1. Introduction

Self-assembled, epitaxially grown quantum dots (QDs) are ideal building blocks for lasers with superior specifications [1–3] and single-photon sources [4]. They are relatively easy to implement into devices and usually do not exhibit blinking or photobleaching effects. Optically pumped micropillar microcavities containing single quantum dots have recently been demonstrated as single-photon sources [5, 6]. Pillar microcavities with embedded semiconductor quantum dots have been fabricated mainly via electron beam lithography and reactive ion etching. Only recently, focused ion beam milling was employed for cavities operating in the visible [7–9] and the ultraviolet spectral region [10]. Post-growth focused ion beam milling was used for fabrication and fine tuning of such micropillars even for the group-III-nitrides [11] and recently for the conventional GaAs system [12]. These sources can be highly efficient as the high semiconductor refractive index collects a large fraction of the spontaneous emission into the waveguide mode due to total internal reflection at the sidewalls. The high-finesse microcavity can further enhance the emission into the mode when it is tuned into resonance with the dot transition. Several (classical-light-) devices like vertical-cavity surface-emitting lasers or all-optical switches are based on such microresonators and therefore the precise knowledge of their mode structures is crucial for design and optimization. Electrical pumping would be very beneficial for application, which could be realized relatively easy with all-monolithically integrated semiconductor quantum dots as shown recently using electrically contacted InAs quantum dots in AlAs/GaAs micropillars [13]. Electrical pumping can also be done in the easily dopable (Al,Ga)InP material system [14], which is an alternative to the II-VI material-system and capable of emitting light in the red, orange, and yellow range. In our approach, we embedded self-assembled InP QDs within (Al_0.20Ga_0.80)_0.51In_0.49P barriers to achieve emission from these nanostructures within the visible red spectral range [15] and therefore at the detection maximum of common Si detectors. In contrast to common systems, this property is highly advantageous, for example, for free space quantum cryptography and quantum computation [16] or polymer optical fiber (POF) applications which demand for devices operating at the red absorption minimum at 650 nm [17].

2. Fabrication

The sample structure was fabricated by metal-organic vapor-phase epitaxy (MOVPE) with standard sources (trimethylgallium, trimethylindium, trimethylaluminum, arsine, phosphine, silane, carbon tetrabromide) at low pressure (100 mbar) on (100) GaAs:Si substrates oriented 6° toward the [111]A direction. The bottom distributed Bragg reflector (DBR) consists of 45 λ/4-pairs of silicon doped AlAs:Si/Al_0.50Ga_0.50As:Si grown at 750°C followed by a 3λ/4 thick AlAs layer. The single-layer of self-assembled InP QDs was grown using the Stranski-Krastanow growth mode [18] by depositing 2.1 monolayers (ML) of InP at 650°C and a growth rate of 1.05ML/s, followed by a 20 s growth interruption for ripening the QDs. The QDs were placed in the center of a 18 nm thick (Al_0.20Ga_0.80)_0.51In_0.49P barrier surrounded by (Al_0.55Ga_0.45)_0.51In_0.49P confinement layers, all together forming a one-λ-cavity. The top DBR consists of 36 λ/4-pairs of highly carbon doped Al_0.50Ga_0.50As:C/Al_0.95Ga_0.05As:C with linearly graded interfaces grown at 750°C. The doping gradient of the bottom and top DBR was zero, so the doping concentration was held constant throughout the growth of each DBR. An Al_0.98Ga_0.02As oxidation layer was inserted after the growth of the second λ/4-pair above the cavity. This layer was inserted to have the ability to form a current restricting aperture in case of intended electrical current injection. The authors refer to Ref. [19] for further details on electrically pumped lasing of this structure. The structure was designed to have a normal-incidence Bragg resonance wavelength between 1.827 eV and 1.920 eV at room temperature, depending on the radial wafer position. The complete growth process was in-situ monitored by a LayTec EpiR-M in-situ reflection measurement setup [20]. An overall QD density of approximately 5.5×10¹⁰ cm⁻² was determined by atomic force microscope measurements on not overgrown, comparable QDs [15]. The averaged QD height is about 4 nm with diameters of around 40 nm [15]. The pillar microcavities with diameters between 1.26 and 5.70µm, providing a three-dimensional light confinement due to total internal reflection at the resonator sidewalls, were milled out of the planar cavity with a 30 kV Ga⁺ focused ion beam system (FIB).

For micro-photoluminesecene (µ-PL) measurements, the samples were cooled down to 4K using a He flow cryostat and excited by a pulsed super-continuum fiber laser with a repetition rate of 50MHz and pulse widths of approximately 150 ps. The excitation wavelength of 570 nm was selected using an acoustic-optically tunable filter with a full width at half maximum of approximately 3 nm. The light to and from the sample was guided confocally through a 100× microscope objective (NA=0.45) and a beam splitter, focusing the laser spot down to a diameter of approximately 1µm, using a piezoactuator. The optical distortion occuring from the cryostat window was not compensated. The luminescence was dispersed by a 0.5m spectrometer and detected using a thermoelectric-cooled charge coupled device (CCD) camera when taking spectra with an effective resolution of approximately 100 µeV or two avalanche photodiodes (APDs) in a Hanbury-Brown and Twiss-type setup [21] when performing second-order autocorrelation measurements.

3. Experimental

Figure 1 displays scanning electron microscope images as an example of the FIB milled structures used for the experiments. Even for small diameters a circular, cylindrically shaped microresonator pillar can be fabricated [Fig. 1(a)]. The inset of Fig. 1(a) shows a cross section of the multilayer stack. As can be seen, the whole structure exhibits a very homogeneous growth. Due to precise control of the milling parameters, the FIB fabrication process led to very smooth sidewalls and a high aspect ratio, as presented in the magnification of one microresonator pillar in Fig. 1(b). A typical µ-PL spectrum of such a microresonator with a radius of 2.1 µm is presented in Fig. 2(a), showing the fundamental HE_1,1 mode at around 1.849 eV and several higher HE- and EH-transverse modes which are resulting from the three-dimensional light confinement within the pillar. The spectral positions of the transverse mode energies have been calculated by modeling the pillar cavity as a waveguide with an effective refractive index. By using a standard transfer-matrix method the longitudinal mode in the planar cavity is calculated, giving the longitudinal electric field amplitude. An effective refractive index n ₁ averaging over the entire pillar cavity is obtained by weighting the refractive index at each point in growth direction with the longitudinal electric field amplitude:

 

Fig. 1. Scanning electron microscope images of the FIB milled structures. (a) Two micropillars with different diameters. The inset in (a) displays a cross section cut of the investigated DBR cavity and a magnification of the cavity region. (b) Magnification of one micropillar showing the smooth sidewalls.

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Surface roughness and the finite milling depth of around 8 µm was neglected. The electromagnetic field in the lateral direction can then be calculated by modeling the pillar microcavity as a homogeneous dielectric waveguide of cylindrical shape with an index of refraction n ₁. By solving the transverse wave equation, the pillar cavity modes are obtained. The calculated mode positions indicated by the vertical lines in Fig. 2 (a) are in excellent agreement with the values obtained in the experiment. The inhomogeneously broadened emission of the quantum dot ensemble is centered at 1.820 eV and has a full-width at half-maximum (FWHM) of 140 meV at 5K (due to the QD size distribution). Therefore, the fundamental modes of the pillar microcavities exhibit a detuning of around 30 meV which is still enough to “feed” all modes of the microresonator pillars over a large spectral band. Further, the diameter dependency of the spectral mode positions of different microresonator pillars was investigated and compared with theory [Fig. 2(b)]. For all investigated pillars the mode positions can be precisely calculated, showing a typical behavior [22]: first, the fundamental mode wavelength decreases with radius, and second, the energy mode spacing gets larger with decreasing radius. One has to point out that the slight misfit of measured and calculated data for small radii is due to the thickness gradient profile on the 2-inch wafer, occuring from growth. As the pillars are separated several tens of micrometers, the normal-incidence Bragg resonance wavelength changes slightly, which was not considered for the calculation of the radius dependency. The errors resulting from the measurement of the diameter (±50 nm) and the spectral energies (±100 µeV) of the pillars are not visible within the used scale. To see the influence of the micropillar geometry on the resonance linewidth, the quality factors (λ/Δλ) of the pillars are plotted in the inset of Fig. 2(b) as a function of the nominal pillar radius (triangles). A maximum quality factor of 3650 was obtained for a 5.7 µm diameter micropillar. For decreasing radii the quality gets lower due to increasing scattering losses at the sidewalls. A simple model (straight curve) presented in Ref. [23] is able to describe the scaling of the quality factor with radius and was fitted to the experimental data. The model relates the additional losses to the field amplitude of the transverse mode profile at the resonator edge, expressed by

 

Fig. 2. (Color online) (a) Micro-photoluminescence spectrum of a micropillar with a radius of 2.1 µm. The vertical lines display the calculated energies of the transverse modes, showing excellent agreement with the measurement. (b) Calculated radius dependency (straight curves) of the first six higher transverse modes and measured mode energies (circles). The inset is showing the obtained quality factors (triangles) and the theoretical behavior (straight curve).

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with quality factor Q(r), planar cavity quality factor Q ₀ and an additional scattering term Q _scattering which characterizes the optical quality of the sidewalls. Absorption losses are not included as they are hidden intrinsically in the planar quality factor Q ₀. The scattering term is proportional to the fundamental mode intensity I(r) at the resonator edge, divided by the resonator radius of the different micropillars. The fundamental radial intensity distribution is proportional to the square of the first kind Bessel function I(r) ∝ J ² ₀(k_tr), with k_t = n ² ₁ k ² ₀−β ² which was calculated previously for the transverse modes, effective refractive core index n ₁, propagation constant β, proportionality constant ε, and radial coordinate r. In order to get many supporting points and a high accuracy, k_t was calculated with a step size of 100 nm. The experimental data is fitted with the model, giving ε = 2.8×10⁻⁸ µm⁻¹ and a planar quality factor of Q _0,fit = 4950±550. This value fits well to the measured planar quality factor of around Q _0,meas = 5300±250, obtained from reflectivity measurements. Using the transfermatrix method a planar cavity quality factor Q ₀ of approximately 10 000 was calculated for the microcavity. Here, the losses occuring from the free-carrier absorption within the DBRs, the high QD density and growth inaccuracies are some factors which are responsible for the lower measured Q ₀.

By increasing the detuning between QD-ensemble and the fundamental modes of the pillar microcavities up to approximately 50 meV by using a different position on the wafer, it is possible to address a single QD solely.

 

Fig. 3. (Color online) Normalized micro-PL spectra of a microresonator pillar with a diameter of 1.26 µm excited with around 300 Wcm⁻² (upper spectrum) and around 40 Wcm⁻² (lower spectrum) at 4 K. The vertical lines display the calculated energies of the transverse modes, while the dashed rectangle marks the background contribution (B). The autocorrelation measurement (inset) showing the highly non-classical light statistic, was performed with around 375 Wcm⁻² for shorter integration times.

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In Fig. 3 the spectrum of a microresonator pillar with a diameter of 1.26 µm is shown for an excitation power density of around 300 Wcm⁻² (upper spectrum) and around 40 Wcm⁻² (lower spectrum) at 4 K. Here, mainly one single QD, which exhibits a FWHM of 590 µeV, is contributing to the fundamental HE_1,1 mode at around 1.874 eV. From the previous results, one would expect a quality factor of approximately 750 [see inset in Fig. 2(b)] for the fundamental mode of this micropillar, which corresponds to a linewidth of approximately 2.5 meV. Therefore, the linewidth can be primarily attributed to the QD, as the mode is only partially “fed”. For high excitation powers a significant background contribution (red rectangle labeled B) arises, which is manifested in the non-zero onset of the spectrum. The authors would like to point out, that there are still approximately 680 QDs arranged spatially within this microresonator pillar (r = 0.63 µm), which is probably one reason for the high background at high excitation powers. Even by taking into account the sidewall damage occuring from the FIB milling, which is typically in the range of 10−40 nm [24], there are still more than 600 QDs within this micropillar. In future, the QD density has to be reduced using either more complex epitaxial fabrication scenarios (e. g. annealing techniques) or highly advanced prepatterning and overgrowth methods, as it was shown recently [25] for obtaining site-controlled QDs in microresonators. The higher transverse modes mentioned above are also only partially “fed”, here only the HE_2,1 and the EH_1,1 modes can be identified for low excitation powers. The higher energetic peaks at around 1.885 eV and 1.905 eV with low intensity do not correlate to the calculated higher transverse modes, indicating the emission of several other QDs within the microresonator pillar, probably due to the broad linewidth of the modes or leaky modes. Photon correlation measurements have been performed on the fundamental mode with an excitation power density of around 375 Wcm⁻² to demonstrate single-photon emission under pulsed excitation from the QDs in this pillar (see inset of Fig. 3). The suppression of coincidences at zero delay (τ = 0) is equivalent to (20±3)% of the calculated Poisson-normalized level. This indicates a decrease in multiphoton emission events by a factor of approximately 5 for the QD emission when compared to a Poissonian source of the same average intensity. The residual, unwanted peak at τ = 0, resembles the influence of detector noise and uncorrelated background (B) which is clearly visible in the spectrum. For clearness, this background is symbolically marked with the shaded rectangle in Fig. 3. According to Ref. [26] a signal (S) to background (B) ratio of ρ = S/(S+B) = 0.92 can be calculated for background correction of g⁽²⁾(τ=0). Using g⁽²⁾ _corr.(0)=[g⁽²⁾(0)-(1-ρ ²) ]/ρ ², the background correction results in g⁽²⁾ _corr.(0)=0.06±0.03. The signal intensity on the APD, being therefore a statistical sum of regulated single-photons and a weak background of Poisson-statistical photons, was approximately 5000 cts./sec. Saturation was achieved for an excitation density of 750 Wcm⁻², giving a count rate of around 6400 cts./sec. In a simple approximation one can neglect the poissonian occupation of states during the excitation process and intensity reducing effects, e.g. dark states etc. Then, at saturation, each excitation pulse corresponds to one emitted photon, giving a total emission rate equal to the repetition frequency of the laser (50 MHz). Therefore, when considering the collection efficiency of the setup (η _setup≈0.15, measured using a HeNe-Laser) and an optimum single-photon emission rate of 50 MHz, an overall single-photon extraction efficiency of η _extraction = 0.67×10⁻³ could be estimated. This value is quite low, as one would expect a much higher efficiency. According to [27] the optimal extraction efficiency can be estimated by:

with Q(r) being the quality factor of the pillar, planar cavity quality factor Q ₀ and Purcell factor F_P. As the authors did not observe any Purcell effect (F_P = 1) for the presented micropillars, an optimal extraction efficiency around η _{extraction,optimal} = 7.5×10⁻² would be expected. To deliver a deeper insight into the coupling of the QD to the mode, temperature dependent measurements up to 50K were performed on this micropillar. Figure 4(a) displays the corresponding temperature dependent spectra, excited with a power density of around 300 Wcm⁻². All resonances are shifting parallel to smaller energies with elevated temperature. The extracted emission energy of the resonance (circles) is compared with the energy shift of a typical QD in (Al_0.20Ga_0.80)_0.51In_0.49P barrier layers without cavity (triangles) [15], shown in Fig. 4(b). Both exhibit a nearly identical energy shift of 2.5 meV from 5K up to 50 K, which is in the same range as the calculated FWHM of the fundamental mode. This energy shift is about 5 times larger than the measured energy shift of the planar cavity mode within the used temperature range. Therefore, we conclude, that the observed resonance corresponds to a QD, shifting within the fundamental mode. Further, the integrated PL intensities of the coupled QD are depicted versus temperature in Fig. 4(c). With increasing temperature, the intensity enhances, having a maximum at around 40K and quenches again for higher temperatures. It seems, that the QD has a higher energy than the fundamental mode and is redshifted towards the mode with increasing temperature, resulting in higher intensities. Above 40K the intensity is reduced. Here, the QD might be partly tuned out of resonance again and/or the quantum efficiency of the QD is accessorily reduced with elevated temperatures due to the thermal reemission of carriers out of the QD. These two effects are overlapping and it is not possible to extract the real detuning as the temperature behavior of the QDs quantum efficiency, which could be very low at all, is not known. Therefore, the low extraction efficiency could be due to the detuning of the QD, a reduced quantum efficiency, and free carrier light absorption within the highly doped DBRs (n_acceptor ≈ 4×10¹⁹ cm⁻³, n_donator ≈ 2×10¹⁷ cm⁻³).

 

Fig. 4. (Color online) (a) Temperature dependent spectra of a micropillar with 1.26 µm diameter. The dashed vertical lines are guides to the eye and mark the positions of the higher transverse modes. The redshift of the emission energy of the fundamental mode (circles) is compared with the behavior of a typical QD in (Al_0.20Ga_0.80)_0.51In_0.49P barrier layers without cavity (triangles), showing an identical shift. In (c) the integrated intensities of the fundamental mode is shown.

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Nevertheless, despite the low extraction efficiency, a single-photon source was realized in this manner. By suppressing the background contribution, e.g. by using (quasi-) resonant optical excitation and additionally reducing the doping concentrations, the overall efficiency should be greatly enhanced.

4. Conclusion

Within this work, focused ion beam etched microresonator pillars based on InP quantum dots embedded in (Al_0.20Ga_0.80)_0.51In_0.49P barrier layers were demonstrated, showing a distinct transverse mode behavior. It was shown that the theoretical calculations are in excellent agreement with the experiments. Quality factors up to 3650 were presented. By using a large spectral detuning between quantum dot ensemble and normal-incidence Bragg resonance wavelength in addition with a small pillar diameter mainly one single quantum dot can be coupled to the fundamental mode. It was therefore possible to record single-photon emission characteristics of this pillar.