Abstract
A modified Fang–Howard (FH) wavefunction with two parameters for two-dimensional electron gas is proposed. The modified wavefunction takes an extra parameter compared to FH wavefunction. The two parameters are determined by using the variational method to minimize the ground level; analytic approximate expressions are derived for the two parameters. It is shown that the finite barrier can lower energy level of electron gas; the wavefunction takes finite value at interface. This is more reasonable than the original Stern wavefunction. The new wavefunction is compared with previous wavefunction based on the rectangular-well approximation, and is applied to an ultra-thin gate oxide MOSFET. The calculated tunneling current-voltage curves are in good agreement with experimental data.
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