciences and technology
Physical Sciences
Physics
Physics, Applied
Science & Technology
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
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Summary:A mathematical model for a semiconductor heterojunction diode at equilibrium based on kinetic theory of inhomogeneous systems is presented. A generalized Boltzmann equation for variable effective mass is obtained from Marshak and van Vliet's extended Wannier-Slater Hamiltonian [Solid-State Electron. 21, 417 (1978)]. An Ehrenfest correspondence procedure has shown that only forces due to variation in band-edge energy and electric potential energy arise; the supposed force arising from the spatial gradient of effective mass does not exist. The diode model consists of three separate regions: two regions of homogeneous material composition and a finite interface region of inhomogeneous composition. Boltzmann's equation is solved in each region as a function of arbitrary electric potential. Physically reasonable boundary and continuity conditions are also established. Closed-form analytical solution of our model equations does not appear to be possible because of the coupling with Poisson's equation. To demonstrate the implications of our model without resorting to a numerical investigation, we make some reasonable simplifying assumptions to derive a new built-in potential formula. The formula suggests that an error exists in the currently accepted formula. The error is particularly large when carrier effective density-of-states ratios across the diode are appreciably greater than unity.
ISSN:0021-8979
1089-7550
DOI:10.1063/1.351774