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Gallium Evaporation Behavior for Purification in Molecular Beam Epitaxy
Kyungjean Min, David Johnson and Kevin Trumble
Abstract High mobility GaAs/AlGaAs heterostructure have been achieved at Purdue University through in-situ distillation of the source Ga prior to growth. A significant amount of Ga is lost during distillation and growth. To evaluate the Ga behavior during MBE operation, the evaporation rate from a planar source of liquid Ga in a crucible is analyzed, correcting for transmission probability according to Clausing theory. The transmission probability which depends on the diameter and receding depth of the liquid surface in the crucible, explains condensation of Ga particles by collision for the vertically standing crucible. The good agreement furthermore suggests that the usual tilt of the cell has little effect on the flux.
Keywords Gallium purity Molecular beam epitaxy (MBE) Langmuir-Knudsen equation
Molecular Beam Epitaxy (MBE) is state-of-the-art deposition technique that produces high quality two dimensional electron gas (2DEGs) with high electron mobility by using modulated doping methods from separated elemental source effusion cells under ultra-high vacuum conditions. At Purdue University, GaAs/AlGaAs heterostructures have been grown by MBE with an electron mobility greater than 35 x 106 cm2/Vs when using a Ga source with an initial purity of 8N (99.999999%) Ga, but a lower electron mobility of 25 x 106 cm2/Vs was obtained when a 7N (99.99999%) Ga source was used [1, 2].
The ultra-high electron mobility attained at Purdue MBE was recently shown to depend mainly on the purity of Ga source , as well as the uniformity of molecular
K. Min (H) • D. Johnson • K. Trumble
© The Minerals, Metals & Materials Society 2017
A. Allanore et al. (eds.), Materials Processing Fundamentals 2017,
The Minerals, Metals & Materials Series, DOI 10.1007/978-3-319-51580-9_8
beam pattern associated with angular flux distribution of the source in MBE . Therefore, the investigation of Ga evaporation behavior in the Purdue MBE geometry can contribute to the understanding of correlation between Ga evaporation during in-situ distillation for the geometry used in the MBE is of interest.
From the principle of kinetic theory, Langmuir derived the equation of maximum rate of evaporation from free solid surfaces. Langmuir calculated evaporation rate and vapor pressure of tungsten from filaments in vacuum for a range of temperatures and compared with experimental results. The calculated evaporation rate of tungsten measured in a vacuum agreed with the experimental results .
Knudsen developed the evaporation theory for the isothermal effusion cell with small orifice. Knudsen employed the coefficient that was multiplied to the Langmuir equation and pressure of vacuum reservoir that was subtracted from the Langmuir equation. Those terms give an effect of condensation of evaporated particles to surface .
Clausing added the condensation factor due to collision between particles inside a crucible to the Knudsen equation and derived the flux of angular distribution. Clausing divided the evaporation behavior of particles into four different cases under the consideration of collision and derived the probability factor including those four cases .
More recently, Krasuski calculated the flux of angular distribution on the exit of crucible that has a cylindrical shape by using Monte Carlo simulations based on Clausing’s derivation. Krasuski found the flux has significant variation depending on different angles .
For the growth of the GaAs/AlGaAs heterostructures described above, the source Ga was distilled within the MBE chamber for further purification. During distillation, and even during growth, a significant amount of Ga is lost. In addition, the evaporated amount of Ga in distillation could not be measured due to the characteristics of MBE experiment to be perfectly evacuated and blocked from outside during operation. By estimating the evaporation amount by thermochemical analysis during distillation and growth, the behavior of Ga during MBE operation and the lost amount of Ga will be numerically analyzed.
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