# UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences. Professor Chenming Hu.

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1 UNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 130 Spring 2009 Professor Chenming Hu Midterm I Name: Closed book. One sheet of notes is allowed. There are ten pages of this exam including this page. Problem 1 30 Problem 2 20 Problem 3 35 Problem 4 15 Total 100

2 Physical Constants Electronic charge q C Permittivity of vacuum F cm -1 Relative permittivity of silicon Si / Boltzmann s constant k x 10-5 ev/ K or J K -1 Thermal voltage at T = 300K kt/q V Effective density of states N c 2.8 x cm -3 Effective density of states N v 1.04 x cm -3 Silicon Band Gap E G 1.1 ev Intrinsic carrier concentration of Si at 300K n i cm -3

3 Problem 1 Minority carrier concentration versus position plots are often used to describe the situation inside semiconductor devices. A linear plot of the excess minority carrier concentration on the N-side of two ideal P + -N diodes maintained at room temperature is pictured below. The P-side doping (N a, N-side doping (N d and the cross-sectional area are the same in both diodes. Assume low-level injection conditions prevail. p N Diode A N side Diode B x (a Are both diodes forward, zero, or reverse biased? [3pts] Forward bias (b Which diode has higher bias? Briefly explain. [5pts] Diode A. p N 0 = p N0 e qv kt 1, since p NA 0 > p NB 0 and p N0A = p N0B V A > V B (c Which diode has higher minority carrier lifetime on the N-side? Assume that the hole mobility of diode A and B are the same. Briefly explain. [5pts] Diode B. L = Dτ, since L B > L A and D A = D B ( μ A = μ B τ B > τ A (d Which diode has higher current? Briefly explain. [5pts] Diode A. J p = qd dp dx, since D A = D B and dp A dx > dp B dx J pa > J pb

4 (e Given the plot of p N in dashed lines in the following figure, add n N in solid lines for diode A and B and label them. [4pts] P N and n N Diode A n N =p N N side Diode B x (f Qualitatively draw J p and J n for diode A and B. Label them clearly. [8pts] J p and J n J n N side J p Diode A Diode B x

5 Problem 2 (a Given below is a menu consisting of various fabrication processes you are familiar with. Using only these given processes, complete the sequence of steps to fabricate the structure given below. (Hint: All given processes may or may not be required, and the same process maybe used multiple times. Processes Available: Thermal annealing (diffusion Epitaxy Anisotropic Etching CVD (Chemical Vapor Deposition Isotropic Etching Nanoimprint CMP (Chemical-mechanical polishing Lithography Thermal oxidation ALD (Atomic layer deposition Ion implantation Sputtering SiO 2 P+ N SiO 2 Cu TiN SiO 2 Starting from a N-type silicon wafer [5pts] Thermal oxidation Lithography Isotropic Etching Ion implantation Thermal annealing Starting from SiO 2 [5pts] Lithography Anisotropic Etching Sputter TiN CVD Cu CMP (b Briefly explain the difference between positive and negative photoresists. [4pts] The exposed regions are removed for positive photoresist, while the unexposed regions are removed for negative photoresist. (c Why does wet lithography provide better resolution? Briefly explain. [3pts] When light enters the water, its wavelength is reduced by the refraction index of water, 1.43, and therefore the lithography resolution is improved. (lithography resolution = kλ (d What motivates the IC industry to use increasingly larger silicon wafer size? Briefly explain. [3pts] More dies of chip can be sliced out of a larger wafer size. Therefore the cost per chip is reduced.

6 Position of E F (ev Carrier concentration n or p (cm -3 Problem 3 Doping concentration plays an important role in changing the physical and electrical properties of a doped semiconductor. You are given an N-type silicon semiconductor: (a Draw carrier concentrations n and p versus doping concentration in T=300K. Do the calculation to specify the left and right intercept of the line. [4pts] n=n d p=n i 2 /N d (b Draw the position of Fermi level versus doping concentration in T=300K. Do the calculation to specify the left and right intercept of the line. [7pts] Ec Ec Ev 0.0 n = N d = N c exp E F E c kt E F = E c + kt ln N d N c

7 Mobility (arbitrary unit Thermal velocity (10 5 m/s (c Thermal velocity at T=300K and N d =10 15 cm -3 is m/s. Draw thermal velocity versus doping concentration in 300K and 580K. Do the calculation to specify the intercepts of the lines. [4pts] v th = 3kT m T, therefore it s independent of doping concentration (d i. Qualitatively draw electron mean free time versus doping concentration at 300K and 600K, given that τ mn at 300K, cm -3 is six times of τ mn at 600K, cm -3. (No need to do calculations [4pts] K 600K 0 ii. At 300K, what scattering mechanism dominates at low (10 15 cm -3 and high (10 18 cm -3 doping concentration respectively? [3pts] Low (10 15 cm -3 : Phonon scattering High (10 18 cm -3 : Columbic (impurity scattering iii. At 600K, what scattering mechanism dominates at low (10 15 cm -3 and high (10 18 cm -3 doping concentration respectively? [3pts] Low (10 15 cm -3 : Phonon scattering High (10 18 cm -3 : Phonon and impurity both have effect (free 1.5 points!

8 Diffusiom constant (arbitrary unit Mean free time mn (arbitrary unit (e Qualitatively draw electron mobility versus doping concentration at 300K and 600K. Briefly explain how you get the curves. (No need to do calculations [4pts] K 600K 0 μ n = qτ mn m n, therefore mobility curves are the same shape of mean free time. (f Qualitatively draw electron diffusion constant versus doping concentration at 300K and 600K. Briefly explain how you get the curves. [6pts] K 300K 0 D n = kt q μ n, therefore, the diffusion constant curves are the same shape except the one at 600K should be doubled up the value.

9 Problem 4 N+ N P + L = 0.1μm Consider the above silicon diode. Assume that N + and P + regions are heavily doped that E c = E f in the N + region and E F = E V in the P + region. The doping in the N-type region is cm -3. Assume that the N layer is thin enough that it is completely depleted. (a Sketch the energy band diagram for this diode. Do not be concerned with the exact shape of E c (x in the depletion region. [2pts] E c E f E v (b Find the built in potential (φ bi of the given diode in Volts. [2pts] Built in potential (φ bi = Bandgap = E g /q = 1.1V (c Qualitatively draw the electric field in the semiconductor as a function of x under the condition of (i V=0V (ii V r (reverse bias = 2.2 V on the same plot. (Hint: You may assume that the depletion region is entirely contained in the N region only. No need to do calculation [4pts] E 1. No depletion in P + and N + region V r = 2.2 V V r = 0 V 2. Slope = de = qn d >0 dx ϵ 3. Slope 2.2V = Slope 0V 4. Area of E at V r = 2.2 V = 3 area of E at V = 0 V x

10 (d Call the diode in part (a diode A. Now consider another diode B with the identical N + -N-P + structure except doping of N region is cm -3. Qualitatively draw the electric field at V=0V of diodes A and B as a function of x in the same plot. [4pts] E Diode B Diode A 1. No depletion in P + and N + region 2. Slope = de = qn d >0 dx ϵ 3. Slope of E of diode B = 2 Slope of E of diode A 4. Area=φ bi are the same (e Does diode A or B has higher breakdown voltage? Briefly explain why. [3pts] x Diode A has a higher breakdown voltage. Because diode A has a lower peak electric field at a given bias. Therefore, diode A has to reach E crit (E crita =E critb at a higher voltage.

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