Variation of Fermi Energy Level with Temperature and Impurity Concentration in 'n'-Type Semi Conductor

VARIATION OF FERMI ENERGY LEVEL WITH TEMPERATURE AND IMPURITY CONCENTRATION IN 'n'-TYPE SEMI CONDUCTOR

When the temperature is increased some electrons in E_d level may be shifted to conduction band and hence some vacant sites will be created in E_d levels. Therefore the Fermi level shifts down to separate that empty levels and the filled valence band level as shown in Fig. 2.17, for the doping level of N_d = 10²¹ atoms/m₃.

From the Fig. 2.17 it can be seen that for the same temperature, if the impurity atoms i.e., doping level is increased (N_d = 10²⁴ atoms/m³), the electron concentration increases and hence the Fermi level increases.

Note: E_i is the fermi energy level of the intrinsic semiconductors given just as reference energy level in order to indicate that the variation of E_F can fall only upto E_i.

Ionisation Energy of Donor

To find the ionisation energy of donor equation (8) can be written as

n_e = Ce ̄^ΔE/2K_B^T, where C is a constant

If a graph is plotted between log n_e and 1/T we get lines (Fig. 2.18) for various values of donor impurity levels. From the slope - ΔE/2K_B, the value of ionisation energy of donor can be calculated.

Note: If T is very high then the slope become - E_g/2K_B as that of intrinsic semiconductor.

Results

•Density of electrons (n_e) in conduction band is proportional to the square root of donor concentration (N_d).

•When temperature is increased the Fermi level falls below the donor level and may approach only upto E_i (Fermi level of the intrinsic semi conductor).

Electrical Conductivity of n-type

We know the electrical conductivity (σ) is given by

σ = n_e e (μ_e +μ_h)

For n-type semiconductor the acceptors are at the most zero. Therefore the mobility of charge carriers (holes) is zero. i.e., μ_h = 0.

σ =n_e e μ_e