GATE EC 2014 Set 4 — Question 19
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Electronic Devices → Semiconductor Physics → Intrinsic & Extrinsic Semiconductors
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Question
In the figure, is plotted as a function of , where is the intrinsic resistivity of silicon, is the temperature, and the plot is almost linear.
The slope of the line can be used to estimate
Correct answer
(A) band gap energy of silicon (E_g)
Solution
The intrinsic resistivity is the reciprocal of intrinsic conductivity :The intrinsic carrier concentration is given by:Substituting into the expression for :Taking the natural logarithm on both sides:This equation is of the form , where and . The slope of the plot of versus is:Since (Boltzmann constant) is a known constant, the slope can be used to estimate the band gap energy of the semiconductor (silicon in this case).
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