Quantum dots in amorphous matrix

 

J. Endres1, S. Daniš1, V. Holý1, M. Mixa1, V. Valeš1, M. Buljan2

 

1Department of Condensed Matter Physics, Charles University, Prague, Czech Republic

2Rudjer Boskovic Institute, Zagreb, Croatia

jan.endres@seznam.cz

 

Systems of quantum dots (QDs) in amorphous matrix are intensively studied because of their prospective technological applications. Their advantages are tunable electrical properties depending on the size, like band gap, electro/photoluminescence, high optical nonlinearity or charge storage for a long time. Thus it can be used in lasers, solar cells, photodetectors , high-speed memories and other optoelectronic devices. Metal QDs in amorphous matrix are recently investigated as well, namely due to interesting magnetic behavior (superparamagnetism, for example). Regularity of QDs system and uniformity of QDs sizes is important for good physical properties.

Ordering of QDs originates in preferential nucleation of QDs in minima of chemical potential on the surface, which correspond with surface energy, during the growth. In the case of QDs in crystalline matrix is ordering caused by elastic forces originated from mismatch of lattice constants of materials in adjacent layers. On the oder hand amorphous matrix ordering is obtained due to diffusion and surface morphology. In such system QDs are ordered into crystal-like lattice only in small blocks, see [1, 2]. Nearly periodic arrangement of QDs in the entire multilayer can be achieved by ion beam irradiating, when the sample is irradiated by ion beam under given angle and the places of ions flyby become a nucleations centers, see [3, 4].

We will study the structure of QDs systems (size, shape, ordering in matrix). X-ray scattering methods are suitable for this purpose. These methods are nondestructive and irradiated volume is large so we obtain averaged information from many irradiated dots. We will primarily use x-ray diffraction, reflectivity and possibly GISAXS. We can use other method like TEM, but it is destructive method, in which the sample is destroyed at preparation for experiment. Ordering of QDs in (SiO2 + Ge)/SiO2 multilayers was studied by M. Buljan et al., see [1-4], ordering of QDs in (SiO2 + Ni)/SiO2 multilayers is studied recently.

Growth of QDs multilayer can be simulated via kinetic Monte Carlo method (KMC). In [5] KMC was used for growth of QDs in a crystalline matrix. Each QDs layer was created on atomically flat wetting layer (WL). Chemical potential μ was in form

                                    (1)

where x is point on surface, μ0 is reference value of chemical potential, w is the volume density of elastic energy, γ is the surface tension, κ is the surface curvature and V0 is the atomic volume. Due to atomically flat WL the third term is zero and the chemical potential is affected only by elastic energy as mentioned above. We modified this approach for simulating the growth of QDs in amorphous matrix. In this case the second term in equation (1) is zero and chemical potential is affected only by the third term. Surface shape of covering layer above one QD is approximated by Gauss function, see [1]. For the whole surface with index j3 we use equation

                    (2)

where j1 and j2 are indices which describe positions of dots in the layer j3 and f denotes Gauss function

                                                    (3)

with full width at half maximum σ and C is a factor, which determines the contribution of layer with index j3 – 2. Preliminary results of simulation show, that QDs in second layer are preferentially created in the minima of surface height, i.e. in places with minimal curvature, see Figure 1 and 2.

Figure 1. Positions of QDs in the part of the first layer and height of surface above them.

 

Figure 2. Positions of QDs in the part of the second layer and curvature of surface below them. The QDs lie in the valleys on the surface, i.e. in the minima of the surface energy.

 

 

 

References

1.     M. Buljan, U. V. Desnica, M. Ivanda, N. Radić , P. Dubček, G. Dražić, K. Salamon, S. Bernstorff, and V. Holý, Physical Review B, 79, (2009), 035310.

2.     M. Buljan, U. V. Desnica, G. Dražić, M. Ivanda, N. Radić, P. Dubček, K. Salamon, S. Bernstorff, and V Holý, Nanotechnology, 20, (2009) 085612.

3.     M. Buljan, I. Bogdanović -Radović, M. Karlušić, U. V. Desnica, G. Dražić, N. Radić, P. Dubček, K. Salamon, S. Bernstorff, and V. Holý, Appl. Phys. Lett., 95, (2009), 063104.

4.     M. Buljan, I. Bogdanović-Radović, M. Karlušić, U. V. Desnica, N. Radić, N. Skukan, G. Dražić, M. Ivanda, O. Gamulin, Z. Matej, V. Valeš, J. Grenzer, T. W. Cornelius, H. T. Metzger, and V. Holý, Physical Review B, 81, (2010), 085321.

5.     M. Mixa, V. Holý, G. Springholz, and G. Bauer, Physical Review B, 80, (2009), 045325.

 

 Acknowledgement