BJT and graph of charge density over position

[KasraMohammad]

Say you are given the problem of constructing the charge density vs position graph of a BJT(lets take a NPN BJT under equilibrium conditions for example). Now, it is a given as to how a NPN BJT Energy Band Diagram would look like through intuition or a google search. Using only the information at hand, namely the Energy Band Diagram of the NPN BJT under equilibrium, how do you go about constructing the charge density vs position graph for it?

And if the above is known how to do, how would you construct the charge density vs. position graph if one would add to the problem that the NPN BJT is actually now under active mode biasing condition?

 

[Valkarie]

To construct the charge density vs position graph for a NPN BJT under equilibrium conditions, you would need to first calculate the charge density at each region of the BJT. This is usually done by solving the Poisson's equation for each region and using the Fermi-Dirac Distribution to determine the charge density. Once the charge density has been calculated at each region, you can then plot it against the position (x-axis) within the BJT on a graph. If the NPN BJT is now under active mode biasing conditions, then the calculation of the charge density becomes more complicated. The charge density for each region will now not only depend on the Fermi-Dirac Distribution, but also on the applied bias voltage. To calculate the charge density in this case, one would need to solve the Poisson’s equation with the added effect of the applied bias voltage. Once the charge density has been calculated, it can then be plotted against the position on a graph as before.