Final answer:
In order to find the donor impurity concentration, use the formula n = 1/(q*R*d), where q is the electron charge, R is the resistivity, and d is the electron mobility. The resistivity at T=200 K is approximately 3.33 Ω·cm, and at T=400 K is approximately 6.67 Ω·cm.
Step-by-step explanation:
To find the donor impurity concentration, we can use the formula:
n = 1/(q*R*d)
where n is the donor impurity concentration, q is the electron charge (1.6 x 10^-19 C), R is the resistivity (5 Ω·cm), and d is the electron mobility (approximately 3000 cm^2/V·s for silicon).
Substituting the given values:
n = 1/(1.6 x 10^-19 C * 5 Ω·cm * 3000 cm^2/V·s)
n ≈ 1.04 x 10^16 impurities/cm^3
To find the resistivity at T=200 K and T=400 K, we can use the formula:
R2 = R1 * (T2 / T1)
where R1 is the resistivity at T=300 K (5 Ω·cm), T1 is the initial temperature (300 K), T2 is the new temperature (200 K or 400 K), and R2 is the new resistivity.
Let's calculate the new resistivities:
- R2 at T=200 K = 5 Ω·cm * (200 K / 300 K) ≈ 3.33 Ω·cm
- R2 at T=400 K = 5 Ω·cm * (400 K / 300 K) ≈ 6.67 Ω·cm
Your question is incomplete, but most probably the full question was:
An n-type silicon sample has a resistivity of 5Ω−cm at T=300 K.
a.) What is the donor impurity concentration?
b.) What is the expected resistivity of the material at T=200 K and T=400 K ?