This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: NATIONAL UNIVERSITY OF SINGAPORE EXAMINATION FOR
(Semester I: 2006/2007) EE2004 / EE2004E — ELECTRONIC DEVICES November/December 2006  Time Allowed: 2.5 Hours INSTRUCTIONS TO CANDIDATES: 1. 9‘95"!” 7. This paper contains FIVE (5) questions and comprises EIGHT (8) printed pages.
Answer all questions. Start each question on a new page. All questions carry equal marks. Programmable calculators are not allowed in this examination. The use of the textbook “Semiconductor Physics and Devices” by DA. Neamen
(McGrawHill) is allowed. The textbook can be annotated, but no other material, such as
sheets of paper, which is not part of the textbook, is permitted. The following information can be used where applicable: Elementary charge 6 = 1.60 x 1019 C Planck constant h = 6.625 x 10'34 13 Speed of light in vacuum c = 2.998 x 108 m s"1 Boltzmann constant k = 1.38 x 10‘23 JK'1
= 8.62 x 105 eV K‘l Thermal energy (T: 300 K) kT = 0.0259 eV Free electron mass m0 = 9.11 x 10'31 kg Permittivity of free space so = 8.85 x 10‘14 Fem—1 For silicon at 300 K:
Bandgap Eg = 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
Electron affinity x = 4.01 eV
Relative permittivity of silicon a, = 11.7 Relative permittivity of silicon dioxide 8, = 3.9 A list of equations is given in the APPENDIX for your reference. Q.l (a) (b) (d) EE2004/EE2004E Electronic Devices / Page 2 The semiconductor in this question is a non—uniformly doped silicon sample of
uniform crosssection, and length 10pm. Its energy band diagram is shown in
Fig. Q.1a. It is manufactured from ptype silicon that was originally uniformly doped
with 1017 cm‘g’ acceptors, followed by nonuniform doping with donors along its
length. In this question, use the following parameters: temperature = 300 K, intrinsic
carrier concentration nl = 6.95x109 cm"3 , electron mobility ,un 21500 cm2 /V.s ,
and hole mobility ,up = 450 cm2 / V.s . The carrier mobilities may be assumed to be
independent of doping concentration. Determine the donor concentration at x = 0 and at x = 10m. (3 marks)
Determine the resistivity of the silicon at x = O and at x = 10m. (2 marks)
The sample is now at thermal equilibrium. (i) Sketch the hole concentration as a function of x (on a linear plot). Indicate the
values at x = O and at x = lOum. (ii) Sketch the electron concentration as a function of x (on a linear plot). Indicate
the values at x = O and at x = 10pm. (iii) Sketch the potential as a function of x, and indicate the potential difference
between x = 0 and at x = 10pm. (iv) Sketch the electric field as a function of x. Indicate the values at x = 0 and at
x = 10pm. (v) Determine the hole drift current density at x = O and at x = 10pm. Sketch the
hole drift current density as a function of x, and indicate the values at x=0andatx=10um. (Vi) Sketch the hole diffusion current density as a function of x, and indicate the
values at x = 0 and at x = 10m. (12 marks) The sample is biased externally with a voltage source as shown in Fig. Q.1b. The
voltage along the bar is measured using an ohmic metal contact probe and a voltmeter as shown. Sketch the measured voltage as a function of x along the bar, and brieﬂy explain its shape.
(3 marks) Question Q.1 is continued on page 3. EE2004/EE2004E Electronic Devices / Page 3 Intrinsic Fermi Level El:i _________ C
0.4eV 
EF _$________________;'L‘=
§ aEV
x=0 +10um X Figure Q.1a — Energy band diagram of sample Voltmeter Figure Q.1b — External applied bias, and voltage measurement Q2 (a) (b) A onesided pn junction has a junction capacitance of 50 nF/cm EE2004/EE2004E Electronic Devices / Page 4 ' An abrupt Si pn junction of uniform crosssection has an acceptor
concentration N A :1017 cm‘3 on the pside, and donor concentration
N D =1016 cm"3 on the nside. At T =300K , the excess minority carrier
concentration generated by the forwardbias voltage at the edge of the spacecharge region on the pside is 1014 cm”3 . Take the intrinsic carrier concentration,
nl =1.5x1010 cm‘3. (i) Calculate the applied forwardbias voltage. (6 marks) (ii) Calculate the ratio of the electron current to the hole current within the depletion
region of this pn junction. The electron and hole mobilities are 500 cmZ/Vs
and 350 cmZ/Vs, respectively. The minority carrier lifetimes in the ntype silicon and in the ptype silicon are 2 us and 200 ns, respectively.
(7 marks) 2 measured at a reversebias of 1V and at T = 300K. The builtin potential at thermal equilibrium is 0.7V. Calculate the impurity doping concentration of the lowdoped side.
(7 marks) Q.3 EE2004/EE2004E Electronic Devices / Page 5 An npn bipolar transistor has a cross sectional area of 10—4 cm2 and is biased in the forward—active mode (Fig. Q3). The table below provides some data on the transistor
at this particular bias — these include the diffusion coefficients of the holes and
electrons in the emitter, base, and collector regions, and the minority carrier
concentration in the base, n B (x). Collector x F——I—>
0 B x
"305) 0 JCB x Figure Q.3 D” =6.5cm2/s 1),, =15cm2/s 1),, = 25cm2 /s = 4.75 ><1018 cm‘4 = 4.45 x1018 cm‘4 Find the following transistor parameters: (a) Base transport factor, (1T, (5 marks)
(b) Common emitter current gain, ,8 , (5 marks)
(c) Hybrid7r incremental resistance, r”, (5 marks) ((1) Transconductance, gm. (5 marks) EE2004/EE2004E Electronic Devices / Page 6 Q4 (a) The C—V characteristics of a MOS capacitor fabricated on ptype silicon was
measured at 1 MHz. The threshold voltage of the MOS device is +0.7 V. The
measured capacitances at — 5 V and + 5 V are 450nF/cm2 and SOnF/cmz, respectively. Find the gate oxide thickness and maximum depletion width under
thermal equilibrium. (10 marks) Figure Q.4 (b) Based on the NMOSFET transistor shown in Fig. Q.4, the drain current equation was
derived as follows: The drain current I D is related to the channel charge density Q” by the charge
transit time tTR through the equation ID=—QnWZ ,and tTR L tTR= —— where vd is the drift velocity.
Vd
2
VD L L
Since v =— E: —— , z =_.._—_
d ,un #11 L TR Vd .unVD and the inversion charge Q, is
Qn = *COX (VG — VT) where C0 X is the gate capacitance per unit area, then, W
ID = #11 TCOXU/G ’VT)VD What is the problem with this derivation? Discuss the validity of the expression for
ID above and suggest improvements that can be made to the derivation. With these improvements, obtain a new expression for ID.
(10 marks) EE2004/EE2004E Electronic Devices / Page 7 Q5. The threshold voltages of N— and PMOSFETs in Fig. Q.5a are +0.6V and —O.6V,
respectively. The channel lengths of both N and PMOSFETs are 1 um while the
channel widths of the N— and PMOSFETs are ’10 um and 30 um, respectively.
V61 and V62 are shorted and connected to Vin . V31 V62
Vout Vss = 0 V "Willi llllllll WW all!Ill!!!llllllllllll lllll‘%é%l‘lllll Will! ”Hill!!!“ “III3 v“ comm Figure Q.5a (a) Draw a circuit diagram corresponding to the cross section of the device shown in
Fig. Q.5a. (5 marks) (b) Sketch the input—output characteristics (Vow vs. Vin) when Vin swings between
0 to 5 V. (5 marks) (c) If the channel widths of both N and PMOSFETs are identical, how will the input
output characteristics curve in part (b) be changed? Explain the reason for such a change. (5 marks)
(d) VGl and VG2 are then disconnected and V0“, is grounded. The capacitancevoltage characteristics between VGZ and VSS are then measured at a frequency of lMHz and the C—V curve as shown in Fig. Q.5b is obtained. Is the CV curve measurement
result correct? Explain. (5 marks) Figure Q.5b END OF QUESTIONS EE2004/EE2004E Electronic Devices / Page 8 APPENDIX (1) General
1. Photon energy E = hf = ha) = hc/l . , sogrA
2. Capamtance of a parallel—plate capacrtor C = d
(11) Semiconductor Equations 2 1. Law of mass action Pono = "i 2. Electron concentration at thermal equilibrium "0 = NC exp[—— (EC — EF )/ kT l or no =nz eprEF —EFl.)/kTJ
Hole concentration at thermal equilibrium P0 = N V CXP[— (E F “ E V )/ le
OI‘ p0 =I’li CXpKEFi —EF)/kTJ
1
. F 'D' d't'bt‘ f t' E=—————~—
3 arm irac is n u ion unc ion fF( ) 1+exp[(EEF)/kT]
4. Conductivity o = e(n,un + pyp)
5 Current densities d”
 J” =en,un£+eDn—d—
x
dp
Jp = epyPE—er If;
6. Einstein Relation J = _D_p = k_T
#n it p e
7. Continuity Equations for minority carriers 6" p = +1 aJn + g' _ 5n}!
. . . at e 8x " Tn
(lowlevel injection)
9’2... _l§_‘{_P_ + g' _. @n
at 2 6x p IF
END OF PAPER ...
View
Full Document
 Spring '08
 Tan

Click to edit the document details