To understand how the conductivity of a semiconductor like a diode depends on temperature, we need to consider the following:
1. Initial Conductivity and Temperature: At a base temperature of 25°C, semiconductors exhibit a certain level of conductivity. For simplicity, let’s assume this initial conductivity is 1 arbitrary unit.
2. Temperature Coefficient: The temperature coefficient indicates how much the conductivity changes per degree Celsius. Roughly, for many semiconductors, the temperature coefficient can be around 0.045 (unit per degree Celsius).
3. Temperature Change: If there is a temperature change from the initial 25°C to a new temperature (e.g., 50°C), we must account for how this change affects the semiconductor’s conductivity.
To calculate the new conductivity, we use the following relation:
[tex]\[ \text{New Conductivity} = \text{Initial Conductivity} \times \left(1 + \text{Temperature Coefficient} \times (\text{Temperature New} - \text{Temperature Initial}) \right) \][/tex]
Here are the given values:
- Initial Conductivity ([tex]\( \sigma_0 \)[/tex]): 1 arbitrary unit
- Temperature Coefficient ([tex]\( \alpha \)[/tex]): 0.045 per °C
- Initial Temperature ([tex]\( T_0 \)[/tex]): 25°C
- New Temperature ([tex]\( T \)[/tex]): 50°C
Now, let’s substitute these values into the relation:
[tex]\[
\text{New Conductivity} = 1 \times \left(1 + 0.045 \times (50 - 25)\right)
\][/tex]
[tex]\[
\text{New Conductivity} = 1 \times \left(1 + 0.045 \times 25\right)
\][/tex]
[tex]\[
\text{New Conductivity} = 1 \times \left(1 + 1.125\right)
\][/tex]
[tex]\[
\text{New Conductivity} = 1 \times 2.125 = 2.125
\][/tex]
Thus, when the temperature increases from 25°C to 50°C, the conductivity of the semiconductor increases to 2.125 units. This result implies that as temperature rises, the number of charge carriers in the semiconductor also increases, leading to higher conductivity.
In summary:
- At 25°C, the initial conductivity is 1 unit.
- With an increase in temperature to 50°C, the new conductivity becomes 2.125 units.
