Description

where 𝐸𝑔(0) is the value of the bandgap energy at 𝑇 = 0𝐾. For silicon, the parameter values are 𝐸𝑔(0) = 1.170𝑒𝑉, 𝛼 = 4.73 × 10−4𝑒𝑉/𝐾, and 𝛽 = 636𝐾. Plot 𝐸𝑔 versus T over the range 0 ≤ 𝑇 ≤ 600𝐾. In particular, note the value at
𝑇 = 300𝐾.

2. The figure below shows the parabolic E versus k relationship in the conduction band for an electron in two particular semiconductor materials, A and B. determine the effective mass (in units of the free electron mass) of the two electrons.

3. (a) For silicon, find the ratio of the density of states in the conduction band at
𝐸 = 𝐸𝑐 + 𝑘𝑇 to the density of states in the valence band at 𝐸 = 𝐸𝑣 − 𝑘𝑇.
(b) Repeat part (a) for GaAs.

4. Determine the probability that an energy level is empty of an electron if the state is below the Fermi level by (a)𝑘𝑇, (b)5𝑘𝑇, and (c)10𝑘𝑇.

5. (a) The Fermi energy in silicon is 0.30𝑒𝑉 below the conduction band energy 𝐸𝑐 at 𝑇 = 300𝐾. Plot the probability of a state being occupied by an electron in the conduction band over the range 𝐸𝑐 ≤ 𝐸 ≤ 𝐸𝑐 + 2𝑘𝑇.
(b) The Fermi energy in silicon is 0.25𝑒𝑉 above the valence band energy 𝐸𝑣. Plot the probability of a state being empty by an electron in the valence band over the range 𝐸𝑣 − 2𝑘𝑇 ≤ 𝐸 ≤ 𝐸𝑣.

6. The probability that a state at 𝐸𝑐 + 𝑘𝑇 is occupied by an electron is equal to the probability that a state at 𝐸𝑣 − 𝑘𝑇 is empty. Determine the position of the Fermi energy level as a function of 𝐸𝑐 and 𝐸𝑣.

7. (a) Calculate the temperature at which there is a 10−8 probability that an energy state 0.60𝑒𝑉 above the Fermi energy level is occupied by an electron. (b) Repeat part (a) for a probability of 10−6.