Question

Assumc that in an n-type gallium arsenide semiconductor at T = 300 K, the electron concentration varies linearly from 1X1018 to 7X1017 cm-3 over a distance of 0.10 cm. Calculate the diffusion current density if the electron diffusion coefficient is Dn= 225 cm2/s.

Answer 1

The diffusion current density in the n-type gallium arsenide semiconductor is 2.88 x 10^-5 A/cm².

Step-by-step explanation:

To calculate the diffusion current density, we can use the equation:

j = -qDn(dn/dx)

where j is the diffusion current density, q is the charge of an electron (-1.60 x 10-19 C), Dn is the electron diffusion coefficient (225 cm²/s), and (dn/dx) is the change in electron concentration per unit length.

In this case, the change in electron concentration is (7 x 1017 cm-3 - 1 x 10^18 cm-3) = -3 x 1016 cm-3, and the length over which it changes is 0.10 cm. Plugging these values into the equation, we get:

j = (-1.60 x 10^-19 C)(225 cm²/s)(-3 x 10^16 cm-3 / 0.10 cm) = 2.88 x 10-5 A/cm²

Answer 2

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.