Question

Using this formula:

nᵢ = 5.2 x 10¹⁵T³/² exp (-E/2KT)

T stands for temperature.
-Eg = -1.12
k = 1.38E-23
Find ni for temperatures:
a) 300 Kelvin
b) 293.15 Kelvin
c) 343.15 Kelvin
d) 233.15 Kelvin
For reference, in part a, ni for 300 Kelvin is supposed to equal 1.08E10, so if you do not get that through your work, you are doing something wrong.

Answer 1

Intrinsic carrier concentration ni can be calculated for different temperatures using a given formula that takes into account the temperature in Kelvin, the energy bandgap, and the Boltzmann constant. The formula includes an exponential term, and Eg must be converted to joules before calculation. Examples provided show how to calculate ni for various temperatures.

Step-by-step explanation:

To calculate the intrinsic carrier concentration ni for various temperatures, we will use the formula:

ni = 5.2 x 1015T3/2 exp (-Eg/2KT)

Where:

• T is the temperature in Kelvin,
• Eg is the bandgap energy (-1.12 eV for silicon),
• K is the Boltzmann constant (1.380649 x 10-23 joule per kelvin).

First, we convert Eg to joules (since K is in joules per kelvin):

Eg = -1.12 eV * 1.602 x 10-19 J/eV

For each temperature, we then calculate ni as follows: