CHINESE JOURNAL OF PHYSICS VOL. 40, NO. 1 FEBRUARY 2002




First-Order Correction to the Semi-Infinite Electron Gas Model of the Inversion Carriers at a Semiconductor-Insulator Interface

T. L. Li*1 and T. W. Tang2

1Department of Applied Physics, National Chia-Yi University,

300 Hsueh-Fu Road, Chiayi, Taiwan 600, R.O.C.

2Department of Electrical and Computer Engineering,

University of Massachusetts Amherst, Amherst, MA01003, USA
(Received June 27, 2001)

The Semi-infinite Electron Gas (SEG) model in the literature is extended to explicitly include the potential energy gradient to first-order, leading to the First-Order Semi-infinite Electron Gas (FOSEG) model of this work. To study the validity of the conventional and the first-order models, the density of states and the carrier density of a triangular potential are computed by both models, and are compared with the exact solution. The field-induced state density in the conventionally forbidden bandgap can be modeled by the first-order approximation because of its explicit inclusion of the potential gradient. Comparison of the carrier density shows that, when there are enough quantum levels below the Fermi level, the first-order results match the exact solution better than the conventional model, especially at locations beyond the classical turning point associated with the Fermi energy.

PACS. 73.20.At - Surface states, band structure, electron density of states.
PACS. 73.40.Qv - Metal-insulator-semiconductor structures.
PACS. 71.10.Ca - Electron gas, Fermi gas.

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