SUPPLEMENTARY MATERIAL
Optical properties of individual site-controlled Ge quantum dots
Martyna Grydlik1,2,3,*, Moritz Brehm1,2*, Takeshi Tayagaki4,5, Gregor Langer1, Oliver G. Schmidt2,3, and,
Friedrich Schäffler1
1 Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz,
Altenbergerstrasse 69, 4040 Linz, Austria
2 Institute for Integrative Nanosciences, IFW Dresden, Helmholtzstr. 20, Dresden 01069, Germany
3 Center for Advancing Electronics Dresden, CfAED, TU Dresden, Germany
4 Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
5 Research Center for Photovoltaics, National Institute of Advanced Science and Technology, 1-1-1
Umezono, Tsukuba, Ibaraki 305-8568 Japan
Determination of the activation energies
We are using fits to Arrhenius plots for the determination of the activation energies (EA) contributing
to the quenching of the wetting layer (WL)-related photoluminescence (PL) signal. A commonly used
formula is given in the main text of the manuscript by:
IWL(TPL) = I0∙(1+A1∙exp(-EA1/kBTPL)+ A2∙exp(-EA2/kBTPL))-1 ,
(Eq. S1)
where IWL(TPL) and I0 are the integrated PL intensity of the WL for a given TPL, and at10 K,
respectively, A1 and A2 are scaling coefficients, EA1 and EA2 are the activation energies and kB is the
Boltzmann constant.
Here, we consider a nanostructure -system and, thus the proposed transitions involve nanostructures
with different dimensionalities. Consequently, an additional temperature-dependent pre-factor
considering the dimensionality of the effective density of states in the final and the initial state should
in principle be taken into account1:
IWL(TPL) = I0∙(1+A1∙Tf-i∙exp(-EA1/kBTPL)+ A2∙Tf-i ∙exp(-EA2/kBTPL))-1 ,
(Eq. S2)
where Tf-i is attributed to the temperature-dependence of the effective density of states in the final state
(f) and the initial state (i).1 For our system we consider the hole-transfer from the wetting layer to the
quantum dots (QDs), which leaves us with three different possibilities. In all cases the wetting layer
(thickness about 0.43 nm) is a two-dimensional (2D) nanostructure and, thus i = 1. For the QDs the
situation is more complex:
(a) If we consider the QDs as zero-dimensional (0D) objects then f = 0. Consequently a pre-factor
of T-1 appears in Eq. S2.
(b) If the QDs are considered as two-dimensional objects, i.e. real confinement only exists in
growth direction, then f = 1 and Eq. (S2) is reduced to Eq. (S1). This case of equal
dimensionality of the carrier density of states in initial and final state is obviously widely used
in literature, by using Eq. (S1) and also in the main text of this manuscript.
(c) If the QDs would be large, i.e. rather three-dimensional (3D) objects than nanostructures, then
f = 3/2 and the pre-factor becomes T1/2.
Supplementary figure S3: Arrhenius plots of the integrated PL-intensity of the WL (P exc = 170
µW) using a linear abscissa (i) and logarithmic abscissa (ii). Fits using a single and two
activation energies are plotted in blue and red, respectively. (a) (i) and (ii) Fits using a prefactor
of T-1,i.e. considering a transition from 2D to 0D, (b) (i) and (ii) Fits using a prefactor of T0 (2D
to 2D) and (c) (i) and (ii) Fits using a prefactor of T1/2 (2D to 3D).
The fits to the Arrhenius plots in Fig. S3 are using temperature-dependent pre-factors (a), (b) and (c).
Note, that the quality of the fits can be evaluated more clearly in the double-logarithmic Arrhenius
plots (Figs. S3(ii)) than in traditional Arrhenius plots using a linear abscissa, shown in Figs. S3(i).
From Fig. S3 it follows that independently of the temperature-dependent pre-factor the PL data cannot
be fitted using a single activation energy (blue curves in Fig. S3). Using two different activation
energies result in a lower EA of about 5 meV linked to the Δz-HH (i.e. Δz –electrons and heavy holes,
HH) exciton binding energy in the quantum-well potential formed by the WL.2,3 The higher activation
energy of about 25 meV is attributed to charge carrier refilling from the WL to the QDs over the
energy barrier formed by the thinner WL at the periphery of the dots, as described in the main text of
the manuscript.
References
1. M. Wachter, K. Thonke, R. Sauer, F. Schäffler, H.-J. Herzog, and E. Kasper,
“Photoluminescence of confined excitons in MBE-grown Si1-xGex/Si(100) single quantum
wells,” Thin Solid Films 222, 10-14 (1992).
2. C. Penn, F. Schäffler, G. Bauer, and S. Glutsch, “Application of numerical exciton-wavefunction calculations to the question of band alignment in Si/Si1-xGex quantum wells,”
Phys. Rev. B 59, 13314 (1999).
3. Y.-H. Kuo, and Y.-S. Li, “Direct-gap exciton and optical absorption in the Ge/SiGe
quantum well system,” Appl. Phys. Lett. 94, 121101 (2009).