Ce 231 Final Exam
University of Waterloo
Department of Electrical & Computer Engineering
E&CE 231 Final Examination - Spring 2000
Aids: Formula Sheets (attached), Scientific Calculator
Time Allowed: 3 hours
Exam Type: Closed Book
Instructor: C. R. Selvakumar
Date: August 10, 2000
Max Marks: 100
Instructions:
Answer all questions in PART-A and any two questions in full from PART-B.
State your assumptions clearly. Be concise, precise and clear in your answers
General assumptions to be made when not specified in a question:
(a) Assume that the semiconductor is Silicon.
(b) Assume that the temperature T = 300K
(c) Use the data given in the formula sheets where needed.
(d) Use the following expressions for the Effective Density of States in the …show more content…
(8 marks)
2b) Derive an expression for the common emitter current gain $ ($ = IC/IB), in terms of the doping densities in the different regions, thickness and carrier diffusivities and diffusion lengths. Assume that there is no recombination in the neutral base or in the space-charge layers. Also, assume that the conventional reverse saturation current of the reverse-biased diode, IC0, is negligible. Assume that short-region approximation is valid in the base and that the bandgap narrowing in the emitter is important. No need to solve continuity equations and you can assume the expected carrier distributions.
(12 marks)
2c) Obtain the modified Ebers-Moll (EM) equations from the original EM equations given in the formula sheet. Sketch Common-Base output characteristics based on the modified EM equations and show the Forward
Active Region of operation, Saturation Region and Cut-off Region. (10 marks)
3a) A silicon n-p-n transistor has an emitter doping NDE = 1020 cm-3 and a base doping NAB = 1016 cm-3. The emitter is 1 µm thick and assume that the hole diffusion length in the emitter is 0.1 :m. The base is 0.35 :m thick and you …show more content…
Prove that the quantity Q p ≈ qAL p pn 0 e
V
Vt
(10 marks)
Page 2
4a) Consider an n-channel MOSFET and explain how the MOSFET operates using key band diagrams (along source, channel and drain and vertically along the metal gate, oxide and the channel region) and cross-sectional diagrams. State clearly wherefrom the channel electrons come and explain how this is controlled by the gate voltage.
(10 marks)
4b) With reference to an n-p-n transistor, explain what is Early Effect and how it arises. Using an approximate sketch show the Early Voltage. Clearly illustrate your answer with the aid of carrier profiles and common-emitter output characteristics. (10 marks)
4c) Contrast the Temperature-dependence of Avalanche Breakdown Mechanism and
Zener breakdown Mechanism. Illustrate your answer with sketches of Reverse bias I-V characteristics giving physical reasons.
(10 marks)
Page 3
E&CE 231
1/4
Formula Sheet
C.R.Selvakumar
E&CE 231 Formula Sheet
3
1
4π
*2 g c (E) = 3 (2m n ) ( E − E C )) 2 ; (E ≥ E c ) h 3
1
4π
*2
2 g V (E) = 3 2m p ( E V − E)) ; (E ≤ E V
Department of Electrical & Computer Engineering
E&CE 231 Final Examination - Spring 2000
Aids: Formula Sheets (attached), Scientific Calculator
Time Allowed: 3 hours
Exam Type: Closed Book
Instructor: C. R. Selvakumar
Date: August 10, 2000
Max Marks: 100
Instructions:
Answer all questions in PART-A and any two questions in full from PART-B.
State your assumptions clearly. Be concise, precise and clear in your answers
General assumptions to be made when not specified in a question:
(a) Assume that the semiconductor is Silicon.
(b) Assume that the temperature T = 300K
(c) Use the data given in the formula sheets where needed.
(d) Use the following expressions for the Effective Density of States in the …show more content…
(8 marks)
2b) Derive an expression for the common emitter current gain $ ($ = IC/IB), in terms of the doping densities in the different regions, thickness and carrier diffusivities and diffusion lengths. Assume that there is no recombination in the neutral base or in the space-charge layers. Also, assume that the conventional reverse saturation current of the reverse-biased diode, IC0, is negligible. Assume that short-region approximation is valid in the base and that the bandgap narrowing in the emitter is important. No need to solve continuity equations and you can assume the expected carrier distributions.
(12 marks)
2c) Obtain the modified Ebers-Moll (EM) equations from the original EM equations given in the formula sheet. Sketch Common-Base output characteristics based on the modified EM equations and show the Forward
Active Region of operation, Saturation Region and Cut-off Region. (10 marks)
3a) A silicon n-p-n transistor has an emitter doping NDE = 1020 cm-3 and a base doping NAB = 1016 cm-3. The emitter is 1 µm thick and assume that the hole diffusion length in the emitter is 0.1 :m. The base is 0.35 :m thick and you …show more content…
Prove that the quantity Q p ≈ qAL p pn 0 e
V
Vt
(10 marks)
Page 2
4a) Consider an n-channel MOSFET and explain how the MOSFET operates using key band diagrams (along source, channel and drain and vertically along the metal gate, oxide and the channel region) and cross-sectional diagrams. State clearly wherefrom the channel electrons come and explain how this is controlled by the gate voltage.
(10 marks)
4b) With reference to an n-p-n transistor, explain what is Early Effect and how it arises. Using an approximate sketch show the Early Voltage. Clearly illustrate your answer with the aid of carrier profiles and common-emitter output characteristics. (10 marks)
4c) Contrast the Temperature-dependence of Avalanche Breakdown Mechanism and
Zener breakdown Mechanism. Illustrate your answer with sketches of Reverse bias I-V characteristics giving physical reasons.
(10 marks)
Page 3
E&CE 231
1/4
Formula Sheet
C.R.Selvakumar
E&CE 231 Formula Sheet
3
1
4π
*2 g c (E) = 3 (2m n ) ( E − E C )) 2 ; (E ≥ E c ) h 3
1
4π
*2
2 g V (E) = 3 2m p ( E V − E)) ; (E ≤ E V