Have you ever wondered what the material delivery efficiency of standard MBE effusion cells actually is? We typically spend on average £2k a year on source materials and £1.5k a year on substrates. We slice our substrates into 11.4 x 11.8 mm2 pieces and get 12 from a 2” wafer. This means our substrate usage efficiency is around 80%. This is the price we pay for cleaving square pieces out of circular substrates. This means we are using £1.2k out of our £1.5k of wafers and losing some £300 a year directly into the recycling bin.
But what about our £2k of cell material?
Well we buy a 240g charge of As every 3 years. This means we load 1.93 x 1024 atoms into our system every 3 years. We grow on average 1 µm a day, on a ~10 x 10 mm2 active area, 280 days a year for 3 years. This is 84 mm3 of GaAs or 1.86 x 1021 As atoms. That means out of 1.93 x 1024 As atoms we put into our system only 1.86 x 1021 actually end where we want them i.e. in our epilayers. That is 0.1%. Ouch, 99.9% material wasted!
Ok, just breathe. We know As is pretty wasteful, it is so gaseous that it goes everywhere. What about our group III’s?
Well we buy a 30g charge of Ga every 6 months. This means we place 2.6 x 1023 Ga atoms in our small 10cc effusion cells every 6 months. We still grow the same 1 µm a day, 87% of which is Ga. We grow this for 140 days in 6 months on our same ~10 x 10 mm2 active area. This is 12 mm3 of GaAs or 2.7 x 1020 Ga atoms. That is also an efficiency of 0.1%.
So out of our £2k a year on material we are only using £2 usefully. The other £1.998k ends up plastered all over the chamber walls, caking shutter blades and gathering in a large pool at the lowest point on the system.
Can we do anything to improve the situation? Sadly for standard effusion cells the answers is: very little.
We could reduce the cell-substrate distance. In the extreme case you could have the sample at the cell orifice, however the temperature rise when opening the shutter would be horrendous and group III cells tend to spit material too. The cell-sample distance is related to the number of sources, and assuming you want 10 cells and a pyrometer pointed towards your sample the current distances are already the lowest possible.
We could reduce the cell’s orifice with a Ta aperture. Effusion cells are designed to create a uniform flux across a certain sample area however they also spray material non-uniformly in almost every direction. In our case the sample area is 4x less than intended, so we could potentially achieve 4x the efficiency (a jaw dropping 0.4%) by reducing the orifice. The minimum aperture is related to the required flux uniformity, and in most cases this is optimized at the time of manufacture too.
We could also lower the deposition rate. There are some fixed time intervals for MBE, like the time the shutters are closed whilst the oxide is being removed and whilst samples are being transferred. When you grow at 0.1 ML/s you are losing 10x less material than when you grow at 1 ML/s in these fixed times. Of course some times lowering the deposition rate does not help. When you are growing a 5 nm / 5 nm GaAs/AlAs superlattice, for example, it does matter what the deposition rate is since (assuming the growth rates of the two cells are identical) the atomic equivalent of 5nm of Ga will be deposited on the Ga shutter whilst it is closed during the 5nm AlAs layer, and vice versa. The efficiency increase depends on the ratio of growth time to preparation time. If we grow a 100 period 5 nm / 5 nm superlattice at 0.11 ML/s we waste 0.37x less material than if we grow at 0.55 ML/s but the total sample growth is increased by 1.9x. This comes down to throughput, the data in this article is gathered for a deposition rate of 0.55 ML/s, 0.000001 ML/s is very efficient but…
With the orifice and the 0.11 ML/s growth rate the efficiency of a Ga cell would be 1%. This is certainly better, but still extremely wasteful.
The final option is to used valved sources. Whilst valved sources are not particularly effective for high vapour pressure elements like As and P, Sb can be delivered with much higher efficiency because it behaves more like an Architypal molecular beam than a gas source. Valved sources are pretty standard for group Vs but what about group IIIs? Well e-Science are currently introducing their Valved Titan effusion cells for Ga and In. A valved source has two distinct advantages over a standard cell. On the one hand the material wastage is significantly reduced, since the cell can be idled hot with the valve closed. On the other hand, varying the valve position can enable instantaneous changes in deposition rate. A fully valve sourced III-V MBE system is certainly amongst my MBE dreams.