Question

6. Explain the variation of carrier concentration of an extrinsic semiconductor with respect to 1/7 shown in the plot below:

Answer 1

The diagramme can be constructed as -

Inttinsic Saturation (extrinsic) lonization High T Low T 1/ K')

Majority carrier concentration vs. inverse temperature for an extrinsic semiconductor. In the ionization regime, donor atoms are partially ionized. Then in the saturation regime where donors are fully ionized and carrier concentration is a constant. Finally, at high temperatures there is the intrinsic regime where it behaves like an intrinsic semiconductor. The temperatures corresponding to these depend on the donor concentration.

The vertical dotted line marks room temperature.will not change the conductivity. Thus, electrical devices can be formed with very little variation in their electrical properties during normal operating temperatures.

Low temperature regime (T < Ts) - At absolute zero there are no ionized carriers. Valence band is full and the donor level is full and conduction band is empty. As temperature is increased, electrons are excited from the valence band and the donor level to the conduction band. But since the valence band ionization energy is of the order of eV , at low temperature the number of electrons excited from it are negligible compared to the electrons from the donor level. So the valence band contribution can be ignored and only electrons from the donor level are excited to the CB. This regime is called ionization regime and extends up to a temperature until all the donor electrons are ionized. The electron concentration (in CB), in the ionization regime, is given by

of the Jaka (en aş) = -

∆E is the ionization energy of the donor level i.e. the energy difference between the donor level and the conduction band.

Medium temperature regime (Ts < T < Ti) - Above the saturation temperature the donor levels are completely ionized so that n = Nd. As temperature keeps increasing there comes a temperature when the electrons from the valence band (intrinsic carriers) becomes comparable in concentration to Nd. This temperature is called the intrinsic temperature, T.

A ionization regime at low temperature, a saturation regime where the electron concentration is nearly a constant, and a intrinsic regime where the semiconductor behaves like an intrinsic semiconductor. In Si, this saturation regime is around room temperature so that the carrier concentration is a constant and independent of temperature.

Thus doping in a semiconductor has 2 functions :-

1. It increases the conductivity by preferentially increasing either electron or hole concentration. The conductivity can be precisely tuned by controlling the type and amount of dopant.

2. The majority carrier concentration is a constant and temperature independent (near room temperature) so that small temperature variations.