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ECEN 231 QUESTION ONE (30 Marks) a) Find the length of a silicon bar having a S-um x 4-um cross section and having free-electron and hole densities of 104/em? and 10!°/cm? respectively, so that 0.2 mA current flows when 1 V is applied end-to-end. Use in = 1200 cm’/V.s and pp = 500 cm?/V.s. (4 marks) b) Differentiate between Avalanche breakdown and Zener Breakdown (2 marks) uy lov + +4 ut +r ¢ 0 _ uy vo 6 vf 4 ‘ - fa) {b) Figure Q1_b c) Figure Q1_b (a) shows the waveform of the, input voltage in figure Q1_b (b), sketch the waveform of the output voltage vo (2 marks) d) Proof that if diode current increase by a factor of 10, the voltage across the diodeis approximately 60 mV (5 marks) e) State three differences between BJTs and MOSFETs (3 marks) f) An NMOS transistor with &, = 4 mA/V? and V;= 0.5 V is operated with Ves = 1.0 V. i) At what value of Vas does the transistor enter the saturation region? (2 marks) ——————~ ji) - What value of 7p insaturation? omnes sere (2 marks) g) Assuming no interface charge due to defects and/or traps, would decreasing the oxide thickness/increasing the oxide capacitance of an n-channel MOSFET increase, decrease, or leave essentially unchanged the following parameters i) the flat band voltage, Vr? (2 marks) ii) the threshold voltage, Vr? (2 marks) iii) the subthreshold slope? (2 marks) Support your answer h) Using the given circuit in Figure Q1_h and assuming the positive sign on the secondary side of the transformer indicates the terminal is positive during the positive half cycle, fill in the table (2 marks) “Transforming Lives through Quality Education” . Page 2 of 6 i ey tee ECEN 231 ¥, = Vpsinaw = Figure Qi_h cycle ON diode Off diode Positive half cycle De Du br 3 Negative half cycle D Bap Or Ose u QUESTION TWO (20 Marks) . a) A PN junction is initially designed to have Na= 107° cm? manufacturing the doping concentration used was Na=! Find the percentage change in; i) Built-in potential (4 marks) ii) Depletion width (4 marks) iii) Depletion region penetration depth in the, (4 marks) b) A variable reverse bias voltage 2 V to 5 V is aj ef the junction specified in (a), i) Explain how the depletion W is affected (3 marks) ii) Explain how the junction capacitance is affected (3 marks) iii) Calculate the maximum depletion width {2 marks) “Transforming Lives through Quality Education” Page 3 of 6 ~ We COmPpave Resstare e Ane alsy As ol es S- U0 bar Pup) Eaves A> Wx: sky mh ECEN 231 QUESTION FOUR (20 Marks) a) Explain the working of a MOS capacitor (5 marks) b) Sketch the typical output characteristics of an N-Channel MOSFET and show different operation regions (4 marks) ¢) An NMOS transistor with kn = 5 mA/V? and V; = 0.4 V is operated with Vos = 0.6 V. At what value of Vps does the transistor enter the saturation region? What value of ip is obtained in saturation? (5 marks) d) A circuit designer intending to operate a MOSFET in saturation is considering the effect of changing the device dimensions and operating voltages on the drain current Jp. The following were the findings: i, | When the channel length is doubled the /p reduced by half. ii, | When the channel width is doubled the /p doubled. iii. | When the overdrive voltage is doubled the Jp is 4 times Jp. Justify the designer's findings mathematically. - (6 marks) QUESTION FIVE (20 Marks) A ee a) Sketch the typical output characteristics of'a NP transistor and label the operation regions al le: (4 marks) b) Measurement of an "pn BJT in a particular circuit shows the base current to be 14.46 pA, the emitter current to be T.460 mA, and the base-emitter voltage to be 0.7 V. For these conditions, calculate a, B, and Js. ~ (6 marks) c) Given a BJT circuit, explain how you would determine whether the transistor is saturation mode (4 marks) d) An npn transistor having Js = 105A and £ = 100 is connected as follows: The emitter is grounded, the base is fed with a constant-current source supplying a de current of 10 »A, and the collector is connected to a 5-V de supply via a resistance Rc of 3 kQ. Assuming that the transistor is operating in the active mode, find Var and Vc, then use these values to verify active-mode operation. (6 marks) “Transforming Lives through Quality Education” Page 5 of 6 ECEN 231 Constants and Basic formulas Physical Constants: Vacuum permittivity: & = 8.85 x 10 F/em Planck's constant: hh = 6.63 x 10°4 J-s Speed of light: c=3.0x 10" cni/s Electronic charge: = gq = 1.60x 10°C Electron rest mass: me = 9.11 x 10%! kg Boltzmann coustant: ke = 1.38 x 10° J/K Thenmal energy at 300K: kT = 0.0259 eV Energy unit conversion: LeV=1.60x 10%) Si materi . Band gap energy at 300 K: Ey = 1.124eV Relative permittivity: ¢ = 11.7 Effective mass of electron: m, == 1.08m, for density of states, — m, = 0.26m, for conductivity Effective mass of hole: m, =0.81m, for density of states, m1, = 0.3977, for conductivity Mobility: Ha = 1400 em/V's, Mp = 470 cm/V's, Diffusion coefficient: Da = 36 cn"Vs, Dp = 12 cm*/s ~~ ~ Effective density of states at 300K: ~ Nc = 2.82 x 10 cm? Ny = 1.83 x 10"? cm? Intrinsic carrier concentration at 300K: m= 8.2.x 10° cm? mya BT a3 10% om K™ Junctions and Diodes tenmn(e) Wanctsy= i i BIT igs bee = AygD rg St LL EL bid 2) 1 D badd deeded 
