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How electron temperature is obtained from a practical current-voltage characteristics curve?

How electron temperature is obtained from a practical current-voltage characteristics curve?

 

How electron temperature is obtained from a practical current-voltage characteristics curve

Figure 1: A practical current-voltage characteristics

 

The electron temperature can be estimated using the following equation

{\begin{array}{l}\;\;\;\;\;\;\;I_e=I_{esat}exp(\frac{V_B-V_p}{T_e})\\\\\Rightarrow\frac{I_e}{I_{esat}}=exp(\frac{V_B-V_p}{T_e})\\\\\Rightarrow\ln(\frac{I_e}{I_{esat}})=\frac{V_B-V_p}{T_e}\\\\\Rightarrow T_e=\frac{V_B-V_p}{\ln({\displaystyle\frac{I_e}{I_{esat}}})}\\\end{array}}

Where

Te=Electron temperature

Isat=Electron saturation current

 

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