# ANALOG ELECTRONICS QUESTIONS

1. Which of the following semiconductors are transparent, partially transparent, non-transparent for visible light (λ = 0.4–0.7 μm): Si, GaAs, GaP, and GaN
2. Band gap of Si depends on the temperature as Eg = 1.17 eV − 4.73 × 10−4 T2T + 636. Find a concentration of electrons in the conduction band of intrinsic (undoped) Si at T = 77 K if at 300 K ni = 1.05 × 1010 cm-3.
3. Electron mobility in Si is 1400 cm2 V−1s−1. Calculate the mean free time in scattering (Relaxationszeit) of electrons. Effective mass is m∗e/m0 = 0.33.
4.  Calculate thermal velocity of electrons and holes in GaAs at room temperature. Effective masses are m∗e/m0 = 0.063 and m∗h/m0 = 0.53.
5.  Hole mobility in Ge at room temperature is 1900 cm2 V−1s−1. Find the diffusion coefficient.
6.  Calculate dielectric relaxation time in p-type Ge at room temperature. Assume that all acceptors are ionized. Na = 1015 cm−3, ǫ = 16, μp = 1900 cm2 V−1s−1.
7. Calculate dielectric relaxation time in intrinsic Si at 300 K. ǫ = 12, μn = 1400 cm2 V−1s−1, μn = 3.1 μp.
8.  Find Debye length in p-type Ge at 300 K if Na = 1014 cm−3. Assume that all acceptors are ionized, ǫ = 16.
9. Calculate the ambipolar diffusion coefficient of intrinsic (undoped) Ge at 300 K. μn/μp = 2.1, μn = 3900 cm2 V−1s−1.
10.  Holes are injected into n-type Ge so that at the sample surface _p0 = 1014 cm−3. Calculate _p at the distance of 4 mm from the surface if τp = 10−3 s and Dp = 49 cm2/s.
11.  Find the built-in potential for a p-n Si junction at room temperature if the bulk resistivity of Si is 1 cm. Electron mobility in Si at RT is 1400 cm2 V−1 s−1; μn/μp = 3.1; ni = 1.05 × 1010 cm−3.
12.  For the p-n Si junction from the previous problem calculate the width of the space charge region for the applied voltages V = −10, 0, and +0.3 V. ǫSi = 11.9
13.  For the parameters given in the previous problem find the maximum electric field within the space charge region. Compare these values with the electric field within am shallow donor: E ≈ e/ǫSia2 B, where aB is the Bohr radius of a shallow donor, aB =ǫSi~2/m∗ e e2 and m∗ e/m0 = 0.33.
14. Calculate the capacity of the p-n junction from the problem 2 if the area of the junction is 0.1 cm2.
15.  n-Si of a p-n Si junction has a resistivity of 1 cm. What should be the resistivity of p-Si so that 99 % of the total width of the space charge region would be located in n-Si (p+-n junction)?
16.  At room temperature under the forward bias of 0.15 V the current through a p-n junction is 1.66 mA. What will be the current through the junction under reverse bias?
17. For a p+-n Si junction the reverse current at room temperature is 0.9 nA/cm2.
18. Calculate the minority-carrier lifetime if Nd = 1015 cm−3, ni = 1.05 × 1010 cm−3, and μp = 450 cm2 V−1 s−1.
19.  How does the reverse current of a Si p-n junction change if the temperature raises from 20 to 50 ◦C? The same for a Ge p-n junction. Band gaps of Si and Ge are 1.12 and 0.66 eV, respectively.
20.  Estimate temperatures at which p-n junctions made of Ge, Si, and GaN lose their rectifying characteristics. In all cases Na = Nd = 1015 cm−3. Assume that Eg are independent of the temperature and are 0.66, 1.12, and 3.44 eV for Ge, Si, and GaN, respectively. Intrinsic carrier concentrations at room temperature are nGei = 2 × 1013,nSii = 1010, and  nGaNi = 10−9 cm−3.
21. A silicon p+-n-p transistor has impurity concentrations of 5×1018, 1016, and 1015 cm−3 in the emitter, base, and collector, respectively. If the metallurgical base width is 1.0 μm, VEB = 0.5 V, and VCB = 5 V (reverse), calculate (i) the neutral base width, and (ii)the minority carrier concentration at the emitter-base junction. Transistor operates at room temperature.
22.  For the transistor from the previous problem calculate the emitter injection efficiency,γ, assuming that DE = DB and the neutral base and emitter widths are equal (xE = xB).
23.  For the same transistor calculate the base transport factor (αT ) assuming the diffusion length of the minority carriers in the base of 3.5 μm.
24. Diffusion length of the minority carriers in the base region is 4 μm. Calculate the base width at which the base transport factor is 0.99, 0.9, and 0.5.
25.  A Si n+-p-n transistor has dopings of 1019, 3×1016, and 5×1015 cm−3 in the emitter,base, and collector, respectively. Find the upper limit of the base-collector voltage at which the neutral base width becomes zero (punch-through). Assume the base width (between metallurgical junctions) is 0.5 μm.
26.  What profile of the base doping results in a uniform electric field in the base?
27.  For a non-uniform doping profile of the base resulting in a mean electric field of 104 V/cm compare the drift and diffusion transport time at room temperature of the minority carriers through the base (xB = 0.5 μm).
28. For a Si transistor with DB = 50 cm2/s and LB = 3.5 μm in the base and B = 0.5 μm estimate the cut-off frequencies in common-emitter and common-base configurations.
29. For an ideal Si-SiO2 MOS capacitor with d = 10 nm, Na = 5 × 1017 cm−3, find the applied voltage at the SiO2-Si interface required (a) to make the silicon surface intrinsic, and (b) to bring about a strong inversion. Dielectric permittivities of Si and SiO2 are 11.9 and 3.9, respectively. T = 296 K.
30. A voltage of 1 V is applied to the MOS capacitor from the previous problem. How this voltage is distributed between insulator and semiconductor?
31.  An ideal Si-SiO2 MOSFET has d = 15 nm and Na = 1016 cm−3. What is the flat-band capacitance of this system? S = 1 mm2, and T = 296 K.
32. For the MOSFET from the previous problem find the turn-on voltage (VT ) and the minimum capacitance under high-frequency regime.
33. For a metal-SiO2-Si capacitor with Na = 1016 cm−3 and d = 8 nm, calculate the minimum capacitance on the C-V curve under high-frequency condition. S = 1 mm2, and T = 296 K.
34. Find a number of electrons per unit area in the inversion region for an ideal Si-SiO2 MOS capacitor with Na = 1016 cm−3, d = 10 nm, V = 1.5 V, T = 296 K.
35. Turn-on voltage of the MOS from the previous problem was found to be shifted by 0.5 V from the ideal value. Assuming that the shift is due entirely to the fixed oxide charges at the SiO2-Si interface, find the number of fixed oxide charges.
36. Assume that the radiative lifetime τr is given by τr = 109/N s, where N is the semiconductor doping in cm−3 and the nonradiative lifetime τnr is equal to 10−7 s. Find the cutoff frequency of an LED having a doping of 1019 cm−3.
37.  For an InGaAsP laser operating at a wavelength of 1.3 μm, calculate the mode spacing in nanometer for a cavity of 300 μm, assuming that the group refractive index is 3.4.
38. Assuming that the refractive index depends on the wavelength as n = n0+dn/dλ(λ− λ0), find the separation _λ between the allowed modes for a GaAs laser at λ0 = 0.89 μm,L = 300 μm, n0 = 3.58, dn/dλ = 2.5 μm−1.
39. An InGaAsP Fabry-Perot laser operating at a wavelength of 1.3 μm has a cavity length of 300 μm. The refractive index of InGaAsP is 3.9. If one of the laser facets is coated to produce 90 % reflectivity, what should be the minimum gain for lasing, assuming the absorption coefficient of the material α to be 10 cm−1?