Free electron and hole model of semiconductor conductivity

We will now expand the free electron model from NetLogo model 13.4.1 to model semiconductors. So, now it will be a free electron and hole model. Note a few differences between this and the original model:

  • There is a band-gap slider. This determines how much energy it takes to excite a valence electron to create a free electron-hole pair. This happens probabilistically in the model based on temperature, set the with temperature slider. The higher the temperature, the more likely for an electron-hole pair to be generated.
  • There is no slider for scatter probability. Instead, the scatter probability is modeled as a linear function of temperature. It is displayed below the temperature slider.

Use this model to answer the questions below.

Exercise 13.10.1: Semiconductor model
Not Currently Assigned

Take about 10 minutes to complete this exercise.

  1. Try varying the the band-gap and the temperature. Under what conditions will the semiconductor conduct electricity? Why is this?

  2. Set the band gap to 4, and the voltage to 2. Create a plot of the relationship between temperature and current and explain what you see. I know the current numbers bounce around - just do your best!

  3. The equation for the conductivity of a conductor is $\sigma = n |e| \mu_e$ (Eq. 13.8.1). Write down an equation for the conductivity of a semiconductor. Which of the variables are functions of temperature?