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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 abruptjunction longbased silicon pn diode consists of an ntype region that is
uniformly doped with donors at a concentration of 1018 cm_3, and a ptype 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 ptype 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 ntype region. (ii) Determine the position of the conduction band edge relative to the Fermi level
for the neutral ptype 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 ptype region is found to be 8.0 pm. (i) Determine the width of the depletion layer in the ntype region. Sketch the
spacecharge 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 smallsignal 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) Q3 (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 builtin 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 ntype.
Discuss how the arsenic doping concentration should be modiﬁed. (5 marks) The capacitancevoltage characteristic curve of a reference MOS capacitor fabricated
on a ptype silicon wafer is measured as shown in Figure Q.3. Other MOS capacitors
are also fabricated with some variations of process conditions. Sketch the CV
curves of the other MOS capacitors under the conditions below, superimposed on the CV 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/Vs. The threshold voltage is deﬁned as the gate voltage at which the drain
current: 1 HA. ..... ..+5V
........ Figure 0.4 Determine the onstate drain current.
(5 marks) Determine the offstate 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 offstate 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 onstate 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 = —q1£12—
4 Izursor2
2. Photon energy E = hf = ha) = hC/l
. . gogrA
3. Capac1tance of a parallelplate 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. FermiDirac 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 (lowlevel injection) Excess minority carrier concentrations as a
function of time, decaying from initial excess carrier concentrations. Excess minority carrier recombination rate under lowlevel injection conditions. Poisson’s equation Excess carrier concentration with respect to
position for an abrupt pn junction diode under lowlevel injection conditions Excess carrier concentration at the edges of the
space—charge region of an abrupt pn junction diode under lowlevel injection conditions. Minority carrier diffusion lengths. Injected current densities across an abrupt, longbase 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 densityvoltage equation for 20. 21. 22. 23. 24. 25. 26 27 28. 29 an abrupt, longbase 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 emitterbase 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 nchannel 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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