3.8.1.1 CHANG's Model

A frequently used model is the generalized trap-assisted tunneling model presented by CHANG et al. [202,203]. The current density reads

$$J = \ensuremath {\mathrm{q}}\int_0^{\ensuremath{t_\mathrm{diel}}}... ...hrm{T}}(x) \frac{P_1(x) P_2(x)}{P_1(x) + P_2(x)}\,\ensuremath {\mathrm{d}}x \ ,$$ (3.123)

where $A$ denotes a fitting constant, $\ensuremath{N_\mathrm{T}}(x)$ the spatial trap concentration, and $P_1$ and $P_2$ the transmission coefficients of electrons captured and emitted by traps. Using $\ensuremath{\tau_\mathrm{c}}\sim P_1/P_2$ and $\ensuremath{\tau_\mathrm{e}}\sim P_2/P_1$, this expression reduces to (3.122). A similar model was used by GHETTI et al. [169]

$$J = \int_0^{\ensuremath{t_\mathrm{diel}}}\ensuremath{C_\mathrm{T}... ...ath{J_\mathrm{in}}+ \ensuremath{J_\mathrm{out}}}\,\ensuremath {\mathrm{d}}x \ ,$$ (3.124)

who assumed a constant capture cross section $\ensuremath{C_\mathrm{T}}$ for the traps. The symbols $\ensuremath{J_\mathrm{in}}$ and $\ensuremath{J_\mathrm{out}}$ denote the capture and emission currents. Essentially the same formula was used by other authors as well [200,204].

A. Gehring: Simulation of Tunneling in Semiconductor Devices