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An equilibrium model of the semiconductor heterojunction diode based on kinetic theory

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2 Author(s)
Le Coz, Y.L. ; Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180‐3590 ; Tiersten, H.F.

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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.

Published in:

Journal of Applied Physics  (Volume:72 ,  Issue: 3 )

Date of Publication:

Aug 1992

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