1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE TECHNICAL QUALIFYING EXAMINATION May , 2008 NAME__________________________________________________________ Topic Area: 6.012 – Microelectronic Devices and Circuits General Instructions: 1. Please do all of your work in the spaces provided in this examination booklet. If you need additional sheets, be sure to put your name and the name of the examination on each sheet. 2. At the end of the examination, please put this booklet and any extra pages you have used in the envelope provided Special Instructions for 6.012 • Some possible useful formulas and material properties are included on pages 14-20 • Where required, make reasonable approximations and state them clearly. • Partial credit will be given for setting up problems without calculations. No credit will be given fro answers without reasoning. • Every numerical answer should have the proper units next to it. Points will be subtracted for answers without units or incorrect units. For examiner’s use only: Satisfactory ______________ Marginal ______________ Unsatisfactory ______________2Problem 1 [40 points] Diodes D1 and D2 are identical except for their cross sectional areas: A2 = 10 A1. They are connected in series as shown below. (a) [5 points] What is the incremental resistance between X and Y? rXY = _________________ (b) [5 points] What is the difference between the two voltages V1 – V2? [Zero is not acceptable answer] V1 – V2 = _____________________________________3 The n+-p diode (D1) has the following characteristics: A1 = 10 μm x 10 μm, Nd = 1020 cm-3, Na =1017 cm-3, Wn = 0.5 μm, Wp = 1 μm. Use De=20 cm2/s and Dh=5 cm2/s. For this problem assume that recombination only occurs at the contacts. No recombination in Space Charge Region (SCR) or Quasi-Neutral Regions (QNR’s). (c) [5 points] Calculate the value of the saturation current, IS. {Assume xp=0.11 μm} IS = _______________4For 1(d), 1(e) & 1(f), the diode is forward biased such that ()15 310ppnx cm−= . (d) [5 points] Calculate the applied voltage, VD. VD = _______________ (e) [10 points] Calculate the ratio of electron current density to hole current density, K=Je/Jh, in the p-quasi-neutral-region (p-QNR). Explain your reasoning. [You can assume that xp << Wp and –xn << -Wn, that is, the widths of both SCR's are much smaller than those of the QNR's] K = _______________5(f) [10 points] Assume that for charge neutrality()()pppxnx′′≈ , where popppxpp −= )(' and noppnxnn−= )(' . Since we are at Low Level Injection (LLI) condition ()pp ponx p⎡⎤<<⎣⎦, you can assume that ()pp popxp′<< . Calculate the magnitude of the electric field in the p-quasi-neutral region (p-QNR). {Hint: Remember that there is a concentration gradient for majority carriers too!} E = _________________6Problem 2 [40 points] A 3-terminal MOS structure is fabricated on a p-type silicon substrate with a n+-doped Si gate (Nd=1020 cm-3); the gate material thermal equilibrium potential is φn+=0.55 V . The substrate doping is Na=1017 cm-3, and the oxide thickness, tox=10 nm. The doping of the n+ contact region is Nd=1020 cm-3. (a) [5 points] What is the value of the contact junction, n+-p, built-in potential, φJ? φJ=______________ (b) [5 points] What is the value of the flatband voltage, VFB? VFB=______________ n+VV+ - -V CB GBn+pBCG+ -+ ---V CB GBn+pBCGVV+ -+ --V CB GBn+pBCG+ -+ -V CB GBn+pBCGn+- +7(c) [15 points] With VCB1=0 V and VGB1=5V find the inversion charge density (charge per unit area), q*N1. q*N1 =_________________8 (d) [15 points] A contact-to-body voltage, VCB2=3 V is applied. Find the gate-to-body voltage VGB2 at which the magnitude of the channel charge is equal to its value for VGB=5 V, VCB=0, i.e. q*N2 (VGB2, VCB=3V)= q*N1 (VGB1=5 V, VCB1=0). Explain clearly. VGB2=______________9Problem 3 [40 points] You are given the multistage amplifier with device data shown below. Transistors M4, M7, M9, and Q1 constitute the four amplifier stages and the rest of the transistors form the bias circuitry. All MOSFETs are nominally biased in saturation and the BJT is in the forward active region of operation. Also: • Assume that the body of each MOSFET is connected to the source. • For parts a – c, neglect channel length modulation, i.e. λ = 0, and basewidth modulation, i.e. |VA| → ∞. PMOS NMOS BJT VTp = -0.7V VTn = 0.7V βF = βo = 100 μpCox = 25μA/V2 μnCox = 50μA/V2 VA = | 20 |V λp = 0.05V-1 λn = 0.05V-1 VCESAT = 0.2V (W/L)p =40/2 (W/L)n = 20/2 M2M1M3M6Q1vOUTM7M8M102.5 VvsVBIASRS+−+−IREF100 μAM5M4M9-2.5 V10(a) [5 points] Determine the current through each leg of the circuit i.e. the drain current of M3, M5, M6, M9 and M10?. ID3______________________ ID5______________________ ID6______________________ ID9______________________ ID10______________________ (b) [5 points] Determine VGS for M1 and VSG for M2. VGS1=______________________ VSG2=______________________11(c) [10 points] Calculate the output resistance of the amplifier, Rout. Rout=_______________12(d) [15 points] Calculate the voltage gain, Av0=vout/vin of the amplifier. {hint: You must include the output resistance of supply current source transistors} Av0=___________________13(e) [10 points] For this part you are also given that C*ox=3 fF/μm2, from which you can calculate the gate-source capacitance, Cgs, of the MOSFETs. You are also given that the gate-drain capacitance per unit width in
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