# Carrier Actions

 Recombination Generation Let's Draw! Related Topics

### Plotting & Problem Solving

Given a band diagram, there are many things you can interpret from them:
1. If the Fermi level is present and flat, the semiconductor is in equilibrium.
2. If the Fermi level is above mid-gap, it is doped with donors and n-type.
3. If the Fermi level is below mid-gap, it is doped with acceptors and is p-type.
4. If there is band bending, there is an electric field being applied or the doping is not uniform.
From this interpretation, other plots can be determined. For example, plotting the concentration of electrons and holes, the electric field, the electrostatic potential, and Jdrift and/or Jdiffusion.

Steps for plotting no and po

1. Make axes (remember carrier concentrations are never negative)
2. Find where no= po (use this point as reference because it would be ni)
3. Note where po= ni and/or no= ni,
4. Where EF > Ei, no > ni and po < ni,
5. Where EF < Ei, no < ni and po > ni,
6. Plot (remember this is on a semi-log scale)
7. To verify (or a shortcut), it should look like Ec (for p) or Ec inverted (for n)
Steps for plotting E
1. Make axes (remember to leave room because E can be negative)
2. Find where E = 0 (places where Ec is flat)
3. Find where E < 0 (Ec would have a negative slope going from left to right)
4. Find where E > 0 (Ec would have a positive slope going from left to right)
5. Note when the slope changes (it starts going positive/negative or to 0)
6. Note when the slope is the steepest (that's where the largest E would be)
7. Plot (remember to plot on a linear scale)
Steps for plotting V
1. The simplest way is to plot Ec upside down, taking some point as reference.
Steps for plotting Jdrift and Jdiffusion
1. Note the equations for Jndrift and Jpdrift.
2. Find E (using the steps described above)
3. Find n and p (using the steps described above)
4. Find and plot where Jdrift = 0 (remember in equilibrium J = 0)
5. Determine polarities (use the slope of the electric field)
6. Plot
7. Plot Jndiffusion by taking the mirror image of Jndrift
8. Plot Jpdiffusion by taking the mirror image of Jpdrift
* Remember, since the plot for carrier concentrations is exponential and the plot for the electric field is linear, the resulting plot will be exponential.
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