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.

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: In growth rate

Faebian Bastiman

InGaAs QW and InAs QDs are popular active regions in opto-electronic devices. In Little Known MBE facts: RHEED oscillations (2) a concept was introduced to establish the In growth rate from a known Ga growth rate but what about an accurate and independent determination of the In growth rate? Well, conveniently there are several options.

The first method is simple. All you need is a rather expensive InAs(100) substrate and its lattice parameter: 6.05840 Å. RHEED oscillations can be performed for In on InAs in an identical manner as for Ga on GaAs. The required As flux for maximum RHEED oscillations for any given ML/s growth rate should be ~87% the As flux needed for GaAs; this maintains the 1.6:1 ratio on InAs. If you don’t know why read Little known MBE facts: Crystal hopping. One thing with InAs is that the demand for As over pressure rises significantly with increased substrate temperature. So if you need more than ~1.6:1 it implies that the substrate temperature is too high.

The second method uses the idea of adding and subtracting RHEED oscillation growth rates for ternaries introduced in Litte Known MBE facts: RHEED oscillations (2). In this way the growth rate of GaAs and InGaAs can be used to find the InAs growth rate. To test, try growing a QW of In_0.06Ga_0.94As of 10nm total thickness and employ a little maths and logic: In_0.06Ga_0.94As is effectively 9.4 nm of GaAs and 0.6 nm of InAs deposited at the same time. If you use a GaAs growth rate of 0.94 nm/s (for example), the whole QW should take 10 seconds to grow. An InAs growth rate of 0.6 nm/s will then give you the desired thickness and composition. If not, and you are certain about your GaAs growth rate, the InAs growth rate is wrong. As an added check of composition-thickness, a simple 3QW structure can be grown as shown in Figure 1 (below). The RT PL peak wavelength varies as a function of both InGaAs thickness and composition: e.g. [In] = 6%, 10nm QW should give RT PL ~900nm.

The third method is very useful for very low growth rates. It involves using the S-K transition which occurs when ~1.8ML of InAs is deposited on GaAs(100). There is an abrupt RHEED transition from streaks to spots which is highlighted in figure 2 (below). The actual S-K transition is a little imprecise since it relies heavily on temperature (particularly where non-unity In sticking coefficients are in question). It also is less accurate at higher growth rates, since the exact moment of the transition is subjective and at >0.25ML/s the timing depends on how accurate you are with your stopwatch. You will certainly want to make 3 attempts and average the times. Luckily 1.8ML of InAs can be readily flushed from GaAs with a brief (5-10 minutes) anneal at ~600°C under As flux and then you can cool the sample back to ~500°C and try again.

The fourth option is a clever trick you can play if you have access to a phosphorus source. The III-V alloy In_1-xGa_xP is lattice matched to GaAs at room temperature for x = ~50%. This little fact means you can grow 250nm of In_0.5Ga_0.5P/GaAs(100) and then analyse the exact composition with XRD peak splitting. When the Ga and In growth rates are identical the composition will be exactly In_0.5Ga_0.5P (just make sure In sticking is unity by growing around 480°C). Also if you are using RHEED oscillations you can accurately determine your Ga growth rate with GaAs RHEED oscillations, then work out your InGaP growth rate from RHEED oscillations AND discover the optimum III:V ratio for phosphorus growth at the same time. The fact that one method utilises 250nm of material and the other utilises 30ML means you can also get an idea of how those pesky shutter transients are affecting things.

The fifth and final option is a little super-lattice (SL) on an InAs(100) or a GaSb(100) substrate. Ideally, you will need access to antimony (Sb) and that way you can grow an GaSbAs/InAs(100) or a InAsSb/GaSb(100) lattice matched SL. Lattice matching at room temperature means the substrate peak and SL-average-composition peak coincide and will only see the satellite peaks. You can also utilise binary super-lattice InAs/GaSb but you may get strange effects from the interfaces unless you know what you are doing (more on that later). This technique relies on prior knowledge of the Ga growth rate (again) but can also provide interfacial and structural quality information.

The actual method(s) you use is largely a matter of personal preference and intended application. If you are trying to work out the growth rates so you can grow InGaP/GaAs(100) lattice matched bulk it makes little sense to utilise a InAs/GaSb SL to work out the growth rates. The nice thing is that with so many ways to double-check the actual growth rate should (in theory) be very accurate indeed.

Little known MBE facts: Crystal hopping: GaAs and InP

Faebian Bastiman

GaAs and InP are two very popular material systems for opto-electronic devices. After measuring and calculating and cross-referencing your Ga, In and Al growth rates on GaAs(100) with a variety of techniques the time has finally come to grow on InP(100). Hurray. However for some reason the growth rates have gone awry! The ML/s growth rate you get on InP is 108% what your very careful and accurate measurements tell you is 1ML/s on GaAs. Worse your µm/h growth rate is 112% out. How can I quote your growth rate error with such startling accuracy?

Well, the fact is there is no error in the growth rate. The discrepancy comes because GaAs and InP have a lattice constant of 5.65338 Å and 5.86860 Å, respectively. When you are talking about 1ML/s on GaAs you are talking about a flux of 6.258 x 10¹⁴ atoms/cm²/s. In fact you should say 1 monolayer of material with the lattice parameter of GaAs per second or for short: 1 ML/s_GaAs. Since 1ML/s_InP is in fact 5.807 x 10¹⁴ atoms/cm²/s, when you put down 1ML_GaAs you are in fact depositing 1.08 ML_InP. The ML growth rate of different material systems is proportional to the square of the lattice constant: 

The square term comes from the fact you are only worrying about a 2D ML on the (100) plane, and hence you are only concerned with the ratio of area of the face of the zinc blende unit cell. The larger discrepancy on the µm/h growth rate comes from the fact you are now looking at a ratio of the volume of the zinc blende unit cell. Thus the term is proportional to the cube of the lattice constant: 

This is a good example why the growth rate should be quoted in terms of the substrate independent unit of atoms/cm²/s.

Little known MBE facts: Growth rate (2): Super-lattices

Faebian Bastiman

Superlattices (SLs) were first discovered by their rather unique X-ray diffraction properties, and so it should come as no surprise that SL creation and XRD characterisation continue to go hand in hand. Rather than get into a semantic debate about where a SL starts and a multi-quantum-well MQW structure ends let’s concentrate on designing a useful structure to determine our growth rate. We want the XRD plot to have well defined satellite peaks so we will want >15 periods and we probably want to average over at least 4 satellite peaks (2 negative and 2 positive) so we will want a period of >10nm. A useful test structure is shown in figure 1 (below) which has the SL nomenclature [GaAs₁₀AlAs₁₀]₁₅.

The 004 ω-2θ scan of this structure is shown in figure 2. A simple peak splitting and periodicity analysis can tell us our growth rates. So what we have just done with 300nm of deposited material is to calibrate both the Ga and Al growth rate. You can do that with 30ML of material and RHEED oscillations. So why bother?

 Well the fact is the SL is telling you more. Firstly, you can vary the thickness of the two layers, whilst even maintaining the same period if you wish, and that will allow you to establish exactly what the shutter transients are doing. Secondly the quality of the XRD can give indications on the interfacial roughness and structural quality of the SL. Thirdly, you can also do RT-PL on the structure which can quickly tell you the width of the GaAs layer from the peak wavelength (just ensure the AlAs is thick enough to avoid wave-function over lap!) and that can allow you to gauge the opto-electronic quality of the GaAs:  a useful little test structure indeed.

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 Al_xGa_1-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 Al_0.3Ga_0.7As 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 In_xGa_1-xAs. The resulting increase in growth rate will allow you to determine the InAs growth rate (GR) since:

GR_InGaAs = GR_GaAs +GR_InAs

This conveniently means we you can accurately determine your growth rate and composition for any and all Al_xGa_1-xAs or In_xGa_1-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 2^nd ML starts on the wide islands before the 1^st ML is fully formed and so on for the 3^rd and 4^th 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: 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.