Exercise 3.1
The thermal equilibrium hole concentration in silicon at T = 300 K is p0 = 2×105 cm−3. Determine the thermal-equilibrium electron concentration. Is the material n type or p type?
Exercise 3.2
In silicon at T = 300 K, it is found that Na = 7 × 1015 cm−3 and p0 = 2 × 104 cm−3. (a) Is the material n type or p type?
(b) What are the majority and minority carrier concentrations?
(c) What must be the concentration of donor impurities?
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Exercise 3.3
A silicon device is doped with donor impurity atoms at a concentration of 1015 cm−3. 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 Ec − EF from the T = 300 K value to the maximum tem- perature value determined in part (a).
(c) Is the Fermi level closer or further from the intrinsic value at the higher temperature?
Exercise 3.4
Silicon is doped at Nd = 1015 cm−3 and Na = 0.
(a) Plot the concentration of electrons versus temperature over the range 300 ≤ T ≤ 600 K.
(b) Calculate the temperature at which the electron concentration is equal to 1.1 × 1015 cm−3.
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Exercise 3.5
GaAs at T = 300 K is doped with donor impurity atoms at a concentration of 7 × 1015 cm−3. Additional impurity atoms are to be added such that the Fermi level is 0.55eV above the intrinsic Fermi level. Determine the type (donor or acceptor) and concentration of impurity atoms to be added.
Exercise 3.6
A compensated p-type silicon material at T = 300 K has impurity doping concentra- tions of Na = 2.8 × 1017 cm−3 and Nd = 8 × 1016 cm−3. Determine the
(a) hole mobility (b) conductivity (c) resistivity
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Exercise 3.7
Consider a semiconductor that is uniformly doped with Nd = 1014 cm−3 and Na = 0, with an applied electric field of E = 100 V/cm. Assume that μn = 1000 cm2/V · s and μp = 0. Also assume the following parameters:
Nc = 2 × 1019(T/300)3/2 cm−3 Nv = 1 × 1019(T/300)3/2 cm−3 Eg = 1.10eV
(a) Calculate the electric-current density at T = 300 K.
(b) At what temperature will this current increase by 5 percent? (Assume the mobilities are independent of temperature.)
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Reference
1. Neamen, Donald A. Semiconductor physics and devices: basic principles. McGraw- hill, 2003.
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