ELEC_315_Final_December_2019_coirrected

Name: Number: Page 1 of 11 ELEC 315 Final December 2019 Closed Book. Only pens, pencils allowed. No calculators. Time: 120 minutes. Equation list and periodic table provided on last 2 pages. This examination consists of 11 pages. Please check that you have a complete copy. You may use both sides of each sheet if needed. Page # MAX GRADE 2 23 3 13 4 27 5 16 6 15 7 21 8 21 9 8 TOTAL 140 IMPORTANT NOTE: The announcement “stop writing” will be made at the end of the examination. Anyone writing after this announcement will receive a score of 0. No exceptions, no excuses. All writings must be on this booklet. The blank sides on the reverse of each page may also be used. Each candidate should be prepared to produce, upon request, his/her Library/AMS card. Read and observe the following rules: No candidate shall be permitted to enter the examination room after the expiration of one- half hour, or to leave during the first half-hour of the examination. Candidates are not permitted to ask questions of the invigilators, except in cases of supposed errors or ambiguities in examination-questions. Caution - Candidates guilty of any of the following, or similar, dishonest practices shall be immediately dis missed from the examination and shall be liable to disciplinary action: -Making use of any books, papers or memoranda, calculators, audio or visual cassette players or other memory aid devices, other than as authorized by the examiners.- Speaking or communicating with other candidates.-Purposely exposing written papers to the view of other candidates. The plea of accident or forgetfulness shall not be received. Student Number READ THIS

Name: Number: Page 2 of 11 1. (5) Imaginary permittivity can be used to help describe: (i) The effect of resistance in a dielectric True False (ii) Loss-related mechanisms True False (iii) Heat generating mechanisms True False (iv) Inductance related phenomena True False (v) Capacitive storage True False 2. (4) The dielectric constant of Barium Titanate (a crystalline compound of barium, oxygen and titanium) is an impressive 3000 at room temperature at 60 Hz, while diamond is 5.66. Explain. 3. (5) In diodes, breakdown is (right – wrong): (i) Always by Zener Breakdown. True False (ii) Occurs in reverse bias. True False (iii) Can be due to tunneling from the p-side Conduction True False Band to the n-side Valence Band (iv) Is usually due to avalanche breakdown in lightly doped True False pn-junctions. (v) Can be used for voltage regulation True False 4. (5) At a junction between two materials, energy levels are present on each side. For the following configurations, indicate whether electrons will on average move left or right (use arrows) or if the state is at equilibrium (double ended arrow): 5. (4) What happens to the potential energy of an electron as it becomes confined within some distance of the nucleus? (right – wrong): (i) It goes up as 1/distance. True False (ii) It goes down as -1/distance 2 . True False (iii) It goes down, but kinetic energy goes up. True False (iv) Radiation is released by orbiting electrons, preventing electron-proton anihilation. True False

Name: Number: Page 4 of 11 10. (6) A material is coated with metal on both sides to form a parallel plate capacitor of area, A , and thickness, d . A voltage, V , is applied. If the real part of the dielectric constant is  ’ r , and the imaginary part is 10 -3 times lower (  ’’ r =  ’ r / 1000), derive an expression for the rate of power loss at frequency,  . (2) In each charge/discharge cycle, what is the ratio of stored to dissipated energy? 11. (5) True or False? (right – wrong): (i) In paramagnetic materials the B field inside the material is REDUCED relative to the applied field due to the effect of the field on spins. (ii) In diamagnetic materials the B field is INCREASED relative to the applied field due to the effect of the field on orbiting electrons. (iii) Most materials are diamagnetic. (iv) The remnant magnetic field is the B field produced by a ferromagnetic material when no current or external magnetic field is applied. (v) The coercive field is the H-field needed to bring a magnet’s B field to 0. 12. (14) Sketch the band diagram of a PN junction under Forward Bias at an applied voltage, V A . Assume a band gap E g . In your diagram (a) Label the conduction and valence band edges, and (b) the Fermi level(s) . (c) Sketch the densities of carriers , d n /d E , d p /d E on both sides. (d) Label the n and p sides (e) Show the applied bias potential, e V A and (f) Indicate on which side the positive voltage is applied with a “+”.

Name: Number: Page 5 of 11 13. A molecule is composed of one positively and one negatively charged atom. A sinusoidal electric field, E(  ) , is applied to the molecule. Assume that each atom has a mass, m and opposite charges, +e , and –e . The stiffness of the bond between them is, k . (i) (3) What is the sum of the displacements,  (t) , of the two atoms relative to their equilibrium separation, in a low frequency field ( E = E o sin  t )? (ii) (2) What is the dipole moment, p , at low frequency, in terms of E and K ? (iii) (2) Write an expression relating field, mass, acceleration, speed, displacement, stiffness and damping, b : (assume the two masses move symmetrically, displacing equally in opposite directions). (iv) (7) Sketch a bode plot of the displacement response (showing magnitude and phase). (v) (2) What is the phase shift between E and displacement at high frequencies?

Name: Number: Page 7 of 11 15. (6) A depletion region is modeled as having an ionized charge density described by:  = -eN A - , where x p is the width of the depletion region that starts at x=0 , on the left hand side, and extends until it meets the n- doped side at x = x p . Derive an expression for the field as a function of position for 0< x < x p . 16. a) (3) Label remnance and coercivity for material C . b) (3) Which material (C or D) is best for use in an permanent magnet? – explain. c) (2) What do you expect the local slopes of the B-H curves to be when the field has reached saturation? e) (4) Given a relative permittivity,  r , find and expression for the B field generated by applying a modest current, I in a long solenoid of length L , filled with material D having N turns. f) (3) What is the inductance of this coil? D B C H

Name: Number: Page 8 of 11 17. (4) Which system(s) could be approximated by a 3D particle in a box model (circle the best answer(s))?: (a) An atom (b) A thin (1 nm diameter), long (1 mm) wire (c) A thin (1 nm) layer of silicon between two layers of silicon dioxide (d) A chunk of silicon that is l  l  l ? 18. (6) Derive the density of states for a 3D infinite particle in a box with sides of length L . Show your work. 15. (6) (a) An isotropic piezoelectric material of thickness z = 1 mm and width x = 10 mm, has coefficients d 33 = d ZZ =2 x 10 -10 m/V and d 31 = d ZX =1 x 10 -10 m/V. How much bound charge is generated per unit area,  , in the z and x axes when a force per unit area (stress) of 10 7 Newtons per square meter is applied in the z-direction? (provide a numerical answer)? (5) What is the ratio of the voltage generated in the x -diretion to the voltage in z ?

Name: Number: Page 10 of 11 Equations and Constants hv=KE+  λv=c 3D Time dependent: 3D Time independent: Eψ ( r )=− ℏ 2 2 m ∇ 2 ψ ( r )+ U ( r ) ψ ( r ) E − U = ℏ 2 ( k x 2 + k y 2 + k z 2 ) 2 m , where k i = n i  / L i in a 3D square well w/ sides of length L x x L y x L z . U=-q/( 4  ε o r) σ =(  e n o +  h p o ) e v=  E j=  E R=L/σ/A g ( E )= ( 2 m ¿ ) 3 / 2 2 π 2 ℏ 3 E 1 / 2 = 4 π ( 2 m ¿ ) 3 / 2 h 3 E 1 / 2 (3D) when E C - E F >> kT and n o <10 18 cm -3 . when E F - E V >> kT and p o <10 18 cm -3 . n i 2 = n o p o . V bi = e ( N A − x p 2 + N D + x n 2 ) 2 ε 1/2 1/2 2 ( ) bi A D A D D A V N N w e N N N N                               kT ~ 0.026 eV at 300 K. h =6.63×10 -34 J·s. e =1.6×10 -19 Coulombs m e = 9.11×10 -31 kg proton rest mass, m p = of 1.67×10 -27 kg Si at 300 K: N C =4x10 19 cm -3 , N V =2.31x10 19 cm -3 . n i =10 10 cm -3 Band gap E g = 1.12 eV j ⋅ℏ⋅ ∂ ψ ( ⃗ r ,t ) ∂ t =− ℏ 2 2 ⋅ m ⋅∇ 2 ψ ( ⃗ r ,t )+ U ( ⃗ r ,t )⋅ ψ ( ⃗ r ,t ) f ( E )= 1 1 + exp [ ( E − E F )/ kT ] n o = N C exp [ − ( E C − E F ) kT ] ( ) exp F V o V E E p N kT         

Name: Number: Page 11 of 11 I = I o [ exp ( eV A kT ) − 1 ] Parallel plate C=ε r ε o A/d dissipation factor = tan  = ε”/ε’ = P loss /P transmitted Voltage 2 V     , ∇ ∙E = ρ free ε , ∮ E∙ ^ ndA = Q free ε , Electric Field E =− ∇ V  o = 8.85  10 -12 C/m/V P = χε o E ε r =(1+ χ ) σ bound = P ∙ n ε r ε o = ε’+jε” P i = d ij T j S i = d ij E j dF =Id l × B T=m×B K=M×n B =  H =  r  o H 0 enclosed Closed Loop B ndS I     ⃗ ⃗  . conduction Closed enclosed Loop H ndS I    ⃗ ⃗  .  o =4  10 -7 N  A -2 Visible Spectrum ~ 400 nm to 750 nm.