Ln sigma vs 1/T curve for p-type semiconductor

In summary, the ln (σ) versus 1/T curve for a p-type semiconductor has a negative gradient at low temperatures, a flat region at a saturation point, and a positive gradient at higher temperatures. The impurity level in the band structure diagram affects the shape of the curve by determining the energy level at which electrons can contribute to the conductivity. This curve is different from that of an n-type semiconductor, which would have a positive gradient at low temperatures and a negative gradient at high temperatures.
  • #1
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Homework Statement



a) Sketch a schematic band structure diagram for a p-type semiconductor. Mark the energy of the top of the valence band, the bottom of the conduction band and the impurity level on the diagram.

b) Sketch the ln (σ) versus 1/T curve for a p-type semiconductor, where σ is the conductivity and T is the temperature. Explain how the shape of the curve relates to the energy levels in the diagram in part a).

The Attempt at a Solution



b) The diagram I found in my notes has ln (σ) on the y-axis and 1/T on the x-axis, and there is a line with a negative gradient, and then it is flat where there is saturation and then the line has a negative gradient again. But I am not sure whether this is for an n-type or p-type semiconductor. I could only find one diagram in my notes and nowhere seems to tell me how the graph looks different for an n-type or p-type semiconductor.

Do the graphs look different for n-type and p-type semiconductors? Please help.
 
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  • #2


Hello, the graphs for n-type and p-type semiconductors do indeed look different. For a p-type semiconductor, the ln (σ) versus 1/T curve will have a negative gradient at low temperatures, indicating a decrease in conductivity. This is because at low temperatures, there are fewer thermally excited electrons available to contribute to the conductivity. As the temperature increases, the curve will become flatter, indicating a saturation point where the conductivity reaches a maximum value. This is due to the impurity level in the band structure diagram, which acts as a trap for the thermally excited electrons, preventing them from contributing to the conductivity. As the temperature continues to increase, the curve will have a positive gradient, indicating an increase in conductivity due to more electrons being thermally excited and able to contribute to the conductivity. The impurity level in the band structure diagram also plays a role in the overall shape of the curve, as it determines the energy level at which electrons can be excited and contribute to the conductivity. Therefore, the shape of the ln (σ) versus 1/T curve is directly related to the energy levels in the band structure diagram. I hope this helps!
 

1. What is the significance of the Ln sigma vs 1/T curve for p-type semiconductors?

The Ln sigma vs 1/T curve is a graphical representation of the conductivity (sigma) of a p-type semiconductor at different temperatures (1/T). It is used to determine the activation energy of the semiconductor, which is a measure of how easily electrons can move through the material. This information is important for understanding the electrical properties and potential applications of the semiconductor.

2. How is the Ln sigma vs 1/T curve obtained for p-type semiconductors?

The curve is obtained by plotting the natural logarithm of the conductivity (Ln sigma) on the y-axis against the inverse of temperature (1/T) on the x-axis. The data points are usually obtained by measuring the conductivity of the semiconductor at different temperatures and then using a mathematical formula to calculate the Ln sigma value.

3. What is the expected shape of the Ln sigma vs 1/T curve for p-type semiconductors?

The curve is expected to be linear, with a negative slope. This is because the conductivity of p-type semiconductors decreases as temperature increases due to the decrease in the number of holes (positive charge carriers) available to conduct electricity.

4. How does the activation energy affect the Ln sigma vs 1/T curve for p-type semiconductors?

The activation energy affects the slope of the curve. A higher activation energy results in a steeper slope, indicating a larger decrease in conductivity with increasing temperature. This means that the semiconductor has a larger band gap and is less conductive at higher temperatures. On the other hand, a lower activation energy results in a shallower slope, indicating a smaller decrease in conductivity and a more conductive semiconductor at higher temperatures.

5. What are the practical applications of the Ln sigma vs 1/T curve for p-type semiconductors?

The curve can be used to determine the activation energy of a p-type semiconductor, which is important information for designing and optimizing electronic devices such as transistors and solar cells. It can also be used to compare the properties of different p-type semiconductors and to study the effects of doping and other factors on the conductivity of these materials.

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