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 Ga0.99982Si0.00018As. 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:
- a 1 – 2um thick doped GaAs layer on an undoped substrate and perform SIMS or Hall measurements
- a 1 – 2um thick doped GaAs layer on a doped substrate and perform SIMS or CV measurements with a CV profiler
- 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.