Question

For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (\(T\)) dependence of free electron concentration (\(n\))?

• A. A
• B. B
• C. C
• D. D

Hint:

For n-type semiconductors, remember that at lower temperatures, donor saturation keeps \(n\) constant, while at higher temperatures, thermal generation of intrinsic carriers causes \(n\) to increase.

Answer 1

The Correct Option is A

Step 1: Understand the temperature dependence of carrier concentration in n-type silicon.
In non-degenerately doped n-type silicon: 1. At low temperatures (high \(1/T\)), the majority carrier concentration \(n\) is dominated by donor ionization and becomes saturated, showing little variation with temperature.
2. At high temperatures (low \(1/T\)), intrinsic carrier generation due to thermal excitation begins to dominate, leading to an increase in \(n\). Step 2: Analyze the behavior of the plot.
1. At low \(1/T\) (high temperatures), intrinsic excitation causes an increase in carrier concentration.
2. At high \(1/T\) (low temperatures), donor saturation results in a plateau in \(n\). Step 3: Identify the correct plot.
Among the provided options, only plot (A) correctly depicts this behavior:
Saturation of \(n\) at high \(1/T\) (low temperatures).
Increase in \(n\) at low \(1/T\) (high temperatures) due to intrinsic excitation. Final Answer: \[ \boxed{{(1)}} \]