Electronic Resource
[S.l.]
:
American Institute of Physics (AIP)
Journal of Applied Physics
72 (1992), S. 971-975
ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.351774
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