固態電子元件導論 第三章習題 Introduction to Solid-State Electronic Devices Homework #3 指導教授: 張廖貴術 教授 繳交期限: 3/27 1. The bandgap energy in a semiconductor is usually a slight function of temperature. In some cases, the bandgap energy versus temperature can be modeled by 𝐸𝑔 = 𝐸𝑔 (0) − 𝛼𝑇 2 (𝛽 + 𝑇) where Eg(0) is the value of the bandgap energy at T = 0 K. For silicon, the parameter values are Eg(0) = 1.170 eV, α = 4.73 x 10-4 eV/K, and β = 636 K. Plot Eg versus T over the range 0 ≦T≦600 K. In particular, note the value at T = 300 K. 2. The forbidden bandgap energy in Ge is 0.66 eV. (a) Determine the minimum frequency of an incident photon that can interact with a valence electron and elevate the electron to the conduction band. (b) What is the corresponding wavelength? 3. The energy band diagram for silicon is shown below. The minimum energy in the conduction band is in the  direction. The energy in this one-dimensional direction near the minimum value can be approximated by 𝐸 = 𝐸0 − 𝐸1 𝑐𝑜𝑠𝛼(𝑘 − 𝑘0 ) where k0 is the value of k at the minimum energy. Determine the effective mas of the particle at k = k0 in terms of the equation parameters. 4. The Fermi energy level for a particular material at T = 300 K is 5.50 eV. The electrons in this material follow the Fermi-Dirac distribution function. (a) Find the probability of an electron occupying the energy at 5.80 eV. (b) Repeat part (a) if the temperature is increased to T = 700K. (Assume that EF is a constant.) (c) Determine the temperature at which there is a 2 percent probability that a state 0.25 eV below the Fermi level will be empty of an electron.