Abstract
The treatment of exchange energy in inversion layers is extended to take the layer thickness into account when only the lowest subband is occupied by electrons. The exchange energy of electrons in Si is close to the zero-thickness limit obtained previously. Wave functions are only slightly contracted because of exchange. The exchange energy in excited subbands is smaller in magnitude, and has a smaller variation with wavevector, than in the lowest subband. Estimates based on a three-dimensional local density approximation give the approximate magnitude of the exchange energy but do not give its dependence on the spatial extent of the wave function correctly and cannot account for image effects.