Hi Bhanu,

Interesting question... The 2DEG forms because the conduction band edge falls below the Fermi level at the GaN side of the interface. The equilibrium band structure is a function of the intrinsic band gap of the materials (with the vacuum energies lining up across the interface), the static net polarisation charge and the redistribution of the free electrons.

So simply put the 2DEG forms at the GaN side of the interface because it is energetically preferable for it to do so. Remember that every charge has a counter-charge, and the entire system should be neutral. The positive charge in the AlGaN side isn't due to empty donor states, it is due to bond polarisation... if it were due to trap states then yes, we would expect some recombination at that point, and the 2DEG density would definitely be affected. But as it is the most convenient place for the electrons to congregate is on the GaN side, in very close proximity to the positive polarisation charge at the interface.

Of course it is typical to use an AlN interlayer between the GaN channel and AlGaN barrier to further confine the 2DEG wavefunction to the GaN side. This reduces the risk of random alloy scattering from the barrier layer and has additional advantages from a material growth perspective. Check my paper on that here: http://scitation.aip.org/content/aip/journal/apl/103/8/10.1063/1.4818645

This is my interpretation of the system, but it would be interesting to get the take of more experience researchers in this forum. Of course we're always happy to be corrected...!

Good luck.

Recombination with positive sheet charge happens only when the positive charge is due to empty states. These states are normally neutral and full. When they emit an electron they become positively charged and empty. The 2DEG charge would then be due to the electrons emitted by the donors. These electrons can be reabsorbed again. In modulation doped HEMTs in GaAs, the 2DEG is formed by emission of electrons from a remote donor state. Even there, it is still energetically favorable for the electrons to not recombine with the donor states but form a mobile 2DEG instead.

The positive charge at AlGaN/GaN interface is due to spontaneous and piezoelectric polarization which has an entirely different physical origin. Polarization always comes in dipoles and cannot be neutralized in conventional ways. There is no "donor/acceptor" state for polarization charge. That is why we say that the 2DEG charge comes from surface donors. If the 2DEG electrons have to recombine, it will be with the surface donor states.

Hi Matthew and Geetak,

Thank You for responses.

@Geetak:

I did not get some part of your answer. 

"These states are normally neutral and full. When they emit an electron they become positively charged and empty. The 2DEG charge would then be due to the electrons emitted by the donors. These electrons can be reabsorbed again."  

Which states are you talking about here?

Can you please elaborate on this part?

Thank you

This question is basic and interesting.

On contacting the two materials, they will go to thermal equilibrium state, by exchanging mobile charges and heat till the fermi level gets equal all over the  structure. I described this process before. The result is a steady state charge distribution in the heterojunction in form of a dipole layer around the hetero face composed of one side from holes in the side of Al GaN and  a free electron layer in the GaN surface.

Because of the equilibrium the density of these charges is on the average constant with time.They are a consequence of the different work functions of the two materials.

This phenomenon is general and occurs also for homojunctions such as pn junctions.

when the dipole is composed of mobile charges, its charges will be pulled to each other by electrostatic forces and therefore one speaks from a two dimensional gas. The thickness of the two dimenional gas is limited by the diffusive tendency of the electrons.

This is not the great issue in your subject. You asked about the recombination possibility of electrons with holes. 

I want put some fundamentals concerning recombination:

Recombination occurs when an electron meets a hole, therefore it is a microscopic local process and it occurs when electrons wnd holes are present in the same volume.

Any semiconductor material in equilibrium has in very location electros and holes such that p0 n0=ni^2. Really there is recombination in every location, and since the the material is in equilibrium no and p0 must be kept constant on the average, and therefore a electron hole generation consequently occurs.

This process is called thermal generation, and hence

the recombination rate = thermal generation rate and so the material remains in equilibrium.

This means that there is recombination which is balanced by thermal generation since the material is in thermal equilibrium.

Net recombination occurs when there is excess mobile charge concentration and net generation occurs when when there is net deficiency in the mobile charges, that is pn< p0 n0.

Bet wishes 

Hi Bhanu,

Sorry for the confusing wording. By 'states' I'm referring to the case where positive charge at the heterojunction is formed not due to polarization but due to donor states at that interface. In this case the donor states emit their electrons which form the 2DEG. This is what happens in AlGaAs/GaAs HEMTs. This case is different from the polarization case (AlGaN/GaN) where the positive charge is due to polarization and the donor states are not at the heterojunction interface but are at the surface. In both cases, 2DEG electrons come from donor states but the location of the donor states is different. Also, electrons leave the donor states to form a 2DEG in both cases because overall it results in reduction of electron energy. If the energy was not being minimized, electrons would rather stay trapped in the donor states and not form a mobile 2DEG.

I don't know if that makes it more clear.

Hi Geetak,

Thank You

It is more or less seems clear as of now.

This concept of 2DEG formation due to polarization is very new to me and has not sunk in well yet. I keep getting new doubts everyday. I will keep posting my doubts.                 Hoping to get response in future as well :)

Hi All,

I have some more doubts regarding the polarization of a material leading to re-orientation of carriers.

We always talk about heterostructure when it comes to explaining the re-orientation of of electrons due to polarization. 

Now, let us consider just AlGaN (no heterostructure), it still has some polarization (spontaneous polarization and no piezoelectric polarization), which means there are +ve and -ve sheet charges at the two ends of the AlGaN bar, which implies that there is a constant electric field in the AlGaN bar, which again implies that there has to be movement of carriers. But, here we don't have a place where carriers can be confined, and they can neither recombine with the sheet charge as explained above (sheet charge is not because of vacancy etc.).

So, how will be the distribution of carriers in steady state?                                               Will electrons and holes accumulate in the two ends to compensate for the charges without recombining?                                                                                                             How will Ec and Ev align?

Now, what happens if we make ohmic contact at the two ends and short them?     Will there be an impulsive current before it reaches steady state?

Thanks

Hi Bhanu,

I do not believe this will be the case. In an AlGaN/GaN heterostructure the 2DEG occurs because the band gap and polarisation discontinuities cause the conduction band to drop below the Fermi level. In bulk AlGaN I believe the polarisation will just act to modify the band bending at the upper and lower surface... my understanding is that the free carriers resulting from the background n-type dopants would screen out these effects in the material except for at the boundaries. Perhaps in a very thin layer you might see some effects such as you describe, but more than likely in this case the layer would be part of a heterojunction (i.e. in a quantum well or HEMT) and again it would be the relative difference at the interface which would be important.

Hi Matthew,

I agree that it will always be a part of a hetero-junction. But, hypothetically, let us consider a AlGaN bar (no hetero-structure), I am interested to know the band alignment and carrier distribution in it.

Will there still be band-bending in the steady state condition? Will the sheet charge in the two ends of the bar neutralize? But, going by the logic that these are polarization charges and they don't recombine, it seems they will always be there and attract opposite charges. So, there will be movement of carriers. What will be the final distribution of carriers?  What if we short the two ends?

You are talking about screening. There has to be re-distribution of carriers even for screening.  

Thanks

Band bending will always occur in any situation at a semiconductor boundary regardless of whether it is air, vacuum, insulator, semiconductor or metal. This is due to the discontinuation of the crystal structure which forces the unpaired bonding electrons into new electornic states, which may be within the (bulk) band gap. These states are ubiquitous at the boundary and therefore force the Fermi-level to 'pin' at some energy, which results in the bending of the conduction and valence bands. Look up what happens at Schottky junction for a more thorough explanation of this.

I believe that in bulk AlGaN something similar will occur, and the polarisation effects will only act to contribute to the overall bending. Because the polarisation charge is a function only of the composition and strain, the electric field (i.e. voltage gradient) associated with it will become less intense with increased thickness.

So at each end of the AlGaN bar there may be a slight accumulation of electrons or holes, but this would be a secondary effect and I don't think it would be measureable. The fact that we discard the polarisation effects at the GaN buffer/substrate interface in contemporary HEMT design is a sign for this: that interface is just too far away from the active 2DEG region to have any importance.

Theoretically, spontaneous polarization is a bulk property of the material. So even if have just bulk AlGaN or bulk GaN, there should be polarization. This means that accumulation of electrons and holes should happen at the ends of the crystal. Confinement can happen at the ends as the carriers will be sitting against the vacuum energy level. If you make an ohmic contact at the two ends, it might behave like a p-n junction.

However, I think these are hypothetical scenarios because it is literally impossible to have surfaces without surface states. Also making ohmic contacts is also a tricky concept and will introduce complications. In the end, both ohmic contacts and surface states can change the properties at the surface. It is therefore extremely difficult, if not impossible, to detect such charge separation in bulk polar materials. Therefore, typically we only discuss polarization at heterojunctions.

If you want to understand modern theory of polarization in more detail, see this reference (http://link.springer.com/chapter/10.1007/978-3-540-34591-6_2). It is pretty involved but I hope it helps clear up some concepts about bulk polarization vs polarization discontinuities.