Chapter 4 where and are the values at 300 K. (a) Silicon(K)(eV)(cm) (b) Germanium (c) GaAs(K)(cm)(cm)_ Plot_(a) By trial and error, K(b) By trial and error, K_ At K, eV At K, eV or or eV Now so cm_ For K, eV For K, eV For K, eV(a) For K, (b) For K, (c) For K, _(a) Let Then To find the maximum value: which yields The maximum value occurs at (b) Let Then To find the maximum value Same as part (a). Maximum occurs at or _ where and Then or _ Plot_ Plot_ Silicon: , eV Germanium: , eV Gallium Arsenide: , eV_ (K)(eV)()(eV)_(a) meV(b) meV_ Let constant Then Let so that We can write so that The integral can then be written as which becomes _ Let for Then Let so that We can write Then or We find that So _ We have For germanium, , Then or The ionization energy can be written as eV eV_ We have For gallium arsenide, , Then The ionization energy is or eV_(a) eV(b) eV(c) cm(d) Holes(e) eV_(a) eV(b) eV(c) cm(d) eV_(a) eV eV(b) cm(c) p-type_(a) eV cm eV cm(b) eV eV cm_(a) eV cm eV cm(b) eV eV cm_(a) p-type(b) eV cm eV cm_(a) cm cm(b) cm cm_(a) eV(b) eV(c) cm(d) Holes(e)