GaN quantum dots

Molecular beam epitaxy

For strained layer systems the Stranski-Krastanow growth regime has been established as a reliable self-assembling method for coherently strained quantum dots. Typically, the layer growth starts two-dimensional (2D) but upon exceeding a critical layer thickness a transition to three-dimensional (3D) islands is observed. For this transition to occur, the energy balance between surfaces, interfaces, and edges is decisive. When 3D islands form, the surface energy plus the energy of edges is increased as more surface area and edges are formed as compared to 2D growth. At the same time, strain energy is decreased as strained material is removed from the highly strained 2D layer and transferred into less strained quantum dots. In total, the QD formation process succeeds if the energy gain due to strain relaxation surpasses the energy budget required for newly created surfaces and edges. Strain energy increases with lattice mismatch and layer thickness, whereas surface energies depend on crystallographic orientation but also on specific surface terminations.

GaN layers when pseudomorphically grown on AlN(0001) buffer layers are compressively strained by 2.5% due to mismatch of the lattice constants of the basal planes (a_GaN=3.189 A vs. &ain=3.11 A). As known from the InGaAs/GaAs system, this is about the lower limit for the Stranski-Krastanow mode [6]. Variations of the surface energy may therefore become significant for the 2D/3D growth mode transition to take place. In MBE growth, this complexity manifests in the sensitive dependency of QD formation on the stabilization of a Ga-bilayer on the growth surface. In such a case, only 2D growth is observed up to the limits of plastic relaxation where dislocations form. This is understood as the consequence of a highly enhanced nitrogen diffusivity on the surface. However, 2D growth is established for Ga/N >1 in the case of plasma-assisted (PA) nitrogen cells and Ga/N <1 in the case of radio-frequency-assisted (rf- assisted) ammonia cells used for the nitrogen supply [7, 8]. If growth conditions are favoring Ga-bilayer formation, the formation of QDs is achieved by applying a growth interruption under vacuum. Thereby, excess Ga atoms evaporate from the surface and stoichiometry between Ga and N is established. Under stoichiometric conditions, however, 3D islands are energetically favored and QDs rapidly appear on the surface [9]. Quantum dots are also obtained if growth conditions are chosen which avoid the Ga-bilayer formation. For PA-MBE such conditions refer to growth using Ga/N-ratio <1. The critical layer thickness at which the 2D/3D transition starts is determined to about 2.5-3 monolayers (ML) GaN [10]. Up to about 8 ML GaN, QD feed on material transfer from the GaN wetting layer (WL), which is consumed until 2.5 ML of GaN remain in the wetting layer. This is illustrated in Fig. 5.1, where the high-resolution transmission electron microscope (HRTEM) image of a 3 QD layer stack is shown. Each QD layer was

Fig. 5.1. HRTEM image of QDs on AlN(0001)/sapphire. In the inset, the wetting layer thickness of 2.5 MLs is resolved. (Reprinted with permission from [10], © 2002 American Institute of Physics.) formed during a 120 s long growth interruption after deposition of a 3 ML thick GaN layer under Ga-rich conditions. The thin continuous dark line connecting the QDs is referred to as the remainder of the wetting layer. In the inset the thickness of the WL is resolved to 2.8 MLs. Typical MBE growth temperatures for GaN-QDs are similar to growth temperatures of thick, two-dimensional layers, i.e., 680-800°C. An exponential increase of the density from 3-10¹⁰ cm~² to 2-10¹¹ cm~² is observed when the GaN thickness is increased from 2.8 MLs to 6 MLs [9]. Once QDs are formed during growth interruptions the supply of nitrogen stimulates Ostwald ripening, i.e., small dots dissolve and large dots grow in size [7]. Well-defined shapes of truncated hexagonal pyramids with a lateral size between 10-25 nm and 2-5 nm height are found both in TEM and AFM measurements. The side facets of the dots belong to {1103} crystallographic planes which make an angle of 32° with the (0001) basal plane of the wurtzite structure in GaN. This shape is preserved during AlN cap layer growth because of the very low intermixing of Ga and Al atoms at the interface between GaN and AlN [12].

Vertical stacking of up to 200 QD planes is reported in the GaN/AlN system [11, 13]. Capping layer growth by AlN results in planarization of the growth front if the layer thickness exceeds the average QD height [12]. Vertically correlated QDs are found for AlN spacer layer thicknesses <8 nm [14]. An example of vertically correlated dots is displayed in Fig. 5.2. Instead of a random dot distribution in each plane an arrangement into vertical columns is found. One can also notice the lateral size increase of the dots in the upper planes. The vertical correlated growth is due to local strain fields in the AlN matrix surrounding the GaN QDs. For small AlN spacer layer thicknesses the strain fields may protrude to the growth plane of subsequent QDs, thereby reducing locally

Fig. 5.2. TEM image of vertically correlated QDs on AlN(0001)/sapphire. A threading dislocation runs through the left column of dots. (Reprinted with permission from [11], © 1998 American Institute of Physics.)

Fig. 5.3. Evolution of shape and emission properties of vertically correlated QDs. Left) Dependence of lateral QD size and aspect ratio on stacking number. Right) Spectra of the ensemble luminescence. The inset shows the narrowing of the spectral width of the luminescence. (Reprinted with permission from [13], © 2004 American Institute of Physics.)

the free energy for QD formation. Uncorrelated stacks of QDs are observed for spacer thicknesses of 20 nm in MBE. The analysis shown in Fig. 5.3 reveals an increase of the lateral QD size from about 25 nm to 50 nm along with a reduction of the statistical size broadening. Thereby, the ground state optical transition undergoes a red-shift and the FWHM of the ensemble luminescence becomes narrower. A detailed survey of the epitaxy of GaN quantum dots by MBE is given by Daudin [15].