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,*

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

*The Fermi function at is approximately,*

*.*

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

*.*

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

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

*The term,*

*.*

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

*.*

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

*, **where*

* is the gap between the conduction band and valence band.*

*Similarly, for an intrinsic material, **the product of ** and is, *

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

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

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

and .

The hole concentration is,

.

The volume of the source region is

.

The number of holes is,

**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.com, buy 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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