UNIVERSITY COLLEGE LONDON
EXAMINATION FOR INTERNAL STUDENTS
MODULE CODE ELEC214P
ASSESSMENT ELEC214PA
PATTERN
MODULE NAME Electromagnetic Theory and Semiconductor
Devices
DATE Wednesday 9 May 2018
TIME 14:30
TIME ALLOWED 3 hrs
This paper is suitable for candidates .who attended classes for this
module in the following academic year(s):
Year
Suitable for all candidates
EXAMINATION PAPER CANNOT BE REMOVED FROM THE EXAM HALL. PLACE EXAM
PAPER AND ALL COMPLETED SCRIPTS INSIDE THE EXAMINATION ENVELOPE
2016/17-ELEC214PA-001-EXAM-Electronic and Electrical Engineering 126
© 2016 University College London
TURN OVER
ELEC 214P

Physical constants
IVelocity ofpropagation of an electromagnetic wave in vacuum c= 1/~&of-lo = 3 x 108 ms­
Permittivity ofvacuum or air: cQ) = 8.85 x 10-12 Fm-I •

Permeability ofvacuum or air: f1D = 47l' x 10-7 Hm-I .

Intrinsic impedance ofvacuum or air: 770 =~f-lo / &0 = 377 Q or 1201t Q.

&SI =11.9 &0
&GaAs = 13.1 &0
&S10 =3.9 &0
2
h =6.63 X 1O~34 Js
k=1.38xlO-23 JK-1
q=e=1.6xlO-19 C
mass of electron = 9.11 x 10-31 kg
For GaAs D =10 cm 2 s-1 and D =22 D p n p
For silicon D =12.5 cm2s-1 p
For silicon N
c
=2.78x 1019 cm-3
For silicon N j =21.5xlOlO cm-3
For silicon f-le =1350 cm2V-1s-1
For silicon X =4.01 eV
Answer TWO questions from Section A and TWO questions from Section B
Use SEPARATE answer books for each section.
Page 1 of6
TURNOVER
ELEC 214P

SECTION A
ANSWER TWO QUESTIONS FROM THIS SECTION
1. (a) (i) For an arbitrary vector field F define and give a mathematical expression of the flux of
F through an arbitrary surface n [4 marks]
(ii) If F is F=rr2 sinB, calculate the flux of F through a sphere of radius a centred in
the origin. [5 marks]
Note: The surface element on the surface ofa sphere ofradius r in spherical coordinates
is given by dO. = r r2 sinBdBdrp.
(iii) Explain in words and give an expression for the continuity condition or conservation of
charge explaining the meaning of each of the terms. [4 marks]
(b) Use Ampere's law in differential fonn and Gauss's divergence theorem to demonstrate that
across any closed surface the total flux of the sum of conduction current and displacement
current is zero.
[4 marks]
(c) An electromagnetic wave in vacuum has frequency.l6, wavelength Ao, wavenumber ko, and
velocity c. When it enters a dielectric medium characterised by flO and G = 4.su,what are the
frequencyf, wavelength 4, wavenumber k, and velocity v of the wave in this medium?
[2 marksJ.
(d) A uniform plane wave of frequency 20 MHz propagates in a non-dissipative medium in the
positive z-direction. A probe located at z = 0 measures the phase to be 98°. An identical
probe at z = 2m measures the phase to be -150 aUhe same time. What is the relative dielectric
constant of the medium?
[6 marks]
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CONTINUED
ELEC 214P
2. (a) Using Faraday's law in differential fonn, find the magnetic field corresponding to the
following electric field propagating in free space:
. E =yEy =yEo cosaxcos(OJt - pz)
[6 marks]
Note: 'VXF=(BFz _ BFyJi+(BFx _ BFz)y+(BFy _ BFxJz

By Bz Bz Bx Bx By

(b) Define the (real) Poynting vector P;:> for real, time-varying fields and explain the meaning of
the total flux. of P;:> across a closed surface Q that surrounds a volume V. Establish, without
derivation, an equation showing the conservation of power in. the volume V and explain the
meaning of each tenn.
Define the complex (or time-average) Poynting vector S for time-harmonic fields and give
an expression that relates it to the real Poynting vector P;:> •
[6 marks]
(c) At a large distance from an ant~nna, the radiated field is a radially propagating wave and its
electric field is given by: E(~,B,t)=010sinB cos(OJt-kr) [Vim]. Find the associated
r
magnetic field and the instantaneous power density (or instantaneous Poynting) vector. Find
then the total instantaneous power radiated by the antenna using a spherical surface ofradius
r centred on the antenna, placed at the origin.
[7 marks]
Repeat the calculations using the phasor expressions for the electric and magnetic fields to
find the complex power density and from this, the total radiated power. Show that this result
corresponds to the time average of the total instantaneous radiated power found before.
[6 marks]
Note: In spherical coordinates the surface element is given by: dn = i r2 sinB dB d¢ and the
7i
relations between unit vectors are: ixO=

. 0
that the average: ! fT cos2 (OJt - kr) dt = i where T is the period.

To .

Page 3 of6
TURNOVER
ELEC 214P

3. (a)A beam of light travelling in air is incident normally on a side of an isosceles prism of
refractive index n = 1.35. It is then reflected on a face coated with a perfect conductor and
finally emerges from the front at point (c), and from the other side, at point (b) at an angle ()
as shown in Fig. 3.1. The polarisation of the beam is
perpendi~ular to the plane of~cidence(the plane ofthe figure).E a
Calculate the angle () shown in the figure. [2 marks]
Ifthe amplitude ofthe electric field ofthe incident beam is Eo,
c
calculate the amplitude of both emerging beams ignoring
multiple reflections inside the prism.
[6 marks]
How will this change if the perfect conductor coating is Fig. 3.1
completely removed?
. [3 marks]'
Note: Since we are only interested in the amplitude, ignore the phase change in reflection
and transmission at the interfaces.
The expressions for the reflection and transmission coefficients for a wave with parallel
polarisation with incidence an'g1e (); from a medium with permittivity 6 1 into another of
permittivity 62 are:
cos (}i - ~p2 - sin2 ();
r .1 =.------:.-~====

cos(); +~p2 - sin2 (}i

For normal incidence, the transmission coefficient between a medium 1 and a medium 2
2F; . (going from 1 to 2) is: 112 = F; .J0. if the permeability f..l ofboth media are the same.
q+ ~ .
(b) Electromagnetic compatibility specifications require that some electronic circuits should be
shielded from ambient electromagnetic radiation with an attenuation of at least 150 dB at 1
MHz. A box made' from aluminium sheet needs to be designed for this purpose and the
available sheets are: 0.2, 0.3, 0.4, 0.5 and 0.7 mm thick. Choose the minimum thickness
necessary to satisfy the specification.
[14 marks]
Note: Neglect multiple reflections. .
The conductivity of aluminium is (j = 3.78xl07 Q-lm-l and the skin depth at 1 MHz is
0= 81.9 /-lm.
Remember also that the intrinsic impedance of a conductor is: Z = ;'0 (1 + j)
Page 4 of6
CONTINUED
ELEC 214P

SECTIONB
ANSWER TWO QUESTIONS FROM THIS SECTION
4. (a) Sketch, and fully label, Energy Band Diagrams for the following:
(i) p-type silicon [3 marks]
(ii) the metal gold (Au) and [3 marks]
(iii) p-type silicon when in contact with gold (Au) [4 marks]
(iv) With reference to the diagram in (iii) describe why this structure behaves as a diode
when electrically biased.
[4 marks]
(v) This type ofdiode is considered to be unipolar in nature relying on thermionic emission
to operate. Explain what is meant by the terms in italics and how this device differs from
a p-n junction diode. . .
[4 marks]
(b) Calculate the theoretical barrier height, built-in potential barrier and maximum electric field
in a metal-semiconductor junction diode at zero bias. Take the semiconductor to be Si with
3an electron affinity of4.01eV and a doping level ofND = 1 X 1016 cm- , and the metal to be W
with a work function of4.55eV.
[7 marks]
PageS of6
TURNOVER
'I
ELEC 214P 'l
5. (a) In a bipolar junction transistor (BJT), the common base current gain, a, can be expressed as: '
a= raTO
Give a name and definition of each of the tenns r, aT and 0. Go on to give a mathematical
expression for each in tenns of the currents expected within a BJT in the forward-active mode
of operation, defining the meaning ofthe tenns within your expressions.
[11 marks]
(b) In a BJT the common-emitter gain, fJ, is defmed as:
fJ=Ie / In
where Ie is the collector current and In the base current. Give a mathematical expression for ,
the relationship between' fJ and a. Assuming the values of r, aT and 0 to be equivalent, what
value must they take to give a common-emitter gain value of 100?
[4 marks]
(c) Describe the nature of the Early effect that is found when operating BJTs. Include a suitable
sketch to illustrate your answer. Add a second sketch, which enables you to define the Early
Voltage. What problem does the Early effect cause, and what technological approach can be
implemented to reduce its effect? What problem is created by the solution you have
suggested?
[10 marks]
6. (a) For a silicon MOS structure describe what is meant by the tenns accumulation, depletion and
inversion. Give a mathematical expression for the capacitance of the MOS structure under
each of these conditions.
[6 marks]
Sketch, and fully label, anideal C-V curve for a silicon MOS structure. Describe the effect of
the measurement frequency on this curve.
[7 marks]
Describe the effect of fixed oxide charges and interface charge effects on the C-V curve,
including modified sketches.
[6 marks]
(b) Consider an n-channe1 MOSFET with W = 15J,I.m, L= 2Jlm and Cox = 6.9 x 10-8 F/cm2.
Operation in the non-saturation region gives a drain current for VDS = 0.10 volts which is
1D = 35J1A at VGS = 1.5V is 1= 75J1A, at VGS value = 2.5V. Determine.(i) the inversion carrier
mobility and (ii) the threshold voltage VT.
[6 marks]
Page 6 of6
END OF PAPER