3.8.1 Model Overview

Numerous models have been presented to describe trap-assisted tunneling in the gate dielectric of MOS devices. These models usually share the equation for the current density which is given by an integration along the gate dielectric [197]:

$$J = \ensuremath {\mathrm{q}}\int_0^{\ensuremath{t_\mathrm{diel}}}... ...mathrm{c}}(x) + \ensuremath{\tau_\mathrm{e}}(x)}\,\ensuremath {\mathrm{d}}x \ .$$ (3.122)

In this expression $\ensuremath{N_\mathrm{T}}$ denotes the trap concentration, and $\ensuremath{\tau_\mathrm{c}}$ and $\ensuremath{\tau_\mathrm{e}}$ denote the capture and emission times of the considered trap. Since both processes - capture and emission - must happen in sequence, they both determine the current density. However, differences exist in how the capture and emission times are calculated. Some models use constant capture and emission cross sections to calculate the respective times. Another important point is the distribution in space, where the traps are usually assumed to follow a GAUSSian distribution. The distribution in energy is also crucial. Commonly it is either assumed that traps have a GAUSSian distribution in energy or that they are located at a certain energy level below the dielectric conduction band. The assumption of a discrete energy level for specific trap types is backed by spectroscopic analyses [198]. Additionally, the tunneling process can either be elastic, where the energy of the tunneling electron is conserved, or inelastic, where the energy of the tunneling electron changes. Recent studies and experiments have shown strong evidence for the tunneling process being inelastic [199,200,201].

Subsections

• 3.8.1.1 CHANG's Model
• 3.8.1.2 IELMINI's Model
• 3.8.1.3 Compact Trap-Assisted Tunneling Models

A. Gehring: Simulation of Tunneling in Semiconductor Devices