Two-Dimensional Surface Electron Gas

Part of the Microdevices book series (MDPF)


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:
$$\frac{{\mathrm{d}}^{2}\phi } {\mathrm{d}{x}^{2}} = - \frac{q} {\epsilon {\epsilon }_{0}}\left [{n}_{\mathrm{n}0}({e}^{q\phi /{k}_{\mathrm{B}}T} - 1) - {p}_{\mathrm{ n}0}({e}^{-q\phi /{k}_{\mathrm{B}}T} - 1)\right ].$$
The electrical field distribution is
$$E = -\frac{\mathrm{d}\phi } {\mathrm{d}x} = \pm {\left (\frac{2{k}_{\mathrm{B}}T} {\epsilon {\epsilon }_{0}} \right )}^{1/2}F(\phi ),$$
$$F(\phi ) ={ \left [{n}_{\mathrm{n}0}\left ({e}^{q\phi /{k}_{\mathrm{B}}T} - \frac{q\phi } {kT} - 1\right ) + {p}_{\mathrm{n}0}\left ({e}^{-q\phi /{k}_{\mathrm{B}}T} + \frac{q\phi } {kT} - 1\right )\right ]}^{1/2},$$
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.


Landau Level Inversion Layer Surface Recombination Velocity Capacitance Spectrum Subband Energy 
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Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  1. 1.Shanghai Institute of Technical Physics, CASShanghaiChina
  2. 2.East China Normal UniversityShanghaiChina
  3. 3.SRI InternationalMenlo ParkUSA

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