Semiconductors

JEE Main level, single correct, medium

29 of 209

Question 29 of 209

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are 1015 atoms/cm310^{15}\text{ atoms/cm}^3 and 1018 atoms/cm310^{18}\text{ atoms/cm}^3, respectively. Which one of the following statements is true ?

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Answer: (B) The depletion region width is more on p-side compared to that in n-side

In a p-n junction diode, the total charge on both sides of the depletion region must be equal to maintain charge neutrality.

Let xpx_p and xnx_n be the widths of the depletion region on the p-side and n-side, respectively. Let NAN_A and NDN_D be the doping concentrations on the p-side and n-side.

The charge neutrality condition is given by:
NAxp=NDxnN_A x_p = N_D x_n

Given NA=1015 atoms/cm3N_A = 10^{15} \text{ atoms/cm}^3 and ND=1018 atoms/cm3N_D = 10^{18} \text{ atoms/cm}^3.

Substituting the values, we get:
1015xp=1018xn10^{15} x_p = 10^{18} x_n

xp=103xnx_p = 10^3 x_n

Since xp>xnx_p \gt x_n, the depletion region penetrates more into the lightly doped side. Therefore, the depletion region width is more on the p-side compared to that in the n-side.

Answer: The depletion region width is more on p-side compared to that in n-side

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