Prof. Sung-Jin Choi Spring 2014 Final Exam: Semiconductor Engineering (I) 2014.06.19 7:00 ~ 10:00 PM (3 hours) Write your name and ID on first page DO NOT open exam booklet until instructed to do so Answer questions and explain your all steps on the exam paper Use back-side of the sheets, if necessary Student ID: Name: Signature: Problem 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total Score assigned 30 30 30 30 40 20 40 30 30 30 30 30 30 20 420 Score earned Thank you for your kind efforts during the semester. Good luck with your excellent future! Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 1. (30 points: each 15 point) Answer the following questions. (a) Find the drift current density (Jdrift) for the silicon sample with doping concentrations (Na = 0, Nd = 1016 /cm3) at room temperature (T = 300 K). Use that the electric field is 10 V/cm, electron mobility (μn) is 1350 cm2/V·sec, and hole mobility (μp) is 480 cm2/V·sec. (b) The electron concentration is linearly varied from 1018 /cm3 to 7 × 1017 /cm3 within 0.1 cm for the n-type GaAs sample at T = 300 K under equilibrium state. Find the electron diffusion current density. Assume that the electron diffusion constant (Dn) for GaAs is 225 cm2/sec. Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 2. (30 points: each 10 point) A silicon device at T = 300 K has the following geometries: d = 10-3 cm, W = 10-2 cm, and L = 10-1 cm. The following parameters are also measured: Ix = 0.75 mA, Vx = 15 V, VH = +5.8 mV, and Bz = 1000 gauss = 10-1 tesla. (a) What is the conductivity type (n or p-type)? Explain briefly for your answer. (b) Find the majority carrier concentration. (c) Find the majority carrier mobility. Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 3. (30 points: each 15 point) At T = 300 K, the doping concentration of an n-type silicon sample is given by Nd (x) = No·exp(-ax) where a is 1(μm)-1. (a) Draw the energy band diagram for this sample, including Ec, EF, Ev, and EFi at equilibrium state. (b) Find the built-in electric field for this sample. Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 4. (30 points: each 15 point) As for the n-type silicon sample with the electron concentration (no) of 1014 /cm3 under equilibrium state, answer the following questions. (a) When light is illuminated into this sample, the electron-hole pairs of 1013 /cm3 are generated for every μsec. Assume that the life time for both electrons and holes is 2 μsec. Find the electron (n) and hole (p) concentration for the steady-state condition. Hint: Use the equations, n = no + δn, p = po + δp where δn and δp are the excess carrier concentrations. (b) From above results, draw the energy band diagram for the sample, including quasiFermi levels (EFn, EFp). Note that the relative locations of quasi-Fermi levels should be shown. Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 5. (40 points: each 10 point) At T = 300 K, the silicon pn junction with Na = 1016 /cm3, Nd = 1015 /cm3 is given. Answer the following questions. (a) Find the built-in potential at equilibrium state. (b) Find the depletion width at p-type silicon (xp), the depletion width at n-type silicon (xn), and total depletion width (W). (c) Find the maximum electric field at metallurgical junction. (d) Find the total depletion width when the reverse bias (-5V) is applied. Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 6. (20 points) At T = 300 K, the silicon pn junction with Na = 1018 /cm3 is given. The maximum electric field is 3 × 105 V/cm when the reverse bias of -25 V is applied. Find the ntype doping concentration (assuming full ionization). Hint: built-in potential (Vbi) is negligible, compared to the reverse bias of -25 V. Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 7. (40 points) For the silicon pn junction, the doping profile is given as follows. Assume that the depletion region width at an n-type region (xn) is larger than xo. Answer the following questions. Nd - Na Nd Nd/2 xo x -Na (a) Find the built-in potential (Vbi) using Na, Nd, ni, or kT, and draw the energy band diagram of this pn junction. (10 points) Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam (b) Draw and find the charge density (ρ) for each region. (15 points) ρ -xp xo xn x Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam (c) Draw and find the electric field for each region. (15 points) E -xp xo xn x Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 8. (30 points: each 10 point) The potential in the depletion region of a silicon pn junction under equilibrium state is determined to be V ( x) Vbi W W x 1 sin where - x . 2 2 2 W (a) Establish an expression for the electric field as a function of position, E(x), in the depletion region (-W/2 ≤ x ≤ W/2) and sketch E(x) versus x. (b) Establish an expression for the charge density as a function of position, ρ(x), in the depletion region (-W/2 ≤ x ≤ W/2) and sketch ρ(x) versus x. (c) Determine and sketch ND – NA versus x in the depletion region (-W/2 ≤ x ≤ W/2). Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 9. (30 points: each 15 point) A silicon pn junction has Na = 1019 /cm3 and Nd = 1016 /cm3. The applied voltage is 0.6 V (forward bias). (a) What are the minority carrier concentrations at the depletion region edges under above the forward bias condition? (b) What are the excess minority carrier concentrations? Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 10. (30 points) The pn diode current can be expressed as: J =( qD p pno Lp + qDn n po Ln )(exp qV qV -1) = J s (exp -1) where Js is saturation current density. kT kT J (current density) Semilog plot 10-6 10-9 10-12 V (a) Derive the inverse slope (unit: mV/decade) of the diode current at forward bias (T = 300 K). (10 points) (b) As the temperature increases, explain whether the inverse slope of the diode current is increased or decreased. What is the value of the inverse slope at T = 500 K? (20 points) Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 11. (30 points: each 10 point) Consider the following parameters in a silicon pn junction (T = 300 K): Na = Nd = 1016 /cm3 Dn = 25 cm2/s Dp = 10 cm2/s ni = 1010 /cm3 τp0 = τn0 = 5 × 10-7 s εsi = 11.7 (relative permittivity) (a) Find the saturation current density. Hint: use the equation in problem 10. (b) Find the total current density at the forward bias of 0.65 V using the answer (a). (c) The total current far from the junction in the n-region at the forward bias of 0.65 V will be majority carrier electron drift current, i.e. J (total) will be the same as Jn (drift only) at far from the junction in the n-region. At this moment, find the electric field, E, using the drift current equation. Use the mobility (μn) of 1350 cm2/Vsec. Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 12. (30 points: each 10 point) Assume a silicon p+n junction at T = 300 K. [1/C’]2 -0.855 V VR (reverse bias) (a) Find the built-in potential from the graph. (b) If the slope is 1.32 × 1015 (F/cm2)-2(V)-1, what is the n-type doping concentration (Nd)? (c) From the obtained Vbi (in (a)) and Nd values (in (b)), find the p-type doping concentration (Na). Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 13. (30 points: each 10 point) The following figure is a dimensional plot of the steady state carrier concentrations inside a silicon pn junction diode maintained at T = 300 K. n or p (log scale) pp 1014 106 np 103 -xp 1015 nn 105 pn 102 x xn (a) Is this diode forward or reverse biased? Explain briefly how you arrived at your answer. (b) What are the p-side and n-side doping concentration? (c) Determine the applied voltage, Va. Semiconductor Engineering Date: 2014. 06.19 Prof. S.-J. Choi Final Exam Problem 14. (20 points) Consider two ideal pn junctions at T = 300 K, having exactly the same electrical and physical parameters except for the bandgap energy of the semiconducting materials. The first pn junction has a bandgap energy of 0.525 eV and a forward bias current of 10 mA with Va = 0.255 V. For the second pn junction, design the bandgap energy so that a forward base voltage of Va = 0.32 V will produce a current of 10 μA.
