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. )
To find the charge carrier density at 175°C, we need to use the equation:
n2 = n1 * exp[(Eg / 2k) * (1 / T1 - 1 / T2)]
Where:
n1 is the charge carrier density at temperature T1 (31°C)
n2 is the charge carrier density at temperature T2 (175°C)
Eg is the bandgap of GaAs in eV (1.42 eV)
k is the Boltzmann constant (8.617333262145 x 10^-5 eV/K)
T1 and T2 are the temperatures in Kelvin (31°C = 304K, 175°C = 448K)
Let’s plug in the values to calculate the charge carrier density at 175°C:
n2 = 2.25x10^6 * exp[(1.42 / (2 * 8.617333262145 x 10^-5)) * (1 / 304 - 1 / 448)]
First, let's calculate the term inside the exponential:
(1.42 / (2 * 8.617333262145 x 10^-5)) * (1 / 304 - 1 / 448) = 17.03149
Now, let's calculate the exponential term:
exp(17.03149) = 2.182 x 10^7
Finally, let's calculate the charge carrier density at 175°C:
n2 = 2.25x106 * 2.182 x 10^7 = 4.885 x 10^13 cm^-3
Therefore, the charge carrier density at 175°C is approximately 4.885 x 10^13 cm^-3.