Question

Gallium Arsenide
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The charge carrier density of GaAs at 31o C is 2.25x106 cm-3.
What is the charge carrier density (in cm-3) at 175oC?

(The bandgap of GaAs is 1.42 eV. )

I am trying with arrhenius relationship but get confused over "charge carrier density"

Answer 1

charge carrier density here means how many electrons per cm^3
will go into conductivity band

For temp1, 31C -> 304.2K

2.25*10^6 = exp( - 2.275*10^-19 / (1.381*10^-23 * 304.2))

For temp2, 175C -> 448.2K

x = exp( - 2.275*10^-19 / (1.381*10^-23 * 448.2))

put this into wolfram alpha

(2.25*10^6/x) = exp( - 2.275*10^-19 / (1.381*10^-23 * 304.2)) / exp( - 2.275*10^-19 / (1.381*10^-23 * 448.2))

=> 8.09*10^13