CARLETON UNIVERSITY. FINAL EXAMINATION December 2016

Transcription

1 CARLETON UNIVERSITY FINAL EXAMINATION December 2016 DURATION: 3 HOURS Department Name & Course Number: Electronics 4705 Course Instructor(s): Tom Smy AUTHORIZED MEMORANDA CALCULATOR (Not Programmable) Students MUST count the number of pages in this examination question paper before beginning to write, and report any discrepancy immediately to a proctor. This question paper has 15 pages. This examination question paper MAY NOT be taken from the examination room. There are 11 questions on the exam. Attempt all questions. Note that the questions are not equally weighted. I suggest you attempt the questions you know best first! There are 178 marks. I think :-) Student Name: Student Number: 1

2 1. Basic Quantum Mechanics (15 Marks total): Sketch a finite electron potential well showing the important features. (2 Marks) (a) (7 Marks) With reference to the sketch write down: i. The time independent Schrodinger s Eq. with the appropriate potential. ii. The appropriate boundary conditions. iii. Describe when quantization of electron energy occurs. (b) (3 marks) Sketch ψ(x) for the first few energy states. (c) (3 Marks) Sketch ψ(x) for the first few energy states greater then the finite potential well height. 2

3 2. Quantum Mechanical Tunneling (10 Marks) Describe what Quantum Mechanical Tunneling is. In particular: (a) Contrast it with the classical situation. (b) Sketch a wave-function for a case of tunneling. (c) What effects the degree of tunneling present? (d) Give an example of a situation when tunneling is important. 3

4 3. Electrons in crystals (Total Marks 20): When describing the electron behaviour in materials we use an E versus k relationship (E(k)). (a) (2 marks) Describe what this relationship is. Specifically what are E and k. (b) (2 marks) What is the E(k) relationship for an electron in a single infinite well? (c) (2 marks) What is the E(k) relationship for perfectly free electrons? (d) (4 marks) Draw an E(k) relationship for free but periodic electrons? How does it differ from the perfectly free electron case? (e) (2 marks) Draw a characteristic E(k) relationship for electrons in a periodic potential with a barrier present. (f) (4 marks) For this case how does the barrier height/width effect the relationship? (g) (4 marks) When we have an electric field present what information about the electron behavior does the E(k) relationship give us? 4

5 (Electrons in crystals Extra page for work.) 5

6 4. Band Structures (Total 25 Marks): (a) (10 Marks) For a crystal of finite size: i. How does the finite size of the crystal effect the potential used in Schrodinger s Eq? ii. How does this change in the potential effect the band structure (E vs k)? iii. Why can bands only accept a finite number of electrons and therefore fill up? iv. If we had small periodic molecule of 20 atoms how many states would you expect to be present in each band? 6

7 Band Structures:(cont.) (b) (5 Marks) What does the band structure of a metal, intrinsic semiconductor, and insulator look like. Draw band structures for each material. (c) (5 marks) Describe in words and with respect to a semiconductor band structure: The Density of States of function The Fermi-Dirac function (d) (5 marks) Describe how the two functions are used to obtain the electron density in a semiconductor. A sketch would be good. 7

8 5. Integrated Circuit Fabrication (Total Marks: 15) (a) (5 Marks) Describe the process of photolithography used in IC fabrication (b) (10 Marks) Describe the steps needed to create a fabricated structure containing: An n region in a p doped wafer A single layer of insulator with a contact cut to the n region An etched metal contact/line to the n region 8

9 6. Schottky Diode: (Total Marks: 12) (a) (2 Marks) Draw the physical structure of a Schottky Diode for an n-type semiconductor. (b) (4 Marks) Draw the band structure at equilibrium and under reverse bias. (c) (6 Marks) Explain the operation of the device in terms of the physical currents flowing in both directions. 9

10 7. Bipolar Junction Transistor: (Total Marks: 10) (a) (7 Marks) Explain why for an NPN bipolar transistor the collector current is given by I c = I c0 eqvbe/kt in forward active operation (base-emitter fwd biased/base-collector reverse biased). Specifically why is it exponentially related to V BE and there is no dependence on V BC? (b) (3 Marks) Can we create an NPN bipolar transistor by connecting two PN diodes backto-back with a metal wire? Why or why not? 10

11 8. Optical Fiber (Total Marks: 10) (a) (2 Marks) If we consider a fiber to be a simple optical structure what fundamental effect do we take advantage of to guide the light? (b) (6 Marks) If we look at the fiber as an electromagnetic problem we find from the solution that modes are present. What are modes and what causes them to exist in this case? (c) (2 Marks) We usually want a fiber to operate using a single mode why? 11

12 9. Optical Devices: (Total Marks: 12) (a) (6 marks) What are the three basic electron transitions that occur in a semi-conductor which involve photons? Describe the transitions. (Use pictures!) (b) (2 marks) If we wish to create an optical amplifier using optical fiber how do we need to modify/alter the fiber? (c) (4 Marks) Would it be possible to make a fiber laser using an optical fiber. How? Can you see any advantages/disadvantages of such a device? 12

13 10. PN Diode Lasers/Detectors (25 Marks). PN diodes can be used for photonic (optical) purposes. (a) (10 Marks) If you wished to design a laser using a pn diode how would you modify the simple structure? Clearly give reasons for each modification and explain it s role in the laser operation. (b) (5 Marks) What would be the two types of electromagnetic modes present in the laser? (c) (5 Marks) What two factors would determine the frequency of operation of the laser? 13

14 PN Diodes. (Cont) (d) (5 Marks) If you wished to design a photodiode using a pn diode how would you modify the structure? Again give reasons for each modification and explain it s role in the detector operation. 14

15 11. MEMS and Nanotechnology: (Total Marks: 24) (a) (2 marks) How would you define the difference between MEMS and nanotechnology? (b) (4 marks) In MEMS process technology describe the role of sacrificial layers. (c) (4 marks) What is a carbon nanotube? Does it have a band structure and why or why not? (d) (6 marks) What is a quantum dot? How big would it be? (e) (6 marks) Propose an application of quantum dots. Explain how the quantum nature of the dot is used. 15