Modeling the Radial Growth of Self-Catalyzed III-V Nanowires

Abstract

A new model for the radial growth of self-catalyzed III-V nanowires on different substrates is presented, which describes the nanowire morphological evolution without any free parameters. The model takes into account the re-emission of group III atoms from a mask surface and the shadowing effect in directional deposition techniques such as molecular beam epitaxy. It is shown that radial growth is faster for larger pitches of regular nanowire arrays or lower surface density, and can be suppressed by increasing the V/III flux ratio or decreasing re-emission. The model describes quite well the data on the morphological evolution of Ga-catalyzed GaP and GaAs nanowires on different substrates, where the nanowire length increases linearly and the radius enlarges sub-linearly with time. The obtained analytical expressions and numerical data should be useful for morphological control over different III-V nanowires in a wide range of growth conditions.

Theory of MOCVD Growth of III-V Nanowires on Patterned Substrates

“…In self-catalyzed VLS growth of GaAs and other III-V NWs (usually, by MBE [ 35 ]), Ga droplet serves as a non-stationary reservoir of Ga which may either swell or shrink during growth depending on the V/III flux ratio [ 29 , 33 ], or even self-equilibrate to a certain stationary size [ 36 , 37 ]. In the Au-catalyzed VLS growth of III-V NWs, Au-rich alloy droplets can stabilize the droplet volume.…”

“…In dense NW arrays with , linear NW growth law in the second stage is obtained from Equations (1) and (6) in the form similar to Refs. [ 29 , 32 , 33 , 34 ]. It is interesting to note that the three growth modes yield different radius correlations of the NW growth rate or N—inverse exponential dependence on given by Equation (9), inverse radius dependence given by Equation (11) and dependence given by Equation (12).…”

“…Therefore, the central object for the NW growth kinetics is the total volumetric current of group III atoms into the NW (measured in nm 3 /s). This current is used to increase the NW volume and possibly the droplet volume on the NW top according to [ 32 , 33 , 34 ] …”

“…Furthermore, the axial NW growth rate should remain continuous even if the Ga diffusion length is limited by surface incorporation according to Refs. [ 32 , 33 , 34 ]. I speculate that this unphysical discontinuity is due to the absence of any pitch dependence in Equation (23).…”

“…[ 32 ], and the differences between the re-emission and surface diffusion mechanisms of material exchange between the substrate and NWs have been further discussed in Refs. [ 33 , 34 ].…”