Department of Electrical and Computer Engineering: Final Examination

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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 Conduction Band (NC) and in the Valence Band (NV) respectively: 3
2

3

3

3

 m   T  2 −3

N C = 2.5 × 1019 
 cm
 m 0   300 
*
n

 m*  2  T  2
p
−3
19
N V = 2.5 × 10 
 m   300 cm


 0

PART -A
1a) Consider a Silicon p+-n diode with the following doping densities: NA = 1019 cm-3 and ND is 1016 cm-3. The diode has an area of 100 µm by 20 µm.
(i)
Without doing any calculations, sketch the capacitance versus reverse voltage (VR) starting from VR = 0.
(4 marks)
(ii)
Calculate the voltage at which you will obtain the minimum
capacitance and also determine (calculate) the minimum
capacitance at that voltage.
(10 marks)
(iii)
Derive the mathematical relations you use in calculating the quantities in (ii) above.
(16 marks)
1b) Assuming that the p+ region and the n-region of the diode described in 1a) above are ‘long’ compared to the minority carrier diffusion lengths in those regions, show how you would obtain the complete Current-Voltage (I-V) Characteristic of the diode. You can assume that there is no recombination in the space-charge layer and you need not solve the continuity equation. Sketch the electron and hole current distributions in the entire device.

(10 marks)

Page 1

PART B
2a) Draw a clearly labelled band diagram of an n-p-n transistor under thermal equilibrium and superimpose on it a band diagram of the same transistor when it is under normal forward active mode of operations.

(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 can use the values of mobilities and lifetimes given in the tables in the formula sheet to determine the electron diffusion length in the base. Verify that the short-region approximation is applicable to the base. Assume that the carrier recombinations in the neutral base an in the emitter-base depletion layer are zero. When this transistor is operating in the normal forward active mode with 0.6 volts forward bias across the emitter-base junction and a 2 volt reverse bias across the collector-base junction, what is the collector current density (JC) and the base current density (JB) ? You can assume that the...
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