Carrier Actions
Plotting & Problem Solving
Given a band diagram, there are many things you can interpret from them:

If the Fermi level is present and flat, the semiconductor is in equilibrium.

If the Fermi level is above midgap, it is doped with donors and ntype.

If the Fermi level is below midgap, it is doped with acceptors and is
ptype.

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 J_{drift} and/or J_{diffusion}.
Steps for plotting n_{o} and p_{o}

Make axes (remember carrier concentrations are never negative)

Find where n_{o}= p_{o} (use this point as reference
because it would be n_{i})

Note where p_{o}= n_{i} and/or n_{o}=
n_{i},

Where E_{F} > E_{i}, n_{o} > n_{i}
and p_{o} < n_{i},

Where E_{F} < E_{i}, n_{o}
< n_{i} and p_{o} > n_{i},

Plot (remember this is on a semilog scale)

To verify (or a shortcut), it should look like E_{c} (for
p) or E_{c} inverted (for n)
Steps for plotting E

Make axes (remember to leave room because E
can be negative)

Find where E = 0 (places where E_{c}
is flat)

Find where E < 0 (E_{c}
would have a negative slope going from left to right)

Find where E > 0 (E_{c}
would have a positive slope going from left to right)

Note when the slope changes (it starts going positive/negative or to 0)

Note when the slope is the steepest (that's where the largest E
would be)

Plot (remember to plot on a linear scale)
Steps for plotting V

The simplest way is to plot E_{c} upside down, taking some
point as reference.
Steps for plotting J_{drift} and J_{diffusion}

Note the equations for J_{n}_{drift} and
J_{p}_{drift}.

Find E (using the steps described above)

Find n and p (using the steps described above)

Find and plot where J_{drift }= 0 (remember in equilibrium
J = 0)

Determine polarities (use the slope of the electric field)

Plot

Plot J_{n}_{diffusion} by taking the mirror
image of J_{n}_{drift}

Plot J_{p}_{diffusion} by taking the mirror
image of J_{p}_{drift}
* Remember, since the plot for carrier concentrations is exponential and
the plot for the electric field is linear, the resulting plot will be exponential.