Little known MBE facts: RHEED oscillations (3)

Faebian Bastiman

I was recently reading a nanowire publication and I was reminded of another means of calibrating the group V flux that I used in my III-Sb days. This is the preferred method for III-Sb epitaxy, however  it is also applicable to general III-V growth. In the following I will use GaAs as an example.

The first step is to establish your Ga growth rate using the method in my RHEED oscillations (1) post. Then convert this into atoms/nm2/s using the method in my flux and growth rate post. Finally, you can then calculate the atomic flux of the Ga cell versus temperature using the method in my Arrhenius plot post.

Then set the As cracker to a value that you wish to determine in atomic flux, for example set it to 25 % open. Set the Ga cell temperature to give you a flux of 0.069 atoms/nm2/s [i.e. 0.1 ML/s growth rate on GaAs(100)]. Open the Ga shutter and record the RHEED oscillations in the usual manner. As long as the As flux is larger than the Ga flux you should obtain a growth rate of 0.1 ML/s ± an error of up to 5% depending on how well the RHEED intensity oscillated. Note the error gets larger the fewer oscillations you obtain. Hopefully you can get at least 10 oscillations.

Next double the Ga cell’s flux to obtain a growth rate to 0.2 ML/s and (importantly) leave the As flux set to the original value. You will need to leave the Ga cell to settle for 10 minutes after changing its temperature.  As long as the As flux is larger than the Ga flux you should be able to obtain a growth rate of 0.2 ML/s ± 5%. The magnitude of the As flux compared to the Ga flux is key to this method. Keep increasing your Ga flux until (eventually) the RHEED oscillations no longer yield the growth rate determined by the Ga cell. When this happens the growth rate is no longer dictated by the Ga flux, it is dictated by the As flux. You can check this by increasing the As flux and repeating the measurement that gave the lower than expected growth rate.

If you plot out all your data points you should obtain a graph like the one shown in Figure 1. You can see that starting at small Ga flux, the growth rate initially increases linearly until eventually it becomes As poor (Ga rich) and the growth rate is limited by the As flux. The growth rate you obtain under these As poor (Ga  rich) conditions indicates the As growth rate in ML/s. 0.5 ML/s in this example. You can then convert the As growth rate into an As flux using my flux and growth rate post once more.

Rheed 3 fig

How to grow your first sample: As capping

Faebian Bastiman

Having a metallic As source offers us the ability to create a very useful protective epilayer: an As cap. Once you have grown a layer you may want to remove the sample from your system and for example transfer it into a neighbouring system or send it to a collaborator for analysis. As soon as you remove the sample from vacuum the surface will of course oxidise. Oxidation cannot be avoided, however if you deposit an As cap of sufficient thickness before you remove the sample only the As will oxidise and your III-V epilayer surface will remain perfectly intact. Once the sample is safely bask inside a vacuum system, one need only heat it to ~300 °C and the As sublimes. A quick look with RHEED will show the original reconstruction is even preserved.


How does one deposit an As cap?

You can deposit an As cap on any surface. In this example I will discuss depositing an As cap on GaAs(100). At the end of your epilayer growth you will typically observe an As-rich (2×4) reconstruction. If you want to know what a reconstruction is see my What is a reconstruction? post. Essentially to deposit a cap all you need to do is fully open the As and turn off the sample heating. However there are a few things to consider:

Firstly, As2 tends to create a better cap than As4, so wherever possible you should use As2.

Secondly, the As cap grows very slowing whilst the substrate is above 100°C and it is preferable to cool the substrate down to 0°C in order to rapidly form a cap.

Thirdly, not only As but every other background species will readily condense onto the substrate at 0 °C including the hydrocarbon, water vapour, oxides and other undesirables lurking inside your vacuum.

In order to ensure the highest purity of your surface, it is a good idea to pre-protect the GaAs by creating an even more As-rich reconstruction than the (2×4). The reconstruction of choice is called a c(4×4). The c(4×4) is simply created by holding the substrate at 500 – 540 °C  in a moderate As flux for several minutes.

Test it yourself. Align the RHEED along the [-110] azimuth so you can see the 4x of the (2×4) shown in Figure 1a and then lower your substrate temperature until the 2x pattern of the c(4×4) appear as shown in Figure 1b. You may be asking yourself why a c(4×4) reconstruction has a 2x pattern. Well if you look closely at the reconstruction in Figure 1b you will see it is not simply a 2x, it is a pair of 2xs. The 2x at the top is out of phase with the 2x at the bottom (i.e. the lines on the RHEED screen do not line up). The 2x at the bottom is in fact exactly half way between the 2x at the top.

As cap v2

Rotate the sample to the [110] azimuth. You will see the exact same pair of 2x reconstructions there too. The c(4×4) looks the same along both [110] and [-110] azimuths. What is going on? Well the reconstruction’s unit cell is not aligned to the same directions as the (2×4). It is in fact centred on the original [100] and [010] directions of the (001) surface, which means it is at 45° to the (2×4) reconstruction.

The c(4×4) is composed of 1.75 ML of As on Ga. That  is a full ML of As plus another ¾ of a ML of As on top of that. This is significantly more As than the ¾ of a ML of the (2×4) reconstruction. The As of the upper ¾ ML of the c(4×4) are back bonded onto the As of the lower full ML, meaning that the As on the upper layer “sees” no Ga at all. Which more importantly means that the Ga in the buried layer is protected from contamination. The As dimers of the upper ¾ ML  arrange  themselves 3 abreast in a “brickwork pattern” and it is this arrangement that gives the pair of 2xs on the RHEED screen.

The c(4×4) is therefore perfect to pre-protect the epilayer. Once it has formed, simply ramp the substrate down to 0 °C  (or as low as you can go) and watch the RHEED. To get a more even As cap you can start the substrate rotation again now.

Once the substrate gets down below 100 °C you should find that the 2x is replaced by the 1x pattern shown in Figure 1c. This is because a thin amorphous As layer now exists on top of the c(4×4) and all you can see are the bulk lattice rods. As the amorphous As layer gets thicker, the RHEED beam can no longer penetrate through to the substrate and the RHEED pattern becomes the amorphous haze shown in figure 1d. This is probably somewhere around 5 – 10 nm thick. It may take >30 minutes from the moment the ramp down was started to the time the amorphous pattern is completed, depending on the background sample heating and the rate of cooling you can create inside your particular MBE chamber.

The As growth rate is highly temperature dependent. You want a final thickness of about 15 nm and from experience this takes about an additional 5 minutes after the amorphous RHEED has appeared. In order to get a more accurate estimate of the As cap growth rate, you can first create the c(4×4), then ramp down to 400°C, then turn off the As flux and leave the sample to equilibriate at 0°C  for half an hour, then apply the As flux and monitor the time it takes to create the amorphous pattern, then triple it. If you want to be really accurate with your cap thickness I suggest you perform cross sectional SEM on the sample and extract the cap thickness.

The As cap is not only useful to protect your epilayer ex situ, but can be used to perform two temperature calibrations at ~300 and ~400 °C  (in order to do that see my Making a static reconstruction map post.

How to grow your first sample: (2×4)/(4×2) transition 

Faebian Bastiman

The (2×4)/(4×2) RHEED transition is a very useful flux calibration point, since it tells you when your As and Ga fluxes are equal. I described what a (2×4) and a (4×2) reconstruction are in my What is a reconstruction post. In this post I will explain how to spot the transition with RHEED.

First of all you need to produce a good starting (2×4) surface. In order to do that follow the steps in my Oxide remove post. With the Ga shutter closed and an As overpressure incident on the sample you should see the As-rich (2×4) reconstruction on your RHEED pattern (Figure 1a). How can you be sure this is a (2×4) and not a (4×2) in disguise?

You can be 99% certain that if you are annealing at a temperature around 15 °C below the oxide remove temperature and the As flux that you are supplying is sufficient to grow GaAs that this is a (2×4) reconstruction. You can test very simply by stopping the rotation so you can see the 4x on the [‑110] azimuth and reducing the temperature. Reduce the temperature until a 2x appears. Rotate to 90° to the [110] azimuth. Still 2x?

If yes, then this a c(4×4) and the early reconstruction was a (2×4). Return to the original temperature and retrieve your (2×4). Note if you want to know what a c(4×4) is read my As cap post.

If no, and you are looking at a 4x, then this is now a (2×4). Remain at this temperature.

If no, and you are also not looking at a 4x, then something is very, very wrong with your sample. Are you sure it is GaAs(100)?

Assuming you have found your (2×4) make sure it looks like the one in Figure 1. If not change your temperature by 5 – 10 °C and your As flux by 10-20% and try to get the best (2×4) you can. You will note that in Figure 1a on the [‑110] azimuth the 4x rods are fairly short and bright even if the 2nd order rods are not very clear. The 2x on the [110] azimuth is simply a 2x and cannot give you any quality information at this point.

Try opening the Ga shutter. Does your 4x change to look like Figure 1b? It should. The Ga flux breaks up the static (2×4) and creates some disorder. This disorder results in an elongation of the 4x rods and an overall decrease in the intensity. The 2x on the other hand does not really change. You can consider Figure 1b as the dynamic (2×4), where “dynamic” means “growing”.

RHEED Ga to As

We are about to search for the Ga-rich (4×2) pattern. In your first few attempts do not rotate the sample, but rather keep the RHEED pointing along the [110] azimuth and looking at the 2x pattern. During the search the 2x will change into a 4x on [110] and the 4x will change into a 2x on [-110]. You can see the Ga-rich reconstructions in Figure 1d.

The problem with performing the transition without rotation is that you are only seeing the transition at the point the RHEED beam is hitting with the Ga and As flux pattern present at that point. This As/Ga ratio can be very different from the one created whilst rotating, since when you rotate you create a more even flux across the wafer. On the other hand since both the starting and ending reconstructions have both a 2x and a 4x azimuth it is not so obvious when the transition has happened until you have some experience looking at it.

So with the rotation off, the Ga shutter open and the 2x on the [110] azimuth on the screen close the As shutter (or close your cracker valve if you do not have a shutter).

Am I serious?


Close the As shutter for a few seconds and watch the RHEED, it should quite rapidly turn into a 4x like Figure 1d. Once it does open the As shutter again and make sure the 2x returns. When the As flux is greater than the Ga flux, you see the 2x of the (2×4) when the Ga flux is greater than the As flux you see the 4x of the (4×2). In the extreme case we just witnessed the Ga was of course practically infinitely bigger than the As flux.

Ok step 2 is a little less brutal… with the rotation off, the Ga shutter open and the 2x on the [110] azimuth on the screen… half the As flux. Wait 15s. Did the 4x appear? If yes return to the original As flux, if no half the As flux again. What you are doing is performing a binary search. You take the lowest As flux you know gives you a 2x and the highest As flux you know gives you a 4x and you apply the average of the two and see if you get a 2x or a 4x. Always wait the same 15s between flux changes for consistency.  

You may notice on your search that the 2x creates a rather dim 3x rather than the desired 4x (Figure 1c). This is a mixed reconstruction between the (2×4) and (4×2) that many people overlook. It is weak on both [110] and [-110] azimuths and hence probably lacks the long range order of the (2×4) and (4×2) reconstructions. The low intensity makes it difficult to say whether it is a (3×1) or a (3×4) or a (3×6) and indeed the physical surface of the GaAs could be made up of domains of each.

Once you have found the maximum As flux that gives you a 4x on the [110] in 15s, return to the original As flux that gave you the 2x on the [110]. In the third step gradually reduce the As flux from the start value toward the value you found and watch the RHEED pattern evolve. Double check the As flux you believe gives you a 4x on the [110] is reproducible and get familiar with the process.

Finally set the substrate rotation to around 0.2 revolutions per second and perform the third step again. The As flux required to create the 4x on the [110] azimuth may be a little different this time. With the rotation on you will see the 2x on the [-110] azimuth for the first time. Take a closer look at the reconstructions in Figure 1d.

The dynamic 4x you get when you are Ga rich is much sharper than the dynamic 4x you get in Figure 1b. This is because that whilst the Ga breaks up the As-rich (2×4), the Ga only ever improves the Ga-rich (4×2). Hence the dynamic 4x of Figure 1d is similar to the static 4x in Figure 1a. Note too that the 2x in Figure 1d is very different. There exist some extra bright spots at the bottom of the image that are much dimmer in the 2x of Figure 1a and cannot be seen in Figure 1b.

Hopefully you are now familiar with the process and can readily ascertain the maximum As flux required to create a (4×2) reconstruction in 15s. This is called the “1 to 1” point. The point at which the As flux is approximately equal the Ga flux. You could argue that the Ga flux is slightly higher than the As flux, since the surface turns Ga rich; however they are approximately equal. More importantly this transition is very repeatable. You need to make sure you always do the test in the same way. i.e. you must always wait 15s and always do the test at this temperature. Otherwise the flux will vary from check to check. It is worthwhile observing that variation yourself.

Once you have found this point you can calculate your fluxes in the system independent units of atoms/nm2/s (see Flux determination post) and state the atomic fluxes in any journal articles you write.

Little known MBE facts: Making a static reconstruction map

Faebian Bastiman

A static reconstruction map is one of the most useful items in your MBE arsenal. The map charts RHEED reconstructions against group V flux and applied power (or inferred temperature). Most reconstructions are stable over a wide set of temperatures and fluxes, however luckily for us they undergo very abrupt transitions. The map can enable you to return to any flux-temperature reference point with high accuracy even in the absence of any knowledge of the actual absolute temperature. However, with suitable inferences the absolute temperature can be stated to within ±10 °C in most cases.

The actual map is different for every substrate and depends on the number of reconstructions. Undoped GaAs is a good substrate to start with since it has 4 static reconstructions in the flux-temperature range of interest to an MBE grower: i.e. 300 – 650°C. Note that doped GaAs absorbs thermal energy more readily than undoped GaAs, which means for a given applied power doped GaAs is always hotter than undoped. Thus the map must be repeated for the doped and undoped version. That is true for all substrates, though is less obvious for those with narrow band gaps.

The map itself is generated in a several stages. It begins with defining your parameters. For GaAs this range of As fluxes (0 – 300 mil of movement in the As cracker’s needle valve in my case) and the range of your heater power (0 – 100W in my case). The second stage involves gathering flux data. A monitoring ion gauge (MIG) can be used to record the beam equivalent pressure (BEP) for each As needle valve position (see table for example data and ranges). The BEP needs converting into system independent ML/sGaAs or preferably atoms/nm2/s utilising the method in Little known MBE facts: flux determination.


The Omicron MBE-STM system has no reliable thermocouple so the heater power is used in place of temperature in the first instance. Most MBE systems possess a thermocouple located behind the heater element that accurately tracks the temperature at a fixed position from the heater element. However both form a suitable reference and either can be used.

The third stage is sample preparation. Remove the oxide as described in Little known MBE facts: oxide removal and deposit enough material (50 nm is sufficient) to create a clear (2×4) reconstruction. This can then be annealed under a lower As flux (0.5 ML/s at normal growth temperature is sufficient) to achieve a flat surface. Cool the sample until a strong c(4×4) is observed and then (with the As flux at 1ML/s) switch off the heater power and periodically check the RHEED until an amorphous pattern is observed and all 1x spots have vanished. You have just deposited an As cap. Once the RHEED is amorphous the As valve can be fully closed. A nominal heating power can be supplied to prevent the manipulator freezing in the presence of the LN2 cooling 0.2W in my case. This is not essential but certainly preferable.  Just make sure the nominal heating does not desorb the cap! Once all As has been purged from the system (typically several hours) the next stage can begin.

The fourth stage is data gathering. Create a 2D table with As flux on the y axis and heater power on the x axis. With no As flux, start heating the sample in small steps (0.05A in my case). Watch for the As cap desorbing with the RHEED and a c(4×4) RHEED pattern emerging. Mark it down in the table. This represents 300±10°C.  Continuing with no As flux, continue incrementing the heater power/current. C(4×4) is stable with no As flux until 400±10°C, at which point on the [-110] azimuth the 2x near the top will transform into a 4x pattern. This is caused because the patches of (2×4) coexist with the c(4×4) on the surface. The is the c(4×4)/(2×4) transition, mark it as “mix” for short. Continue with no As flux until (2×4) replaces the c(4×4). The (2×4) will remain until around 475±25°C where a (nx6) pattern emerges. The pattern is weak and it is unclear whether n is 3 or 4. At this point, to avoid damaging the sample, open the As to the first position (10 mil in my case). The surface should immediately become (2×4) once more.

At this point keep the heater power fixed and increase the As flux in small steps. The (2×4) will mix once more at an As flux of ~0.8ML/s and will thereafter give way to c(4×4). Continue to chart out the range of fluxes and temperature and eventually the data should resemble the table below.

The fifth and final stage involves interpretation of the raw data. We have already marked 300, 400 and 500°C with some error bar. The earlier oxide remove power can be marked as 600±20°C. Plotting the power vs temperature allows the other temperatures to be extracted from a line of best fit. The temperatures from ~400 to ~540°C can now be readily located with a known As flux by utilising the c(4×4)/(2×4) “mix” transition. If your aim is publication or dissemination you can now create a graphical plot of your data, though for personal use the table retains greater fidelity.

Little Known MBE facts: RHEED oscillations (2)

Faebian Bastiman

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:


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.

Little Known MBE facts: RHEED oscillations (1)

Faebian Bastiman

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.

[1] J.H. Neave, B.A. Joyce, P.J. Dobson and N. Norton, Appl. Phys. A 1983 31(1):1

Little known MBE facts: Temperature determination and RHEED

Faebian Bastiman

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