3.5 Quantum Mechanical Aspects

As a HEMT channel is formed by heterolayers with typical channel widths of 10 nm-20 nm, a highly quantum mechanical situation is encountered. The typical geometrical width is smaller than the de Broglie length of 26 nm in GaAs, as pointed out by Shur in [257] and also given in Appendix B. This work treats the channel in a classical approach. This section supplies some basic estimates of the error introduced with respect to the material systems used. Based on the stationary Schrödinger equation

$$-\frac{\hbar^2}{2 m^*} \frac{\delta ^2 \psi(z)}{\delta z^2}+ V(z) \psi(z) = E_m \psi(z)$$ (3.128)

typically a one-dimensional analysis is performed. With no ${\it V}_{\mathrm{DS}}$ voltage applied a very precise analysis can be performed, as e.g. in [70,318]. A fully quantum mechanical two-dimensional analysis is rendered complicated due to the boundary conditions required [1].