3.8.1.2 IELMINI's Model

Considerable research has been done by IELMINI et al. [205,206,207,208] who describe inelastic TAT and also take hopping conduction into account [209,210]. They derive the trap-assisted current by an integration along the dielectric thickness and energy

$$J = \int_0^{\ensuremath{t_\mathrm{diel}}} \,\ensuremath {\mathrm{... ...uremath{{\mathcal{E}}_\mathrm{T}},x)\, \ensuremath {\mathrm{d}}{\mathcal{E}}\ ,$$

where $\tilde{J}$ denotes the net current flowing through the dielectric, given as the difference between capture and emission currents through either side (left or right), as shown in Fig. 3.16

$$\tilde{J}(\ensuremath{{\mathcal{E}}_\mathrm{T}}, x) = \ensuremath... ...{\ensuremath{f_\mathrm{l}}(\ensuremath{{\mathcal{E}}_\mathrm{T}},x)}\right) \ ,$$

where $f_\mathrm{T}$ is the trap occupancy, ${\mathcal{E}}_\mathrm{T}$ the trap energy, $W_\mathrm{c}$ the capture rate, and $\ensuremath{f_\mathrm{l}}$ the energy distribution function at the left interface. The symbol $\ensuremath{N_\mathrm{T}}^\prime$ denotes the trap concentration in space and energy. IELMINI further develops the model to include transient effects and notes that in this case, the net difference between current from the left and right interfaces equals the change in the trap occupancy multiplied by the trap charge

$$(\ensuremath{J_\mathrm{cl}}- \ensuremath{J_\mathrm{el}}) + (\ensu... ...suremath{N_\mathrm{T}}\frac{\partial \ensuremath{f_\mathrm{T}}}{\partial t} \ ,$$ (3.125)

an observation that will be revisited in Section 3.8.2.4. The main shortcoming of this model, despite its sophistication, is the assumption of a constant capture cross-section.

Figure 3.16: Schematic capture and emission currents through the left and right interfaces of the dielectric layer.

A. Gehring: Simulation of Tunneling in Semiconductor Devices