Final answer:
The diffusion current density in an n-type gallium arsenide semiconductor can be calculated using the formula j = -qDn(dn/dx), where j is the diffusion current density, q is the charge of an electron, Dn is the electron diffusion coefficient, and (dn/dx) is the change in electron concentration with respect to distance.
Step-by-step explanation:
To calculate the diffusion current density, we can use the formula:
j = -qDn(dn/dx)
where j is the diffusion current density, q is the charge of an electron (-1.6 x 10⁻¹⁹ C), Dn is the electron diffusion coefficient (225 cm²/s), and (dn/dx) is the change in electron concentration with respect to distance.
Plugging in the given values, we have:
j = -(-1.6 x 10⁹ C)(225 cm²/s)((7 x 10¹⁷ cm⁻³ - 1 x 10¹⁸ cm⁻³) / 0.10 cm)
Simplifying the expression, we get:
j = -3.6 x 10^-20 C/s
Therefore, the diffusion current density is -3.6 x 10⁻²⁰ C/s.