find the intrinsic concentration, ni for silicon at 300k.given that Eg =1.12V Ao=5.85×10^5 q=1.6×10^-19C K=1.38×10^23J/K. using ni= Ao T^3/2 exp(-q/KT . Eg/2).
To find the intrinsic concentration (ni) for silicon at 300K using the given formula ni= Ao T^(3/2) exp(-q/KT * Eg/2), we need to substitute the given values into the equation. Let's break it down step by step:
1. Substitute the given values into the formula:
- Ao = 5.85 × 10^5
- q = 1.6 × 10^-19 C
- K = 1.38 × 10^23 J/K
- Eg = 1.12 V (this needs to be converted to Joules)
- T = 300 K
2. Convert the value of Eg from volts to Joules:
- Since 1 eV = 1.6 × 10^-19 J, we can convert Eg by multiplying it with the conversion factor:
Eg(J) = Eg(V) * q = 1.12 V * 1.6 × 10^-19 J/V = 1.792 × 10^-19 J
3. Substitute the converted values back into the formula:
ni = Ao * T^(3/2) * exp(-q / KT * Eg / 2)
ni = 5.85 × 10^5 * 300^(3/2) * exp(-(1.6 × 10^-19 C) / (1.38 × 10^23 J/K * 300 K) * (1.792 × 10^-19 J) / 2)
4. Simplify the equation using the given values:
ni = 5.85 × 10^5 * 300^(3/2) * exp(-1.6 × 10^-19 C * (1.792 × 10^-19 J) / (1.38 × 10^23 J/K * 300 K * 2))
5. Calculate T^(3/2) to solve the equation:
T^(3/2) = 300^(3/2) = (300^3)^(1/2) = 27000000^(1/2) ≈ 5196
6. Substitute the value of T^(3/2) back into the equation:
ni = 5.85 × 10^5 * 5196 * exp(-1.6 × 10^-19 C * (1.792 × 10^-19 J) / (1.38 × 10^23 J/K * 300 K * 2))
7. Perform the remaining calculations:
ni = 5.85 × 10^5 * 5196 * exp(-1.6 × 10^-19 C * 1.792 × 10^-19 J / (1.38 × 10^23 J/K * 300 K * 2))
ni = 5.85 × 10^5 * 5196 * exp(-0.256)
8. Calculate the final result:
ni ≈ 9.65 × 10^9
Therefore, the intrinsic concentration (ni) for silicon at 300K is approximately 9.65 × 10^9.