Diffusion of carriers in a double heterostructure

[EmilyRuck]

Hello!
Double heterostructures are used in LEDs and lasers to provide both the confinement of the charge carriers and the confinement of the generated light.
This image is a comparison between a homojunction and a heterojunction.
As regards the unbiased junctions, when the n region and the p region come into contact, the electrons of the n region diffuse in the p region despite the higher energy values of the conduction band.
Heterojunctions are built to confine the charge carriers; the central region (which will be the active region) has the conduction band limit which is lower than the conduction band of the left and right regions; the valence band limit is instead higher than the "neighbour". In the image, an electron from the right region could diffuse into the central one; but what can certainly prevent the electrons to diffuse from the central region to the left one, "climbing" and following the conduction band?
In a pn traditional junction, electrons can climb bands as written before; why should this case be different?

 

[EmilyRuck]

For example, let's refer to this document, page 7, figure (a). If electrons migrated from the right (n-AlGaAs) region to the central (GaAs) region, overstepping that high barrier potential, how can we be sure that they won't also overstep the barrier between the central and the left (p-AlGaAs) region?
Figure (a) is referred to a zero-bias condition. A forward bias would be even worse, the barriers will be lower!

 

[espen-4]

To be sure that a carrier does not cross a barrier you have to design the step to be high enough so that the probability of the carrier crossing the barrier is close to zero. The probability of a carrier crossing a step goes as exp(-E/kT) where E is the energy step across the barrier, T is the temperature in Kelvin and k is the Boltzmann constant. So, the probability decreases very fast as the step energy increases. Also, as the temperature decreases the probability decreases because the carriers have less energy at low temperature.

 

[EmilyRuck]

To be sure that a carrier does not cross a barrier you have to design the step to be high enough so that the probability of the carrier crossing the barrier is close to zero.

Ok and thank you! As far as you know, which could be a typical height choosen for barriers in heterostructures? (For example, in the case of AlGaAs - GaAs - AlGaAs)

 

[espen-4]

I do not know the typical height, but I think a height of 100 meV should be sufficient for a device operating at room temperature. For lower temperatures an even lower step height would be sufficient in order to trap the carriers in the low gap material.
You also need to look at how the band alignment changes as you go from undoped to doped layers. The Fermi levels must be aligned. This is easy to find in textbooks. My favourite being Streetman: Solid state Electronic Devices.