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] Page 2 of6 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
