Little known MBE facts: High Purity Material

Faebian Bastiman

I was asked recently what purity of material a user should use in their MBE system. Here the grower was referring to the number of “N’s”. The N of the material is a reference to its purity and is actually the number of nines: Material that is 99% pure and 1% impure is termed 2N. 99.5% is termed 2N5, the “2N5” tells you it is at least half way to being 3N. Of course this does not tell you what the impurities are specifically, however you can assume they are made up of all the things you do not want in your III-V thin film layers (Zn, Cu, Fe, Sn, Hg, Ca, Te, etc) and a few III-V elements that you do not need to worry too much about (you are, after all, growing III-Vs anyway).The purity of material will ultimately determine the quality of your thin films, since any impurities in your cell material will likely incorporate as unintentional dopants in your layers.

If you are growing metals (for example MnAs) you are not too worried about unintentional doping and you may use a maximum of 5N5 material (99.9995%). If you are growing electronic or opto-electronic grade semiconductors (for example GaAs) you will want higher purity. Ultimately the highest you can get commercially is 9N (99.9999999%), however I would not recommend you all rush to the shops and buy such expensive material for general research. 9N is exponentially more expensive than 8N, 8N is exponentially more expensive than 7N. Similarly the ultimate background doping you can achieve with 9N is an order of magnitude lower than with 8N, and the same applies when comparing 8N to 7N. Before I suggest the appropriate material quality, let’s do a thought exercise with GaAs…

GaAs has a lattice constant of 0.565338 nm, and therefore an atomic density of 4.42 x 10²² cm^-3. When opto-electronics people (specifically detector people) talk about background doping requirements they say that 10¹⁵ cm^-3 is already good.  This means they would like the unintentional doping level to be 5×10⁷ times lower than the atomic density. In this case 7N5 would be the appropriate choice for you group III and V material. One could argue that you should use 7N5 for all materials and that replacing a specific material with 8N is a waste of money. However this “all or nothing” philosophy is not really justified since unintentional doping is accumulative, and hence replacing your group IIIs with 8N might reduce your background doping from high 10¹⁵ to low 10¹⁵. Thus 7N5 to 8N is a good choice for opto-electronic research, and 9N is only for exceptional high mobility cases or world record attempts. Moreover, if you are simply experimenting with a new opto-electronic alloy and not so interested in device quality at this stage 6N5 is acceptable. Note that the source material is only one factor in your ultimate achievable material quality, for more information read my Optimum Quality post.

Finally consider the dopant material. When we dope a semiconductor we typically dope in the 10¹⁶ to 10¹⁹ cm^-3 range depending on the application. At 10¹⁹ cm^-3 the dopant is around 10⁴ times lower in atomic density than the III or V species. This means the doping fluxes are around 10⁴ times lower that the group III and V fluxes and hence any impurities introduced into your system from the dopant source will also be 10⁴ times lower. Add to this that when you dope the alloy you are “trying” to add impurities and you can say that 6N is already a very good grade for dopant material and 5N may even be suitable.

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.

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 2^nd 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”.

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?

Yes.

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.

MBE Dreams: Efficiency of Effusion Cells

Faebian Bastiman

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.

Post bake tasks: Dealing with dopants

Faebian Bastiman

After your bake out you can establish the relationship between temperature, flux and growth rate for your group III sources using Post bake tasks: Arrhenius plot. This is very useful, since it enables you to estimate the growth rate from a cell temperature to within 2%, that is just ± 0.02 ML/s when your target is 1ML/s. The estimate remains valid for a few weeks, until the cell is sufficiently depleted. After which you need to re-calibrate the temperature, flux and growth rate relationship, however only for a single value this time since in the relationship:

The values of E and k never change, and all you need to do is find the new value for A”. Actually what you are proving with this experiment is that MBE effusion sources obey the laws of thermodynamics. That is that the value for activation energy (E) in eV for a certain element is identical to established data, any small fluctuations are purely instabilities in the measurement instrument: the monitoring ion gauge head (MIG). Since effusion cells obey the laws of thermodynamics you can predict the flux (in atoms/nm²/s) for any cell once you have a single calibration point.

What about doping cells?

The problem with doping cells (like Si or Be) is that the actual flux is too low to register with a MIG. When pushing the Si cell to >1350°C to measure Si, you are probably simply measuring N from the decomposition of the PBN crucible. When you push the Be cell to 1100°C to measure Be, you are evaporating £1 of Be per second. Hardly worth it. The fact is you do not need to measure the Si and Be fluxes. Since effusion cells obey the laws of thermodynamics you know that Si and Be will evaporate with an activation energy of -4.11 eV and -3.10 eV respectively from established values in the literature (vapour pressure data from Wikipedia for example). This means you only need to establish a single calibration point for each cell and then use the value of A” for that cell to extrapolate to all doping values of interest.  Figure 1 shows some nominal flux values for In, Ga, Al, Be and Si each scaled to their A” (i.e. atoms/nm²/s/A”) for comparison.

Before you gather your own data, consider what doping is. Doping is growing a very dilute ternary. Think about it. GaAs has a lattice parameter (a) of 0.565338 nm. With 8 atoms per a³ for zincblende that is 4.423 x 10²² atoms/cm³. Half of them Ga, and half of the As. When you want a Si doping of 4 x 10¹⁸ atoms/cm^-3 you in fact want to grow Ga_0.99982Si_0.00018As. This means that the Si flux in atoms/nm²/s can be established from knowledge of the attained doping level and Ga flux in atoms/nm²/s. The doping density depends on the magnitude of both the Ga flux and the Si flux. And so, you can double the doping by either doubling the Si flux, or halving the Ga flux (and hence halving the GaAs growth rate). It therefore useful to work out your Si and Be fluxes in terms of atoms/nm²/s so that are directly comparable to the Ga flux.

Your calibrated doping fluxes will only be valid until the cell starts to deplete, similar to the group III source. Handily you are utilizing x10⁴ less dopant material than you are group III material. So the dopant cell temperature vs flux relationship should be stable to within 2% for x10⁴ as long, ~192 years. Well perhaps this is a little hyperbolical, but it should be stable for 5-10 years.

To do all this you still need one calibration point. You can grow:

1. a 1 – 2um thick doped GaAs layer on an undoped substrate and perform SIMS or Hall measurements
2. a 1 – 2um thick doped GaAs layer on a doped substrate and perform SIMS or CV measurements with a CV profiler
3. a p-i-n diode and perform CV measurements

If you possess doping cells, but none of these capabilities you will hopefully be able to find a collaborator who can provide a free one off calibration. If not, two commercially profiled samples per every 10 years will not break the bank. For SIMS profiling contact LSA.

Post bake tasks: Group III flux: Arrhenius plots

Faebian Bastiman

After a thorough cell outgas (Post-bake tasks: Cell outgas) you are ready to record the beam equivalent pressures (BEPs) of the group III cells. This is doubly useful as on the one hand it allows you to establish a working range for the cell and on the other it enables you to gather some quantitative data for growth rate estimation to within 2% (see below). Here we will focus on the Al, Ga and In cells. To collect your flux data first insert the monitoring ion gauge (MIG) into the beam path. Next ramp the cell to the starting temperature and allow it stabilize at that temperature. Typical temperatures for group III sources are given in the table of figure 1. It is good practice to first heat the cell to T_outgas for 30 minutes, then cool down to the T_high value for a further 15 minutes and gather data in a descending temperature sequence. That way the cell is outgassed before use and before each subsequent reading. In is also good practice to double check each reading after a period of 5 minutes to ensure the cell is stable at the temperature of interest.

Use the method outlined in Little known MBE facts: Flux determination to obtain each flux value by subtracting the background flux from the BEP flux. Collect data in steps of 25 °C waiting 15 mintues each time for the cell to stabilize at the new temperature. Once the data is gathered plot it in your favourite graphical analysis software (here I use Origin Lab) and you should have data similar to that shown in figure 2a. Note the discrepancy in data for the Ga1 and Ga2 cells. This is caused by the slight difference in capacity and slight difference in the angle the atomic flux makes to the MIG. Regardless of the absolute value, the envelope (shape) of the curve is the same.

The envelope of Figure 2a describes the Arrhenius data for each of the sources. Using the modified Arrhenius equation in figure 3 and defining an appropriate fitting equation inside the Origin fitting tool, the constants A, E and C can be calculated for these particular cells. Unfortunately small nuances in the fitting can lead to significantly different values for A, B and C in the modified Arrhenius. To make things simpler we can use the far right approximate (a basic Arrhenius), where A” is variable, E is the activation energy of the element, k is the Boltzmann constant (in eV = 8.6173E-5) and T is the absolute temperature (in K). Instead of plotting the basic Arrhenius, we can plot log(flux) vs 1000/T  and create a nice linear plot for simple linear fitting: y = mx + c. The full formula and working is shown in Figure 3.

For example:

Assume we plot log(flux) vs 1000/T for the Al cell, where the flux is the BEP flux in mBar, the log is in base e (i.e. natural log) and T is in K. We get a value for the slope (m) = -34.11 and the intercept (c) of 8.92. The intercept is our value for log(A”) in Figure 3, but the slope needs converting into an activation energy. To do this we need to multiply it by 1000 (because we plotted 1000/T) and then multiply it by the Boltzmann constant, k. The value comes out at -2.94 eV. It is negative because we are using y = c – (-)mx for our fit in the second equation of Figure 3.

The values for E should come out to be the activation energies from the literature, and, together with the log(A”) value, we can now predict the flux (in mBar) for a given cell temperature using the third equation in Figure 3. Some typical values for E and log(A”) are shown in the  table of Figure 3.

 

 

 

Since the flux reading is directly proportional to the growth rate we have a direct means of setting the growth rate. To do that you will need to find out what your value for F is in the table of Figure 3 using the method outlines in Little known MBE facts: Growth rate and flux. Since the flux calculated by the value in Figure 3 comes out in mBar, F has units of atoms/nm²/s/mBar. The values for F in this case are very large since 1 x 10^-7 mBar is around 1 atom/nm²/s. This is another good reason to work in nA for BEP since 1 nA is around 1 atom/nm²/s and the numbers are therefore more convenient (see Note below). You can now change the BEP from the system dependent values of nA/mBar to the system independent values of atoms/nm²/s. 

The cell ‘s flux is only stable for a short period of time owing to (i) consumption of material, (ii) material degassing and (iii) redistribution of the material inside the cell. Hence the flux data gathered will only be valid for a short period. It is good to refresh the flux data once a week. This can be done automatically with the appropriate software (see MBE Dreams: Software).

Note: The fluxes in this article were gathered on an EPIMAX PVCi, and hence are in units of mBar. The ion gauge had a tungsten filament and the controller was operated with an emission current of 1mA and 19% sensitivity.  The new EPIMAX PVCx displays the collector current in the unit of nA in addition to pressure values. The units of nA and mBar follow a simple linear proportional correlation, the unit of choice is therefore simply user preference. The unit of nA is somewhat nicer to handle since the gathered fluxes will be in the 0.1 to 100 nA range and you can dispense with the obligatory 10^-9 to 10^-6 needed to express mBar.

Little known MBE facts: Flux determination

Faebian Bastiman

A flux monitor or monitoring ion gauge (MIG) is a very useful tool for MBE growth.  The principle is rather simple: insert an ion gauge head into the beam path and instead of monitoring the background pressure you can monitor the beam equivalent pressure (BEP). Each elemental species responds differently to ionisation and detection, and the angle of incidence and temperature difference also affect the final measured values. Handily any given cell is in a fixed position relative to the MIG. The ionisation potential is a constant and the effect of temperature differential is small over a 100°C range.

Gathering flux data is straight forward. For an effusion cell (e.g. Ga, In, Al or Bi) you simply need to vary the cell temperature over the range of interest and note down the flux when the shutter is open and when the shutter is closed. Typically the measurement may take 10-60s to stabilise. When you subtract the shutter closed “background” from the shutter open “measured” flux you end up with an “actual” flux for that cell temperature. The As and P cracker or Sb valved sources are quicker. With the source set to operating temperature you just need to step the valve position through the available range. Stabilisation times will vary and to some extent the background flux is moot since the background is predominantly the group V species being monitored.

The result so far is a system dependent BEP determination for each cell. This is useful for you, but not for anyone reading your publication and attempting to repeat the results. What you want is a system independent atomic flux determination. In order to achieve that you need to do a little more work.

The group III cells’ flux can be calibrated in terms of ML/s from RHEED oscillations using Little Known MBE facts: RHEED oscillations (1). This can be converted into atoms/nm²/s using the method in Little Known MBE facts: Growth rate and Flux. We now have a system independent flux in atoms/nm²/s for all our group III species, but what about group V?

Let’s take As as an example. Using the static map you created in Little known MBE facts: Making a static reconstruction map you can estimate the As flux that is necessary to retain a As-rich (2×4) reconstruction at a growth temperature of 580°C. In Little known MBE facts: Group V overpressure we called this flux As_As. When growing GaAs we also need to balance the incident Ga flux with an additional As flux: As_Ga. Thus the total As, As_total = As_As + As_Ga. This enables a good number of RHEED oscillations (>30) and maintains a (2×4) during growth with very dim 2^nd order rods. What happens if you reduce the As flux when growing? Well when you reduce the As to less than As_total and open the Ga shutter for a few seconds the RHEED will be a slightly weaker (2×4). Close the Ga. Reduce the As flux further. Open Ga for 5s, check the RHEED and close the Ga. Eventually the RHEED will be (1×1), reducing the As further will result in a Ga rich (4×2) pattern (for more information see my (2×4)/(4×2) post). At the point where the (1×1) emerges the As_Ga part of the As_total flux and Ga flux are equal. If you now subtract As_As that you estimate at this temperature from the As_total that gave you a (1×1) you have a value of BEP that represents the atoms/nm²/s of As atoms that is exactly equal to the atoms/nm²/s of Ga. So if this growth rate is 1ML/s, that is 6.258 atoms/nm²/s of Ga and therefore also 6.258 atoms/nm²/s of As.

The atoms/nm²/s for P and Sb can be can be calculated using the method outlined for As above, providing of course you have III-P and III-Sb substrates to grow the binary on. The other method is to grow a dilute ternary i.e. GaAsP or GaAsSb and with knowledge of the composition and As fluxes you can estimate the P and Sb fluxes. The problem is you are estimating the flux in atoms/nm²/s “incorporated” as oppose to atoms/nm²/s “incident”. The lattice site competition and other complications that arise when growing group V ternaries mean the incident and incorporated are significantly different. Another means of checking is to “grow” a layer of pure group V, like Sb or Bi, at 0°C and assume the sticking coefficient is unity. The thickness of this layer can be measured with SEM and then you can estimate the incident flux utilising the atomic density of the amorphous film. Though clearly the pyrophoric nature of P precludes it from this kind of experiment.

Little known MBE facts: Growth rate and flux

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/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. 

Little known MBE facts: Group V overpressure

Faebian Bastiman

 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:

As_total = As_As + As_Ga

As_Ga is temperature independent. The As_Ga 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 As_As is temperature dependent, but Ga independent. At the optimum MBE growth temperature for GaAs formation (~600 °C) the As_As 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.