Low-density patterned InAs quantum dot arrays

Quantum information science is a developing field of study that can benefit a variety of applications^1,2 such as secure communications, quantum computing, and quantum sensing. Quantum computing is ever more in the spotlight with the ability, in principle, to crack encryption algorithms and to advance science ranging from pharmaceuticals to materials discovery. Sensing devices are also being intensely developed for areas such as imaging brain activity and testing fundamental physics like gravitational waves. The basis for all of these technologies is the qubit, which requires a scalable physical system that can also be well-characterized. However, scalable production remains challenging due to the inhomogeneity of qubits in the current materials’ platform.

We are investigating a scalable, molecular beam epitaxy (MBE) grown material system where the bases for our qubits are low-density InAs quantum dots grown in patterned nanoholes on GaAs substrates. The goal is to position one quantum dot (QD) per photonic crystal cavity (PCC), which is spaced every 10 μm. A 10 μm spacing is important to accommodate a continuous array of our PCC device design, where each individual PCC device is up to 8 μm wide. The PCC will eventually serve as a proof-of-concept device for studying the QDs in optically integrated systems.

MBE grown QDs typically nucleate arbitrarily across the sample surface, thereby forming randomly distributed QDs. There are numerous studies^3–8 that have found patterning arrays of nanoholes in the substrate surface before growth is a method to overcome the random distribution nature of QD growth. Adatoms arriving at the surface during growth preferentially fill in the edges of the patterned holes due to the presence of dangling bonds, making these edges the preferred nucleation sites for QD growth. In these previous studies, pit periodicities range from 100 nm to 12.5 μm and pit sizes range from 30 to 100 nm wide. However, significant challenges remain. Patterning substrates introduces impurities and defects at the growth interface that lead to broad linewidths and weaker signals in QD photoluminescence (PL) measurements. To grow successfully in patterned nanoholes, a thick buffer layer cannot be grown, as this would disrupt the morphology of the nanoholes. This generally causes low optical quality QDs despite efforts to address the optical quality.

In 2004,³ Kiravittaya et al. compared the width and the height of patterned and unpatterned quantum dots. The samples were grown at a substrate temperature of 470 °C. The average height for an array periodicity of 210 nm was found to be 19.37 nm, with the corresponding unpatterned dots at 11.59 nm tall. For an array periodicity of 160 nm, the average height was found to be 17.80 nm, with the corresponding unpatterned dots at a height of 13.73 nm. Overall, patterned QDs are found to be slightly larger than unpatterned QDs. Subsequent growth does not exhibit relaxation of these QDs.

In 2006,⁵ Kiravittaya et al. successfully grew patterned, low-density GaAs QDs with linewidths of 70 μeV, which is only 20–50 μeV larger than conventionally grown QDs. The linewidth increase is attributed to elongation of the nanohole during buffer layer growth. In 2009,⁶ Mereni et al. studied MOVPE grown inverted tetrahedral In_xGa_1 − xAs QDs in (111) GaAs with linewidths of 90 μeV. After removing the substrate, the QDs achieved linewidths of 18 and 19 μeV. However, (111) GaAs can be very difficult to be grown on and not ideal for a scalable device. Jöns et al.⁷ made advances in 2013 with Stranski–Krastanov growth of patterned InAs QDs spaced 12.5 μm apart. The samples were grown at a substrate temperature of 510 °C. The authors used strain induced islanding to grow a second layer of QDs over the initially patterned QDs. This second layer of QDs exhibited linewidths of 13 μeV. Yet this study only demonstrated up to 40% occupancy of QDs in the patterned nanoholes. Most recently in 2017,⁸ Sapienza et al. demonstrated site selection of InAs QDs using atomic force microscopy and PL to identify QDs in between lithographically defined markers. Although prepatterning does not hinder the QDs in this study, this method of identifying QDs for devices is tedious and time consuming and is therefore unsuitable for scalable production of devices. In this article, we present progress on achieving a high QD occupancy with simultaneous low-density spacing. Future work will address optical quality but is beyond the scope of this paper.

Nanofabrication of patterned substrates necessarily involves oxidizing the surface of the substrate prior to MBE growth. This oxide must be removed while maintaining the pattern integrity for a successful growth. For a standard thermal deoxidation,⁹ the substrate is heated above 580 °C in the presence of an As₂ overpressure. The chemical reaction, $Ga2O3+2GaAs→3Ga2O+As2$⁠, of the gallium oxide surface with the underlying GaAs substrate leads to the formation of Ga₂O, which is easily removed with heat. Unfortunately, this method of oxide removal causes the surface to become pitted, and on a patterned substrate, these pits compete as nucleation sites for the QDs. Wet chemical etching¹⁰ can be used to remove the surface oxide from fabrication and purposely induce a thin protective oxide layer that is then thermally desorbed. This is done with an H₂SO₄/H₂O₂/H₂O 5:1:1 etching solution. However, this still leaves a thin layer of Ga₂O₃ that can lead to some pitting on the sample surface.

The most common method of oxide desorption for patterned wafers is to use a hydrogen flux^10,11 prior to growth. This is done at 400 °C under hydrogen overpressure. The reaction $Ga2O3+4H−→Ga2O+2H2O$ creates the more volatile oxide, Ga₂O, on the surface. However, an available port on the tool is required for a hydrogen source.

We have instead opted to use a gallium-assisted deoxidation^9,12,13 for our patterned substrates. This technique uses a gallium flux in the absence of arsenic. The more volatile oxide is formed through the chemical reaction $Ga2O3+4Ga→3Ga2O$⁠. Various studies have investigated this technique, depositing between 0 and 10 monolayers (MLs) of gallium at substrate temperatures ranging between 420 and 540 °C. Initially, the oxide is thinned uniformly with the supplied gallium. Then, patches of oxide-free GaAs appear on the surface. The supplied gallium either continues to thin the oxide or travels across the clean surface to a remaining region of oxide. However, an excessive supply of gallium can lead to gallium droplets forming on the surface; so care must be taken to provide only the required amount of gallium.

Our system has several criteria to enhance adatom mobility for the low-density array and to eventually continue into the full device growth. First, there is no buffer layer to maintain the hole morphology. Second, we are working with a higher gallium deposition rate. Using a short pulsed gallium-deoxidation method enables us to use the same gallium flux for both deoxidation and growth. This means we can use a higher GaAs growth rate for further device growth.

Finally, we are using a higher growth temperature to enhance the adatom mobility for the 10 μm pit spacing. However, there are both advantages and disadvantages to use a higher growth temperature for deoxidation and growth. First, it was found⁴ that the higher mobility of the gallium atoms decreases the amount of time it takes for the deposited gallium to react with the remaining patches of oxide. Second, it was observed in a previous study¹³ that the gallium atoms migrate to the bottom of the holes during deoxidation and fill in the nanoholes due to the higher adatom mobility at higher substrate temperatures. The nanoholes in this prior study were etched 18–22 nm deep. To counter this effect, we are starting with deeper patterned nanoholes as described below.

The growth takes place in an OSEMI Nextgen MBE system equipped with gallium, indium, and arsenic (valved cracker) effusion cells, where the beam flux monitor is located in the plane of the wafer.

Samples are patterned and grown on 500 μm (100) GaAs. Patterned samples are fabricated and used for growth within 2 weeks to limit the amount of surface oxide formed prior to growth. Samples are fabricated first by making lithographically defined etch markers, which is a pattern of crosses and squares surrounding the nanohole array. The pattern is defined using a Raith EBPG5200 e-beam tool. These markers are etched 1 μm deep using a low-bias chlorine inductively coupled plasma etcher. The nanohole array is then defined using the e-beam tool in between the etch markers. The array consists of pits with patterned widths of 50, 80, and 110 nm and periodicities of 0.25, 0.5, 1, 5, and 10 μm. Nanoholes are etched using a H₂SO₄:H₂O₂:H₂O 1:8:800 acid solution for 30 s. Pits are 40–50 nm deep after etching with a slightly slanted sidewall and widen to 70, 100, and 130 nm, respectively. Samples are cleaned in a 80 °C ultrasonic bath with N-Methyl-2-pyrrolidone, acetone, and isopropyl alcohol and then dipped in a HCl:H₂O 1:3 acid solution prior to being loaded in the MBE.

The deoxidation and subsequent growth are conducted in an OSEMI Nextgen MBE system equipped with gallium, indium, and arsenic (valved cracker) effusion cells, where the beam flux monitor is located in the plane of the wafer.

For a thermal deoxidation, samples are heated to 620 °C under an As₂ overpressure of 1 × 10⁻⁵Torr for 10 min and monitored by in situ reflection high energy electron diffraction (RHEED). All sample temperatures are measured using band-edge thermometry in transmission. These samples are subsequently either used for QD growth or cooled and removed from the MBE for further analysis.

Gallium-assisted deoxidized samples are heated to 540 °C in the absence of an arsenic overpressure. The sample is exposed to a gallium flux equivalent to a 12 ML/min growth rate in 1 s pulses with 30 s pauses for a total deposition of 7–8 ML. The sample is then annealed in an As₂ overpressure of 1 × 10⁻⁵ Torr for 5 min and then either proceeds to QD growth or is cooled and removed for analysis.

After deoxidation, the substrate temperature is dropped to 515 °C, and the arsenic valve position is reduced to an As₂ overpressure of 5 × 10⁻⁶ Torr. Then, 1.7 ML of InAs is deposited at a growth rate of 0.02 ML/s followed by a 100 s pause. An additional 0.3 ML of InAs is deposited six times, for a total of 3.5 ML, with 100 s growth interrupts between each deposition. The arsenic shutter is open throughout the process. The sample is then cooled and removed for analysis.

The in situ RHEED pattern is monitored throughout the growth. Figures 1(a)–1(d) show RHEED images at various stages in the deoxidation process. At 1 ML of gallium deposition, the RHEED reconstruction pattern is dim and spotty. By 3 ML deposition of gallium, a faint 2 × 4 pattern is visible. After 5 ML deposition of gallium, the 2 × 4 pattern becomes streakier and brighter. By 7 ML, a faint 3 × 1 pattern is observed indicating a transition to a gallium rich surface and complete deoxidation. During the subsequent arsenic anneal, the RHEED pattern stays streaky and becomes brighter. In Fig. 1(e), the RHEED pattern indicates gallium droplets that have solidified into GaAs mounds during the arsenic anneal after deoxidation and before InAs deposition. RHEED exhibits large and bright chevrons due to the deposition of excessive gallium during deoxidation, where the surface becomes faceted from the solidified GaAs mounds. Therefore, a 7 ML deposition of gallium is determined to be optimal for substrate deoxidation in this work. After deoxidation, Fig. 1(f) shows the RHEED pattern following the deposition of 1.7 ML InAs after deoxidation, where the RHEED pattern becomes slightly chevroned. This indicates the formation of InAs QDs on the sample surface. It is likely that the pattern remains partially streaky due to the large spacing between QDs.

Samples are analyzed with scanning electron microscopy (SEM). During a standard thermal deoxidation under an arsenic overpressure, a pit density of 134/μm² is observed on the surface immediately after deoxidation and before growth. The QD density is found to be 124/μm² on samples that continue with QD growth on thermally deoxidized substrates. This is comparable to the pitting density prior to InAs deposition. As shown in Fig. 2(a), the pattern has become surrounded by pits, which developed during thermal deoxidation. Figure 2(b) confirms the pattern is no longer visible and is indistinguishable from randomly located (i.e., unpatterned) QDs after QD growth. This demonstrates the necessity to use a deoxidation method that preserves the fidelity of the pattern.

Following the successful deoxidation with 7 ML gallium and the subsequent InAs QD growth, the samples are evaluated for occupancy in the nanoholes by varying their width and periodicity. Figure 3 illustrates the percent occupancy of QDs in the various types of nanoholes. An upward trend in percent occupancy is observed as the array periodicity gets larger for the stated growth conditions. Nanohole arrays with periodicities of 0.25 and 0.50 μm were found to have less than 50% occupancy. For the 1 μm array, the 70, 100, and 130 nm wide nanoholes have occupancies of 47%, 61%, and 75%, respectively. A small dip is observed for the 70 nm nanohole of the 5 μm array, which has an occupancy of 42%. This dip in the upward trend of QD occupancy could be caused by incomplete deoxidation in this area of the array. The 100 nm nanohole of the 5 μm array was found to have an occupancy of 78%, and the 70 and 100 nm nanoholes of the 10 μm array have occupancies of 89%. These QDs are about 20 nm tall and fill the width of the nanohole. In future growths, these QDs will be capped and flushed to an appropriate height for PL measurements. The 130 nm nanoholes for 5 and 10 μm arrays are not included in the plot since they formed InAs rings around the nanoholes instead of QDs inside the holes. The mechanism of this behavior is not presently understood.

The upward trend of QD occupancy as a function of the array periodicity can be explained by the choice of growth conditions. By using a higher InAs growth temperature than similar cited studies and low arsenic overpressure, we are able to take advantage of migration enhanced epitaxy¹⁴ and virtual surfactant growth.^15,16 The indium adatoms are able to freely migrate across the surface of the sample before stabilizing and incorporating at the step edges of the nanoholes. This is due to the energy supplied from the growth temperature and the low probability of finding other arsenic and indium adatoms. As more adatoms fall into the nanoholes, there is less chance that adatoms find each other on the surface and incorporate as unintended (i.e., out-of-pattern) dots.

It is likely that the surface becomes temporarily indium rich during wetting layer deposition due to the low arsenic conditions, thereby acting as a virtual surfactant to promote adatoms over the nanohole step edges. This has been shown previously by Ohtake and Ozeki to produce large, disperse InAs islands similar to the morphology and density of our patterned 10 μm arrays. A moderate amount of InAs will desorb from the sample surface instead of incorporating due to the high growth temperature. For smaller array periodicities, there is not enough InAs that is deposited and stays on the surface to fill in the dense nanohole arrays with QDs. For larger array periodicities, indium adatoms that do not find the sparse nanoholes will likely desorb from the substrate instead of incorporating as QDs outside the patterned nanoholes.

We have shown an improved InAs QD occupancy by controlling the growth conditions and the periodicity of the nanoholes on patterned substrates. We have also presented successful patterning of single QDs with an occupancy of 89% in 10 μm spaced nanoholes. This is a critical step forward for their implementation in quantum devices. Having a known location and a low density of single QDs enables a scalable platform for patterning and production of micrometer-scale devices for sensing and computing. Additionally, we implemented gallium deoxidation with our desired growth conditions for subsequent low-density patterned QD growth. Moving forward, we plan to implement a column of QDs in between the patterned substrate and the optically active QD, which is intended to create a buffer layer and address the weak photoluminescence and broad linewidths typical of patterned QDs.

The authors would like to thank the staff at the University of Delaware Nanofabrication facility, especially Kevin Lister and Paul Horng, for their guidance in the process development. This project is funded by the National Science Foundation (NSF) under Award No. DMR-1609157.