Solid State Electronics Final Exam 2022/2023 PDF

Module Code 22ECE02C Final Examination 2022/2023 Module Title Solid State Electronics Module Leader: Semester: Dr. Sameh Osama...

Module Code 22ECE02C Final Examination 2022/2023 Module Title Solid State Electronics Module Leader: Semester: Dr. Sameh Osama One, Jan 2023. Equipment allowed Scientific calculator Instructions to Students The exam is in two sections. Answer all questions in Section A and any two questions from Section B. The exam paper is double sided five pages long, not including this page The allocation of marks is shown in brackets next to each question. Write your answers in the answer booklet provided, not on the exam paper. Assume any missing information and state your assumptions clearly. This examination is Two hours long. 22ECE02C Solid State Electronics Final Exam – S1 2022/2023 Section A: Answer all questions Q1 [Total: 40 marks] a) A semiconductor at 300 K is characterized by the energy band diagram shown in figure 1. Use the cited energy band diagram to answer the following questions. Figure 1 a) Sketch the electrostatic potential inside the semiconductor [5 marks] b) Determine where the semiconductor is degenerate. [5 marks] c) Sketch roughly the electron and hole concentration (not to scale). [5 marks] d) Do equilibrium conditions prevail and why? [5 marks] e) Give an expression for the kinetic energy of the electron shown on the diagram [5 marks] f) Sketch the electric field inside the semiconductor [5 marks] g) Sketch the electrostatic charge inside the semiconductor [5 marks] h) Assume that the semiconductor has been heated by a way or another so that the [5 marks] temperature reaches 300 K +ΔT, re-sketch the energy band diagram while illustrating the effect of the temperature on the Fermi-level position. Page 1 of 5 22ECE02C Solid State Electronics Final Exam – S1 2022/2023 Section B: Answer two questions only Q2 [Total: 30 marks] The Fermi-Dirac distribution is given by: 1 f FD (E ) = ( E − E F ) / KT 1+ e a) Plot the Fermi-Dirac distribution (x-axis) vs. energy (y-axis) at 0 K and [5 marks] temperature T > 0 K with indicating the Fermi level in the graph. b) Write the integral form used to calculate the electrons concentration in terms [5 marks] of the density of states gc (E). You have to indicate clearly the integration limits. c) Write the integral form used to calculate the electrons concentration in terms [5 marks] of the density of states gv (E). You have to indicate clearly the integration limits. d) Giving the electron concentration as: [5 marks] 3/ 2 ( E F − E c ) / KT  2 m e* KT  n = N ce with N c = 2    h2  Discuss the energy band diagram for a n-type semiconductor under doping level of Nc, assume Boltzmann statistics are applied. e) Giving the hole concentration as: [5 marks] 3/ 2  2 m KT  * p = N v e ( Ev −E F ) / KT with N v = 2   h 2  h  Discuss the energy band diagram for a p-type semiconductor under doping level of Nv, assume Boltzmann statistics are applied. f) Show with the aid of sketches, the impact of mass action law for [5 marks] semiconductor under thermodynamic equilibrium towards a constant total number of carriers in both intrinsic and extrinsic semiconductors. Page 2 of 5 22ECE02C Solid State Electronics Final Exam – S1 2022/2023 Q3 [Total: 30 marks] Si p-n diode has the following parameters: Nd = 1018 cm-3, Na =1015 cm-3, Dp =8 cm2/s, Dn =15 cm2/s, τn =1µs, τp =0.01µs, ni = 1010 cm-3,VT =25.9 mV at 300 K, ε =11.7 εo, εo =8.854× 10-14 F/cm, A=1 mm2, and q =1.6× 10-19 Hint: the depletion region in the n-side can be given by: 1/ 2  2 N a  1   x no =   V o   q N d  N a + N d   a) At what value of applied potential Va, the depletion region potential [5 marks] barrier will tends to zero. b) Draw the energy band diagram and carrier distribution at applied [5 marks] voltage Va =+0.5V. c) Find the ratio [Wd (at Va=+0.5) / Wdo at thermal equilibrium, and [5 marks] comment on your answer. d) Consider the given p-n junction is turned to be p-i-n junction, where i [5 marks] indicates intrinsic region. Sketch the p-i-n cross-section energy band diagram under thermodynamic equilibrium. e) For (d), plot the carrier concentration across the junction. [5 marks] f) Re-sketch (d) when 0.5 V is applied on the junction. [5 marks] Page 3 of 5 22ECE02C Solid State Electronics Final Exam – S1 2022/2023 Q4 [Total: 30 marks] a) The C-V characteristic exhibited by an MOS-C (assumed to be ideal) is displayed in Figure 4 Figure 4 a) Draw the MOS-C energy band diagram corresponding to point (2) on the [5 marks] C-V characteristic b) Draw the block charge diagram corresponding to point (1) on the C-V [5 marks] characteristic. c) Roughly sketch the electric field inside the oxide and the semiconductor as a [5 marks] function of position. d) Find an expression for the maximum depletion width Xdm for the given [5 marks] MOS-C e) For n-channel MOSFET, sketch the variation of the space charge density in [5 marks] the semiconductor of a MOS capacitor as a function of the surface potential showing the different regions. You must explain the functional dependence in each part of the graph. f) Sketch the I-V curve of the MOSFET, with indicating its three regions of [5 marks] operation Page 4 of 5 22ECE02C Solid State Electronics Final Exam – S1 2022/2023 Constants Carrier unit charge (q) = 1.6 ∗ 10−19 𝐶 KB (in eV) = 8.617333262×10−5 h = 6.62607004 × 10-34 m2 kg / s εo = 8.85×10−12 F⋅m−1 At 300 K, KT = 0.026 eV At 300 K for silicon: Energy gap = 1.1 eV Intrinsic carrier concentration = 1010 cm-3 Atomic Concentration = 5  1022 cm-3 Electron mobility = 1350 cm2 V-1s-1 Hole mobility = 450 cm2 V-1s-1 Effective density of states in the CB = 2.81  1019 cm-3 Effective density of states in the VB = 1.16  1019 Page 5 of 5