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 Toutgas for 30 minutes, then cool down to the Thigh 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.

Slide1_crop

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.

Slide2_crop

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.

Group 3 Arr 2

 

 

 

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 (W) 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.

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8 thoughts on “Post bake tasks: Group III flux: Arrhenius plots

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    • I do not know where you can get them directly, but try searching for vapour pressure for the substance you want and then reverse engineering the activation energy using Arrhenius fitting.

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