Photocurrent - Microelectronic Devices and Circuits - Exam, Exams of Microelectronic Circuits

Download Photocurrent - Microelectronic Devices and Circuits - Exam and more Exams Microelectronic Circuits in PDF only on Docsity! 1 University of California at Berkeley College of Engineering Dept. of Electrical Engineering and Computer Sciences EE 105 Final Examination Spring 2002 Prof. Roger T. Howe May 18, 2002 ________________,_________________ Your Name (Last, First) Guidelines Closed book and notes; three 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.); use your time wisely. Good luck! Score Problem Points Possible Score 1 30 2 25 3 25 4 20 Total 100 2 1. CMOS two-stage photocurrent amplifier [30 points] V - = - 1.5 V Given: µnCox = 50 µA/V2, VTn = 1.0 V, λn = 0.05 V-1 µpCox = 25 µA/V 2, VTp = -1.0 V, λp= 0.05 V -1 M1: (W/L)1 = 256/1 (µm/µm) M7: (W/L)7 = 32/1 (µm/µm) M2: (W/L)2 = 256/1 ( µm/µm) V+ = 1.5 V IREF = 10 µA M4 M1 M3 M7 M9 RL M11 M3: (W/L)3 = 16 /1 (µm/µm) M4: (W/L)4 = 32 /1 (µm/µm) M5: (W/L)5 = 256/1 (µm/µm) M6: (W/L)6 = 128/1 (µm/µm) M8: (W/L)8 = 32/1 (µm/µm) M9: (W/L)9 = 64/1 (µm/µm) RS = 100 kΩ RL = 100 kΩ M5 M8 M10 M2 M6 Illuminated Photodiode Model: RS is M10: (W/L)9 = 512/1 (µm/µm) M11: (W/L)9 = 64/1 (µm/µm) iout Neglect the backgate effect. (a) [3 pts.] Find the numerical values of the DC drain currents for transistors M1, M10, and M2. You can assume that all transistors are saturated, that the DC output voltage is VOUT = 0 V, and that channel length modulation can be neglected. ID1 = ________ µA -ID10 = ________ µA -ID2 = ________ µA 5 (f) [5 pts.] Find the numerical value of Ai (the low-frequency short-circuit current gain -- a two-port parameter.) Again, you should make reasonable approximations in order to save time and pencil lead! Ai = ___________ (g) [4 pts.] Find the maximum amplitude MAXOUTi ,ˆ of the output current iOUT,(t) in µA which avoids clipping. Note that the value of the load resistor is RL = 100 kΩ. =MAXOUTi ,ˆ _________ µA 6 (h) [3 pts.] Sketch the transfer curve iOUT vs. iS where the output current is in µA and the input current is in nA = 10-9 A. Consider the input source to be “large signal” for this part and neglect RS. Provide your own appropriate scale -- your sketch should be consistent with your answers to parts (f) and (g). If you couldn’t solve these parts, you can assume that the overall short-circuit current gain is 75 and that -1.2 V < vOUT < 0.9 V (not the correct answers, of course). iOUT [µA] iS [nA] 7 2. Frequency Response of a CMOS Photocurrent Amplifier [25 points] Cox = 2 fF/µm2, Cov = 0.1 fF/µm, Ldiff = 2 µm, NMOS: Cdb = 0.5 fF/µm2, PMOS: Cdb = 0.3 fF/µm2 V - = - 1.5 V Given: µnCox = 50 µA/V2, VTn = 1.0 V, λn = 0.05 V-1 µpCox = 25 µA/V2, VTp = -1.0 V, λp= 0.05 V-1 M1: (W/L)1 = 256/1 (µm/µm) M7: (W/L)7 = 32/1 (µm/µm) M2: (W/L)2 = 256/1 (µm/µm) IREF = 10 µA M4 M1 M3 M7 M9 RL ,CL M11 M3: (W/L)3 = 16 /1 (µm/µm) M4: (W/L)4 = 32 /1 (µm/µm) M5: (W/L)5 = 256/1 (µm/µm) M6: (W/L)6 = 128/1 (µm/µm) M8: (W/L)8 = 32/1 (µm/µm) M9: (W/L)9 = 64/1 (µm/µm) RS = 100 kΩ CS = 100 fF RL = 100 kΩ CL = 100 fF M5 M8 M10 M2 M6 Illuminated Photodiode Model: CS Is M10: (W/L)9 = 512/1 (µm/µm) V + = 1.5 V RS Iout Device Capacitance Data: IN OUT X (a) [4 pts.] What is the numerical value of the total capacitance Cin between the input node IN and small-signal ground (in fF)? You can consider any node connected to a DC voltage source through a diode-connected MOSFET to be effectively at small-signal ground. Also, assume VSB1 = 0 V. List all relevant capacitances symbolically (e.g., Cgs1) before calculating their values. Cin = _________fF 10 (g) [3 pts.] What is the –3dB frequency ω1 for this amplifier in Mrad/s, according to the open-circuit time constant method? If you couldn’t do parts (a)-(f), you can assume here that Cin = 120 fF, CX = 225 fF, and τout = 35 ns – all incorrect answers, of course. ω1 = _______Mrad/s (h) [2 pts.] The bandwidth is not high enough, so you decide to add a 3rd stage. Which CMOS 3rd stage, if any, would improve the bandwidth of this amplifier? Circle one answer and justify it. Circle one: 1. CS 2. CG 3. CD 4. None Justify your choice in one or two sentences: 11 3. New CMOS amplifier configuration [25 points] n-well (dark) select (both) poly (clear) metal (clear) n-well (dark) oxide (dark) select (both) contact (dark) oxide (dark) 3 4 poly (clear) contact (dark) metal (clear) 1 µnCox = 50 µA/V2, VTn = 1.0 V, λn = 0.05 V-1 µpCox = 25 µA/V2, VTp = -1.0 V, λp= 0.05 V-1 Node Voltages: 1: Input, 2: VDD = 2.5 V, 3: VSS = 0 V; 4: Output 12 µm 6 µm 1 µm 1 µm y [µm] 0 1 2 3 A A’ 2 Cox = 2 fF/µm2 n-well CMOS process: starting material: boron-doped silicon, conc. 1 x 1016 cm-3 1. Deposit 500 nm of thermal silicon dioxide and pattern using the well mask 2. High-energy phosphorus implant; rapid-thermal anneal to form 2 µm-deep well with only a 0.5 µm-wide lateral spread of phosphorus under the well mask pattern (through the end of the process) 3. Etch off oxide, deposit 500 nm of silicon dioxide, pattern with oxide mask 4. Grow a 2.5 nm-thick gate oxide 12 5. Deposit 250 nm of heavily phosphorus-doped polysilicon and pattern with poly mask 6. Implant boron using photoresist patterned with the select mask (dark field) as an implant mask; strip resist. 7. Implant arsenic using photoresist patterned with the select mask (clear field) as an implant mask; strip resist. 8. Rapid-thermal anneal to form 0.25 µm-deep regions that spread laterally by LD = 0.1 µm. Net doping conc. for both n and p type source/drain regions: 5 x 1018 cm-3. The polysilicon layer is n-type at the end of this step. 9. Deposit 500 nm of silicon dioxide and etch 502.5 nm of oxide with the contact mask 10. Deposit 500 nm of aluminum and pattern using the metal mask (clear field). (a) [5 pts.] Draw the cross section along A-A’ on the graph below. The locations of the mask edges have been indicated on the x axis scale for your convenience. Label any ion- implanted regions in the substrate. - 0.25 y (µm) z (µm) 0.25 0.5 1 0.75 -0.5 Edge of select mask 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 -1 -0.75 Edge of select mask Edge of oxide mask 3 Edge of oxide mask Edge of con- tact mask Edge of metal mask 1.5 1.25 (b) [4 pts.] Draw the schematic of the circuit corresponding to this layout, including the connections for all four terminals and the (W/L) ratios of any MOSFETs in the circuit. Note that nodes 1-4 are defined below the schematic on p. 11. 15 4. Feedthrough model [20 points] Vd + - Cp Cp Rb + - Ix Iin If Rm Iin + - Vout Ideal Transresistance Amplifier MR This circuit model represents substrate feedthrough around a MEMS resonator (MR). (a) [5 pts.] Find an expression for the phasor feedthrough current If in terms of the drive voltage Vd. Do not simplify the expression for this part. (b) [5 pts.] Find an expression for the output voltage Vout,f due to If (that is, with Ix set to 0 A). Your answer should be expressed as Vout,f / Vd and must be reduced to the form of one pole and a numerator proportional to ω2. 16 (c) [5 pts.] On the graph below, plot the magnitude Bode Plot for the transfer function Vout,f / Vd. The parameters are: Cp = 500 fF, Rb = 500 Ω, and Rm = -1 MΩ. If you couldn’t solve part (b), you can plot the transfer function: 1 2 , /1 ωω ω j K V V s fout + = where K = 5 x 10-16 s2 and ω1 = 8 x108 rad/s. ω (rad/sec) |Vout,f / Vs| dB 60 80 104 105 106 107 108 109 1010 1011 40 20 0 -20 -40 -60 -80 1012 -100 -120 -140 17 (d) [5 pts.] If a drive voltage waveform is vd(t) = 100 mV cos[(10 Mrad/s)t] is applied to the input, what is the output voltage waveform due to feedthrough, vout,f (t)? Use your results from parts (b) and (c), or the alternative transfer function given in part (c)