Monte Carlo Simulation of the Self-Organized Growth of Quantum Dots with Anisotropic Surface Diffusion

Modelling of the composition segregation effect during epitaxial growth of InGaAs quantum well heterostructures

“…Surface diffusion of adatoms takes place by short-range hopping occurring with a probability proportional to ν = ν 0 exp(−E d /kT ), where ν 0 is the typical frequency of the surface vibrations of adatoms (∼10 13 s −1 ), k is the Boltzmann constant, T is the temperature and E d is the activation energy of surface diffusion which takes into account the adatom's interactions with both the underlying layer and its neighbours in the growing monolayer [22,23,[28][29][30][31][32],…”

“…The quantities E s and E N are to be regarded as effective diffusion barriers which depend on the type of the adatom and the local configuration of its initial state [31]. We used the values of E Ga s = 1.3 eV and E Ga−Ga N = 0.3 eV for Ga adatoms as in most previous works [16,22,23,31]. Following the idea of [16], the corresponding energies for In adatoms were taken lower proportionally to the ratio of the corresponding binding energies (E b = 1.73 eV and 1.53 eV for GaAs and InAs, respectively), i.e.…”

“…We took into account the Schwőbel barrier which prevents the migration of adatoms from upper to lower terraces [20]. Its value was taken the same for In and Ga adatoms, equal to 0.1 eV [23].…”

“…Beyond the bond distortion related to the local configuration of an adatom (the number of its nearest neighbours in the growing layer), we reckon the pseudomorphic deformation of the underlying atomic layers on the adatom kinetics. As known, taking into account the deformation of the underlying atomic layers (including the wetting layer and the substrate) is essential for the modelling of the formation of self-assembled quantum dots via the Stranski-Krastanow (SK) mechanism [22,23]. Pseudomorphic strain renormalizes the cation diffusivity on the surface as it has been shown by means of density-functional theory (DFT) calculations for the case of In on the GaAs (0 0 1) surface [24].…”

“…Of course, the local environment of each adatom is taken into account in the spirit of [16] but the psedomorphic deformation of the underlying layers, which does not vary considerably on the atomic scale, affects differently the surface diffusion of the two types of cation atoms on the growing surface and, therefore, contributes to the surface segregation. In our MC procedure the composition and strain profiles are found self-consistently and enter the so-called substrate contribution to the activation energy of surface diffusion [16,22,23]. In the following, the same 4 Structures or strain are called pseudomorphic when the layer is lattice mismatched to the substrate and the strain is accommodated entirely elastically without plastic deformation via formation of crystal defects [21].…”