# Two-Dimensional Surface Electron Gas

• Junhao Chu
• Arden Sher
Chapter
Part of the Microdevices book series (MDPF)

## Abstract

The simplest metal-insulator-semiconductor device structure, shown in Fig. 4.1, includes a metal gate, an insulator layer on a semiconductor surface, and a back metal ohmic contact. t ox is the thickness of insulator and εox is its dielectric constant. The insulator layer lies between the metal gate and the top semiconductor surface. A bias voltage is applied to the metal gate to control the surface potential of the semiconductor surface. When the bias voltage reaches a threshold, the n-type semiconductor becomes strongly inverted. The resulting energy band bending is shown in Fig. 4.2. The potential Φ as a function of displacement x from semiconductor surface is obtained from the one-dimensional Poisson equation. Under nondegenerate and thermal equilibrium conditions, we have:
$$\frac{{\mathrm{d}}^{2}\phi } {\mathrm{d}{x}^{2}} = - \frac{q} {\epsilon {\epsilon }_{0}}\left [{n}_{\mathrm{n}0}({e}^{q\phi /{k}_{\mathrm{B}}T} - 1) - {p}_{\mathrm{ n}0}({e}^{-q\phi /{k}_{\mathrm{B}}T} - 1)\right ].$$
(4.1)
The electrical field distribution is
$$E = -\frac{\mathrm{d}\phi } {\mathrm{d}x} = \pm {\left (\frac{2{k}_{\mathrm{B}}T} {\epsilon {\epsilon }_{0}} \right )}^{1/2}F(\phi ),$$
(4.2)
where
$$F(\phi ) ={ \left [{n}_{\mathrm{n}0}\left ({e}^{q\phi /{k}_{\mathrm{B}}T} - \frac{q\phi } {kT} - 1\right ) + {p}_{\mathrm{n}0}\left ({e}^{-q\phi /{k}_{\mathrm{B}}T} + \frac{q\phi } {kT} - 1\right )\right ]}^{1/2},$$
(4.3)
and n n0 and p n0 are the concentrations of majority and minority carriers in the semiconductor, ε is its permittivity, and q is the magnitude of the electron charge.

## Keywords

Landau Level Inversion Layer Surface Recombination Velocity Capacitance Spectrum Subband Energy
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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