In the company you work as an engineer, you are assigned to determine the electrical conductivity of a new intrinsic semi-conductive material at temperatures of 20 and 100 °C and the band gap (Eg). So you cut out this material in the form of a rectangular prism with a length of 30 cm, a width of 1 cm and a thickness of 2 cm and apply a potential difference of 1 V size by placing the electrodes on the faces shown. In this case, you have observed that the current flows at 0.8A at 20 °C and 12A at 100 °C. According to this information a) calculate the electrical conductivity of the material at 20 °C and 100 °C and b) the band gap of this material.

Question

In the company you work as an engineer, you are assigned to determine the electrical conductivity of a new intrinsic semi-conductive material at temperatures of 20 and 100 °C and the band gap (Eg). So you cut out this material in the form of a rectangular prism with a length of 30 cm, a width of 1 cm and a thickness of 2 cm and apply a potential difference of 1 V size by placing the electrodes on the faces shown. In this case, you have observed that the current flows at 0.8A at 20 °C and 12A at 100 °C. According to this information a) calculate the electrical conductivity of the material at 20 °C and 100 °C and b) the band gap of this material.

I found the electrical conductivity of the material. How can I find the band gap of this material?

Answer 1

I am not certain what you did. But for intrinistic semi-conductors, if you can know :(or calculate) the charge carrier density, it is related

n=constant (e-(bandgap/2kT)
so of you plot ln(n) vs 1/T, the slope is -Egap/2k

you know k, so Egap is then known.

Answer 2

To find the band gap (Eg) of the material, you can make use of the temperature-dependent electrical conductivity data that you have obtained.

The electrical conductivity (σ) of a material can be related to the band gap (Eg) using the Arrhenius equation:

σ = σ0 * exp(-Eg / (k * T))

Where σ0 is a pre-exponential factor, Eg is the band gap energy, k is the Boltzmann constant (8.617333262145 x 10^-5 eV/K), and T is the temperature in Kelvin.

To determine the band gap of the material, you can rearrange the equation and solve for Eg:

Eg = - (k * T) * ln(σ / σ0)

Now, let's calculate the band gap of the material at 20 °C and 100 °C:

a) At 20 °C:
- Temperature (T) in Kelvin: T = 20 + 273.15 = 293.15 K
- Electrical conductivity (σ): σ = 0.8 A (given)
- Pre-exponential factor (σ0) is not provided in the question. You can assume a value based on the characteristics of the material or consult relevant literature for typical values. Let's assume σ0 = 1 S/cm (Siemens per centimeter) for demonstration purposes.

Plugging the values into the equation:

Eg = - (8.617333262145 x 10^-5 eV/K) * (293.15 K) * ln(0.8 A / 1 S/cm)

b) At 100 °C:
- Temperature (T) in Kelvin: T = 100 + 273.15 = 373.15 K
- Electrical conductivity (σ): σ = 12 A (given)
- Pre-exponential factor (σ0) is again assumed as σ0 = 1 S/cm.

Plugging the values into the equation:

Eg = - (8.617333262145 x 10^-5 eV/K) * (373.15 K) * ln(12 A / 1 S/cm)

By calculating the band gap using the above equations, you can determine the energy gap (Eg) of the intrinsic semi-conductive material at both 20 °C and 100 °C.