Fabrication of dense diameter-tuned quantum dot micropillar arrays for applications in photonic information processing

We report on the realization of a dense, large-scale array of 900 quantum dot micropillar cavities with high spectral homogeneity. We target applications in photonic information processing such as optical reservoir computing which can be implemented in large arrays of optically coupled microlasers. To achieve the required spectral homogeneity for the underlying optical injection locking, we calculate and set the diameter of each individual micropillar within the array during the fabrication process by taking the diameter-dependent emission wavelength of the microcavities into account. Using this kind of diameter adjustment, we improve the overall wavelength homogeneity in a 30 × 30 micropillar array by 64% and reduce the standard deviation of the resonance energy distribution by 26% from 352 μeV in the planar unprocessed sample to 262 μeV in the fabricated array. In addition, we present a detailed analysis of the device quality and the diameter control of the micropillar’s emission wavelength, which includes important information for the effective application of the developed fabrication method for the realization of highly homogeneous micropillar arrays in the future.

We report on the realization of a dense, large-scale array of 900 quantum dot micropillar cavities with high spectral homogeneity. We target applications in photonic information processing such as optical reservoir computing which can be implemented in large arrays of optically coupled microlasers. To achieve the required spectral homogeneity for the underlying optical injection locking, we calculate and set the diameter of each individual micropillar within the array during the fabrication process by taking the diameter-dependent emission wavelength of the microcavities into account. Using this kind of diameter adjustment, we improve the overall wavelength homogeneity in a 30 × 30 micropillar array by 64% and reduce the standard deviation of the resonance energy distribution by 26% from 352 µeV in the planar unprocessed sample to 262 µeV in the fabricated array. In addition, we present a detailed analysis of the device quality and the diameter control of the micropillar's emission wavelength, which includes important information for the effective application of the developed fabrication method for the realization of highly homogeneous micropillar arrays in the future. © 2018 Author(s

I. INTRODUCTION
The development of high-quality quantum dot (QD) micropillar cavities has enabled numerous studies and advances in the field of cavity-enhanced nanophotonic devices. Besides the investigation of fundamental light-matter interaction in the single-QD regime of cavity quantum electrodynamics (cQED), 1,2 appealing applications of QD-micropillars include single-photon sources with close to ideal optical properties 3,4 and high-β QD-microlasers 5 showing even single-QD lasing effects. 6 More recently, the study of externally controlled QD-microlasers has led to unconventional effects such as partial injection locking in the field of nonlinear laser dynamics. 7,8 Interestingly, so far the related research has almost exclusively focused on individual QD-microcavity systems without taking advantage of coupling these devices to larger systems with enhanced functionality. For instance, network dynamics of coupled microlasers promise exciting applications in advanced photonic information processing such as neuromorphic computing. 9,10 These applications usually set stringent requirements on the fabrication of the microlasers since they rely on an extremely well-defined separation (pitch) between the individual lasers 10 and spectral homogeneity 11 within large scale laser arrays, where photonic neural networks typically require several hundred lasers 12 emitting within a frequency-range of ∼50 GHz (∼200 µeV). The realization of spectrally homogeneous microcavity arrays is not feasible by relying upon post-fabrication tuning methods commonly applied in single-QD experiments using temperature, 2,13 magnetic field, 14,15 or the electrical field. 16,17 This issue is explained by the fact that these parameters mainly influence the emission energy of the excitonic emitters but have only minor effect, if any, on the spectral features of the cavity mode. Additionally, the tuning of individual pillars is not feasible in the case of global temperature or magnetic field tuning. Tuning of individual lasers via electrical contacts too is technologically very challenging and becomes increasingly difficult with increasing network size and density. Therefore, the spectral alignment of a large-scale network of micropillars has to be ensured already in the cavity design and fabrication process of the array, for example, by adjusting the resonance wavelength of each micropillar via its diameter. Interestingly, such "diameter-tuning" of the resonance wavelength has already been applied for individual deterministically fabricated single-QD-micropillars. 4,18 In this work, we report on the application of diameter-tuning to realize large arrays of hundreds of quantum dot micropillars with high spectral homogeneity. For this purpose, we individually tailor the resonance wavelength of single micropillars to compensate for spectral inhomogeneities of the unprocessed planar microcavity. By applying this approach, we achieve high spectral homogeneity of 262 µeV within a large-scale array of up to 900 quantum dot micropillars. Such homogeneity facilitates the interaction between the individual lasers of such arrays and allows them to form a network that can be optically injectionlocked by using an external laser. 11

II. METHOD AND SAMPLE TECHNOLOGY
The fabrication process for dense arrays of quantum dot micropillars starts with the epitaxial growth of a planar microcavity sample by means of metal-organic chemical vapor deposition (MOCVD). The layer design of the planar microcavity consists of a central one-λ thick GaAs cavity sandwiched between a lower and an upper distributed Bragg reflector (DBR) composed of 27 and 23 λ/4-thick Al 90 Ga 10 As/GaAs mirror pairs, respectively. The central GaAs cavity includes a single layer of self-assembled Stranski-Krastanow InGaAs QDs with a density of about 1 × 10 10 cm −2 . During the growth process, the material deposition depends on the radial position of the rotating wafer which causes a radial layer thickness variation of about 2% (3 nm per DBR pair) and, in return, leads to an associated radial dependence of the cavity resonance wavelength. This typical and generally unavoidable radial variation of the resonance wavelength in the epitaxial microcavity growth is illustrated in Fig. 1(a), which shows the resonance wavelength of the planar microcavity from the center to the edge of a 2 inch wafer. For the particular sample of Fig. 1, the cavity exhibits a total radial shift of its resonance by about 25 nm. To realize homogeneous arrays of micropillar lasers, part of this resonance shift has to be compensated by adjusting the pillar diameters within the 300 × 300 µm 2 sample area relevant for the 30 × 30 micropillar array with a pitch of 10 µm chosen in this work. For this purpose, we consider the well-known relation between the micropillar diameter d c and the resonance energy E c of the pillar modes, 19,20 where E 0 is the position dependent resonance energy of the planar microcavity, ε r is the effective dielectric constant of the cavity material, and x ϕ ,r is the n th r zero of the Bessel function J ϕ (x), which has a numeric value of 2.4048 for the fundamental HE 11 mode. We introduced the additional parameter α r which takes the process dependent light confinement into account. It is interesting to note that there exists a trade-off between the achievable spectral compensation and the variations in the pillar emission energy induced by a given diameter accuracy. The E c (d c ) becomes steeper with decreasing diameter allowing for a larger spectral compensation. Consequently, E c becomes more sensitive to small variations in d c which can lead to process related spectral inhomogeneities. On the other side, this behavior allows to adjust the tuning window of this method to a given process accuracy. In practice, we can achieve a spectral compensation of about 5-8 meV in the relevant diameter range of 2-6 µm. To calculate the required diameter for each micropillar in the 30 × 30 array, first α r has to be determined for the chosen etching process as we describe below. Then the resonance energy of the desired sample area needs to be mapped by micro-photoluminescence (µPL) map-scans covering the relevant area of about 300 µm × 300 µm. Here, the pitch between each pixel of the mapscans corresponds to the pitch (10 µm) of the final micropillar array so that each scanned pixel is associated with an individual pillar in the final array. To facilitate the calculation of the pillar diameters according to Eq. (1) with respect to a chosen target emission energy E c , the measured wavelength data from the map-scans are first fitted by a polynomial function of 5th-order. The resulting calculated laser diameter pattern for the 30 × 30 pillar array is then transferred to the sample via electronbeam lithography (EBL) by using a scanning electron microscope equipped with a pattern generator. The process starts with coating of the sample with a SiN layer using plasma enhanced chemical vapor deposition (PECVD). This layer acts as material for a hard mask which ensures a high etch selectivity for the following plasma etching steps. Then the sample is coated with a negative-tone EBL-resist which is exposed using the calculated pattern of the pillar array that can be aligned with an accuracy of about 5 µm to the desired sample area. Afterward, the pattern is transferred into the 500 nm thick SiN layer by a reactive ion etching (RIE) process using a SF 6 plasma. This results in a hard mask with smooth vertical sidewalls, as illustrated in Fig. 1(b). Finally, the pillar structures [Figs. 1(c)-1(e)] are etched by an inductively coupled plasma (ICP) RIE process using a mixed plasma recipe containing Ar 2 , Cl 2 , and BCl 3 . The etching process by which we remove the upper DBR and up to 20 mirror pairs of the lower DBR is optimized to achieve vertical side-walls. We would like to note that process imperfections lead to (unintentional) statistical variations in the pillar diameters with a standard deviation of approximately 30 nm.

III. EXPERIMENTAL SETUP AND OPTICAL CHARACTERIZATION
Optical characterization is performed by means of high resolution µPL spectroscopy. The sample is placed onto a motorized x-y-z stage with sub-µm accuracy in all three dimensions. All measurements are performed at room temperature. Optical excitation is realized by using a diode pumped solid-state laser emitting at 671 nm which is focused via a microscope-objective (NA = 0.4) onto the surface of the sample. An additional x-y-z piezo-stage ensures spatial fine adjustment of the microscope objective. The µPL signal of the micropillar structures is then collected by using the same microscope objective and detected via a grating spectrometer with a spectral resolution of about 20 µeV, where a pinhole is used in a confocal microscope to selectively collect µPL signal from individual micropillars. The setup is automatized to record the PL emission from each individual micropillar in the 30 × 30 array. Here, the x-y-z piezo-stage is used for additional precise autoadjustment for each individual micropillar in the array via an optical feedback-loop. This way, a spectral map is recorded in which each pixel is associated with the spectral information of a single micropillar inside the array.
We first evaluate the quality of the device fabrication by a diameter dependent optical characterization of a series of reference micropillars processed by the nominally same method as used for the micropillar arrays to be discussed below. The results are illustrated in Fig. 2, which shows a typical emission µPL spectrum (a) of a 4 µm micropillar, as well as the cavity Q-factor (b) and the fundamental resonance energy E c (c) vs pillar diameter d c . The 4 µm micropillar cavity shows a distinct mode spectrum with fundamental HE 11 mode at 1.1625 eV (1066.51 nm) and a Q factor of 5450. The emission wavelength of about 1060 nm was chosen in our work to match the requirements of an existing setup for the implementation of optical reservoir computing. The diameter dependent data presented in the lower panels show the typical decrease in the Q-factors with decreasing diameter due to enhanced losses in the small diameter regime. 21 Additionally, when compared to theoretical values of about 16 000 obtained by using finite-element simulations, 22 experimental Q-factors up to 6000 at large diameters indicate absorption losses in non-ideal DBR sections and in the active area. 21 The experimental E c (d c ) dependence shows a pronounced diameter dependent blue-shift and is quantitatively described by Eq. (1). The fit yields E 0 = 1.160 840 eV ± 22 µeV and α r = 0.95 ± 0.01 which were used to calculate the diameter for each micropillar in the homogeneous array according to Eq. (1). It is important to note that successful diameter tuning depends sensitively on the precise knowledge of the process related parameter α r which influences the slope of the E c (d c ) dependence in particular at low diameters. Here, α r is a measure of the lateral light-confinement capabilities of the micropillars and increases with improved lateral light confinement. To obtain better insight into this important parameter, we numerically simulated the diameter dependent mode properties of micropillar cavities under variation of the etching depth for two different DBR compositions and slightly different resonance wavelengths using a commercial finite-element-method solver. 22 Fitting the calculated E c (d c ) dependencies allows us to determine the associated α r parameters [see Eq. (1)] which are plotted in Fig. 2(d) vs the number of etched mirror pairs in the lower DBR for two different material compositions. As expected, α r increases with the number of etched bottom DBR pairs because of higher lateral light confinement. On the other hand, α r is nearly independent of the resonance wavelength and the index contrast in the DBR, which increases slightly by changing the Al content from 90% to 100% due to enhanced vertical light confinement. This result highlights that α r is mainly influenced by the process related lateral mode confinement. For more than 10 etched mirror pairs in the lower DBR, the lateral light confinement becomes independent of the etching depth and α r saturates. This is the regime which we use in our work.
Next we study the effect of diameter tuning on the spectral homogeneity of a processed  Fig. 4(a). (c) µPL map-scan of the HE11 resonance wavelength of the fabricated array. As the color scale shows, the wavelength trend of the unprocessed material gets compensated by the effect of the diameter tuning. micropillar array. The array was fabricated in a sample region, marked in Fig. 1(a), with a significant radial dependence of 2.1 nm/mm of the planar cavity resonance to demonstrate the proposed concept of diameter tuning. This spectral trend is also seen in the resonance map-scan of the unprocessed material in Fig. 3(a), where the resonance wavelength decreases from the top right to the bottom left corner of the map from 1058.33 nm to 1055.84 nm. This change in the resonance is accompanied by additional growth-related local resonance fluctuations throughout the sample region resulting in