# Diffusion current because of internal field of semiconductor

Suppose we have an isolated n-type semiconductor having varying concentrations of carriers over x. After some finite time, the concentration becomes uniform for a given constant temperature. We always say that this is because of diffusion which allows the movement of charge carriers to move from higher to lower concentrations. But shouldn't this diffusion occur because of the repulsive forces between electrons? why do we say it's because of the random motion? (the random motion allowing for the carriers to rearrange should be because of the electric field produced by them due to the gradient of charges). If we see some excess charges added to an isolated conductor, then the electric field produced by these excess charges allows the charges in the conductor to redistribute to settle on the outer surface where the net force experienced by the excess charges is zero. Shouldn't the same principle apply to semiconductors? What exactly is happening inside?

I hope to get a clarified answer. Diagrams will be highly appreciated.

## 1 Answer

I had the same doubt! Here is why. Because there are no excess charges at all! The semiconductor is perfectly charge neutral (always and all the times). There could be excess carriers but not excess charges. This is a fundamental misconception between charges and current. In semiconductors, there are currents with it being charge neutral.

• First, understand that there could be current without having an excess charge (+,-). Charge is the property of matter. But current is due to "moving charged bodies". Within a system, there could be overall zero charge (equal +ve and -ve charged bodies) yet current could be observed because some of the charged bodies were moving. In semiconductors, these mobile carriers are "electrons" where as the immobile charged bodies are "ions".
• Next, understand diffusion. It is not an electrostatic phenomenon. Arguably, every force at its heart is electrostatic. Electrostatic force is one of the four universal forces and the most ubiquitous. But it is not at all qualitative to revert to it so much. Diffusion is a thermodynamic concept. There is thermal energy that sends particles in a system into a random motion. The collision of particles causes "heat". When particles don't collide? They keep on moving in the directions they didn't collide. The spaces into which these particles moved into are more spacious and less concentrated. This is why gases expand. In semiconductors, electrons are believed to be highly mobile and project this behaviour.
• Lastly, there is a day and light difference between semiconductors and metals (conductors). The first step would be to address the atomic bonding, semiconductors have covalent bonds! They share electrons among atoms. After doping, the excess carriers (only) have ionic bonds in it. Whereas, metals, they have metallic bonds. There is a sea of electrons present which is loosely tucked and easy to influence. Not the case with semiconductors. There are many other differences, semiconductors are conceived of quantum mechanics and solid state physics and are beyond Maxwell's Electrodynamics.

But shouldn't this diffusion occur because of the repulsive forces between electrons?

Answer is in Quantum Mechanics. They are said to form "Energy Bands". To say more, electrons here are shared amongst atoms and hold discrete quantum states. This is described acc to Kronig Penny Model in solid state physics. The Ionic bonding of dopant carriers is described by the more familiar Bohr Model. They are very neatly arranged in the lattice together. So no repulsion amongst them.

I'll suggest reading Kittel's or Neamen's book for engineers. Take a stab at Shankar's or Dirac's book too.

• thank you for your answer Commented Oct 31, 2023 at 12:28