# How the Depletion Region of PN Junction changes under Bias

There are several other questions on PN Junctions out there, but I don't think this one has been asked specifically.

I am having a severe misunderstanding of how the depletion region width varies under bias. I know that what I am thinking is incorrect somehow, but I am unsure wear.

I will reference this picture from a textbook I like:

The depletion region is created due to a balance of diffusion and drift current. Diffusion pressure causes holes to travel from the P-side and electrons to travel to the N-side and combine with one another around the junction. This combination leaves behind positive charge on the N-side and negative charge on the P-side. This charge creates an electric field that opposes the diffusion current with a drift current. The width of the depletion region is determined by whatever amount of charge transfer balances the drift and diffusion pressures.

Now, if you have a higher concentration of dopants, you end up with more diffusion pressure which means the electric field must be bigger in order to oppose it, meaning that the depletion/space charge region must be wider. However, what I just said is incorrect, but i don't understand where my reasoning is wrong.

Now again, if you have a higher electric field applied you should get proportionally less diffusion current meaning that the width of the depletion region can be smaller and still fully oppose the diffusion current. This is also incorrect reasoning, but where did i go wrong?

The natural follow up is under forward and reverse bias. During a reverse bias I know that the depletion region grows, and under forward bias it shrinks. I can use Kirchoff's voltage laws and Fermi Levels and tons of other ways to reason out why that MUST be true. But what I CAN'T do is explain what physical motion of holes and electrons and recombination in the system under bias results in the the depletion region shrinking and growing under forward and reverse bias respectively.

Essentially, during the application of a bias, what are the holes and electrons phsyically doing during the transient under this new electric field applied to them? How does the depletion region physically change size?

Feel free to get as technical as needed, but I understand all of this in terms of just using math, but I am looking for a more intuitive understanding. Thanks.

Now, if you have a higher concentration of dopants, you end up with more diffusion pressure which means the electric field must be bigger in order to oppose it, meaning that the depletion/space charge region must be wider. However, what I just said is incorrect, but i don't understand where my reasoning is wrong.

If you understand that there's a built-in voltage, then you should also know that distance and path is unimportant to a voltage. Voltages are scalar. 5V over 1 billion miles is the same as 5V over 2um. Now the electric fields associated with those two voltage are entirely different. Now the reason that the depletion region gets smaller with higher dopants is that there is more static charges exposed in the depletion region. Think of it like this, with a low dopant level I'd have to take 3mm of space to free "20" charges, but if they were a higher density, I'd only have to take 3um to free "20" charges. Remember it's the exposed charges in the depletion region that create the field, not the charges in the drift region.

Now again, if you have a higher electric field applied you should get proportionally less diffusion current meaning that the width of the depletion region can be smaller and still fully oppose the diffusion current. This is also incorrect reasoning, but where did i go wrong?

You went wrong when you thought about the field inside the depletion region effecting things outside the depletion region directly. The field is stuck there. It can't directly effect anything. It does have some secondary effects though. For instance the wider the depletion region, the easier it is to diffuse across the non-depletion areas. This is because there is less distance to the end of the device when there's more length in the field. We use this all the time in BJT's. The other things that a field will do is create a build up of charges on it's edges (You know, all those ones you ripped out to create the depletion region, they want back to where they were). These "free charge" (free because they are able to move, unlike in the depletion region where the charges are held in the atoms of the crystal lattice) areas are actually what is driving the diffusion in the other areas. The free charges are more concentrated by the depletion region than in other places. Again, they want back, but the built in field removes them every time they try so they're stuck at the edge. This creates the "High to Low pressure" that drives diffusion. The higher the field, the more charges you ripped away that want to go back that the field at the boarder resists them, the more concentrated the free charges are, the more diffusion there is. All linked. I'll Try to get picture in here. It really is difficult to see without picture.

Edit: I've found a good Youtube video with all the particles present and a very decent explanation. I hope this helps.

• OK COOL. your first bit about the depletion width varying inversely with dopant concentration makes sense. simply, more charges can move across, meaning that you get a higher charge concentration within the depletion region which creates a larger electric field with less distance. I think I get that. But yes, I struggled visualizing everything you said in the second part. I'm not thinking of the E-Field within the junction, I am thinking of the applied E-field from the bias voltage, which charge carriers in the bulk should be affected by. Or is that wrong too? Commented Mar 4, 2016 at 19:42
• That is wrong. In PN semiconductors the electric field exists solely in the depletion region (any and all electric fields, external, internal, all of them). The bulk region is a diffusion only region. This isn't 100% true all the time, but the amount of field present in the bulk area is so small that it's negligible in every case except breakdown.
– Dave
Commented Mar 4, 2016 at 19:50
• why? is that true? Like... i have a voltage source connected around the junction, shouldn't the create an electric field which exists across the whole thing, including the bulk region? Commented Mar 4, 2016 at 20:01
• Yeah, no. The field will be contained almost entirely in the depletion region. That's why external voltages change the depletion width/ field strength and allow for carriers to either cross or not cross. Diffusion is the dominant mode of transportation in the bulk. Not to say that there's no field whatsoever, it's just so small that we often throw it out of the equations (seriously, it's sub 1% for good diodes). I was also surprised when I learned this. I encourage you to seek text books and other sources on this, because understanding this field and diffusion concept is critical.
– Dave
Commented Mar 4, 2016 at 20:09
• I think you're confused what a depletion region is. There are no free charges (i.e. there are no free electrons or holes there) in the depletion region. In the video, it's where there aren't any bouncing particles where the P and N junction is. Look at the video at 6:57. The depletion region is high-lighted.
– Dave
Commented Mar 4, 2016 at 20:34

Reverse bias means that the P-side is at a higher energy level and electrons need more energy to get from the N to the P-side.

If we increase the reverse bias and the width of the depletion region does not change the electrons don't have enough energy to get to the P-side, therefore diffusion current dominates and that increases the width of the depletion region until we get an equilibrium again.

Another way to think about it, is that for reverse bias the field in the depletion region has to be equal to the externally applied field. The higher the field in the depletion region the more atoms have to be uncovered (ionized). Since the number of atoms that can be uncovered is limited (depending on the doping level) the only way to get more atoms is to have a wider depletion region.

• Ok so we increase the reverse bias, meaning the electric field is stronger from right to left (using the pictures above). This means that electrons want to go left to right. This is the opposite direction that diffusion current would have them go. Which makes the diffusion current effectively weaker. Since the diffusion current is what causes electrons from the N-side to go to the P-side and holes from the P-side to go to the N-side (which is the mechanism that forms the depletion region in the first place) why doesn't it being weaker mean the depletion region shrinks? Commented Mar 4, 2016 at 19:04
• and yea, i get it in terms of KVL and Electric field continuity. I just don't get it in terms of particle motion. Commented Mar 4, 2016 at 19:07
• The drift and diffusion currents are independent of each other. We only consider their net effect. Commented Mar 4, 2016 at 19:12