Techniques for epitaxial site-selective growth of quantum dots

Quantum information science has made recent advances with the potential to revolutionize many technologies that are currently limited by conventional semiconductor devices. Quantum devices are promising for secure communications,¹ quantum computing,² quantum sensing devices,³ and myriad emergent applications that could be realized as the technologies evolve. Many possible implementations of these novel quantum devices have been proposed so far; this review focuses on quantum dot (QD) integration, which is an enabling technology. QDs, sometimes referred to as “artificial atoms,” are nanostructures that confine charge carriers in three dimensions leading to discrete energy levels. Their charge spin and optical properties are highly tunable by changing their size and composition, which makes them versatile for a variety of applications.

Epitaxial methods are often used to achieve the growth of QDs embedded in a solid-state matrix. They can be further processed for device applications via common semiconductor fabrication methods.⁴ However, producing large scale and reliable quantum devices remains a challenge due to the natural inhomogeneity and spatial randomness of self-assembled QDs. Natural variations in size, composition, and shape have a large effect on the quantum states, making it difficult to produce a collection of QDs at the same target wavelength for an intended device application.⁵ In addition, the random nucleation sites of QDs on a sample make it difficult to be processed into device architectures. In this review, the efforts to address these challenges—with a focus on these site-selective QDs—are discussed. The pioneering research by many in QD growth and functionalization, including that of Gossard and co-workers on highly strained QD growth,⁶ QD cap and flush technique,⁷ and QD lasing,^8,9 has helped motivate these efforts toward improved patterned growth.

This review is organized into 11 sections. Section I introduces the basics of QD formation and nanofabrication of patterned substrates. In Sec. II, the first patterned growths and basic formation of molecular beam epitaxy (MBE) grown site-controlled QDs are explored. Section III discusses the effects of changing parameters such as nanohole periodicity, shape, and size. Sections IV and V discuss alternative patterning techniques and materials, respectively. Section VI considers deoxidation methods for the patterned substrates and their effect on the patterning. Section VII discusses buried stressors to improve the quality of patterned QDs. Section VIII discusses QDs grown in inverted pyramids by metalorganic chemical vapor deposition (MOCVD) and related systems. In Sec. IX, the photoluminescence (PL) of the site-selective QDs and the effect on optical quality are explained. The review finishes with a look at theoretical modeling of QD patterning in Sec. X and integration into devices in Sec. XI.

QDs are fabricated by various methods, and QDs embedded in a solid-state matrix are commonly grown by methods such as MBE and MOCVD. Quantum dots are generally grown in a Stranski–Krastanow (SK) (layer-then-island) growth mode. In this growth mode, a thin wetting film is first grown on the substrate. The strain that results from the lattice mismatch between the film and the substrate is then relieved by the formation of nanometer-sized islands.¹⁰ 

In addition to the SK growth mode, a cap and flush technique^4,7 can be employed to control the height of the QDs. For example, when growing InAs QDs in a GaAs matrix, initially GaAs is grown to partially cover the InAs QDs. Then, the top of the QD is removed by raising the substrate temperature, and the remaining QD is capped completely with GaAs. Since the height is generally the smallest dimension of the QD, this technique leads to the increased control of the emission wavelength due to the increased control over the thickness of the QD.

Multiple QDs can be stacked in a crystal matrix,⁴ where one QD is on top of another with a thin barrier layer in between. The barrier layer has to be thick enough to separate the QDs but thin enough to allow strain induced nucleation. For a system of InAs QDs in a GaAs matrix, the tensile strain in the GaAs barrier layer that originates from the first QD layer creates a preferential nucleation site for a new QD. This growth method can be expanded to grow an entire column of QDs; alternating layers of barrier layers and QDs are grown.

Since the epitaxial growth mechanism results in a random distribution of QDs across the surface of the sample, various methods for patterning arrays of preferential nucleation sites for QD growth have been used to achieve the site-selective growth of QDs. Many of these studies were based on the patterning and etching arrays of grooves or nanoholes in the surface of a sample to create preferential nucleation sites for QD growth. Adatoms arriving at the surface during growth preferentially fill in the edges of the pattern due to the presence of unsatisfied bonds. A variation in pattern periodicity, size, and growth parameters further customizes these nanostructures and their applications. However, patterning substrates introduce defects and impurities at the sample surface that lead to broad linewidths in PL, indicating the decreased optical quality of patterned QDs. Developments in the nanofabrication of substrates and in the growth process have improved the quality of these site-selective QDs close to that of self-assembled QDs.

Patterning¹¹ a substrate for subsequent single crystal growth can cause the degradation of QD quality in several ways: residues from pattern processing can be undesirably introduced into the ultrahigh vacuum epitaxial growth chamber, it can damage the substrate during etching so that a high quality single crystal film cannot be grown, or oxide can be formed during processing, interfering with epitaxy. As illustrated in Fig. 1(a), the sample will undergo multiple nanofabrication stages and growths that include lithography, etching, substrate cleaning, and oxide removal.

Lithography¹¹ is used to define the pattern. Due to the desired small feature size, electron-beam lithography (EBL) is typically used for this purpose. Because lithography necessarily involves the uses of polymer materials, subsequent cleaning is needed. Typically, this cleaning consists of a low-energy oxygen plasma followed by dilute wet chemical etching and solvent rinses. During the oxygen-plasma cleaning process, oxides form on the sample surface. While wet chemical cleans help, the residual oxide that remains is removed prior to epitaxial growth with various techniques discussed in this review.

Etching¹¹ creates the nanoholes from the lithographically defined pattern in the substrate surface. Wet etches are preferred for samples that require high surface quality since dry etches degrade surface quality by ion bombardment. These ions can have enough energy to disrupt the lattice and create antisites or vacancies as well as changing the surface stoichiometry which can cause surface states, pin the Fermi level in a different position and cause near-surface doping. Conversely, dry etches are excellent at dimensional control as an anisotropic etch with negligible undercutting of the mask whereas wet etches undercut masks as an isotropic etch, making pattern fidelity a concern.

Single-photon sources are crucial for the creation of quantum computing and sensing devices. The Hanbury–Brown–Twiss experiment gives a measure of the efficiency of a single-photon source. This experiment measures the second order correlation function¹² g⁽²⁾(τ) which describes the probability of a source emitting two photons at the same time. A perfect single-photon source would have g⁽²⁾(0) = 0. QDs coupled to various nanostructures have proved to be reliable single-photon sources. These devices¹³ could be micropillars, microdisks, or photonic crystal cavities. In a micropillar, light is emitted vertically, and confinement is achieved through two Bragg-mirrors in the vertical direction and etched sidewalls in the horizontal direction. A microdisk can emit light from its side and confines light using total internal reflection from all three directions. Photonic crystal cavities confine light in the vertical direction with a suspended slab and an arrangement of etched holes for the horizontal direction. The design of the slab and the holes determines the emission direction.

The first study of site-selective QD growth was done by Mui et al.,¹⁴ where the growth of self-aligned, one-dimensional InAs QDs on gratings was demonstrated. The gratings were patterned onto (001) GaAs substrates with spacings of 0.28, 1, and 5 μm aligned along the [011] or [01-1] direction. After a 50 nm buffer layer, QDs were formed at 525 °C by depositing 1.5 monolayers (MLs) of InAs. For samples with [011] oriented ridges spaced 1 μm, the QDs formed with a density of 12 μm along the B-type sidewalls of the grating, seen in Fig. 2, where (a) is a top down view and (b) is a side view. The preferential In adatom migration toward the B-type sidewall caused a local increase in a InAs layer thickness, which favored QD formation in that area. For the [01-1] grating spaced, the adatoms migrated away from the ridges and formed on the (001) plane. The smallest grating size, 0.28 μm, did not have enough of a (001) plane in between the gratings and subsequently, QDs formed on the sidewalls when the critical thickness was reached.

A second study by Ishikawa et al.¹⁵ showed entirely in situ patterning and growth to grow individual site-controlled InAs QDs. The in situ patterning process steps are shown in Figs. 3(a)–3(f). A photo-oxidized layer was formed on the surface of a clean (001) GaAs substrate. After electron-beam writing, holes were etched using Cl₂ in 12 × 12 array spaced 1 μm apart to a diameter of 200–400 nm and depth of 30–80 nm. The oxide was then removed under an arsenic overpressure, and InAs QDs were formed at a substrate temperature of 460 °C by supplying a varying amount of InAs in 0.2 ML increments with 1 min growth interruptions. The transition from 2D to 3D growth was found to be at 1.4 ± 0.2 ML of deposited InAs, which formed 100–200 nm diameter QDs in the patterned holes. QDs formed on the surface outside the holes were infrequent.

Ishikawa et al.¹⁶ later demonstrated the inclusion of a thin buffer to improve QD quality. In this paper, mesastructures containing an array of small holes were patterned, and a GaAs buffer layer was included before the growth of the QDs. An initial 500 nm buffer layer was grown on prepatterned mesas with sizes 30 and 50 μm wide, and a subsequent surface oxide layer was formed by photooxidation to serve as an e-beam mask. 100 nm diameter holes were written and etched by Cl₂. The oxide mask was removed in an ambient As₄ atmosphere, and a second 10–20 nm buffer layer was grown at 550 °C. The buffer layer caused the patterned holes to become shallower and elongate in the [110] direction. QDs were formed by depositing 1.4–1.6 ML of InAs at 460 °C. The number of QDs that formed in each hole correlated with the hole depth. In 5 nm deep holes, 15–25 QDs were observed. This decreased to 5–15 QDs for 3 nm holes and 1–2 QDs for holes 1.5 nm deep. No QDs were observed in holes with a depth of less than 1 nm. The density of QDs also correlated with the mesa size, where the center of the 30 μm showed very few QDs as compared to the center of the 50 μm mesa. PL emission from these QDs was observed at 1.25 eV with an inhomogeneous broadening of 70 meV.

Kiravittaya et al.¹⁷ reported on the formation of ordered and homogeneous arrays of InAs QDs. Nanoholes with diameters 60–80 nm were patterned on 500 μm wide, 200 nm high mesas. The pattern had a periodicity of 160 nm. A 5.1 nm GaAs buffer layer was deposited at 500 °C followed by 1.5 ML of InAs grown at 470 °C. A second InAs QD layer was grown after a 15 nm GaAs/Ga(Al)As spacer layer at 500 °C. For a deposition amount of 1.8 ML InAs for the second QD layer, QDs in the unpatterned area were found to be randomly distributed with a density of 51 μm⁻². Immediately outside the edge of the patterned area, the density of randomly distributed QDs drastically decreased to 2–3 μm⁻². Inside the edge of the patterned area, QDs filled the patterned areas with some interstitial defects. The AFM image in Fig. 4(a) compares the QD growth of the patterned and unpatterned areas, where Figs. 4(b) and 4(c) correspond to the areas noted in (a). The number of defects decreased further inside the patterned area. When the amount of InAs deposited for the second QD layer was lowered to 1.6 ML, no QDs were observed outside the unpatterned region and size inhomogeneity was observed from the center to the edge of the patterned region. The authors proposed that indium adatoms diffuse first to the center of the mesa where the underlying patterned QDs are buried. These adatoms incorporated as QDs due to the strain field starting at the center and moving outward until all the sites were filled. Then, the strain field worked to repel adatoms, which decreased QD formation close to the patterned area.

A combined study by Gerardot et al¹⁸ explored and compared the two techniques for site-controlled growth shown in the Kiravittaya et al. and the Lee et al. papers by using the localized surface chemical potential and surface strain. After patterning a (001) GaAs substrate using one of these two techniques, a thin GaAs buffer layer was grown at 610 °C with 10 s growth interruptions every 10Å. QDs were then formed by depositing InAs at 550 °C in 0.1 ML steps with 2 s growth interruptions. The surface chemical potential patterning method utilized an In_0.2Ga_0.8As stressor film grown over patterned mesas 150 nm wide with a lattice period of 200–400 nm. A schematic of the stressor film growth is shown in Fig. 5. During a 10 nm buffer layer growth and subsequent stressor film growth, the mesas elongated along the [1-10] and became 50 × 200 nm². The number of QDs on each site could be adjusted with the amount of InAs deposited. Next, a method of strain based growth was investigated by patterning 50 nm deep nanoholes with a diameter of 100–400 nm and a pitch of 0.5–4 μm into the GaAs surface. QDs were formed in the nanoholes when the critical thickness of InAs was deposited. Extra surface QDs formed between the nanoholes when more InAs was deposited. Finally, another method of strain based growth was shown by patterning the substrate using colloidal nanospheres as the lithography mask. A latex sphere suspension was spun onto the GaAs substrate. When the suspension dried, capillary forces drew the spheres together and they packed into an ML hexagonal lattice. After dry etching to a depth of 35 nm and removal of the 240 nm spheres, a triangular lattice was observed in the GaAs surface. When a 15 nm GaAs buffer layer and InAs QDs were deposited, islands with a diameter of 41 nm were observed in the honeycomb depressions.

Variations in pattern periodicity, hole or trench size, use of a stressor layer, buffer layer, and other parameters can have a significant effect on the ordering, size, and homogeneity of patterned QDs. Section III explores some of those parameters and their effects.

A paper by Heidemeyer et al.¹⁹ investigated the effect of pattern periodicity on lateral ordering, size homogeneity, and optical properties. Arrays of 29 nm deep nanoholes and trenches were patterned on top of 200 nm high, 500 μm wide mesas. At 500 °C, an 18 ML GaAs buffer layer was grown followed by 2.1 ML of InAs. The second layer of 2.1 ML InAs was deposited after a 10 nm GaAs/5 nm Al_0.4Ga_0.6As/5 nm GaAs spacer. This resulted in QD-pairs aligned along the [110] direction and directly above the first patterned layer. When the third layer of QDs was grown, the spacer and InAs deposition were repeated. Not all sites were occupied for a pattern period of 103 nm and most QDs formed as a single QD on the site. For a pattern period of 159 nm, most sites were occupied and some QD-pairs were observed. QD-pairs were observed on every patterned site for periods of 185 and 210 nm. An average increase in QD height, from 7.3 to 8.2 nm, was observed with an increasing period. A PL peak shift was also observed from 1.084, 1.087, 1.090 to 1.090 eV for periodicities of 103, 159, 185, and 210 nm, respectively. The corresponding FWHMs were 71, 75.3, 66.2, and 66.7 meV for periods of 103, 159, 185, and 210 nm, respectively. The PL signal corresponded to the buried QD layer and correlated with the surface morphology. The 103 nm period had a broad spectrum and indicated the incomplete formation of the QDs in the sites. The narrow peaks for the 185 and 210 nm periodicities indicated well-developed QD-pairs. The surface morphology is confirmed with AFM images.

A second paper by Schramm et al.²⁰ also studied the effect of different periodicities; however, this study evaluated the growth of patterned grooves with InAs QD chains. To begin, a 500 nm GaAs buffer was deposited on a (001) GaAs substrate. Grooves with periods of 200, 500, 1000, and 2000 nm were patterned in the surface with a depth of 30 nm and oriented in the [010] direction. The regrowth consisted of a 60 nm GaAs buffer grown at 470 °C, and 1.8 ML InAs deposited at 540 °C. The cap was made up of 20 and 50 nm layers of GaAs grown at 540 and 590 °C, respectively. The QD density in the grooves was observed to increase with larger periodicities. The linear density increases from 7 to 18 μm⁻¹ for periods from 200 to 1000 nm and saturated at that periodicity. The average QD height also increased from 8.5 to 15 nm for the 200 and 1000 nm periods, respectively. The PL emission is broad with the QDs emitting above 900 nm. For the increasing periods, the PL emission redshifted to above 1000 nm.

Hole size and shape effects on the growth of site-selective QDs were investigated in a work by Mayer et al.²¹ Initially, a 300 nm buffer layer was grown on a (001) GaAs substrate followed by patterning of the nanoholes. The regrowth started with a 12 nm GaAs buffer and continued with a 20 s annealing step. 1.5 ML of InAs was deposited to form QDs in the patterned nanoholes. With larger hole diameters, an increase in QD occupation was observed, while a larger standard deviation in average, the occupation was observed for smaller hole diameters. Since EBL can vary more for smaller holes, this was likely the cause. The final shape of the hole could also be manipulated by patterning circles versus ellipses. When circular nanoholes were etched, they elongated in the [011] direction during the buffer layer growth. If nanoholes were initially patterned as ellipses in the [0-11] direction, then the buffer layer growth compensated in the [011] direction to create circular nanoholes for InAs deposition. The aspect ratio of the ellipse, controlled by two exposure spots during EBL patterning, was then investigated. The number of QDs per hole was observed to increase with increasing aspect ratio. The higher occupancy of the larger nanoholes tended to be affected by the aspect ratio as compared to the smaller holes. The occupancy of the larger nanoholes could be controlled by using smaller aspect ratios to decrease occupation and larger aspect ratios to increase occupation. And finally, the etch depth of the nanoholes was investigated. Deeper nanoholes were observed to have a higher occupancy of QDs; however, shallower holes had a larger standard deviation in the average number of QDs per hole.

In a letter by Schneider et al.,²² the lithographic alignment of site-controlled QDs was evaluated for the potential of further processing into device structures. An initial 350 nm buffer layer was grown on a (001) GaAs substrate and proceeded by etching lithographic markers to a depth of 1.5 μm into the sample. Small, 30 nm wide nanoholes were etched into the mesas with a periodicity of 1 μm. The subsequent growth at 530 °C consisted of a 12 nm GaAs buffer layer, InAs QD deposition, and a 50 nm GaAs capping layer. The growth showed a 90% single QD occupancy in the patterned nanoholes. Figure 6(b) illustrates the mesa design, and Fig. 6(a) shows an AFM of the QDs in the patterned nanoholes. Metal cross hairs were deposited after growth in between the QDs to determine the positioning accuracy of the grown QDs. A standard deviation of 50 nm was observed from the QDs to the target position at the center of the cross hairs. The previous research²³ found that a 50 nm deviation from the target position corresponded to a 25% decrease in the overlap of the QD with the optical mode based on a W1 waveguide (photonic crystal lattice with one line of holes missing). Based on this result, the use of lithographic markers could position single patterned QDs into arrays of photonic crystal cavities within 50 nm accuracy.

In another study by Heidemeyer et al.,²⁴ the authors showed patterned lateral ordering of QDs under optimized growth conditions. A GaAs buffer layer grown on a (001) GaAs substrate was patterned with mesas 500 μm wide and 200 nm tall. Nanohole arrays 29 nm deep and 90 nm wide were fabricated in the center of each mesa. With a buffer layer deposition of 18 ML GaAs, the lateral size of the holes slightly increased. An additional 8 ML of In_0.25Ga_0.75As formed a QD-pair in the [110] direction. For 36 ML of GaAs deposited, the shape of the nanoholes appeared more regular. Further deposition of InGaAs also formed a similar QD-pair. By 72 ML of GaAs, the holes narrowed in the [−110] direction but remained the same in the [110] direction. There is also a ridge that filled in the center, creating two holes instead of one. When no buffer layer was grown, subsequent InGaAs deposition partially filled the holes and formed the initial stage of a QD-pair. The dots had a diameter of ∼70 nm and were spaced ∼93 nm apart. The second layer of 11 ML of In_0.3Ga_0.7As QDs was deposited following a buffer layer stack consisting of 8 nm GaAs/3 nm Al_0.5Ga_0.5As/2 nm GaAs. The AlGaAs served as a charge carrier confinement layer for PL measurements. Figure 7(c) shows a cross-sectional schematic of the growth along with AFM images of the growth of the first [Fig. 7(a)] and second [Fig. 7(b)] layers of InGaAs QD. PL data of these quantum dots showed a peak at 1.045 eV with an FWHM of 49.5 meV.

A different study also looked at the lateral ordering of QDs. Atkinson et al.²⁵ showed growth of arrays of site-controlled InAs QDs and QD-pairs. A (001) GaAs substrate was patterned with an array of nanoholes 60–100 nm wide and 35 nm deep. The overgrowth proceeded at 520 °C and comprised of a 10 nm GaAs buffer layer followed by 2 ML of InAs and a 3 min anneal under As overpressure before finishing with a 70 nm GaAs capping layer. For a nanohole array of ∼59 nm wide, 53% of the patterned sites were observed to contain single QDs, while the remaining sites contained either a QD-pair spaced 30 nm apart, a QD-pair that was close to combining, or no dot but infilled hole with Ga(In)As. The QD-pairs were formed from a figure-eight shape that emerged in the patterned holes during buffer layer growth. The size distribution for these dots was found to be 5.0 ± 0.1 nm high and 23 ± 5 nm wide. For 100 nm wide nanoholes, two to four dots were formed in each hole with some beginning to coalesce. There was no significant change in single dot size observed for an increase in InAs coverage to 2.35 ML or for pattern periodicities between 400 nm and 2 μm. The PL spectrum showed emission wavelength ranges from 960–1060 nm with the wide variation attributed to the QD size distribution.

McCabe et al.²⁶ investigated various periodicities ranging from 0.25 to 10 μm and pit widths of 70, 100, and 130 nm, where growth conditions were tailored toward high QD occupancy in larger lattice spacings. Samples were grown at 515 °C on (001) GaAs. After deoxidation, the arsenic overpressure was cut in half to 5 × 10⁻⁶ Torr. 1.7 ML of InAs was deposited followed by a 100 s growth interruption. 0.3 ML of InAs was deposited six more times with 100 s interruptions in between. Under the lower arsenic overpressure and higher InAs growth temperature, the samples were observed to take advantage of migration enhanced epitaxy. Due to this, the adatoms had a lower probability of finding other adatoms before incorporating at the step edges of the nanoholes. This caused an increase in QD occupancy as the periodicity increases. For nanohole arrays smaller than 0.5 μm, the occupancy was less than 50%. The 1 μm spacing had occupancies of 47%, 61%, and 75% for nanohole widths of 70, 100, and 130 nm, respectively. The 5 μm spacing had an occupancy of 78%, and the 10 μm spacing saw an occupancy of 89%.

Beyond traditional lithography and etching techniques, there are a number of alternative patterning methods that have been investigated. Scanning tunneling microscopy (STM)-assisted nanolithography investigated by Nakamura et al.²⁷ can be used in conjunction with MBE growth to form site-selected QDs. 30 μm wide mesas were first patterned into a (001) GaAs substrate and then transferred into an STM/MBE system. After deoxidation and buffer layer growth, an array of tungsten containing droplets was deposited on the sample surface by the STM tip, schematically shown in Fig. 8(a). These droplets were sized 20 nm wide and 2 nm tall. The droplets were then overgrown by 15 nm of GaAs, shown in Fig. 8(b), and resulted in nanoholes directly above the droplets, which were 40 nm wide and 4 nm deep. 1.1 ML of InAs in 0.17 ML increments with a 1 min growth interruption was further supplied to the sample at 460 °C to form QDs in each nanohole, as shown in Fig. 8(c). The QDs had an average width and height of 35 and 6 nm, respectively. Each droplet was shown to act as a nanomask with nm precision for subsequent formation of QDs with no QDs observed in between patterned sites.

In a study by Ohkouchi et al.,²⁸ a nanojet probe site-controlled patterning technique was introduced. The technique took place in an AFM/MBE system and used a specially designed AFM probe, which deposited indium droplets on a GaAs substrate. A 500 nm diameter aperture was formed at the tip of an AFM stylus using focused in beam (FIB). The stylus was then mounted in the UHV system and loaded with the indium source material. An applied voltage pulse caused local melting of the indium, which protruded out of the aperture due to a high electric field formed during the voltage pulse. A voltage pulse of 140 V for 10 ms was found to produce relatively uniform indium droplets on the GaAs substrate surface in arrays with periods of 50 and 100 nm. The droplet epitaxy technique could then be utilized to crystalize the droplets under an arsenic overpressure into InAs QDs. Figure 9 illustrates a schematic of this patterning process.

In a further study,²⁹ the authors reported on the progress of the nanojet probe technique for deterministically placing QDs. Using the technique described in the author’s previous report,²⁸ nanodots 30–40 nm wide and 3–4 nm tall with a periodicity of 100 nm were fabricated on a GaAs substrate. Each nanodot was observed to be accompanied by three smaller dots around it, possibly due to the deposition from the tip. The sample was then annealed in an arsenic overpressure of 5 × 10⁻⁵ Torr while slowly raising the substrate temperature to 420 °C. Two subsequent layers of InAs QDs were grown on top of the nanojet QDs by depositing 20 nm thick GaAs spacer layers in between 1.25 ML InAs QDs. An additional 5 nm Al_0.3Ga_0.7As barrier layer was inserted in the second GaAs spacer layer. The PL spectrum exhibited a peak 980 nm and had a broad linewidth of ∼100 meV. This is most likely due to the dot inhomogeneity of the buried nanojet deposited QDs.

Another approach by Bauer et al.³⁰ used cleaved edge overgrowth to order InAs QDs. Layers of AlAs and GaAs were grown at 650 °C on a (001) GaAs substrate. The four different AlAs/GaAs superlattices studied were (1) five periods of 320 Å AlAs/680 Å GaAs, (2) five periods of 200 Å AlAs/400 Å GaAs, (3) five periods of 110 Å AlAs/220 Å GaAs, and (4) ten periods of 200 Å AlAs/200 Å GaAs. The sample was cleaved in situ to expose the (1-10) surface and then continued with QD growth. Figure 10 schematically displays the cleaved edge growth stack. Three monolayers of InAs were deposited at a substrate temperature of 470 °C. The QDs preferentially nucleated on the Al-rich regions of the cleaved edge possibly due to the reduced mobility of In adatoms on Al-rich surfaces. The QD size directly correlated to the thickness of the AlAs layer. QDs on samples 2 and 4 were elongated in the [110] direction and on sample 3 appeared as wires due to the smallest AlAs layer. The PL spectrum showed broad luminescence peaks at 1.325 and 1.356 eV (sample 1), 1.372 eV (sample 4), and 1.389 eV (sample 2), which corresponded to the observed QD sizes.

A letter by Song et al.³¹ reported on MOCVD grown site-controlled InAs/InP QDs fabricated using a local AFM oxidation technique, which exhibited single-dot emission that matches the optical telecommunications band. Initially, a 200 nm InP buffer layer was grown on a (001) InP substrate. Nanometer scale oxide drops were formed in air at room temperature by local AFM oxidation using a negatively biased tip that contacts the sample surface. The dots were spaced 500 nm apart and were 80–110 nm wide with a height of 5–6 nm. The dots were then removed using an HCl solution, which left behind patterned nanoholes 80–110 nm wide and 3–4 nm deep. An anneal before QD deposition decreased the hole depth to 1.7–2.3 nm. 1.4 ML of InAs was deposited at 500 °C and subsequently capped and flushed to a final QD height of 2 nm to obtain light emission in the range of 1.3–1.55 μm. The 200 nm cap was grown at 600 °C. Single PL peaks were observed which mostly matched the telecommunications bands. The peaks ranged in emission from 1.22 to 1.45 μm with a FWHM of ∼0.8 meV.

Finally, a study by Zhang et al.³² investigated FIB patterned GaAs (001) substrates for the growth of site-controlled InGaAs QDs. The FIB patterning adjusted parameters such as accelerating voltage, probe current, dwell time, and pitch. The parameters tested used 20 keV, 5 pA, and either a 1, 5, or 20 ms dwell time. There was also a pattern tested that was made with 20 keV, 40 pA, and a 1 ms dwell time. After patterning, a 20 nm GaAs buffer was deposited at 580 °C followed by 1.5 ML of InAs at 520 °C. During characterization, it was found that short dwell time and small ion beam doses resulted in patterned QDs, while large dwell times and doses formed quantum rings and holes. Room temperature PL studies displayed broad peaks at 878 and 1152 nm, which are the GaAs substrate and QDs, respectively.

Interference lithography is another method of patterning InAs QDs in situ. This method uses a single pulse, four-beam laser that recombines at the sample surface to create an interference pattern. The interference maxima rise in temperature very rapidly while the interference minima remain colder. Adatoms diffuse to the cold regions due to the resulting thermal gradient and form nanoislands. These nanoislands serve as nucleation sites for the InAs QDs. In Wang et al.,³³ this method was used during epitaxial growth to form InAs QD arrays with a 300 nm periodicity. The samples were fabricated on (001) GaAs and the growth proceeded with a 500 nm GaAs buffer layer at 600 °C followed by 1 ML of InAs at 500 °C. The laser was then pulsed to create the patterned nanoislands, which the authors speculate are composed of mostly indium. The QD growth was then completed with an additional supply of InAs and a 10 s growth interruption under an arsenic flux. Trenches were observed to form around the nanoislands, which created preferential nucleation sites for the InAs QDs. The authors successfully showed on more than 30 samples the nucleation of QDs in these trenches. The QDs were found to be 40–50 nm wide and 12–15 nm tall. By increasing the InAs deposition from 1.55 to 1.75 ML, the number of QDs formed at each site increased from 1 to 6. PL analysis of the QDs showed the ground state emission at 1.05 eV with a narrow linewidth of 22 meV.

While patterned QDs tend to be InAs, there can be alternate materials. In this letter by Kiravittaya et al.,³⁴ ordered GaAs quantum dots were grown in an AlGaAs/GaAs heterostructure. Prior to patterning, a 400 nm GaAs buffer, 20 nm Al_0.5Ga_0.5As, and 200 nm GaAs layers were grown on a (001) GaAs substrate. The pattern was then defined to a periodicity of 5 μm and was etched to ∼30 nm deep. The subsequent growth included a 10 nm GaAs buffer, 20 nm Al_0.33Ga_0.67As barrier, 2 nm GaAs QD layer, a second Al_0.33Ga_0.67As barrier, and 100 nm GaAs cap, all grown between 500 and 530 °C. Immediately after deposition of the QD layer, a 2 min growth interruption was applied, which aids the filling of the holes and smoothing of the surface. After the first buffer and barrier, layers were grown to overtop the pattern, the holes elongated in the [110] direction to two to three times the patterned width. The width of the [1-10] direction remained unchanged. Figure 11 illustrates (a) a cross section of the growth stack as well as (b) AFM images of the nanohole morphology with insets showing before (top) and after (bottom) buffer layer growth. The individual PL spectrum showed emission from the QDs between 737 and 788 nm with linewidths between 0.1 and 1 meV. The PL of a single QD displayed neutral and charged exciton lines at 1.6826 and 1.6795 eV, respectively. Single-photon emission was tested by performing a correlation measurement from the exciton transition. The correlation function g⁽²⁾(τ) demonstrated that g⁽²⁾(0) = 0.40, which is less than 0.5, therefore, indicating single-photo emission.

In another letter by Wen et al.,³⁵ Ge QDs patterned on Si substrates were investigated for the nanophotonic bandgap effect. (001) Si substrates were patterned with 90 × 100 nm² periodicity nanoholes. During growth, 7 ML of Ge was deposited for the bottom QD layer followed by 5 ML for each of the subsequent ten QD layers. A 10 nm Si spacer separated each layer. Samples were capped with 100 nm of Si and 17 nm of Al. During analysis, it was found that the resultant 3D QD crystal created a photonic nanocrystal that had THz acoustic phonons with controllable transport properties. Using the 3D finite-difference time-domain method, the phonon scattering caused by the QDs showed two minigaps at 0.34 and 0.7 THz. The optical differential reflection measurements revealed three oscillation components observed at 79, 200, and 344 GHz, where 79 GHz is the acoustic propagation in Si, and 200 and 344 GHz is attributed to coherent acoustic phonons from the Al layer.

The most common method of the GaAs substrate deoxidation is through a thermal desorption, where a sample is heated in an arsenic overpressure to drive off the surface oxide. In Yamada and Ide,³⁶ the isothermal desorption of the surface oxides was investigated. A Si-doped (001) GaAs substrate was cleaned and etched in solvents, and a H₂SO₄:H₂O₂:H₂O (4:1:1) solution prior to loading into the vacuum chamber. Samples were exposed to oxygen pretreatment to grow a thin layer of oxide similar to those seen from in situ EBL. The sample was then heated to 543 °C in the absence of an arsenic overpressure and monitored by a quadrupole mass spectrometer. At 200 °C, a desorption peak for AsO⁺ was observed, followed by an As⁺ peak at 350 °C. At 500 °C, a Ga₂O signal was detected and continued until a sudden, sharp peak indicating the full removal of the surface oxide. These results showed that volatile oxides were removed during the substrate heating, and only the Ga₂O₃ oxide remained above 500 °C, which is removed with the reaction Ga₂O₃ + 4GaAs → 3Ga₂O + 2As₂ (or As₄). The surface Ga₂O₃ uses Ga atoms from the underlying GaAs substrate during this reaction, and the surface eventually becomes Ga-rich after the complete oxide removal. This model explains why thermally desorbed substrates become roughened. The migration of Ga atoms within the GaAs substrate to the oxide for desorption leaves voids which eventually become nanometer-sized pits at the completion of oxide desorption. For this reason, thermal deoxidation is not used for site-selective growth. The naturally formed pits compete with patterned nanoholes for adatoms during the QD growth process and inevitably cause QDs to form outside the intended pattern.

An alternative method for deoxidation utilizes a cracked hydrogen source. This procedure has the advantage over thermal deoxidation in that it does not require high temperatures. This prevents the pitting of the GaAs and leaves a flatter surface prior to growth, which is particularly desirable for site-selective templated growths. In Khatiri et al.,³⁷ this method was investigated using STM to analyze the surface roughness. Samples were outgassed for 15 min at 300 °C under ultrahigh vacuum and then exposed to an overpressure of atomic hydrogen at 2.5 × 10⁻⁵ mbar at 400 °C until a clear RHEED pattern was observed. Samples were then annealed in two steps, first for 5 min at the same temperature and then between 580 and 600 °C under an As₂ overpressure for 5–10 min. The samples were finished with the growth of a GaAs buffer layer at 480–600 °C. The root mean square (RMS) roughness was characterized with the STM after each growth step. Different GaAs substrates were found to have varying deoxidation times. (001) GaAs substrates required up to 40 min of atomic hydrogen exposure, whereas (110) and (111)A GaAs required only 6 and 14 min, respectively. The RMS through each procedural step was also different for each type of substrate. The (001) GaAs had RMS values of 1.8, 1.1, and 1.2 Å for the atomic hydrogen, As₂ anneal, and buffer layer steps, respectively. While the (001) GaAs substrates had better observed values for the atomic hydrogen and As₂ steps, the (110) and (111)A GaAs showed a much greater improvement in RMS through the procedural steps overall. 2.4, 1.6, and 0.6 Å, respectively, were observed for the procedural steps of (110) GaAs, and 2.1, 1.9, and 0.9 Å, respectively, for (111)A GaAs. These differences could be explained by the thickness of the initial oxide or possible variations in the amount of volatile oxides. Most importantly, no pitting is observed on the substrates after deoxidation.

In Atkinson et al.³⁸ and Atkinson and Schmidt,³⁹ a method is investigated to use a gallium flux, an element already installed on the instrument, in the absence of arsenic to desorb the oxide from a patterned sample prior to MBE growth. The more volatile oxide is created through the chemical reaction Ga₂O₃ + 4Ga → 3Ga₂O. The results argue this as a great alternative deoxidation method, which addresses the void creation from Ga atom migration in the substrate to the oxide by supplying Ga to the surface instead. In this study, samples were prepared by growing a 200 nm GaAs buffer on (001) GaAs wafer. An array of holes was patterned and then wet etched to produce nanoholes ranging from 40 to 80 nm in diameter. Following the wet etch, the wafer was cleaned in a variety of solvents and completed with an oxygen-plasma clean. The oxide was primarily formed in the plasma step. The sample was then loaded into the MBE and exposed to a gallium flux of 1 ML per minute in 30 s intervals alternated with 30 s growth interruptions. Various thicknesses of gallium were investigated: 0, 4, 6, 8, and 10 ML. Substrate temperatures were also varied from 420 to 540 °C. After deoxidation, samples were annealed for 2 min at 560 °C in the presence of an arsenic flux. Another GaAs buffer of 8–10 nm was grown prior to the InAs QD growth. The InAs growth was 1.4 ML thick. In unpatterned areas of the wafer, the InAs QD density was found to be less than 5 × 10⁶ cm⁻². The ideal conditions from these experiments of gallium overgrowth for deoxidation were found to be 6–8 ML of gallium at a substrate temperature of 420–460 °C. Also, the nanoholes filled in slightly during the deoxidation, creating a figure-eight shape in the hole. This resulted in a 60% double occupancy and a 40% single occupancy of QDs in the nanoholes.

Finally, another alternative method for deoxidation is by using an indium-assisted deoxidation. The advantage of this method is that excess indium readily desorbs from the substrate at lower temperatures leaving a metallic free surface. This is opposed to excess gallium from a gallium-assisted process which would not desorb until 650 °C and can produce gallium droplets left on the substrate surface. In Hussain et al.,⁴⁰ an indium-assisted deoxidation on patterned substrates was investigated. The (001) GaAs substrates were patterned with 200 nm periodicity holes that measured 550 and 50 nm wide in the [110] and [1-10] directions, respectively, and were etched 20 nm deep. The indium-assisted deoxidation was done at 500 °C in the absence of an arsenic overpressure. In total, the InAs equivalent of 1.5 nm was deposited by a continuous flux on the surface. The sample was then annealed at 560 °C under and As₄ flux for 2 min. After a 10 nm GaAs buffer layer, InAs QDs were deposited in 0.1 ML steps for a total of 1.8 ML at 500 °C. During the desorption step, the nanoholes widened to 80–85 nm laterally and decreased in depth to 9 nm. The nanoholes also maintained their shape better than a gallium-assisted deoxidation, leading to more singly occupied patterned sites over a tenfold stack of QDs. This could be due to leftover InAs in the nanoholes during the anneal which limits GaAs growth in the holes during the buffer growth.

QD lattice sites have been shown to be patterned by underlying stressor layers. The authors of Wu et al.⁴¹ investigated QD columns with STM for the first time. QDs were formed on an unpatterned (001) GaAs substrate by depositing 3 ML of InAs at a substrate temperature of 485 °C. Subsequent layers of QDs form preferentially directly above the previous layer due to strain and were separated by 56 Å GaAs spacer layers. The cross section was exposed to STM analysis by cleaving in situ. QDs were observed to be 30 Å tall and the STM analysis showed that the QDs get wider further up the column. There were also clear regions of InAs and GaAs with some intermingled indium in the GaAs spacer from the wetting layer but showed no evidence of indium diffusion between the QDs.

A report by Nakamura et al.⁴² focused on the fabrication and characterization of stacked InGaAs QDs on prepatterned (001) GaAs. The periodicity of the patterned nanoholes was 200 nm, where the holes had a width of 80 nm and a depth of 25 nm. Initially, 13 ML of In_0.4Ga_0.6As was deposited on the patterned substrate at 530 °C. A 20 nm thick buffer layer consisting of 10 nm GaAs/5 nm Al_0.3Ga_0.7As/5 nm GaAs was grown on top of the InGaAs stressor layer at 500 °C. For sample A, a second 4.6 ML InGaAs layer was then grown. For sample B, three more InGaAs QD layers consisting of 11.5, 5.8, and 5.5 ML were grown followed by two, 1.4 ML InAs layers. Figure 12 shows (a) bright-field and (b) many-beam TEM images of this growth stack. The InGaAs layers were deposited at 530 °C, and the InAs layers were deposited at 500 °C. Sample A was observed to have mostly double dots in lattice site positions with a size of 80–120 nm. Sample B had double and triple dots sized 50–60 nm. This was likely due to an initial elongation of the pits causing a widened strain field. Another feature that could explain this is a 6 nm ridge formed from an imperfectly smooth spacer between dot layers.

QDs self-assembled into lattices by a strained layer were shown by Lee et al.⁴³ Mesas sized 170 nm wide and 25 nm tall were patterned onto a {100} GaAs surface with a periodicity of 250 nm. The mesas were oriented parallel to either the <100>, <110>, or 30° off the <110> direction. After patterning, a 60 nm GaAs layer was deposited at 600 °C followed by an In_0.2Ga_0.8As stressor layer and 10 nm GaAs spacer layer deposited at 510 °C. The sample temperature was raised to 530 °C to deposit 1.7 ML of InAs and form QDs. Each mesa orientation exhibited between 3 and 4 QDs on top of each lattice site with a clear separation between sites. The QDs ranged in size from 27 to 45 nm wide and 4–10 nm tall. A stressor film thickness of 0, 5, 10, 12, 15, and 20 nm was also investigated. Below 5 nm, 0% of QDs were found on the lattice sites. As the stressor film thickness reached 20 nm, 90% of the QDs on each sample were observed on top of a lattice site. PL of the lattice sites showed peaks at 1.16, 1.22, and 1.269 eV, which correspond to the emission of the ground state and excited states, respectively.

This next paper by Kohmoto et al.⁴⁴ examined vertical stacks of QDs patterned by STM-assisted nanolithography. A (001) GaAs substrate was first patterned with nanomasks using the STM-assisted technique, and a thin GaAs buffer layer was deposited. 0.9 ML of InAs was then supplied to the surface in 0.17 ML steps with 1 min growth interruptions. A GaAs/AlAs superlattice spacer layer was grown in between subsequent layers of QDs. The lattice spacing between QDs was patterned to 100 nm, and STM images indicated that most lattice sites were occupied. An STM image after covering the initial layer of QDs with 20 nm of GaAs/AlAl showed a planar surface with some terraces of single ML. Supplying another 0.9 ML of InAs for a subsequent QD layer resulted in elongated disks 0.33 nm tall on the lattice site. An additional 0.4 ML of supplied InAs formed QDs on the lattice site with almost 100% vertical pairing. STM images in Fig. 13 show the progression of this growth investigation: (a) the first QD layer, (b) the spacer layer, (c) the 0.9 ML InAs second QD layer, and (d) a 1.3 ML InAs second QD layer.

Continuing this research, Yang et al.⁴⁵ looked at the effect of periodicity on STM-assisted patterned QD stacks. GaAs substrates were first prepared with 30 μm mesas and a buffer consisting of 350 nm GaAs/100 nm Al_0.3Ga_0.7As/50 nm GaAs. Nanomasks with periodicities of 45, 50, 75, and 100 nm were then patterned on the prepared substrates, and a 10 nm GaAs buffer was grown over the nanomask. The first layer of 1.4 ML InAs QDs was deposited followed by a GaAs/AlAs spacer layer and finished with 1.8 ML of InAs. QDs in the first layer averaged 6 nm tall and 35 nm wide while the second layer averaged 9 nm tall and 45 nm wide. As the periodicity of the pattern decreased, vertical pairing between layers of QDs decreased. For less than a 75 nm period, the probability of pairing became very low. This was likely due to the increased lateral interactions of adatoms. Room temperature PL of the QDs was also investigated. It was found that the FWHM increases with decreasing pitch, which matches with the increased variations in size uniformity observed. This was also likely due to amplified lateral interactions.

Heidemeyer et al.⁴⁶ researched buried stressors to probe the strain field of a previous layer to align QDs on lattice sites and areas of strain energy minima. Mesas on (001) GaAs substrates were patterned with 29 nm deep nanoholes of various periodicities. These samples were overgrown at 500 °C with a stack of 11.3 ML of In_0.3Ga_0.7As/8 nm GaAs/3 nm As_0.5Ga_0.5As/2 nm GaAs/12 ML In_0.3Ga_0.7As. Figure 14 shows images of the periodicities of the (a) 103, (b) 157, (c) 179, and (d) 200 nm arrays. Perfect site control was observed for the 103 nm array. As the periodicity of the array increased, more elongated InAs structures formed between the vertically stacked QDs. This was due to the strain energy minima between the lattice sites increasingly acting constructively, which drove epitaxial growth by chemical potential. The InGaAs material accumulated in areas of energy minima to avoid areas of strain energy maxima.

Different crystal planes can be utilized for self-organization of QDs due to variations in strain energy. Lippen et al⁴⁷ reported on self-organized strain engineering of QDs on (311)B GaAs substrates. After a 250 nm GaAs buffer layer grown at 580 °C, a superlattice was grown consisting of 3.2 nm In_0.37Ga_0.63As/0.7 nm GaAs grown at 500 °C, a 2 min anneal at 580 °C, and finished with a 5.5 nm GaAs layer. Between 1 and 11 periods of this, superlattice was grown. Due to the (311)B GaAs substrate and the low concentration of In in the InGaAs QDs, the QDs do not form by the SK growth mode but instead the surface strain field. For 5 and 10 period superlattices, a distinct arrangement of grouped QDs with a periodicity of 300 nm, a height of 8–10 nm, and a group width of 200 nm was observed. The average group consisted of 11 QDs. When the temperature of the growth was lowered to 470 °C, the ordering went away. The QDs preferred the tensile strain minima, and the observed QD formation pattern offers insight into the underlying strain template.

The growth of pyramidal QDs (PQDs) is another unique approach to location-defined QDs. The pyramid structure provides both the ability to form a thick enough buffer layer to address optical issues and maintain a small enough dimension for quantum size effects.

Large, site-controlled inverted pyramids in (111)B substrates used to grow InGaAs QDs were investigated in Mereni et al.⁴⁸ Tetrahedral recesses with a 7.5 μm pitch were initially patterned in GaAs substrates. Samples were then grown using metalorganic vapor phase epitaxy. A GaAs buffer layer was followed by an Al_xGa_1−xAs gradient layer that varied in composition from Al_0.30Ga_0.70As to Al_0.75Ga_0.25As. A thicker Al_0.75Ga_0.25As was grown to aid as an etch stop layer after growth to flip the apex of the pyramids up on a new substrate and remove the as-grown substrate. Then, GaAs barrier layers and the QD layer were grown between Al_0.55Ga_0.45As confinement layers. Figure 15 schematically illustrates the growth stack. The In_yGa_1−yAs QD layer was varied in composition with y = 0.15, 0.25, 0.35, and 0.45 for samples A–D, respectively. The inset in Fig. 15 shows the emission energy of the QDs for samples A–D. The samples were characterized by as-grown and apex-up post substrate removal. PL characterization was done and found that for the varying In_yGa_1−yAs composition, the wavelength emission ranged from 830 to 882 nm for samples A–D, respectively. The QD ensemble of sample B found the emission energy of the neutral exciton to be 1463.5 meV with a standard deviation of 1.19 meV. Prior to the substrate removal, single QD linewidths were found to be up to 90 μeV and after the substrate removal, a significant improvement was observed with single QD linewidths of 18 and 19 μeV; ensemble linewidths were not available for comparison.

Wong et al.⁴⁹ discuss InAs QD growth on top of GaAs nanopatterned pyramids. The GaAs pyramids were grown on (001) GaAs substrates covered with a SiO₂ mask. The mask was 25 nm thick with 230 nm diameter openings spaced 330 nm apart. The pyramids were grown by MOCVD at 700 °C and form three distinct types of pyramids, labeled as pyramids A, B, and C. SEM pictures and corresponding schematics are shown in Fig. 16. InAs QDs were then deposited on the pyramids at 510 °C and capped with GaAs for PL analysis. Pyramid A was defined by a (001) apex and six facets of {115} and {105}. Pyramid B had facets from {115}, {105}, {311}, and {103} with a (001) apex. Finally, pyramid C was observed to have {111}, {110}, and {311} facets with a (001) apex. The pyramids ranged in height from 30 to 90 nm. The QDs were observed to nucleate on higher index GaAs facets like {115} and {311} and avoid nucleation on the (001) apex, {111}, and {10n} facets. Nucleation on pyramid A took place on (115) and (-1-15) facets with an average of 3 QDs per facet. On pyramid B, two QDs nucleated, one on each of the (311) and (3-1-1) facets. A single QD formed on pyramid C and grew over the (001) apex onto each of the {311} facets. During PL analysis measured at 77 K, the ground state emission wavelength of the QDs was found to range from 1.25 to 1.35 μm for pyramids A–C, respectively. The FWHM of pyramids A, B, and C were observed to be 59, 72, and 79 meV, respectively.

Hsieh et al.⁵⁰ demonstrated the single-photon emission of a QD grown at the apex of a pyramidal mesa. Square mesas 1–2 μm wide were initially patterned on a GaAs substrate before MOCVD growth of a GaAs buffer layer at 600 °C, where the buffer layer tapered down into a pyramid with {124}, {110}, and {111} facets with a (001) apex. The pyramid width was varied from 10 to 500 nm by changing the initial mesa size and the buffer layer thickness. InGaAs QDs were then grown at 500 °C and selectively form at the apex of each pyramid. The QDs were observed to emit in the range of 1.18–1.32 eV. Due to the emission angle of the pyramid-defined QDs versus QDs on the planar substrate, the PL emission was expected to be double that of the planar QDs. However, the PL was only 1.3 times stronger, which could be due to variations across the sample. However, clear antibunching behavior was observed indicating single-photon emission with a g²(0) = 0.36.

Spectral matching with optical cavities of QDs in tetrahedral recesses was investigated by Felici et al.⁵¹ Samples were grown by organometallic chemical vapor deposition on 2 degrees off-(111)B GaAs patterned with a 7 × 7 array of inverted pyramidal recesses with an edge length between 252 and 485 nm and spaced 15 μm apart. This array was surrounded by similar pyramids 500 nm apart to moderate the growth rate and act as sinks during the growth process. An In_0.20Ga_0.80As QD layer was deposited in between GaAs buffer layers. As the size of the pyramid increased, the QD energy was observed to increase by 60 meV presumably from the formation of thinner QDs as the pyramid size increased. A QD energy gradient was also observed from the center to edge of the 7 × 7 array, as illustrated in Fig. 17. It is clear from the figure that the average emission energy increased with the distance from the center, indicating thicker QDs toward the border. These QDs may have been more influenced by the QD sinks surrounding the array. The spectral tuning by pyramid size and growth rate moderation exhibits the possibilities for controlling properties in further device applications.

There are studies that focus on characterizing and improving the optical quality of patterned QDs. Obtaining optical properties of site-specific QDs comparable to unpatterned QDs are of interest. One way to achieve this is by utilizing vertically stacked QDs to increase the distance between the regrowth surface and patterned, optically active QD. Jöns et al.⁵² investigated this alternative. Initially, a 20 period superlattice of 65.7 nm GaAs/77.5 nm AlAs capped with 101.4 nm GaAs was grown and then patterned with 100 nm wide, 18 nm deep nanoholes spaced 12.5 μm. The QD stack consisted of a 5 nm Al_0.75Ga_0.25As/5 nm GaAs buffer followed by 1.5 ML InAs and a 3 min growth interruption. The QDs were capped with 8 nm of GaAs and followed by another 10 min smoothing interruption. A 2 nm Al_0.83Ga_0.17As/2 nm GaAs barrier layer was then grown before the second 1.6 ML InAs QD layer. This second layer was capped with 1.9 nm GaAs and annealed again. The differences in GaAs caps were to help distinguish the emission wavelength of the stressor QD and from the second layer during PL measurements. The entire structure was finished with 137.4 nm GaAs and two periods of 77.5 nm AlAs/65.7 nm GaAs. The QD stressor layer was observed to contain between zero and four QDs at 40% of the lattice sites. The narrowest linewidths observed from the second layer QDs μ-PL were 7 μeV, which is comparable to that of unpatterned InGaAs QDs. The median line widths observed for 40 lattice sites was 13 μeV. This was attributed to the distance achieved between the optically active QD and the regrowth interface. A time correlated single-photon counting measurement showed a lifetime of 0.71 ± 0.04 ns, which is also comparable to unpatterned QD values. Finally, the single-photo emission value of g²(0) = 0.02 indicated these QDs as an excellent single-photon source, which the authors attributed to the very large periodicity between lattice sites.

In this study by Hakkarainen et al.,⁵³ the PL of site-controlled InAs QD crystals was investigated. Samples were prepared by first growing a 100 nm GaAs/100 nm AlGaAs/100 nm GaAs stack at 590 °C on (001) GaAs substrates. Groove patterns 90 nm wide, 30 nm, and with a period of 180 nm oriented along the [011], [01-1], [010], and [001] directions were etched into each sample. The regrowth proceeded at 490 °C with a 60 nm GaAs buffer followed by 2.2 ML of InAs at 515 °C to form QDs in the grooves. The capping layer consisted of a 20 nm GaAs/50 nm AlGaAs/20 nm GaAs stack. After the regrowth buffer layer and before the InAs deposition, the grooves had depths of 7, 18, 12, and 12 nm for the [011], [01-1], [010], and [001]-oriented grooves, respectively. A plateau formed in between the grooves of the [011] orientation but was not observed for the other orientations. This was due to enhanced Ga adatom diffusion in the [01-1] direction which fills the [011]-oriented grooves more and becomes the main contributor to the differences in the QD crystals. The ground state PL peak for the QD crystals was observed at 1180 nm, which blue shifted from 1190 nm for an unpatterned reference sample, presumably from QD size differences. The polarization dependency of the QD crystals was also investigated. The [011]-orientation showed no polarization dependency, while the [01-1]-orientation showed emission polarized along the QD crystal direction. Both the [010] and [001]-orientations exhibited maximized PL emission half way between the QD crystal and the [01-1] direction. The polarizations for these various QD crystal orientations were explained by two mechanisms, QD shape elongation in the [01-1] direction and enhanced PL intensity along the QD crystal direction caused by dot-to-dot interactions. These two effects canceled out in the [011]-orientation, added for the [01-1]-orientation, and caused a rotation in the [010] and [001] orientation from the QD crystal to the [01-1] direction.

Huggenberger et al.⁵⁴ reported narrow PL emission from site-selective QDs as well as integration into device structures. 100 nm wide nanoholes with periods ranging between 200 nm and 10 μm were wet etched onto the tops of 300 × 300 μm² wide mesas. A wet etch was chosen, as opposed to a dry etch in previous studies, to reduce the damage to the substrate during the nanofabrication process. The sample growth started at 545 °C with an 8 nm buffer layer followed by deposition of an InAs QD layer where the amount of InAs was less than the wetting layer thickness such that no QDs form but partially filled the holes. This was overgrown with a layer consisting of 5 nm GaAs/3 nm Al_0.33Ga_0.67As/2 nm GaAs followed by between 0.8 and 1.6 nm of InAs. Samples for PL were flushed to a height of 2 nm and capped with 50 nm GaAs. Samples used in device integration had stacks grown prior to nanohole patterning consisting of a 400 nm p-doped GaAs layer followed by five periods of GaAs/AlAs and finished with a 106 nm intrinsic GaAs layer. After QD growth, the samples were capped with 106 nm intrinsic GaAs and 212 nm n-doped GaAs. Micropillars with Au-ring contacts were fabricated over single, site-controlled QDs. Of the 12 QDs measured, the mean emission wavelength was found to be 906 nm with a standard deviation of 7 nm. The individual QDs had FWHMs of 100 μeV. The QDs inside the micropillars showed successful device integration with an FWHM of 400 μeV.

In a follow up letter,⁵⁵ the authors continued their research with a report on a large statistical study of PL emission from both the QD ensemble and single site-selective QDs. The growth is the same as stated above, except this study focused on nanohole periods of 200, 300, and 350 nm. PL of an ensemble of 130–140 QDs showed an inhomogeneous broadening of 14.4 meV, and the smallest single QD linewidth found was 43 μeV. A study of 87 individual QDs showed 20% of the sites emit with a linewidth of under 100 μeV. The median linewidth was found to be 213 μeV.

A work by Yakes et al.⁵⁶ discussed a method for patterning individual and short chains of QDs without a stressor layer of QDs and utilized a thick GaAs buffer layer. This study started with patterning a GaAs substrate with alternating rows of holes and [−110] lines 30 nm deep and 80 nm wide. With a thick buffer layer growth, the pattern widened in the [110] direction leaving notches at the tops of ridges, as shown in Fig. 18(a). These notches functioned as QD nucleation sites, where the number of QDs in each site is determined by growth conditions, line spacing, and buffer layer thickness, as shown in Fig. 18(b). For a 90 nm buffer layer and InAs QD deposition just under the wetting layer thickness, 1, 2, and 3 QDs nucleate in each site for line spacings of 240, 280, and 320 nm, respectively, seen in Fig. 18(c). When 80 sites were measured for PL, linewidths ranging from 6 to 100 μeV with a median of 19 μeV was observed. This observed range is incredibly narrow and on the order of linewidths for unpatterned QDs. The primary reason for these narrow linewidths was attributed to the thick buffer layer used between the patterned substrate and QD growth.

Simulations can provide information on trends and parameters for improving growth. In this paper, Liu et al.⁵⁷ used computer simulation to create charts based on parameters of the growth of prepatterned QDs and quantum rings. The charts provide useful instruction on approaching patterned growth to achieve either QD or quantum ring growth. The surface was modeled by the diffusion and deposition of atoms, which was controlled by the surface chemical potential. The film and the substrate were assumed to have the same elastic properties, and both the elasticity and surface are isotropic. For prepatterned pits, where the phase diagram is shown in Fig. 19, when either the periodicity or deposition rate was large (zone 1), QDs formed singly during the growth. When both the periodicity and deposition rate was large (zone 3), extra ripples and dots appeared in between the patterned pits. For periodicities and deposition rates that were middling between these two regions (zone 2), initially, additional ripples and dots were observed between the pits. However, with further growth, these features were smoothed and left behind single QDs in the prepatterned holes. For prepatterned humps, where the phase diagram is shown in Fig. 20, a middling pitch distance demonstrated ring growth that progresses with further growth into single QD growth on top of the humps (zone 1). For a small periodicity, only single dots formed but directly between two adjacent humps causing a doubled dot density (zone 2). A very small pitch difference corresponded to QDs located between the patterned humps (zone 3). A small deposition rate first formed incomplete rings and then disordered QDs upon further deposition (zone 4). Large periodicities and growth rates caused ripples and dots to appear between the prepatterned humps (zone 5).

In another report, Lee et al.⁵⁸ explored growth conditions for forming a QD crystal by performing Monte Carlo simulations. The models simulated the formation of QD islands on top of a previous layer of QDs separated by a buffer layer. The simulations used the stress energy tensor Ψ_j, where the vertical and off-diagonal components of the stress energy tensor were considered negligible. The adatoms movement was modeled with the diffusion and was dependent on the stress energy and temperature. An adatom in a position where the stress energy was small had a chemical potential that was low, and where the stress energy was large, the chemical potential was large. These adatoms diffuse, meet, and combine on the sample surface to form QDs. The separation between these islands depended on the diffusion and flux of impinging atoms. For a buffer layer that was small, the chemical potential was reduced in the core region directly above the previous layer due to the strong stress energy. Using too thick of a buffer layer, diminished the stress energy and adatoms nucleated into islands randomly.

Large scale and practical applications of site-controlled QDs cannot be accomplished without successful device integration. This section introduces a few ways, this has been accomplished in the current research. A method of fabricating QDs in devices is to construct the device and QD-like structure from grown quantum wells (QWs). In research by Lee et al.,⁵⁹ an InGaN/GaN QW was dry etched into an array of 120 nm high nano-pillars and then encapsulated in 40 nm of Al₂O₃. The InGaN QW layer was 3 nm thick. This resulted in a QD-like disk at the center of the nanopillar. PL data of a single pillar noted QD emission behavior. This emission wavelength was analyzed for pillar diameters between 16 and 25 nm. As the pillar became smaller, a blue shift was observed due to the quantum confinement in the disk plane. The average emission from the measured QD disks was 2.947 eV as compared to the QW emission at 2.854 eV. The FWHM of the PL data for the QD disks was measured to be 24 meV, which is comparable to SK grown GaN/AlN QDs, but much larger than InGaN SK grown QDs.

A device of particular interest for QD integration is photonic crystal cavities. This can be accomplished with both SK grown and pyramidal QDs. Surrente et al.⁶⁰ investigated pyramidal QDs incorporated into L₁₁ photonic crystal cavities (cavity with a line of 11 holes missing). In each cavity, between 3 and 9 InGaAs/GaAs QDs were integrated. 1 μm of Al_0.75Ga_0.25As and 265 nm of GaAs were initially deposited on a (111)B GaAs substrate. Pyramidal pits were then patterned with a triangular periodicity of 200 nm and a pyramid side length of 160 nm. The remaining growth stack consisted of 2.5 nm GaAs, 0.2 nm In_0.2Ga_0.8As QD, and 5 nm GaAs cap. The photonic crystal pattern etched out after the final growth step matched the 200 nm triangular lattice, and the AlGaAs undercut layer was etched out using an HF solution leaving the GaAs membrane. Ensemble PL data showed a linewidth of 7.4 meV. The cavity modes were identified using polarization-resolved spectroscopy. A peak at 1.4041 eV was attributed to the fundamental L₁₁ cavity mode. MicroPL spectra for each QD cavity system fabricated showed that for any number of QDs patterned inside the cavity, a cavity mode was observed in the expected region.

In a study by Jamil et al.,⁶¹ the authors reported in-plane single-photon emission in a photonic crystal cavity from SK grown site-selective QDs. The samples grown started with 900 nm sacrificial Al_0.7Ga_0.3As followed by a 105 nm GaAs layer. The nanoholes were then patterned and the regrowth proceeded at 470 °C with a 15 nm GaAs buffer, InAs deposition slightly less than the wetting layer thickness, and a 112 nm GaAs cap. This left a QD at the center of a 229 nm slab to aid in the light coupling of a fabricated photonic crystal waveguide. Figure 21(a) shows an AFM image of the patterned, uncapped QDs. The waveguide was then fabricated from the grown sample, as shown in Fig. 21(b), using dry etching and EBL as well as a wet etch to remove the Al_0.7Ga_0.3As sacrificial layer, leaving the device membrane. The patterned QDs were found to have an average offset of 64 nm with a standard deviation of 21 nm from the center of the photonic crystal cavity. The QD was then tuned to couple to the cavity using temperature tuning. In general, coupling QDs to cavities benefits from tuning the emission of the dots and many techniques⁶² have been used but a detailed discussion of such tuning is beyond the scope of this review. Photo autocorrelation measurements were taken to evaluate the device as an in-plane single-photon source. The correlation function g⁽²⁾(0) gave values as low as 0.12 ± 0.05, which indicates strong suppression of in-plane multiphoton events and demonstrates the potential for this system as an on-chip quantum light source.

Precise positioning of the QDs with respect to the device structure is incredibly important for coupling with the device. A PL imaging technique to determine the location of QDs based on markers was presented by Sapienza et al.⁶³ Self-assembled InAs QDs inside a 190 nm thick GaAs layer were first grown on top of a 1 μm thick Al_0.65Ga_0.35As layer. Metal alignment markers were then patterned on top of the growth stack before the PL positioning imaging. The imagine set up consisted of a light emitting diode sent through a 90/10 beam splitter and a 20 infinity corrected objective. This made a 200 μm spot on the sample. The sample then sent reflected light and fluorescence back through the beam splitter to an electron multiplied charged couple device where it was imaged. Using this imaging technique, the QDs were located with less than 10 nm in uncertainty from the alignment marks. Nanophotonic device structures were then fabricated on the QD positions. A g⁽²⁾(0) value of 0.15 ± 0.03 was obtained for the nonresonant, pulsed excitation of the QD emission. Further investigation of the QD excited state showed a single-photon emission value of g⁽²⁾(0) = 0.009 ± 0.005 was achieved, indicating the potential for this technique to help produce quantum light source devices.

In this review, we have presented an overview of site-controlled QD growth. The initial studies by Mui et al.¹⁴ and Ishikawa et al.¹⁵ on the formation of QDs on gratings and in nanoholes demonstrated the possibilities of QD deterministic growth. Subsequent research by Ishikawa et al.¹⁶ showed that the simple inclusion of a buffer layer improved the QDs' optical properties. Various other research studies, both theoretical and experimental, investigated the effect of changing nanohole size and shape, array periodicity, the amount of material deposited for QD formation, and growing multiple layers of QDs. Beyond pattern alterations, studies showed the successful growth from substrates patterned using STM-assisted nanolithography, nanojet probe patterning, cleaved edge overgrowth, AFM oxidation, and FIB patterning. Also, while this review focused on InAs site-controlled growth, research was presented for growth techniques of other QD materials systems such as GaAs/AlGaAs and Ge/Si.

Maintaining pattern integrity and substrate quality was also reviewed through the use of different deoxidation methods. Atomic hydrogen exposure and ML Ga and In deposition were shown to be viable methods for surface oxide removal as opposed to thermal deoxidation, which creates surface pitting.

In an effort to increase the surface buffer layer and improve optical quality, QD growth in pyramidal recesses and on top of tetrahedral mesas was evaluated. In the case of Mereni et al.,⁴⁸ this method produced QDs emitting with linewidths of 18 and 19 μeV, comparable to that of self-assembled InAs QDs. The PL and optical properties were also considered in other studies. Improvements in pattern preparation and increasing buffer layer thickness were shown to consistently produce patterned QDs with linewidths less than 100 μeV. Finally, the successful integration into device structures was presented and showed the ability of these patterned QDs to be single-photon emitters for quantum device applications.

The next steps for site-selective growth of QDs are to continue improving device integration such that small arrays of devices can be realized. This would be an important step in the direction of one day achieving wafer-scale production of quantum devices.

The authors thank D. S. L. Mui, T. Ishikawa, S. Kiravittaya, B. D. Gerardot, C. Schneider, H. Heidemeyer, H. Nakamura, S. Ohkouchi, J. Bauer, Y. Nakamura, S. Kohmoto, M. Felici, M. K. Yakes, A. Jamil, P. Lui, P. S. Wong, and L. O. Mereni for the permission to reuse some materials presented in this paper. L.N.M. was supported by the National Science Foundation (NSF) under Award No. 1609157, and J.M.O.Z. was supported by the National Science Foundation (NSF) under Award No. 1839056. L.N.M. also wishes to acknowledge the COVID 19 pandemic for the time it permitted to work on this review.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.