For intrinsic semiconductors, the intrinsic carrier

For intrinsic semiconductors, the intrinsic carrier concentration ni depends on temperature as follows:

or taking natural logarithms,

Thus, a plot of ln ni versus 1/T (K)–1 should be linear and yield a slope of –Eg/2k. Using this information and the data presented in Figure, determine the band gap energies for silicon and germanium, and compare these values with those given in Table18.3.