Semiconductor devices: PN-junctions

If there were only intrinsic semiconductors, they wouldn't be very technologically interesting, because they mostly act as lousy conductors. If there were only one type of extrinsic semiconductor, they still wouldn't be very technologically interesting - we'd only be able to make already modestly performing conductors a bit better. So what's the big deal?

Most of the interesting technological applications of semiconductors come from putting p-type and n-type extrinsic semiconductors into contact with each other creating what is known as a pn-junction.

NetLogo model 13.12.1 below models a pn junction. It mostly works like the models of conductors and semiconductors we have seen on previous pages, but there are a few key additions needed to model a pn-junction. In the various versions of the free electron (and hole) model on the previous few pages, we assumed that electrons and holes did not exert forces on one another. We assumed that they only felt the force of the electric field from the applied voltage. The reason pn-junctions are interesting, is because they develop a built-in voltage which can influence the flow of the charge carriers. To model this, we have to make a few changes:

We assume that the background "patches" in the model have a charge to balance out the free electrons and holes. Each impurity atom that donates an electron becomes a positive $+1$ ion and each acceptor impurity atom that creates a hole becomes a negative $-1$ ion. The net charge is still zero of course.
At each time step in the model, we calculate an electric field due to the background ions and the distribution of electrons and holes. At each $x$-location, we calculate the charge density by adding up all the charge contributors—the ions (patches) and free charge carriers (electrons and holes). We then calculate the electric field at each x-position by calculating what force a $+1$ charge would feel from the charge density at each x-location. Then, we also calculate potential at each location (relative to the left side of the model) by integrating the electric field from left to right—this is the equivalent of saying "how much energy would we get by moving a charge through each increment of the electric field." We only do this in the x-direction and assume everything is uniform in the $y$-direction.
At each time step, the charge carriers are accelerated by the force from the electric field at their location.

Use the model to answer the questions below and learn more about pn-junctions.

Take about 20 minutes to complete this exercise.

Try running the model with a positive voltage greater than $+1$ (called a forward bias) and a negative voltage less than $-1$ (called a reverse bias). What happens in each case? Consider how the charge carriers are moving and the change in current.

With the voltage set to $0$, what happens to:

The interactions of electrons and holes near the interface.
The charge density across the domain.
The electric field across the domain. Think about the electric field in terms of the force that it applies to a positive charge: $F = q\mathscr{E}$

There are lots of other interesting experiments you can run with NetLogo model 13.12.1. Can you computationally derive rectifying behavior? What happens if you allow for intrinsic carriers to be activated (and how would you do that in the model)? What happens if $p$ is larger than $n$? What happens to your rectifying behavior if the scattering frequency is too large? If you have time, explore these behaviors a bit.

MOSFETs or Metal-Oxide Semiconductor Field-Effect Transistors are on of the most pervasive semiconductor technologies on Earth. We'll discuss in class, but watch the video below in its entirety to better understand how these work - I think it's better than text. It's a bit old - but still relevant, and it rehashes many of the ideas we've introduces in the last few chapters.

Solar cells and LEDs

Solar cells and LEDs both use pn-junctions using the same principles but for opposite purposes.

Solar cells are made of pn-junctions. Light energy then creates intrinsic electron-hole pairs. If the pair is created at the junction, they will be accelerated in opposite directions due to the built-in potential. This creates a current, which can be used to do work.

LEDs use the same principle in reverse. A voltage is applied to push electrons and holes to recombine at the interface. When they recombine, they are going to a lower energy state and the extra energy is emitted as a photon, creating light. The band gap of the material determines how much energy is released which determines the wavelength (and therefore the color) of the light.