Question:
For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (\(T\)) dependence of free electron concentration (\(n\))?
For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (\(T\)) dependence of free electron concentration (\(n\))?
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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.
Updated On: Jan 31, 2025
- \includegraphics[width=5cm]{22a.png}
- \includegraphics[width=5cm]{22b.png}
- \includegraphics[width=5cm]{22c.png}
- \includegraphics[width=5cm]{22d.png}
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The Correct Option is A
Solution and Explanation
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: \[ \boxed{{(1)}} \]
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: \[ \boxed{{(1)}} \]
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