Electronic Devices Paper

Electronic Devices Paper - NATIONAL UNIVERSITY OF SINGAPORE...

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Unformatted text preview: NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION FOR (Semester II: 2004/2005) EE2004 — ELECTRONIC DEVICES April 2005 — Time Allowed: 2 Hours INSTRUCTIONS TO CANDIDATES: 1. This paper contains FOUR (4) questions and comprises NINE (9) printed pages. 2. Answer all questions. Start each question on a new page. 3. The questions carry equal marks. 4. The following information can be used where applicable: Elementary charge e = 1.602 x 10'19 C Planck constant k = 6.626 x 10'34 J s Speed of light in vacuum 0 = 2.998 x 108 m s"1 Boltzmann constant k = 1.381 x 10’23 J K'1 = 8.618 x 10—5 eV K’l Thermal energy (T: 300 K) kT = 0.02586 eV Free electron mass m0 = 9.109 x 10‘31 kg Permittivity of free space 80 = 8.854 x 10‘14 F cm"1 Temperature conversion 0 °C 5 273.15 K 1 Angstrom 1 A E 10‘]0 m For silicon at 300 K: Bandgap E g = 1.12 eV Effective density of states in conduction band N C = 2.80 x 1019 cm"3 Effective density of states in valence band N V = 1.04 x 1019 cm"3 Intrinsic carrier concentration ni = 6.73 x 109 cm"3 Electron affinity x = 4.15 eV Relative permittivity of silicon a, = 11.8 Relative permittivity of silicon dioxide 6, = 3.8 5. A list of equations is given in the APPENDIX for your reference. Q.l (a) (b) (c) (d) EE2004 Electronic Devices / Page 2 An abrupt-junction long-based silicon pn diode consists of an n-type region that is uniformly doped with donors at a concentration of 1018 cm_3, and a p-type region that is uniformly doped with acceptors at a concentration of 1015 cm‘3 . The temperature is 300 K. Give an example of an element that can be used to dope the p-type region. (2 marks) The diode is at thermal equilibrium. You may assume full—ionization of the dopants. Express your answers below in units of eV. 0) Determine the position of the conduction band edge relative to the Fermi level for the neutral n-type region. (ii) Determine the position of the conduction band edge relative to the Fermi level for the neutral p-type region. (iii) Sketch the energy band diagram, indicating the band edge positions relative to the Fermi level. Indicate the value (in eV) of the barrier height on the energy band diagram. (6 marks) The diode is now reverse biased. At a particular reverse—bias voltage, the depletion layer width in the p-type region is found to be 8.0 pm. (i) Determine the width of the depletion layer in the n-type region. Sketch the space-charge density along the length of the diode. (ii) Determine the peak electric field (in V/cm) in the diode. Sketch the electric field along the length of the diode. (iii) Determine the reverse bias (voltage) applied across the diode. (13 marks) The diode is now forward biased. Sketch the small-signal equivalent circuit for the diode, indicating the functional name of each equivalent circuit element. (4 marks) Q.2 (a) (b) (c) (d) (6) 15132004 Electronic Devices / Page 3 An npn bipolar junction transistor is biased with the voltages as shown in Figure Q.2a. Under these biasing conditions, the widths of the neutral regions are as shown in Figure Q.2.b. The transistor is at 300K. The following parameters are given: Minority carrier lifetime Vcc Depletion regions Contact Contact 0V (8) Figure 0.2 Determine the minority carrier diffusion lengths in the emitter, base, and collector regions. Express your answer in inn. (3 marks) Sketch the majority and minority carrier distributions along the transistor in the neutral regions, indicating the position of the emitter and the collector contacts. “Label the electron and hole distributions clearly. Indicate on your sketch the thermal equilibrium carrier distributions, and their values, in the three neutral regions. (Use dashed/dotted/mfferent coloured lines to clearly distinguish the thermal equilibrium carrier distributions). (7 marks) What can you say about the base transport factor of this transistor? Justify your answer. You need not calculate the base transport factor. (3 marks) Determine the electron and hole current densities in the base at the edge of the base- emitter depletion region, stating any assumptions made. (8 marks) Determine the common emitter current gain, stating any assumptions made. (4 marks) Q-3 (a) (b) (c) EE2004 Electronic Devices / Page 4 Gold (Au), with a workfunction of ed) M = 4.8 eV, is contacted to an arsenic doped silicon wafer with a doping concentration of 1x1017 cm‘3 to make a Schottky diode. Determine the Schottky barrier height and built-in potential at 300 K. (5 marks) Now we want to change the Schottky contact of part (a) into an ohmic contact by adjusting the arsenic doping concentration. The silicon type should remain n-type. Discuss how the arsenic doping concentration should be modified. (5 marks) The capacitance-voltage characteristic curve of a reference MOS capacitor fabricated on a p-type silicon wafer is measured as shown in Figure Q.3. Other MOS capacitors are also fabricated with some variations of process conditions. Sketch the C-V curves of the other MOS capacitors under the conditions below, superimposed on the C-V curve of the reference MOS capacitor. Explain the shape of your sketched C—V curve. (i) When the substrate doping concentration is lower; (5 marks) (ii) When a larger amount of positive oxide charge is present at the metal gate / oxide interface; (5 marks) (iii) When a larger amount of positive oxide charge is present at the oxide / substrate interface. (5 marks) C/Cox Figure 0.3 Q4 ((1) (e) EE2004 Electronic Devices / Page 5 A MOSFET is biased as shown in Figure Q4. The gate oxide thickness is 100 A, and the threshold voltage of the transistor is 0.5 V. The channel width and length of the transistor are 10 um and 1 pm, respectively. The subthreshold swing (S) of the device is 100 mV/decade. Assume that the channel electron mobility is constant at 500 cmZ/V-s. The threshold voltage is defined as the gate voltage at which the drain current: 1 HA. ..... ..+5V ........ Figure 0.4 Determine the on-state drain current. (5 marks) Determine the off-state drain current. (5 marks) If channel length modulation is not negligible and the effective channel length (Leff) is 0.8 pm, determine the on—state and off-state drain currents. Assume that the threshold voltage and subthreshold swing remain the same. (5 marks) Determine the linear transconductance (gm) when the drain voltage (VD) = 0.1 V. Ignore channel length modulation. (5 marks) If VB is negatively biased rather than grounded, how will the on-state drain current change? Explain the mechanism underlying the change. (5 marks) END OF QUESTIONS EE2004 Electronic Devices / Page 6 APPENDIX (1) General 1. Coulomb’s force law F = —q-1£1-2— 4 Izursor2 2. Photon energy E = hf = ha) = hC/l . . gogrA 3. Capac1tance of a parallel-plate capac1tor C = a, (II) Semiconductor Equations 2 1. Law of mass action Pono = "i 2. Space—charge density P = 9(1) + N 5 ’ n ‘ N :1 ) 3. Electron concentration at thermal equilibrium "0 = NC expi“ (E C — EF )/ le or no =niexpl(EF ~EFi)/kTJ Hole concentration at thermal equilibrium P0 = NV expi‘ (E F ‘ E V )/ le or p0 =nieprEFl. —EF)/kTJ 4. Fermi-Dirac distribution function f F (E ) = 1 1+ exp[(E-—EF)/kT] 5. Effective density of states in the conduction N 2[ 2m;kT]3/2 C = band h 2 . . . 3/2 6. Effective denSIty of states in the zmyd‘ valence band NV = 2 h 2 7. Conductivity o- : Any" + ppp) 8. Drift mobility . y = ff. * m 9 Current densities d" - J =en,un£+eDn—— " dx d JP = epppr—er a!) 10. Einstein Relation M & kT 11. 12. 13. 14. 15. 16. 17. 18. Continuity Equations for minority carriers (low-level injection) Excess minority carrier concentrations as a function of time, decaying from initial excess carrier concentrations. Excess minority carrier recombination rate under low-level injection conditions. Poisson’s equation Excess carrier concentration with respect to position for an abrupt pn junction diode under low-level injection conditions Excess carrier concentration at the edges of the space—charge region of an abrupt pn junction diode under low-level injection conditions. Minority carrier diffusion lengths. Injected current densities across an abrupt, long-base pn junction. EE2004 Electronic Devices / Page 7 a 6n at e 6x Tn aJ a§n=_l_p+grp_®n t e 6x I], anpo) = 6np(0)exp(-r/rn) amt) = 6pn(0)exp(—t/rp) on R; = p ; = 6p)! In 1,, LE =11 _ xix) dx dxz 6,60 = e (P‘"+ND “JV/1) 8,80 6np(x)=6np(— xp)exp[ 6Pn (x)=&’n (xn exp[" x+x ‘0 19. Ideal diode current density-voltage equation for 20. 21. 22. 23. 24. 25. 26 27 28. 29 an abrupt, long-base pn junction diode. Junction capacitance of an abrupt pn junction diode. Emitter injection efficiency of an npn bipolar junction transistor Common base current gain of a bipolar junction transistor Common emitter current gain of a bipolar junction transistor. Incremental resistance of emitter-base junction under forward bias Transconductance of a bipolar junction transistor . Capacitance of oxide in MOS structure . Capacitance per unit area of oxide in MOS structure Threshold voltage of an n-channel MOS Transistor . Maximum depletion width under inversion in MOS capacitor EE2004 Electronic Devices / Page 8 D D Jo = ei:Ln npo+L—ppno] ’1 P = en2 D" + DP ' LnNA LPND 1/2 C =A 8808,. NAND J ziVo—Vi NA+ND I y=IEn E I an. [—6 E I B= f B i _ fl :1 r1, dV kT F dIC gm‘ dVBE ‘ iaoIE 'I‘C— kT VT A COX = eoxa, ox CIOX_ :on ox VT=VFB—CQO:.+2¢I; =¢MS_ QSS +2VeNA8si¢b +2¢b COX' COX' W _ 25si¢s m eNA EE2004 Electronic Devices / Page 9 30. Drain current in linear region I = [C [ V _V V _lV2 D #nL 0X(G T)D 21) 31. Drain current in saturation region ID = _1_ # [COX (VG _ VT)2 2 " L 32. Transconductance of a MOSFET gm E “’1 D dVG END OF PAPER ...
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Electronic Devices Paper - NATIONAL UNIVERSITY OF SINGAPORE...

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