Download 10 Problems on Microelectronic Circuits - Assignment 1 | ECE 3040 and more Assignments Electrical and Electronics Engineering in PDF only on Docsity! ECE3040 Assignment 1 1. It is found that Si at T = 300K has the intrinsic concentration ni = 1.5 × 1010 per cm3. If the bandgap voltage is VG = 1.11V, show that the constant n0 in the equation ni = n0 µ T 300 ¶3/2 exp µ−VG 2VT ¶ has the value n0 = 3.04× 1025. 2. Copper has two valence electrons per atom, an atomic weight of 63.546 g/mol, a density of 8230 kg/m3, and a conductivity of 5.8 × 107 S/m. (a) If all valence electrons are free, show that the concentration of free electrons is n = 1.56× 1029 electrons per m3. (b) Show that the electron mobility in copper is µe = 2.32× 10−3m2V−1 s−1. 3. Show that the diameter of 1 ft of copper wire required to obtain a resistance of 5Ω is d = 1.44× 10−3 in. 4. Let y = f (x). The percentage fractional change in y per change in x is defined by 1 y × dy dx × 100% The intrinsic concentration of silicon is given by ni = n0 µ T 300 ¶3/2 exp µ−VG 2VT ¶ If VG = 1.11V and is assumed to be independent of temperature and VT = kT/q, show that the fractional percentage change in the intrinsic concentration for silicon at T = 300K is µ 3 2T + VG 2TVT ¶ × 100% = 7.64% per ◦C 5. Let a rod of semiconductor material have a length ∆ , a cross-section area S, an intrinsic concentration ni, an electron mobility µe, and a hole mobility µh. Show that the resistance of the rod can be written as the parallel combination of two resistors Re and Rh given by Re = ∆ niµeqS Rh = ∆ niµhqS 6. A rod of intrinsic silicon is 5mm long and has a diameter of 1.5mm. At room temper- ature, the intrinsic concentration in the silicon is ni = 1.5× 1016 per m3. The electron and hole mobilities are µe = 0.13m 2V−1 s−1 and µh = 0.05m 2V−1 s−1. Use the results of problem 5 to show that Re = 9.06MΩ, Rh = 23.6MΩ, and R = RekRh = 6.54MΩ. 7. In the silicon rod of problem 6, the number of silicon atoms per m3 is 5 × 1028. An acceptor impurity is added to the silicon in the rate of one donor atom per 108 atoms of silicon. Show that the new resistance of the rod is R = 706Ω. Verify that the resistance contributed by the minority electron carriers is negligible. Assume that each acceptor atom contributes one mobile hole. 1
