Question

1. Energy band model a) For silicon, if Eg decreases by 0.078 eV, by what fraction does ni increase (assume T is constant at 300K)? b) If the temperature rises from 300K to 600K, by what additional fraction does n, increase (assume Eg is constant 1.068 eV, you do not need to worry about the decrease from problem a)? c) If we further increase the temperature, Si starts exhibiting semi-metal properties. Think ofa physical reason for this phenomenon. (Assume you haven't melted it).

Answer 1

The expression for the intrinsic carrier concentration is given as follows, (1) | (T)= VN, N, esp - Here, (T) is the intrinsic carrier concentration, N, is the effective density of states in the conduction band, N, is the effective density of states in the valence band, k is the Boltzmann constant, and T is the absolute value of temperature. According to the condition given in the question, if the value of forbidden energy Rap changes by 0.078 eV, then the change in value of the intrinsic carrier concentration is n, (T)= N, P, exp - E+0078 Take the ration of equation (2) by (1), we get n. (1). (N, N) ****227 (T) VINN)

Substitute 0.026 eV for kI in above equation, we get T-448 (T) (T) = 4.48% 12 (T) b) if the value of temperature increases from 300 K to 600 K, the change in intrinsic carrier concentration will be 1068 (T) INN.) exp2k 600 | PA (T) VN, N, P 1068 (-1068 exp 2k X 600 0.078 exp 300 1,(T) - 28831.7* (T) on further heating the system, the density of carrier concentration increases by large amount as seen in part b. More carrier concentration will cause the behavior of silicon as semi-metal