The energy gap of an element is given as 5.9x10* eV. Calculate the intrinsic coherent

To calculate the intrinsic carrier concentration of a semiconductor given the energy gap, we can use the formula that relates the energy gap to the intrinsic carrier concentration. The intrinsic carrier concentration (n_i) can be expressed using the equation:

Understanding the Formula

The intrinsic carrier concentration is given by:

n_i = sqrt(N_c * N_v) * exp(-E_g / (2 * k * T))

Where:

• n_i = intrinsic carrier concentration
• N_c = effective density of states in the conduction band
• N_v = effective density of states in the valence band
• E_g = energy gap (5.9 eV in this case)
• k = Boltzmann's constant (8.617 x 10^-5 eV/K)
• T = absolute temperature in Kelvin

Values Needed for Calculation

To proceed with the calculation, we need to assume a temperature. A common reference temperature is room temperature, approximately 300 K. At this temperature, we can also use typical values for the effective density of states:

• N_c ≈ 1.5 x 10^19 cm^-3
• N_v ≈ 1.5 x 10^19 cm^-3

Plugging in the Values

Now, substituting the values into the formula:

n_i = sqrt(1.5 x 10^19 * 1.5 x 10^19) * exp(-5.9 eV / (2 * 8.617 x 10^-5 eV/K * 300 K))

Calculating the Exponential Term

First, let's calculate the exponential part:

-5.9 / (2 * 8.617 x 10^-5 * 300) ≈ -5.9 / 0.0518 ≈ -113.5

Now, calculating the exponential:

exp(-113.5) ≈ 1.1 x 10^-50

Finding the Intrinsic Carrier Concentration

Next, we calculate the square root term:

sqrt(1.5 x 10^19 * 1.5 x 10^19) = 1.5 x 10^19

Now, we can combine these results:

n_i = 1.5 x 10^19 * 1.1 x 10^-50 ≈ 1.65 x 10^-31 cm^-3

Final Result

The intrinsic carrier concentration for the element with an energy gap of 5.9 eV at room temperature is approximately 1.65 x 10^-31 cm^-3. This value indicates that the material is a very poor conductor at room temperature, which is consistent with the high energy gap.