Abstract:
Direct. tunneling gate leakage current in both n- and p-MOS devices with
ultra-thin gate-oxide is studied. The effects of inelastic scattering of the inversion
carriers, tunneled into the gate-oxide region, on the direct tunneling
gate current are investigated. Coupled Schrodinger's and Poisson's equations
are solved self-consistently.' Open boundary conditions, taking into
account the wave function tail inside the gate-oxide region, are used to solve
Schrodinger's equation within the self-consistent loop. Also, the fraction of
inversion charges inside the gate-oxide region is taken into account in the
solution of Poisson's equation. Inelastic scattering is represented by a collision
time which appears as an imaginary potential in S~hrodinger's equation.
Simulated direct tunneling currents are compared with published experimental
results. Inelastic scattering effects on direct tunneling current are found
to be significant in devices with oxide thickness::::: 2 nm and at lower gate
voltages. Therefore, the existing mismatch at, lower gate voltages between experimental
and simulated direct t,unneling gate currents cim be explained in
terms of inelastic scattering effects. However, for accurate modeling of direct
tunneling current, appropriate spatial and gate bias dependence of collision
time needs to be taken into account. It is also found that carrier effective
mass in gate-oxide region is not a constant, rather a function of the applied
/ . gate bias. Moreover, electron and hole effective masses in gate-oxide region
show opposite ,dependence on gate bias. Physical reasons for this behaviour
are not yet known. Since the same expression of spatial and gate bias dependent
collision time accurately simulates the direct tunneling gate current in
both n- and p-MOSFETs, we believe that our empirical expression contains.
the essential physics of inelastic trap scattering. The contribution of split-off
holes to direct tunneling gate current in p-MOSFETs, particularly at higher
gate voltages, is not negligible. Consequently this contribution should not
be neglected as done in some recent studies.
