A homogeneously impurity doped silicon has

Question

A homogeneously impurity doped silicon has N_DD=1.01x10¹⁶ phosphor/cm³ and N_AA =1.00x10¹⁴ boron/cm³, all of which are ionized. What are the electron and hole concentrations at 21.2°C and 362°C. Use Figure or the experimental formulae given in problem to obtain the accurate value of n_i at these two temperatures.

Problem:-

The experimental formulae for the intrinsic carrier concentration in silicon was obtained by Morin and Malta at the Bell Telephone Laboratories in 1954 from conductivity and Hall voltage measurements over a wide range of temperature in many n-type and p-type impurity doped silicon single crystals. Their results were fitted to give n₁²=1.5x10³³T³exp(-1.21eV/kT) where k is the Boltzmann constant given by (231.3) (k=8.616x10^-5 eV/K, verify k in this unit) and T is the absolute temperature in Kelvin.

Calculate the value of n_i at T=300°C and verify your result with that given by Figure.