335-final
.pdf
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University of Toronto**We aren't endorsed by this school
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ECE INTRODUCTI
Subject
Electrical Engineering
Date
Dec 16, 2024
Pages
17
Uploaded by ChiefMagpie644
UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING FINAL EXAMINATION, December 2018 DURATION: 2.5 hours ECE3351-11 F - Introduction to Electronic Devices Calculator Type: 2 Exam Type: D Allowed Aids: Course textbook, notes Examiner: J. K. S. Poon Instructions: Please write your work in the space provided and the final answer in the box corresponding to the question if available. The exam has 5 parts (Short answers + 4 problems). Each part is worth 20 points. For instructor use only 0.1 0.2 0.3 0.4 0.5 Total Name (last name, first name): Student Number: Page 1 of 17
Useful Constants Constant Planck's constant h Planck's constant h = h/27 Charge of an electron Mass of an electron m0 Boltzrnann's constant k Permittivity of free space € Value 6.626 x 104 m2kg/s 1.055 x 10 m2kg/s 1.602 x 1019 C 9.11 x i01 kg 1.38 x 10-23 J/K 8.854 x 10-12 F/rn Some Properties of Silicon at 300 K Property Value Dielectric constant 11.8 Bandgap energy 1.1 eV Electron affinity 4.0 eV N 2.8 >< 1019 crn3 N 1.04>< io' crn3 Intrinsic carrier concentration 1.1 x 1010 crn3 Electron effective mass (m/m0) 0.26 Hole effective mass (rn/rn0) 0.39 Dielectric constant of SiO2: 3.9 Hyperbolic Functions ex - exsinh(x) = 2 cosh(x) = ex + e 2 tanh(x) = sinh(x) cosh(x) Page 2 of 17
1. (20 points) Short answers (a) (1 point) Sketch the plane with Miller indices (201). Clearly label the lattice constant, a. (a) (b) (2 points) Semiconductors A and B have the same bandgap of 1 eV. A has an indirect bandgap, and B has a direct bandgap. You have material samples of A and B with the same thickness and cross-section area. (b) Which sample absorbs more light? A B Which sample can emit more light? (ii) A B (select answer) (c) (1 point) You have a sample of N-type Sillycon with resistivity pN, and a sample of intrinsic Sillycon with resistivity p,. What value does PN/Pi(c) i/p, approach as the temperature is raised to the melting point of Sillycon? (d) (1 point) The overall charge in the depletion region in (d) Positive Negative Zero a PN junction is . (select answer) (e) (4 points) Quantum confinement changes the density of states. For example, the density of states of quantum wells is constant, and the density of states of quantum wires is proportional to 1/V. What is expected form of the current vs. voltage (It') relation of a PN junction made in materials containing multiple quantum wells, wires, or dots, assuming complete impurity ionization? Will it have the form of I = 10 [exp () - 11? Why or why not? Page 3 of 17
(6 points) Consider a Si NMOS with doping concentration Na and a N poly-Si gate at 300K. Complete the table below for how the threshold voltage, V, changes with the specified change of each parameter. - Na Tox Gate Gate length Vdd Body increased increased replaced with decreased increased changed to Pi- poly-Si P-type Ge* Increased Increased Increased Increased Increased Increased Vt Reduced Reduced Reduced Reduced Reduced Reduced Unchanged I Unchanged Unchanged I Unchanged I Unchanged I Unchanged (select one for each) *The bandgap of Ge is 0.8 eV. (2 points) Briefly describe and sketch one modern transistor structure deployed in the last 5 years that is not bulk CMOS. (h) (1 point) To have a faster (i.e., higher bandwidth, lower (h) v switching delay) transistor at the same Vdd, should Vt be Increased Decreased increased or decreased? (select answer) (I) (1 point) To have a lower leakage current at the same Vdd, (i) V should Vt be increased or decreased? Increased Decreased I(select answer) (j) (1 point) Three doping concentrations are available for a BJT: 1018, w 1017, 1016 CM-3. Which concentration should be assigned to the Nc collector, base, and emitter for optimal operation? NB NE Page 4 of 17
2. (20 points) A PN Junction Solar CelVPhotodetector The figure below shows a Si PN junction at 300 K illuminated with light. The shaded region in the centre is the depletion region. Assume the light is uniformly absorbed in the device. 11111MIT1111111 1,17 1,17 The impurity concentrations are Na = Nd = 1015 cm-3; the mobilities are Pn = 1400 cm2/Vs, pp = 480 cm2Ns; and the minority carrier lifetimes are Tn = Tp = 1 ns. The lengths of the P and N regions are W = WN = 20 pm. The electron-hole pair generation rate is G = 3 x 1018 cm-3 1 in the device. (a) (5 points) What are the minority carrier diffusion lengths in the P and N regions expressed in micrometers? Does the infinitely long diode approximation apply? (a) L (pm) L(pm) Infinite diode approx.? Yes No (select answer) (b) (5 points) Find the expressions for the excess minority carrier concentrations in the P and N regions as a function of V. Assume the usual non-equilibrium boundary conditions for G = 0 hold at the depletion region edges, Xn and -xp. Clearly explain your steps. Do not substitute numerical values yet. Page 5 of 17
(b) (I) n'(x) (ii) p1' (x) Page 6 of 17
(C) (5 points) What is the current density vs. voltage (J vs. ') relation of the diode? Substitute the numerical values to express the current density in iA/cm2. (c) J vs. V (in units of iiA/cm2) Page 7 of 17
(d) (3 points) Sketch the J vs. V relation. Mark the short circuit current density (J) and the open circuit voltage (V00). Indicate on the plot how an increased generation rate modifies the J vs. V relation. (e) (2 points) Mark on the plot in (d) the operation regimes for (i) a solar cell (i.e., a device that generates power), and (ii) a photodetector. Page 8 of 17
3. (20 points) An SOS Capacitor Consider a semiconductor-oxide-semiconductor (SOS) capacitor made out of Si at 300K as shown below. The oxide is ideal (no trapped charges) and has a thickness of To, = 50 nm. The doping concentrations are Na = Nd= 1017 CM-3. T0 VgIE io;1j (Nd) (a) (6 points) Sketch the energy band diagrams at (i) equilibrium, (ii) Vg = 2V, (iii) Vg = -2V. Clearly label the quasi-Fermi energies, conduction and valence band edges. (i) Equilibrium (ii) Vg = 2V (iii) Vg = -2V (b) (3 points) What is the flat-band voltage? Page 9 of 17
(b) Vfb (V) (c) (6 points) What is the threshold voltage? (b)V1(V) Page 10 of 17
(d) (3 points) Sketch the charge distribution when Vg = 2V. Sketch the circuit model to determine the capacitance at Vg = 2V. Give the expressions for the total capacitance, and the capacitances in the N-Si, oxide, and P-Si in terms of the oxide thickness and depletion widths. Charge distribution Circuit model with capacitance expressions (e) (2 points) Sketch the high frequency C-V curve. Page 11 of 17
4. (20 points) Design a MOSFET Design a Si PMOS without body bias for operation at 300 K. The designed MOSFET should have the highest while achieving a threshold voltage of -0.2 V. Below are the device properties that the design is restricted to: Poly-Si gate Supply voltage (i.e., max lVgsl, lVdsl) of 1 V Oxide thickness: 2: 8 nm Channel length ~t 500 nm Channel width = 1 urn Oxide sheet charge density of 10-7 C/cm2 Channel mobility of 200 cm2Ns (a) (12 points) Specify the gate type, substrate doping type, doping concentration, oxide thickness, and transistor length. You can neglect short channel effects. Explain your choices. Page 12 of 17
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(a) Gate doping type: P or N Substrate doping type: P or N Substrate doping concentration (cm-3): Oxide thickness (nm): Transistor length (urn): (b) (4 points) What are the I, and loff of your transistor in (a) at 300K? (b) QiA) loff (pA) (4 points) Sketch the energy diagram and charge distribution diagram when Vgs > V1. Clearly label the quasi-Fermi energies, Er and E. Is the MOS is in inversion, depletion, or accumulation? Energy Diagram Charge diagram Inversion Depletion Accumulation (choose one) Page 14 of 17
5. (20 points) Bipolar Junction Transistors A Si NPN transistor at 300 K has doping concentrations of NE = 1019 cm-3, NB = 1015 cm-3, and Nc = 1014 cm-3. At thermal equilibrium, the neutral emitter, base, and collector widths are 100 nm, 500 nm, and 50 pm. The device cross-section area is 0.5 mm2. In the emitter, base, and collector, the carrier lifetimes are IE = 5 ns, TB = 10 ns, Tc = 100 ns, respectively. - ---------------- I II1. I III I IIII 1111111 11111111 I_r_ILLIJ lO 10' 1 1D' lo",1018 1019 1031 Na + Nd (ions/cm) (6 points) Using the mobility plot above, determine the diffusion lengths in the emitter, base, and collector. Express the answers in units of pm. (a) LE (pm) LB (pm) Lc (pm) (2 points) Does the approximation of short emitter, short base, and infinitely long collector (b) Yes No Reason: apply? Why? Page 15 of 17 1600 1400 1200 1000 - 800 600 400 200 'iT
(c) (3 points) What are the emitter efficiency, common base current gain, and common emitter current gain using equilibrium values? /JF (d) (5 points) Find the width of the quasi-neutral base region for VBE = 0.5 V and VCB = 3 V. (d) WB (nm) Page 16 of 17
(e) (1 point) For the bias values in (d), what is the collector current (Ic)? (d) Ic (mA) (f) (3 points) Sketch (i) the energy diagram for the BJT in cut-oft with IVBCI > IVBEI and (ii) the corresponding minority carrier concentrations in the quasi-neutral regions of the BJT. Clearly label E, E, and the quasi-Fermi energy levels in (i), and the carrier type in each region in (ii). The shaded regions below are the depletion regions. I (i) Enerqy diaqram in cut-off I (ii) Minority carrier concentrations in cut-oft I E B C Page 17 of 17