**Faebian Bastiman**

As a III-V MBE grower you probably take great care to measure your fluxes. A monitoring ion gauge (MIG) is an excellent tool to establish a beam equivalent pressure vs temperature relationship for all your sources. To do so use the method in Post bake tasks: Group III flux: Arrhenius plots. A good cell is relatively stable and hence only one recheck at the start of each day is necessary to confirm the flux is as expected. The measured Ga and As fluxes can then be directed toward a GaAs(100) substrate and hopefully we can find the optimum growth conditions using Little known MBE facts: Group V overpressure. But what is our growth rate?

If you are lucky enough to have a fully functioning RHEED system you can quickly calculate your growth rate in monolayers per second (ML/s) from the RHEED oscillations using the guidance in Little known MBE facts: RHEED oscillations (1). If not, you can still extract the necessary data from SEM, XSTM, TEM, XRD, reflectivity, CV or SIMS. Great! Some even have atomic resolution and the ability to tell you the number of monolayers you have grown, others give lower resolution data and hence a number of units start to accumulate: ML/s, Å/s, nm/min, µm/h. So what unit should we use for our growth rate?

Why… atoms/cm^{2}/s of course! What!? Well the fact is every semiconductor substrate you use has a lattice constant that is known to several significant figures of accuracy. GaAs has a lattice constant (a) of 5.65338 Å. The GaAs(100) plane has 2 atoms per a^{2}, or a density of 6.258 x 10^{14} atoms/cm^{2}. And so our highly precise BEP measurement that resulted in a growth rate of 1 ML/s is in fact 6.258 x 10^{14} atoms/cm^{2}/s. This very conveniently means we can quote our Ga flux in terms of the system independent units of atoms/cm^{2}/s rather than the system dependent BEP units of nA or mBar or µTorr. But how do we switch between the units?

A ML on any zinc blende (100) plane is by definition half the lattice constant (^{a}/_{2}). So for GaAs(100) 1ML/s is 2.82669 Å/s or 0.282669 nm/s. With 3600s in an hour and 1000nms in a µm,1 ML/s equates to 1.0176 µm/h. Which conveniently means 1ML/s is ~1um/h for GaAs(100).

N.B. In order to save yourself the chore adding a perfunctory “x 10^{14}” when talking about your atoms/cm^{2}/s, you may wish to consider the using the units atoms/nm^{2}/s; since 6.258 x 10^{14 }atoms/cm^{2}/s is conveniently 6.258 atoms/nm^{2}/s.

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How can I calculate the flux in atoms/nm^2/s when the only information I have is the BEP in mbar ?

You cannot. You need to know the growth rate to convert.

I wonder why a monolayer on zinc blende structure in half lattice parameter ?

Take a good look at the zinc blende unit cell down one of the six faces here:

http://www.dawgsdk.org/crystal/en/library/zinc-blende#0000

Whilst the unit cell has 4 complete layers before you reach the next unit cell, a ML only has 2 complete layers. Therefore it is half of the unit cell height.

Thank you for your answer and your website, I still wonder why a monolayer is 2 complete layers instead of one since it’s called a “mono” layer ?

Hi Tina,

There are various ways to think about this. For GaAs it is easiest to consider the alloy: GaAs. GaAs requires one full layer of Ga and one full layer of As to make a single monolayer of GaAs.