# Does diffusion current in semiconductor always exist?

According to what I understand, diffusion current is caused by the change in concentration of charge carriers in semiconductor (free electrons and holes) from higher concentration region to lower concentration region due to thermal energy. However, I'm still unsure that if the diffusion current always exist inside crystal. As the concentration drop in higher region and increase in lower region, finally, the concentration in the whole crystal will be equal so no concentration change. Will the diffusion current still exist after that.

Moreover, in non-doping semiconductor (ex: pure Si) the density/amounts of holes and electrons the same so is there diffusion current. Suppose that the diffusion is only 1 dimensional and 1 direction. The charge carriers which diffuse contain both hole and electron then the total charge movement is zero that make the current zero, is it true?

• Current is typically separated into drift (field driven) and diffusion (random walk) pieces. Carriers are always diffusing. In equilibrium, the net diffusion is zero, but each electron or hole is moving about. Sep 22, 2015 at 17:30

In a semiconductor at thermal and diffusive equilibrium, the net current is zero for each of the carrier types, i.e., it is zero both for the electron and hole currents separately. The total current is the sum of the diffusion current (proportional to the gradient of the density of carriers) and the drift current driven by an external field (the electrostatic field in most of the cases for a semiconductor). In brief, in a semiconductor in thermodynamic equilibrium the diffusion current compensates the drift current for each of the carriers separately resulting in a zero net current.

Note that an intrinsic semiconductor at thermodynamic equilibrium may have diffusion and drift currents different from zero but the total net current still be zero due to the compensation of the drift and diffusion currents (this would be the case of an isolated semiconductor crystal placed inside an electric field).

• You might consider it semantics but a device under a field is not in thermodynamic equilibrium (although it can reach a stationary state with no net current). Equilibrium implies no external forces. Several properties that hold in equilibrium are broken by the presence of a field Sep 13, 2021 at 7:40
• You are right. It is not semantics. It is the difference between the equilibrium state (detailed balance holds) and stationary state (detailed balance does not hold) May 7, 2022 at 7:08

The diffusion current serves to equalise charge density everywhere. But in any given crystal at a finite temperature above 0 K, there will be some concentration gradients somewhere for both holes and electrons. This leads to diffusion currents. But note that the magnitude of such currents is very small and it is very difficult to measure them. The same thing also happens in conductors but takes place much faster than semiconductors.

Semiconductors (doped and not, both) has some charge carriers. For penta-valent semiconductors, it is electrons, and for tri-valent semiconductors, it is holes.

And, diffusion of charge carriers always takes place. But, the motion of charge carriers is completely random. And, statistically, the motion of charge carriers in every direction is equally distributed making the net current zero.

So, there is no net current caused by the diffusion of charge carriers.

• I feel the answer should emphasize that this is only true at equilibrium Sep 13, 2021 at 7:35
• This is innacurate. Completely (presumably uniformly) random movement does not imply no net movement. If you have a box of marbles where all of the marbles are in one corner and you move them in random directions within the box you will expect net movement away from the corner. Its the same in semiconductors.
– Matt
Jan 13, 2022 at 0:13

I was not satisfied with any of the answers. And yet the answer feels to be 'straightforward'. The answer is a resounding No. Given a perfect situation, where everything is in equilibrium; There are no external electric fields, no temperature changes, a nice (uniformly doped or intrinsic) semiconductor should not posses diffusion or drift currents. If however, we have a non-uniformly doped material, then things are not so perfect. There is a different kind of equilibrium in this case.

Let's say this material was differentially doped in one dimension 'x'. There are more dopants one side than the other, which keep decreasing with 'x'. In this case, we will observe a diffusion of carriers from the higher concentration end to the lower concentration. Moving carriers connotes current.

What exactly is diffusion? It has nothing (or little) to do with charged carriers in the body, it is not an electric phenomenon but a thermal one. Particles at a given thermal energy are in random thermal movement in the body. They over time just happens to find more spacious avenues and spread out. Fick's law. These particles are charged in this case and cause diffusion current.

But till when? Are these particles always diffusing? Yes and No. Let's divulge the situation better, these carriers are not on their own. They are over their host atoms (dopant or intrinsic). When these carriers diffuse away from their host atoms, they become ions and try to pull carriers back. A very "sticky" equilibrium is reached. So they do have the propensity to diffuse further, but can't.