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GATE-2012 ECE Q26 (electronic devices)

by Krishna Sankar on October 27, 2012

Question 26 on Electronic Devices from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper.

Q26. The source of a silicon (), n-channel MOS transistor has an area of and a depth of  . If the dopant density in the source is , the number of holes in the source region with above volume is approximately

(A)

(B)

(C)

(D)

Solution

To answer this question, had to dig up the copy of Solid State Electronic Devices, Ben G Streetman, Sanjay Kumar Banarjee (buy from Amazon.com, buy from Flipkart.com) and am referring to the content from Section 3.3 Carrier Concentrations.

Electrons in solids obey Fermi-Dirac statistics.  The function  Fermi-Dirac distribution function, gives the probability that an available energy state at will be occupied by an electron at absolute temperature ,

.

The quantity  is the Fermi level and  is the Boltzmann’s constant.

The concentration of electrons in the conduction band is,

, where  is the density of states in the energy range .

The integral is equivalently stated as,

 alt=,  where  alt= is the effective density of states at conduction band edge  alt=.

The Fermi function at  alt= is approximately,

.

So in this condition the concentration of electrons in the conduction band is,

 alt=.

Similarly, the concentration of holes in the valence band is,

 alt=, where  alt= is the effective density of states at valence band edge  alt=.

The term,

.

So in this condition the concentration of holes in the valence band is,

 alt=.

The product of  alt= and  alt= at equilibrium is a constant for a particular material and temperature even if doping is varied.

 alt=where

 alt= is the gap between the conduction band and valence band.

Similarly, for an intrinsic material, the product of   alt= and  alt=  is, 

 alt=

For an intrinsic material, the electron and hole concentration are equal i.e.  alt=.

The constant product of electron and hole concentration can be written as

 alt=

 

With the above understanding, let us try to find the solution to the problem. In our question,

 alt= and  alt=.

The hole concentration is,
 alt=.

The volume of the source region is

 alt=.

The number of holes is,

 alt=

 

Based on the above, the right choice is (D) 0. 

References

[1] GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf

[2] Solid State Electronic Devices, Ben G Streetman, Sanjay Kumar Banarjee (buy from Amazon.combuy from Flipkart.com)

[3] Valence band http://en.wikipedia.org/wiki/Valence_band

[4] Conduction band http://en.wikipedia.org/wiki/Conduction_band

 

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