next up previous
Next: Carrier trapping and Shockley-Read-Hall Up: Electrical model Previous: Calculating the built in

Transport

To describe charge carrier transport, the bi-polar drift-diffusion equations are solved in position space for electrons,

$\displaystyle \boldsymbol{J_n} = q \mu_e n_{f} {\frac{\partial E_{LUMO}}{\partial x}} + q D_n {\frac{\partial n_{f}}{\partial x}},$ (9)

and holes,

$\displaystyle \boldsymbol{J_p} = q \mu_h p_{f} {\frac{\partial E_{HOMO}}{\partial x}} - q D_p {\frac{\partial p_{f}}{\partial x}}.$ (10)

Conservation of charge carriers is forced by solving the charge carrier continuity equations for both electrons,

$\displaystyle {\frac{\partial \boldsymbol{J_n}}{\partial x}} = q (R-G),$ (11)

and holes

$\displaystyle {\frac{\partial \boldsymbol{J_p}}{\partial x}} = - q (R-G).$ (12)

where $ R$ and $ G$ are the net recombination and generation rates per unit volume respectively.

To obtain the internal potential distribution within the device Poisson's equation is solved,

$\displaystyle {\frac{d}{d x}} \cdot \epsilon_0 \epsilon_r {\frac{d \phi}{d x}} = q (n_{f}+n_{t}-p_{f}-p_{t}-N_{ad}),$ (13)

where $ n_{f}$ , $ n_{t}$ are the carrier densities of free and trapped electrons; $ p_{f}$ and $ p_{t}$ are the carrier densities of the free and trapped holes; and $ N_{ad}$ is the doping density.


next up previous
Next: Carrier trapping and Shockley-Read-Hall Up: Electrical model Previous: Calculating the built in
rod 2017-12-08