**Branch :**Computer Science and Engineering

**Subject :**Fundamental of Electronic Devices

## Direct and Indirect Semiconductors

In this section, we describes the Direct and Indirect Semiconductors in brief.

**Direct and Indirect Semiconductors:**

In a typical calculation, a single electron is assumed to travel through a perfectly periodic lattice. The wave function of the electron is assumed to be in the form of a plane wave moving, for example, in the x- direction with propagation constant k, also called a wave vector. The space-dependent wave function for the electron is

where the function U(k_{x},x) modulates the wave function according to the periodicity of the lattice.

- In such a calculation, allowed values of energy can be plotted vs. the propagation constant k.

- Since the periodicity of most lattices is different in various directions, the (E, k) diagram must be plotted for the various crystal directions, and the full relationship between E and k is a complex surface which should be visualized in three dimensions.

- The band structure of GaAs has a minimum in the conduction band and a maximum in the valence band for the same k value (k = 0).

- On the other hand, Si has its valence band maximum at a different value of k than its conduction band minimum.

- Thus an electron making a smallest-energy transition from the conduction band to the valence band in GaAs can do so without a change in k value.

- On the other hand, a transition from the minimum point in the Si conduction band to the maximum point of the valence band requires some change in k.

- Thus there are two classes of semiconductor energy bands; direct and indirect (Fig. given below).

- We can show that an indirect transition, involving a change in k, requires a change of momentum for the electron.

- Band diagrams such as those shown in the above figure are cumbersome to draw in analyzing devices, and do not provide a view of the variation of electron energy with distance in the sample.

- Therefore, in most discussions we shall use simple band pictures such as the band diagram of the metal, insulator & semiconductor remembering that electron transitions across the band gap may be direct or indirect.