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Suppose a 'n'-type wafer is created by d...

Suppose a 'n'-type wafer is created by dopin Si crystal having `5xx10^(28)` atoms/`m^(3)` with 1 ppm concentration of As. On the surface 200 ppm Boron is added to create 'P' region in this wafer. Considering `n_(i)=1.5xx10^(16)m^(-3)` (i) Calculate the denisties of the charge carrier in the n & p regions. (ii) Comment which charge carriers would contribute largely for the reverse saturation current when diode is reverse biased.

Text Solution

Verified by Experts

Here 1 ppm = 1 part per million
= 1 part in 10 lakh
(i) For n-type semiconductor :
(no. of Si atoms in 1 `m^(3)` volume) `to` (no. of As atoms in 1 `m^(3)` volume)
`10^(6) to 1`
`therefore 5xx10^(28) to `(?)
`rArr` Number density of pentavalent As atoms (or) free electron number density).
`n_(e )=(5xx10^(28))/(10^(6))=5xx10^(22)("free electron")/(m^(3))`
Now `n_(e )n_(h)=n_(i)^(2)`
`therefore n_(h)=(n_(i)^(2))/(n_(e ))`
`=((1.5xx10^(16))^(2))/(5xx10^(22))`
`therefore n_(h)=4.5xx10^(9)"hole"//m^(3)" "...(1)`
(ii) For p-type semiconductor:
(no. of Si atoms in 1 `m^(3)` volume) `to` (no. of B atoms in 1 `m^(3)` volume)
`10^(6) to 200`
`therefore 5xx10^(28)to` (?)
`rArr` Number density of trivalent B atoms (or hole number density).
` n_(h)=(200xx5xx10^(28))/(10^(6))`
`therefore n_(h)=10^(25)("hole")/(m^(3))`
Now `n_(e )n_(h)=n_(i)^(2)`
`therefore n_(e )=(n_(i)^(2))/(n_(h))`
`therefore n_(e )=((1.5xx10^(16))^(2))/(1xx10^(25))`
`therefore n_(e )=2.25xx10^(7)("free electrons")/(m^(3))" "...(2)`
Equations (1) and (2) indicate that `n_(h) gt n_(e )`
`rArr` In the reverse bias condition of given pn-junction, holes will contribute majority in producing reverse saturation current.
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