4.61 A new semiconductor material is to be "designed." The semiconductor is to be p type and doped with 5 x 105 cm3 acceptor atoms. Assume complete ionization and assume Na = 0. The effective density of states functions are N = 1.2 x 10" cm and N, = 1.8 x 10" cm at T = 300 K and vary as T. A special semiconductor device fabricated with this material requires that the hole concentration be no greater than 5.08 x 1015 cm-3 at T = 350 K. What is the minimum bandgap energy required in this new material?

4.61 A new semiconductor material is to be "designed." The semiconductor is to be p type and doped with 5 x 105 cm3 acceptor atoms. Assume complete ionization and assume Na = 0. The effective density of states functions are N = 1.2 x 10" cm and N, = 1.8 x 10" cm at T = 300 K and vary as T. A special semiconductor device fabricated with this material requires that the hole concentration be no greater than 5.08 x 1015 cm-3 at T = 350 K. What is the minimum bandgap energy required in this new material?