Excitonic lasing of strain-free InP(As) quantum dots in AlInAs
microdisk
Supplementary Materials
1. Structure and emission spectra of InP/AlInAs quantum dots having 25 nm thick AlInAs
cap.
Fig. SM1 Cross-section TEM
images of InP/AlInAs QDs
having 25 nm cap. The scale
bar is 2 nm (left), 5 nm (upper
right) and 50 nm (lower right).
In Fig. SM1 we present TEM images of InP/AlInAs structure having 25 nm thick AlInAs
cap. In the lower right image having size ~500x500 nm2 one can see a pan-cake-like QD
having lateral size ~300 nm. The height of this QD is 5 nm, which is seen in the left image
taken with atomic resolution.
Low-temperature (10K) micro-PL spectra of these structure consist from a set of sharp lines
(low excitation power observed in the range 810-915 nm (see upper spectra in Fig.2), which
merge into broader band at 810, 850 and 900 nm at higher excitation power. These bands are
related to the emission of QDs.
6.5 OD
6.0 OD
5.5 OD
5.0 OD
Fig. SM2 Low-temperature (10K) -PL spectra of InP/AlInAs QD structure having 25 nm
cap. Excitation power density (from upper to lower) is 1, 3, 10, and 30 W/cm 2.
2. Calculations of electron and hole probability densities for InP(As) QDs.
Our calculations show a strong impact on the localization of the wave functions of the holes,
i.e. from a type-II situation with the holes confined in the AlInAs matrix in the case of pure
InP quantum dot, to that of a complete delocalization both outside and inside of the dot,
which is confirmed by the plots shown in Fig.SM3. This provides the increased emission
intensity of these QDs compared to dots having lower As composition (see Fig.2 in the
paper).
Fig. SM3. Normalized probability density (cross section) electron(top) and hole(bottom)
ground states of InP0.75As0.25QDs. White contour is a QD.
3. Calculations of whispering gallery modes in AlInAs microdisk
Cylindrical symmetry of WGM resonators allows to reduction of the eigenvalue problem
from 3D to 2D via separation of known azimuthal dependence given by a factor exp(±im).
Here, m is an azimuthal mode number, and  is the azimuthal angle. The reduced problem is
solved numerically with COMSOL Multiphysics software using the approach developed in
Ref. [SM1]. In the simulation, we take into account the InP pedestal with a height of 1400 nm
(as homogeneous material with refractive index 3.1), AlInAs microdisk cavity with a height
of 250 nm (as homogeneous material with refractive index 3.4), and surrounding air (with
refractive index 1). The diameters of the microcavity and pedestal are supposed to be equal to
3.2 and 1 m, respectively. The comparison of the experimental spectrum with calculated
eigenmodes is shown in Fig.SM4a and b. The distribution of electric field amplitude |E| for
the identied modes is shown in Fig.SM4c. One can see that the modes TE19,2,2 and TM19,2,2
are hybrid and, therefore, their axial and radial indices are dened conditionally.
The effective mode volume was calculated using the following formula [SM2]:
(c)
Fig. SM4. (a) -PL spectra of a representative InP(As)/AlInAs microdisk (diameter 3.2 m) for power
density 20 W=cm2. (b) Calculated spectrum of the WGM microdisk laser.(c)
The results of the effective mode volume calculations are shown in Table SM1.
Table SM1: Effective mode volumes of the eigenmodes. Refractive index of the microdisk n
= 3.4.
[SM1] Oxborrow M. Traceable 2-D Finite-Element Simulation of the Whispering-Gallery
Modes of Axisymmetric Electromagnetic Resonators // IEEE Transactions on Microwave
Theory and Techniques. 2007. Vol. 55, no. 6. p. 1209-1218.
[SM2] Srinivasan K., Borselli M., Painter O. et al. Cavity Q , mode volume , and lasing
threshold in small diameter AlGaAs microdisks with embedded quantum dots // Optics
Express. 2006. Vol. 14, no. 3. p. 1094-1105
4. Emission decay of whispering gallery modes
In Fig. SM5 data on spectral dependence of emission decay of InP(As) QDs embedded in
AlInAs MD measured in the range 930-940 nm have shown. In this range three whispering
gallery modes at 932, 936 and 938 nm are observed. The emision decay time for these modes
is 1.0, 1.05 and 1.2 ns, respectively, and the decay time of the background is ~1.5 ns. The
faster decay of WGM is due to Purcell effect.
Fig. SM5. Emission intensity (lower and upper) and decay time (upper) spectra of InP(As)
QDs in AlInAs MD at 10 K.
5. Measurements of g2(0)
The nature of the emission also can be determined by the second-order coherence function
(g2) measurement (R. Hanbury Brown and R. Q. Twiss, Nature 177, 27, 1956): g2(0)>1
represents super-Poissonian statistics (thermal light), g2(0)=1 – Poissonian (coherent light)
light and g2(0)<1 – sub-Poissonian (for example, single-photon emission). The second-order
correlation function obtained at 10MHz excitation frequency and measured at the pumping
power density of 228 W/cm2, which is above the estimated lasing threshold, is shown in
Fig.SM6. g2(0) value was calculated by N0/Navg where N0 is the number of integrated counts
of the peak around 0ns delay (within the range of -50 and 50 ns), and Navg is the average
count of the other side peaks (uncorrelated photons). We measured g2(0)=1.01±0.02 which,
ideally, represents the expected coherent light emission. However, we stress that the
interpretation of the obtained results is not straightforward: as it was pointed out previously
(for example in Ref. arXiv:1607.05348), an extra care needs to be taken during the
measurement procedure. To observe clearly the transition from the region of spontaneous
(thermal light distribution) to stimulated emission (coherent/Poissonian distribution), a very
narrow spectral range (< 1μeV) needs to be studied, as the defining features of g2(τ) appear
Fig. SM6. The second-order correlation function obtained at 10MHz excitation frequency and
measured at the pumping power density of 228 W/cm2 InP(As) QDs in AlInAs MD at 10 K.
within the coherence time of the emission. The limitations of our set-up, in particular the
instrument-response-function width of ~400ps and the minimum resolution of 18 μeV, make
the precise measurements complicated and can easily hinder the detection of the spontaneous
light emission type.