Question

An electric field of 100 V/m is applied to a sample of n-type semiconductor whose Hall coefficient is -0.0125 m³/C. Determine the current density in the sample, assuming the electron mobility to be 0.36 m²V⁻¹s⁻¹.

Answer 1

The current density in the sample can be determined using the equation j = nquE, where j is the current density, n is the number of charge carriers per unit volume, q is the charge of the charge carriers, μ is the electron mobility, and E is the electric field. Plugging in the given values: j = (-0.0125 m³/C)(1.6 x 10^-19 C)(0.36 m²V⁻¹s⁻¹)(100 V/m). Simplifying gives the current density: j = -7.2 x 10^20 A/m².

Step-by-step explanation:

The current density in the sample can be determined using the equation:j = nqμE

where j is the current density, n is the number of charge carriers per unit volume, q is the charge of the charge carriers, μ is the electron mobility, and E is the electric field.

Plugging in the given values:j = (-0.0125 m³/C)(1.6 x 10^-19 C)(0.36 m²V⁻¹s⁻¹)(100 V/m)

Simplifying gives the current density:j = -7.2 x 10^20 A/m²

Answer 2

To determine the current density, we can use the formula j = nqυ. The drift velocity can be calculated using the formula υ = μE. Hence, the current density is 7.2 x 10^-22 A/m² and drift velocity is 36 m/s.

Step-by-step explanation:

To determine the current density in the sample, we can use the formula j = nqυ, where j is the current density, n is the number of charge carriers per unit volume, q is the charge of the charge carrier, and υ is the drift velocity of the charge carriers.

The Hall coefficient is given as -0.0125 m³/C, which represents the number of charge carriers per unit volume.

The electric field is given as 100 V/m, which can be used to calculate the drift velocity using the formula υ = μE, where μ is the electron mobility.

Plugging in the values, we have μ = 0.36 m²V⁻¹s⁻¹ and E = 100 V/m. Therefore, υ = (0.36 m²V⁻¹s⁻¹)(100 V/m) = 36 m/s.

Now, let's calculate the current density.

The charge of an electron is -1.6 x 10^-19 C, so q = -1.6 x 10^-19 C.

Plugging in the values, we have j = nqυ = (-0.0125 m³/C)(-1.6 x 10^-19 C)(36 m/s) = 7.2 x 10^-22 A/m².