1 University of California, Berkeley College of Engineering Dept. of Electrical Engineering and Computer Sciences EE 105 Final Examination Fall 2005 Prof. Borivoje Nikolić December 20, 2005 ________________,_________________ Your Name (Last, First) Guidelines Closed book and notes; one 8.5” x 11” page (both sides) of your own notes is allowed. You may use a calculator. Do not unstaple the exam. Show all your work and reasoning on the exam in order to receive full or partial credit. You have 180 minutes (3 hrs.). Good luck! Score Problem Points Possible Score 1 32 2 34 3 34 Total 10021. [32 points] MOS Transistor. The following figure shows the cross-section of a p-well CMOS process. The maximum and minimum voltage in the chip is 5V and 0V respectively. lease use the following parameters: φp+ = -550mV, εSi = 11.7, εSiO2 = 3.9, ε0 = 8.854×10-14F cm-1, ni = 1010cm-3, kT/q = 25mV, Dn = 20 cm2/s, Dp = 10 cm2/s. You can assume μn = 500cm2/Vs, μp = 200cm2/Vs, P-WellP+ Poly GateN+ N+P+ N+N-substrateABCDE1E181E16P-WellP+ Poly GateN+ N+P+ N+N-substrateABCDE1E181E16 (a) [2 pts] To which voltage should terminal E be connected? Explain your answer. VE =3(b) [6 pts] If tox = 5nm, find VFB and VT. (c) [6 pts] If VB = 0V, how would you bias terminals C and D to maximize the drain current? Calculate the maximum drain current for W = 5μm, L = 1μm. VFB = VT = VC = VD = ID =4 (d) [10 pts] If VA = VB = VD = 0V, draw the potential profile across the cutting line (from the gate to n-substrate) when VC = -2V.5(e) [4 pts] With VE = 5V, how would you bias the other terminals to form an npn-BJT operating in forward bias region? (f) [4 pts] If the depth of the n+ regions is 0.2μm, and assuming only lateral conduction, and VBE = 0.7V and no recombination in base region, calculate the maximum IC. for the BJT from part (e).62. [34 points] Bipolar current source. Given: VCC = 5V, βF = β0 = 50, VBE = 0.7V, VCES = 0.1V. RREF = 5kΩ, VA = 20V. q = 1.6 x 10-19 C, kT/q = 25mV, Dn = 25 cm2/s. For all transistors: Emitter area: AE = 25 μm2, emitter width WE = 30 nm, base width WB = 50 nm, emitter doping NdE = 1019cm-3, base doping: NaB = 1017 cm-3, collector doping NdC = 1016 cm-3. (a) [2 pts] Find the current IREF. IREF =7(b) [8 pts] Assuming that Q3 is in the forward active region, find the ratio IOUT/IREF as a function of βF. You can ignore the base width modulation, but do not ignore the base currents. Please leave the answer in the symbolic form. IOUT/IREF =8(c) [4 pts] How does the ratio of IOUT/IREF change if you account for the base width modulation. A qualitative answer is sufficient, if explained well. (d) [6 pts] Sketch the minority carrier concentration profiles in the base regions of transistors Q1 and Q2. Your values at the edges of the depletion regions (x = 0, the edge of the emitter-base depletion region and x = WB, the edge of the base-collector depletion region) should be accurate.9(e) [4 pts] Find the minimum output voltage, vOUT, for which all the transistors operate in the forward active region. (f) [6 pts] Find the small signal output resistance for this current source. vOUT,MIN = ROUT =10(g) [4 pts] Modify the schematic by adding just one extra transistor to minimize the mismatch of IOUT and IREF due to base width modulation.113. CMOS Amplifier [34 points] VDDM1M2IBIASiOUTvINvOUT+M3M4M5M6M7 VDD = 5V, VTn = -VTp = 0.5V, μnCox = 50 μA/V2, μpCox = 20 μA/V2, λn = λp = 0.05 V-1 IBIAS = 100μA. M1: (W/L)1 = 16/1 (μm/μm) M2: (W/L)1 = 16/1 (μm/μm) M3: (W/L)1 = 64/4 (μm/μm) M4: (W/L)1 = 64/4 (μm/μm) M5: (W/L)1 = 4/1 (μm/μm) M6: (W/L)1 = 4/1 (μm/μm) M7: (W/L)1 = 4/1 (μm/μm) Cox = 5fF/(μm)2 Cov = 0.5fF/μm (per unit of transistor width). Input signal has negligible output resistance. Neglect backgate effect for bias and small-signal calculations.12(a) [4 pts] Find DC currents of transistors M1, M2, M3 and M4. ID1 = ID2 = ID3 = ID4 =13(b) [6 pts.] For RL = 100Ω find the maximum and minimum output voltages for which all transistors operate in saturation. (c) [6 pts] For RL= 100kΩ find the maximum and minimum output voltages find the maximum and minimum output voltages for which all transistors operate in saturation. vOUT, MAX = vOUT,MIN = vOUT, MAX = vOUT,MIN =14(d) [6 pts] Find the low-frequency small-signal gain of the amplifier and its output resistance, with RL = ∞. Av = ROUT =15(e) [6 pts] Find the bandwidth of this amplifier. ω3dB =16(f) [6 pts] Estimate the frequency of the second pole of this amplifier. ωp2
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