So you have established your binary GaAs and AlAs growth rates using Little Known MBE facts: RHEED oscillations (1) and now your thoughts are moving to ternaries. The AlxGa1-xAs ternary is fully miscible. [Al] > ~85% are indirect gap materials. If you are using AlGaAs as a carrier confining cladding layer you may want [Al] from 30-40%. So how do we calculate our ternary growth rate?
Well conveniently algebra of epitaxy holds. First find your GaAs growth rate of 0.7ML/s and your AlAs growth rate of 0.3ML/s, separately. Then when you open the two cells’ shutters together you will get Al0.3Ga0.7As growing at 1ML/s. Just remember to suitably increase your As flux to ensure good RHEED oscillations for each measurement and good stoichiometric crystal growth.
On the other hand, you can approach the problem from an entirely different angle. In the growth of InGaAs (for example) you can first accurately determine your GaAs growth rate and then (at a suitably low temperature to ensure unitary In sticking coefficient: <540 °C but good adatom mobility: >500°C) you can add a little In and grow InxGa1-xAs. The resulting increase in growth rate will allow you to determine the InAs growth rate (GR) since:
GRInGaAs = GRGaAs +GRInAs
This conveniently means we you can accurately determine your growth rate and composition for any and all AlxGa1-xAs or InxGa1-xAs ternary alloys on a single sample within a matter of minutes. How very efficient of you.
RHEED oscillations provide a very fast and accurate method of growth rate determination for 2D materials. The principle involves variation of the electron scattering which can be monitored by integrating the primary RHEED spot intensity. The idea being a smooth surface provides an intense, coherent primary spot, whilst a rough surface provides a weak, incoherent primary spot. The degree of roughness corresponds to each fraction of a ML growth with a maximum roughness and hence low intensity for 0.5ML deposited and a maximum smoothness and hence high intensity for the smooth surface after 1 full ML. This is shown diagrammatically in figure 1 (below).
There is actually a lot more going on than meets the eye. To begin with we can determine the growth rate of GaAs and AlAs on GaAs(100). To start you will want to anneal the surface under a low As flux (~0.3ML/s at 600°C) to ensure you have a very flat starting surface. Then you simply set your optimum As growth flux and open the respective Ga or Al shutter and monitor the intensity. Typically a frame grabber card and appropriate software is used, but even the naked eye can discern the first few intensity oscillations.
It is a simple case of counting the number of oscillations (1 oscillation = 1ML) and averaging them over time (in seconds) to determine the growth rate in ML/s.
The oscillations will eventually dampen out, it depends on how smooth the starting surface was and how well you balanced the III:V ratio. 30+ oscillations are good. The reason for the damping is due to the fact that the 2nd ML starts on the wide islands before the 1st ML is fully formed and so on for the 3rd and 4th MLs; hence the system is moving toward some equilibrium surface roughness.
The oscillations may also not be equally spaced. The first few may have a larger or small period than the last 30. This is actually informing you about the growth rate perturbation caused by the shutter transient. This can actually be significant ±20% has been observed on poorly designed or orientated sources. The time and magnitude of the perturbation can have serious consequences, especially when growing thin QWs or SLs where the growth only comprises the shutter transient. The WEZ-type sources with integral shutters from MBE Komponenten utilised on our system have excellent stability and virtually no shutter transients.
 J.H. Neave, B.A. Joyce, P.J. Dobson and N. Norton, Appl. Phys. A 1983 31(1):1
MBE surface characterisation benefits greatly from reflection high energy electron diffraction (RHEED) in situ monitoring. RHEED can give information regarding roughness, surface order, growth rate and even polycrystalline grain size. It also proves a highly repeatable means of temperature determination with reasonable accuracy. The secret is differentiating the three different types of temperature dependence.
Type 1 is flux independent, substrate independent. Being independent of flux and material is very useful, as it means you are also system independent. Unfortunately only a limited number of these points exist. The most obvious one on a III-V MBE system is As cap removal. This is the evaporation of As bulk from any substrate surface. Since this is a property of the As and not the substrate it tells you when any substrate is at ~300 ± 10°C. So you can quickly compare the temperature of S.I. and n+ GaAs and also InAs, InP and GaSb. The RHEED transition is amorphous to single crystalline.
Type 2 is flux independent, substrate dependent. A well known example of a type 2 RHEED transition is oxide removal. All substrates have a specific temperature at which the native oxide thermally decomposes. GaAs is 590 ± 10°C. InAs is 500 ± 10°C. A less well known type 2 transition can be utilised if the substrate has both c(4×4) and (2×4) reconstructions. GaAs and InAs are good examples. Under no external As flux a RHEED transition occurs where As-As bonds supporting the 1.75ML of As of the c(4×4) thermally destabilise and only 0.5ML of As on the (2×4) remains. For GaAs this happens at 400 ± 10°C. For InAs it seems to occur at a similar temperature. For AlAs the c(4×4) to (2×4) appears to be somewhat higher. Regardless of the absolute temperature, type 2 transiton always occur at the same temperature for a given material system, so it can be used as a quick temperature calibration point.
Type 3 is both flux and substrate dependent. A number of static reconstructions exist on III-V substrates. Each happens at a specific temperature under a specific As flux. The reconstructions are c(4×4) to (2×4) to (4×2) and each represents the loss of As from the surface. Hence the larger the As flux the higher the temperature at which the reconstruction transition occurs. Accurate and repeatable temperature determination relies on accurate and repeatable flux determination. However if you calibrate your III:V ratio using the steps in Little known MBE facts: Growth rate and flux the c(4×4) to (2×4) transition can be used to estimate 500 ± 20°C for a 0.5 ML/s As flux.
Which means for GaAs(100) we can determine with reasonable accuracy 300, 400, 500 and 600°C
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/cm2/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 a2, or a density of 6.258 x 1014 atoms/cm2. And so our highly precise BEP measurement that resulted in a growth rate of 1 ML/s is in fact 6.258 x 1014 atoms/cm2/s. This very conveniently means we can quote our Ga flux in terms of the system independent units of atoms/cm2/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 1014” when talking about your atoms/cm2/s, you may wish to consider the using the units atoms/nm2/s; since 6.258 x 1014 atoms/cm2/s is conveniently 6.258 atoms/nm2/s.
It is a well known fact in the MBE community that the group V element should be over supplied during III-V MBE. If pressed a grower will probably recommend a 1.6:1 As:Ga ratio when discussing optimal GaAs growth conditions. When asked why (?) the answer is simple: because these are the optimum conditions. But why ?
Well upon heating GaAs in a vacuum a number of notable phenomena occur. Arsenic is the more volatile of the two species and this fact underpins the observed phenomena. Firstly, the sublimation of As bulk: any amorphous As that condensed on the surface will readily evaporate at around 300 °C resulting in a c(4×4) reconstruction. Secondly, sublimation of As-As dimers: further heating in the absence of an external As flux results in a (2×4) reconstruction appearing in favour of c(4×4) at ~400°C; this represents the loss of As dimers back bonded onto As lattice sites. Thirdly, breaking of the As-Ga bond: continued heating under no external As flux results in a very rough surface as As-Ga bonds break and the upper GaAs surface thermally decomposes into sublimed As and Ga droplets.
To prevent thermal damage above 400°C it is therefore necessary to supply an As over pressure. The actual magnitude is almost irrelevant so long as it is large enough to compensate As loss from the surface. This minimum As overpressure depends on the substrate temperature. Supplying a flux close to the minimum is advantageous since it allows the surface to readily anneal and flatten; and also (from an economical point of view) results in minimal wastage of As.
Supplying a Ga flux to the mix results in GaAs growth. Now the required As flux has two parts, firstly it needs to compensate for As loss, secondly it needs to compensate for the additional Ga on the surface and ensure stoichiometric crystal growth. The total required As flux can therefore be thought of as:
Astotal = AsAs + AsGa
AsGa is temperature independent. The AsGa flux required to compensate the Ga flux is by definition 1:1. A slightly higher flux is recommended to prevent unwanted Ga-Ga interactions on the surface, though fluxes greater than 1.2:1 start to impair adatom mobility (increasing roughness) and increase the chance of point defects (such as anti sites). Conversely AsAs is temperature dependent, but Ga independent. At the optimum MBE growth temperature for GaAs formation (~600 °C) the AsAs flux required to maintain the surface is ~0.3 ML/s; which is a sizable fraction of the typical MBE growth rates of 0.5 – 1.0ML/s. Combining these two constituents means the actual optimum As:Ga flux ratio is (…as an MBE grower I would say…) about 1.6:1.
In the first instance MBE appears to be a rather complicated affair involving pumps, LN2, valves, fluxes and vacuums. A high purity vacuum and effusion sources are essential and require great attention, however when an MBE system is well maintained and operated the problem of MBE growth optimisation becomes trivially two dimensional: A III:V MBE grower ultimately only has control over two parameters (1) the growth temperature and (2) the III:V flux ratio.
Most miscible materials can therefore be optimised within less than 10 sample runs. Take GaAs/GaAs(100) as a thought exercise. A simple assessment of a direct band gap semiconductor like GaAs is a room temperature PL investigation. To differentiate between the epilayer and the substrate we will want to confine carriers and possibly shift the wavelength away from the ~872nm of bulk GaAs at RT. A suitable test structure is shown in figure 1 (below) with a RT PL of ~810nm.
The first thing to do is discern a favourable starting point. The oxide remove temperature is a good starting temperature for optimal GaAs growth (~580°C) and a flux ratio that gives a slightly weak 2×4 pattern and >20 RHEED oscillations before damping is a good flux. The flux ratio can also be estimated by (carefully and quickly) finding the dynamic (2×4)/(4×2) transition by dropping the As flux for a given growth rate. This corresponds to an As:Ga of ~1:1. A good starting point is ~1.6:1, hence the As beam equivalent pressure of the 1:1 can be simply multiplied by 1.6.
Once these basic conditions have been found, a bench mark test structure can be obtained. Then the optimisation can begin. Increase and decrease the As flux by ~10-15% and increase and decrease the growth temperature by 10-20°C. Which of these 5 is the best? Which of these 5 gives the brightest PL with the narrowest FWHM? The cycle can then be repeated until no further improvement in RT PL is observed.
A myriad of III-Vs can be optimised either directly (by RT PL) or indirectly (in the case of AlGaAs) by the effect they have on RT PL of the confined layer. The only encountered notable exception is GaAsBi. Where the miscibility, ordering and phase separation are just some of the added complexity. GaAsBi is actually an excellent system to study as it possesses every complication to MBE growth. The idea being once you can grow bismide you can grow anything.