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GATE-2012 ECE Q26 (electronic devices)

Posted By Krishna Sankar On October 27, 2012 @ 2:38 pm In GATE | No Comments

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






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 [1], buy from Flipkart.com [2]) 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,


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,


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


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

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


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



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

 alt= and  alt=.

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. 


[1] GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf [3]

[2] Solid State Electronic Devices, Ben G Streetman, Sanjay Kumar Banarjee (buy from Amazon.com [1]buy from Flipkart.com [2])

[3] Valence band http://en.wikipedia.org/wiki/Valence_band [4]

[4] Conduction band http://en.wikipedia.org/wiki/Conduction_band [5]


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[1] buy from Amazon.com: http://www.amazon.com/gp/product/013149726X/ref=as_li_qf_sp_asin_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=013149726X&linkCode=as2&tag=dl04-20

[2] buy from Flipkart.com: http://www.flipkart.com/solid-state-electronic-devices-812033020x/p/itmdytczshhgnypr?pid=9788120330207&affid=krishnadsp

[3] http://gate.iitm.ac.in/gateqps/2012/ec.pdf: http://gate.iitm.ac.in/gateqps/2012/ec.pdf

[4] http://en.wikipedia.org/wiki/Valence_band: http://en.wikipedia.org/wiki/Valence_band

[5] http://en.wikipedia.org/wiki/Conduction_band: http://en.wikipedia.org/wiki/Conduction_band

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