A pure silicon crystal at temperature 300 K has electron and hole concentration ( n i ) 1 0 16 per m 3 each and 1 0 21 phosphorus atoms ( n e ) are added per cubic metre. The new hole concentratio

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A pure silicon crystal at temperature 300 K has electron and hole concentration ( n i ​ ) 1 0 16 per m 3 each and 1 0 21 phosphorus atoms ( n e ​ ) are added per cubic metre. The new hole concentration in silicon crystal is

TestHub · Accepted Answer

According to the mass action law for semiconductors:

$n_{e} n_{h} = n_{i}^{2}$

Given the intrinsic carrier concentration $n_{i} = 1 0^{16}$ m $^{- 3}$ .

Phosphorus is a pentavalent impurity, which acts as a donor. Since the number of donor atoms added is much greater than the intrinsic concentration, the new electron concentration is approximately equal to the donor concentration:

$n_{e} \approx N_{D} = 1 0^{21}$ m $^{- 3}$

Substituting the values into the mass action law to find the new hole concentration $n_{h}$ :

$n_{h} = \frac{n _{i}^{2}}{n _{e}}$

$n_{h} = \frac{( 1 0 ^{16} ) ^{2}}{1 0 ^{21}}$

$n_{h} = \frac{1 0 ^{32}}{1 0 ^{21}} = 1 0^{11}$ m $^{- 3}$

Answer: $1 0^{11}$ per m $^{3}$

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