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Reg. No. : ..................................... Name : ..........................................
Third Semester B.Tech. Degree Examination, June 2009 03-303 : SOLID STATE DEVICES (TA) (2003 Scheme) Time : 3 Hours
Max. Marks : 100
Instructions : Answer all questions from Part – A and two questions from each Module in Part – B. Assume appropriate data, if necessary. PART – A 1. Explain the variation of carrier concentrations and Fermilevel position in a semiconductor with increase in doping. 2. The doping profile in a semiconductor is given by ND(x) = N(0)e–ax . If ND(x) >> ni, determine the built in field. Plot its energy band diagram. 3. Show that the maximum resistivity of a semiconductor at a given temperature with −
−1 intrinsic carrier concentration ni is ρ max = (2q n i ) (μnμp )
1 2.
4. Derive a relationship between the dopings (N A, ND) and depletion layer widths (XP, Xn) of an abrupt p-n junction. 5. How does the built in potential of an abrupt pn junction vary with temperature, doping and energy band gap ? Justify your answers. 6. Draw the energy band diagram of an abrupt p-n junction under reverse bias condition. Show the position of quasi-Fermi levels. 7. Plot the o/p characteristics of a p-n-p transistor in common emitter configuration with proper labels. Show the different regions of operation of the transistor. 8. Plot the transfer characteristics and drain characteristics of an n channel enhancement type MOSFET and briefly explain. 9. What is meant by pinch off voltage of a JFET ? Derive an expression for it in terms of channel thickness and doping. 10. Draw the two transistor equivalent of an SCR and explain the principle of operation. (4×10=40 Marks) P.T.O.
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PART – B Module – I 11. a) What are the differences between direct band gap and indirect band gap semiconductors ?
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b) A GaAs sample is doped uniformly such that the electron and hole components of currents are equal in an applied electric field. Calculate the equilibrium electron and hole concentrations and the resistivity of the specimen.
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12. a) Explain a method to measure the majority carrier mobility and concentration in a rectangular semiconductor specimen under thermal equilibrium. Derive the required equations.
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b) A Germanium sample is doped with 5×1013 Arsenic atoms/cm3. Determine the electron and hole concentrations in the specimen and the position of Fermi level at 300K.
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13. a) What are the different scattering mechanisms in a semiconductor ? How do they affect carrier mobility ?
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b) Plot the drift velocity of electrons as a function of applied electric field for a) Silicon b) Gallium arsenide. Explain.
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Module – II 14. a) Derive expression for the built in potential across an abrupt p-n junction. b) An abrupt p+-n silicon junction has breakdown voltage of 400V. The critical electric field is 3×105 V/cm. At 300 K determine i) The doping on the n side ii) depletion layer width at breakdown. 15. a) Derive expression for the diffusion capacitance of an abrupt p-n junction. . b) For an abrupt p-n junction show that qVo = Ecp – Ecn = Evp – Evn = Eip – Ein. 16. a) Derive the I-V relationship for a Schottky diode. b) At 300 K, for a silicon abrupt p-n junction, the resistivity is 0.5 Ω .cm on the p side and 1 Ω .cm on the n side. Determine the built voltage, depletion layer width (Wo) and the maximum electric field (ε mo).
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Module – III 17. a) Plot the minority carrier distribution in an npn transistor in active region of operation and explain.
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b) Derive the following relationships for a BJT i) I C = – α I E + I CBO 5
ii) I C = β I B + (1 + β )I CBO.
18. Derive the I D – VDS relationship for an n channel JFET, stating the approximations clearly. 10 5
19. a) Derive expression for the threshold voltage of a MOS capacitor. b) Calculate the capacitance of a MOS capacitor with silicon substrate of doping NA = 1015 cm–3 under accumulation condition. Given tox = 100° A; ε rox = 3.9, ε si = 11.8, Area of cross section (A) = 10–3cm2 . Properties of intrinsic Si, Ge and GaAs at 300 K Properties
Si
Ge
Ga As
Energy band gap (eV)
1.11
0.67
1.43
Electron mobility (cm2/V.s)
1350
3900
8500
Hole mobility
480
1900
400
1.5×1010
2.5×1013
1.79×106
11.8
16
13.2
,,
Intrinsic carrier concentration (cm–3) Relative permittivity
Constants Plank’s constant (h)
:
6.626×10–34 J.S
Electronic charge (q)
:
1.602×10–19 C
Permittivity of free space ( ε 0)
:
8.854×10–14 F/cm
Velocity of light in Vacuum (c)
:
2.998×1010 cm/s
Boltzman constant (k)
:
1.381×10–23 J/K
Relative permittivity of SiO2
:
3.9
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