VE320- Homework 3 Solved

(a) For silicon, find the ratio of the density of states in the conduction band at 𝐸=𝐸𝑐+𝑘𝑇to the density of states in the valence band at 𝐸=𝐸𝑣−𝑘𝑇. (b) Repeat part (a) for GaAs.
(a) The Fermi energy in silicon is 0.30𝑒𝑉below the conduction band energy 𝐸𝑐at 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 0.25𝑒𝑉above 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.
(a) Calculate the temperature at which there is a 10−8probability that an energy state 0.60𝑒𝑉above the Fermi energy level is occupied by an electron. (b) Repeat part (a) for a probability of 10−6
(a) The carrier effective masses in a semiconductor are m: = 1.21 mo and m; = 0.70 mo. 

Determine the position of the intrinsic Fermi level with respect to the center of the bandgap at T = 300 K. (b) Repeat part (a) if m: = 0.080 mo and m; = 0.75 mo.
Silicon at T = 300 K is doped with boron atoms such that the concentration Of holes is pc, = 5 x 101s cm-N. (a) Find EF — (b) Determine Ee — EF. (c) Determine no. 

(d) Which carrier is the majority carrier? (e) Determine Eh —
(a) Consider a germanium semiconductor at T = 300 K. Calculate the thermal equilibrium electron and hole concentrations for (i) IV,I = 2 x cm-3, No = 0, and 

(ii) No = 1016 cm-VA, = 7 x cm-J. (b) Repeat part (a) for GaAs. (c) For the case of GaAs in part (b), the minority carrier concentrations are on the order of 10-3 cm-3 

What does this result mean physically?

(a) Silicon at T = 300 K is uniformly doped with boron atoms to a concentration of o3 x 1016 cm-Y and with arsenic atoms to a concentration of 1.5 x cm-s. Is the
material n type or p type? Calculate the thermal equilibrium concentrations Of majority and minority carriers. (b) Additional impurity atoms are added such that holes are the majority carrier and the thermal equilibrium concentration is = 5 x 1016 cm-3. What type and concentration of impurity atoms must be added? What is the new value of no

A silicon device is doped with donor impurity atoms at a concentration of 101' cm-Y For the device to operate properly, the intrinsic carriers must contribute no more than 5 percent to the total electron concentration. (a) What is the maximum temperature that the device may operate? (b) What is the change in E, — EF from the T = 300 K value to the maximum temperature value determined in pan (a). (c) Is the Fermi level closer or further from the intrinsic value at the higher temperature?

For a particular semiconductor, = I .50 eV, m; = 10 m:, T = 300 K, and n, = I x 10' cm-3. (a) Determine the position of the intrinsic Fermi energy level with respect to the center of the bandgap. (b) Impurity atoms are added so that the Fermi energy level is 0.45 ev below the center of the bandgap. (i) Are acceptor or donor 
atoms added? (ii) What is the concentration of impurity atoms added?(a) For silicon, find the ratio of the density of states in the conduction band at 𝐸=𝐸𝑐+𝑘𝑇to the density of states in the valence band at 𝐸=𝐸𝑣−𝑘𝑇. (b) Repeat part (a) for GaAs.
(a) The Fermi energy in silicon is 0.30𝑒𝑉below the conduction band energy 𝐸𝑐at 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 0.25𝑒𝑉above 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.
(a) Calculate the temperature at which there is a 10−8probability that an energy state 0.60𝑒𝑉above the Fermi energy level is occupied by an electron. (b) Repeat part (a) for a probability of 10−6
(a) The carrier effective masses in a semiconductor are m: = 1.21 mo and m; = 0.70 mo. 

Determine the position of the intrinsic Fermi level with respect to the center of the bandgap at T = 300 K. (b) Repeat part (a) if m: = 0.080 mo and m; = 0.75 mo.
Silicon at T = 300 K is doped with boron atoms such that the concentration Of holes is pc, = 5 x 101s cm-N. (a) Find EF — (b) Determine Ee — EF. (c) Determine no. 

(d) Which carrier is the majority carrier? (e) Determine Eh —
(a) Consider a germanium semiconductor at T = 300 K. Calculate the thermal equilibrium electron and hole concentrations for (i) IV,I = 2 x cm-3, No = 0, and 

(ii) No = 1016 cm-VA, = 7 x cm-J. (b) Repeat part (a) for GaAs. (c) For the case of GaAs in part (b), the minority carrier concentrations are on the order of 10-3 cm-3 

What does this result mean physically?

(a) Silicon at T = 300 K is uniformly doped with boron atoms to a concentration of o3 x 1016 cm-Y and with arsenic atoms to a concentration of 1.5 x cm-s. Is the
material n type or p type? Calculate the thermal equilibrium concentrations Of majority and minority carriers. (b) Additional impurity atoms are added such that holes are the majority carrier and the thermal equilibrium concentration is = 5 x 1016 cm-3. What type and concentration of impurity atoms must be added? What is the new value of no

A silicon device is doped with donor impurity atoms at a concentration of 101' cm-Y For the device to operate properly, the intrinsic carriers must contribute no more than 5 percent to the total electron concentration. (a) What is the maximum temperature that the device may operate? (b) What is the change in E, — EF from the T = 300 K value to the maximum temperature value determined in pan (a). (c) Is the Fermi level closer or further from the intrinsic value at the higher temperature?

For a particular semiconductor, = I .50 eV, m; = 10 m:, T = 300 K, and n, = I x 10' cm-3. (a) Determine the position of the intrinsic Fermi energy level with respect to the center of the bandgap. (b) Impurity atoms are added so that the Fermi energy level is 0.45 ev below the center of the bandgap. (i) Are acceptor or donor 
atoms added? (ii) What is the concentration of impurity atoms added?