The Drift-Diffusion Equations and Their Numerical Solution

2017 ◽  
pp. 151-192
Author(s):  
Dragica Vasileska ◽  
Stephen M. Goodnick ◽  
Gerhard Klimeck
Keyword(s):  
Numerical Solution ◽  
Diffusion Equations ◽  
Drift Diffusion

scholarly journals WIGNER–POISSON AND NONLOCAL DRIFT-DIFFUSION MODEL EQUATIONS FOR SEMICONDUCTOR SUPERLATTICES

2005 ◽  
Vol 15 (08) ◽  
pp. 1253-1272 ◽  
Author(s):  
L. L. BONILLA ◽  
R. ESCOBEDO
Keyword(s):  
Numerical Solutions ◽  
Inelastic Collisions ◽  
Diffusion Equations ◽  
Electron Interaction ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Hartree Approximation ◽  
Semiconductor Superlattices ◽  
Sustained Oscillations ◽  
Model Equations

A Wigner–Poisson kinetic equation describing charge transport in doped semiconductor superlattices is proposed. Electrons are assumed to occupy the lowest miniband, exchange of lateral momentum is ignored and the electron–electron interaction is treated in the Hartree approximation. There are elastic collisions with impurities and inelastic collisions with phonons, imperfections, etc. The latter are described by a modified BGK (Bhatnagar–Gross–Krook) collision model that allows for energy dissipation while yielding charge continuity. In the hyperbolic limit, nonlocal drift-diffusion equations are derived systematically from the kinetic Wigner–Poisson–BGK system by means of the Chapman–Enskog method. The nonlocality of the original quantum kinetic model equations implies that the derived drift-diffusion equations contain spatial averages over one or more superlattice periods. Numerical solutions of the latter equations show self-sustained oscillations of the current through a voltage biased superlattice, in agreement with known experiments.

Correlating hysteresis phenomena with interfacial charge accumulation in perovskite solar cells

2020 ◽  
Vol 22 (1) ◽  
pp. 245-251 ◽  
Author(s):  
Tianyang Chen ◽  
Zhe Sun ◽  
Mao Liang ◽  
Song Xue
Keyword(s):  
Solar Cells ◽  
Charge Exchange ◽  
Perovskite Solar Cells ◽  
Exchange Model ◽  
Diffusion Equations ◽  
Charge Accumulation ◽  
Drift Diffusion ◽  
Charge Extraction ◽  
Interfacial Charge ◽  
Hysteresis Phenomena

A generalized charge exchange model is introduced into drift–diffusion equations for modeling the charge extraction in perovskite solar cells.

SECOND ORDER BOUNDARY CONDITIONS FOR THE DRIFT-DIFFUSION EQUATIONS OF SEMICONDUCTORS

1995 ◽  
Vol 05 (04) ◽  
pp. 429-455 ◽  
Author(s):  
A. YAMNAHAKKI
Keyword(s):  
Boundary Conditions ◽  
Test Problem ◽  
Fluid Model ◽  
Diffusion Equations ◽  
Robin Boundary Conditions ◽  
Fluid Models ◽  
Drift Diffusion ◽  
Dirichlet Conditions ◽  
Robin Boundary ◽  
Two Fluid

By an asymptotic analysis of the Boltzmann equation of semiconductors, we prove that Robin boundary conditions for drift-diffusion equations provide a more accurate fluid model than Dirichlet conditions. The Robin conditions involve the concept of the extrapolation length which we compute numerically. We compare the two-fluid models for a test problem. The numerical results show that the current density is correctly computed with Robin conditions. This is not the case with Dirichlet conditions.

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