TABLE OF CONTENTS In this appendix, we derive the expressions for the 2DEG (two-dimensional electron gas) density of states and inversion charge density used in Section 4.2.4. A quantum-mechanical treatment of inversion layer is necessary because of the confinement of electron motion in the direction normal to the surface (Stern and Howard, 1967). Note that MKS units are used throughout this appendix (i.e., length must be in meters, not centimeters).
Following an approach in parallel with that of Appendix 3 for the 3-D density of states, one can derive an expression for the density of states of a 2-D gas. Based on quantum mechanics, there is one allowed state in a phase space of volume ( ? y ? p y)( ? z ? p z)= h 2, where p y and p z are the y- and z-coinponents of the electron momentum and h is Planck s constant. If we let N(E) dE be the number of electronic states per unit area with an energy between E and E+dE, then
| (A7.1) |  |
where dp y dp z is the area in the momentum space within which the electron energy lies between E and E+dE, g is the degeneracy of the subband, and the factor of two arises from the two possible directions of electron spin.
If E min is the ground-state energy of a particular subband, the energy-momentum relationship near the bottom of that...
