Size dependent line broadening in the emission spectra of single GaAs quantum dots: Impact of surface charges on spectral diffusion
N. Ha, T. Mano, Y. L. Chou, Y. N. Wu, S. J. Cheng, J. Bocquel, P. M. Koenraad, A. Ohtake, Y. Sakuma, K. Sakoda, T. Kuroda
SSize dependent line broadening in the emission spectra of single GaAs quantum dots:Impact of surface charges on spectral diffusion
Neul Ha, Takaaki Mano, Ying-Lin Chou, Yu-Nien Wu, Shun-Jen Cheng, Juanita Bocquel, Paul M. Koenraad, Akihiro Ohtake, Yoshiki Sakuma, Kazuaki Sakoda, and Takashi Kuroda ∗ National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan Department of Electrophysics, National Chiao Tung University, Hsinchu 30050, Republic of China Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands (Dated: October 12, 2018)Making use of droplet epitaxy, we systematically controlled the height of self-assembled GaAsquantum dots by more than one order of magnitude. The photoluminescence spectra of singlequantum dots revealed the strong dependence of the spectral linewidth on the dot height. Tall dotswith a height of ∼
30 nm showed broad spectral peaks with an average width as large as ∼ ∼ ≤ µ eV).The measured height dependence of the linewidths is in good agreement with Stark coefficientscalculated for the experimental shape variation. We attribute the microscopic source of fluctuatingelectric fields to the random motion of surface charges at the vacuum-semiconductor interface. Ourresults offer guidelines for creating frequency-locked photon sources, which will serve as key devicesfor long-distance quantum key distribution. PACS numbers: 78.67.Hc, 78.55.Cr, 73.21.La
Introduction.
Numerous photonic applications usingsemiconductor quantum dots rely on the discrete anddelta-function-like density of states [1]. However, varioussingle dot spectroscopy studies have confirmed significantline broadening in the photoluminescence spectra that isnormally much broader than the transform limited widthdetermined by the spontaneous emission rate. The linebroadening mechanism is commonly attributed to spec-tral diffusion, where the transition frequency randomlychanges through the fluctuation of a local electric field inthe vicinity of dots [2–5]. The fluctuating spectral linebecomes integrated into a relatively broad peak thanks tothe long time scales of signal integration compared withthose of environmental motion.Some progress has been made in studying the shorttime scale dynamics of the spectral fluctuation. Photoncorrelation measurement can elucidate spectrally diffu-sive photoluminescence with subnanosecond characteris-tic times [6, 7]. The correlation functions routinely showmonoexponent decays, which implies efficient couplingbetween a single dot and a small number of environmentconfigurations. In contrast, resonant fluorescence mea-surements reveal broad-band noise spectra in the 0 . ∗ [email protected] recent work on field-effect devices identifies charge trapsat the barrier/well interface [11] or impurity centers [12]as a dominant field source. Thus, the timescales andmagnitudes of spectral diffusion vary greatly dependingon the sample and the measurement conditions. We stilllack a global understanding of the microscopic mecha-nism of spectral diffusion, however it is needed for devel-oping frequency-locked photon sources as basic elementsin long-distance quantum key distribution, e.g., quantumrepeaters for extending the key transmission distance.In this work we experimentally analyze the dependenceof quantum dot morphology on environment-mediatedspectral broadening. For this purpose we focus on GaAsquantum dots grown by droplet epitaxy, which enables usto continuously control the quantum dot height by morethan one order of magnitude. The morphology tunabil-ity contrasts with that of traditional quantum dot growthusing the Stranski-Krastanow mode, where the dot pro-file is essentially fixed by strain relaxation and surfaceenergies. The spectral linewidth of a single dot emissiondepends strongly on the dot height. The measured heightdependence agrees with that of Stark coefficients alongthe growth direction (normal to the sample surface). Weattribute the source of the electric field fluctuation tothe change in the microscopic configuration of surfacecharges at the vacuum-semiconductor interface [13, 14].Thus, morphology engineering is an alternative route toachieving narrower emitter linewidths without the needfor feedback techniques to suppress spectral fluctuation[15, 16]. Experimental procedure.
GaAs quantum dots wereself-assembly grown in Al . Ga . As by droplet epitaxyon semi-insulating GaAs(100) substrates [17, 18]. Thesedots are free from strain thanks to the negligible latticemismatch between GaAs and Al . Ga . As. After the a r X i v : . [ c ond - m a t . m e s - h a ll ] J un
20 nm50 nm1.5 ML 5 ML 7.5 ML(a)(b) (c)
FIG. 1. (Color online) (a) Three-dimensional AFM imagesfor typical GaAs quantum dots grown by droplet epitaxy onAl . Ga . As(100) with different amounts of gallium deposi-tion θ Ga . (b and c) The average height and the base diameter,respectively, of quantum dots as a function of θ Ga . The errorbars represent the standard deviation of profile statistics. growth of a 100 nm Al . Ga . As layer, different amountsof gallium ( θ Ga ) with 1.5, 2, 3, 5, 7.5, or 10 monolay-ers (ML) were deposited at 0.5 ML/s and 200 ◦ C. Thisstep enabled the formation of gallium droplets. Then,an As flux was supplied at 2 . × − Torr and 200 ◦ C,and the gallium droplets were fully crystalized to GaAsdots. Note that the As flux was roughly two orders ofmagnitude higher than that used for the self-assembly ofquantum ring structures [19].After the dots were grown, the sample was annealedat 400 ◦ C in situ (under a weak As supply) for 10 min,and partially capped with a 20 nm Al . Ga . As layer.The temperature was then increased to 580 ◦ C, whilethe capping continued with a 30 nm Al . Ga . As layerfollowed by a 10 nm GaAs layer. GaAs dots on a 2 MLAl . Ga . As layer were additionally grown on the top ofsamples for atomic force microscopy (AFM) analysis. Fi-nally, rapid thermal annealing was carried out at 800 ◦ Cfor 4 min in a N atmosphere. All the samples withdifferent amounts of θ Ga exhibited well-defined dots; seeAFM top views in Supplementary Fig. 1. The dot den-sity depended only slightly on θ Ga from 1 . × cm − (1.5 ML) to 1 . × cm − (10 ML). Thus, we assumethat the volumes per dot are nearly proportional to θ Ga .We used a continuous-wave laser that emitted at awavelength of 532 nm as an excitation source. The laserillumination generated photocarriers in the Al . Ga . Asbarrier. The excitation polarization was set to be linearin order to avoid a spectral shift of nuclear origin [20, 21].Our confocal setup combined an objective lens with a nu-merical aperture of 0 .
55 and a hemispherical solid immer-sion lens (SIL) with a refractive index of two. The useof the high-index SIL enabled us to reduce the focusingdiameter to ∼ . µ m [22], where approximately 25 dotswere inside the spot. The excitation density was keptsufficiently low so that the carrier population was lessthan 0 .
5, and the influence of strong optical injection online broadening was fairly removed. Photoluminescence (cid:1) (cid:1) (cid:1)
10 nm (cid:1)
FIG. 2. (Color online) Cross-sectional STM topography im-ages of GaAs quantum dots capped with Al . Ga . As. Thewhite dotted lines are guides to the eye that highlight thedot-barrier interface. signals were fed into a spectrometer of a 50 cm focusinglength, and analyzed with a full width at half maximum(FWHM) resolution of 120 µ eV. All the experiments werecarried out at 10 K. Morphology analysis.
Figure 1(a) shows AFM three-dimensional views whose height increases significantlywith the amount of θ Ga . Figures 1(b) and 1(c) show theaverage dot height and the base diameter, respectively,which were determined by statistical analysis. When theamount of θ Ga was increased from 1.5 to 10 ML, the dotheight increased from 2 . ± .
5) to 24 ( ±
5) nm, i.e., bya factor of ten. In contrast, the base size increased onlyby a factor of less than two. Thus, the dot height in-creased considerably as the dot volume increased, whilethe base size remained almost unchanged. The mecha-nism responsible for the volume-dependent aspect ratio isexplained in terms of the two-step crystallization processinvolved in droplet epitaxy, see Supplementary Discus-sion.Figure 2 shows the morphology of GaAs quantum dotscapped with an Al . Ga . As matrix that was measuredusing cross-sectional scanning tunneling microscopy (X-STM) [23]. They have a truncated pyramidal shape,which agrees with the AFM cross-sections of uncappeddots. Thus, GaAs dots are embedded in Al . Ga . Aswhile maintaining their original shape. This is due to thesmall diffusion length of aluminum atoms, which furthergives rise to the formation of a distinct dot-barrier inter-face. This observation is in stark contrast to commonlystudied InAs/GaAs dot systems, where indium atoms dif-fuse efficiently, and composition mixing leads to the de-formation of dots with capping. This shape conservationallows the determination of the shape of embedded dotsfrom AFM measurements of free-standing references
Photoluminescence spectra.
Figure 3(a) shows thespectra of a large ensemble of quantum dots. They weremeasured using long-focus optics. The spectral peaksat ∼ .
51 eV originate from impurity-bound excitons inthe GaAs substrate. Signals associated with quantumdots are observed at 1.85, 1.8, and 1.67 eV in the 1.5,
FIG. 3. (Color online) Comparison of (a) photolumines-cence spectra of a large ensemble of GaAs quantum dots, and(b) those of a small number of dots selected using a micro-objective setup.
2, and 5 ML samples, respectively. The emission peak,therefore, shifts to a lower energy side with increasingdroplet volume. The 7.5 ML sample shows a relativelynarrow peak at 1.55 eV, which is close to the bulk bandgap of GaAs.Figure 3(b) shows the emission spectra of a small en-semble of quantum dots that were spatially selected usinga micro objective setup. The spectra of both the 1.5 and2 ML samples consist of sharp lines, whose linewidthsare close to, or less than, the instrumental response ofour spectrometer. There are around 70 spectral lines,which is approximately three times the expected numberof dots inside a focusing spot. The discrepancy is rea-sonable because each dot is able to generate three to fouremission lines through the formation of different types ofcharged/neutral exciton complexes [24].In contrast, the 5 and 7.5 ML samples exhibit relativelybroad peaks that dominate the emission signals at ener-gies below 1.75 eV. Note that a few sharp lines are alsoobserved at energies higher than 1.8 eV, as found withthe spectral lines of the 1.5 and 2 ML samples. Thus,the broad peaks for low-energy dots and narrow peaksfor high-energy dots are not sample-specific signatures,but universal size-dependent behaviors.Figure 4 shows linewidth statistics as a function ofemission energy. Here we evaluate the FWHM of allthe spectral lines by fitting without distinguishing be-tween the neutral and charged transitions. Such treat-ment is sufficient to clarify the general trend of size-dependent broadening, since the difference between theneutral and charged exciton linewidths is much smallerthan the observed dot-to-dot variation, as confirmed pre-viously [25]. The compiled statistics demonstrate a clearcorrelation between line broadening and emission energy.The smooth transition over the data points of differentsamples confirms that the linewidth reaches several meVfor tall dots, and decreases monotonically to the res-olution limit with decreasing dot height. The similar
FIG. 4. (Color online) Dependence of the linewidth of thespectral line on the emission energy. Gray open circles arethe values averaged over all the spectral lines in each sample. linewidth dependence on emission energies has recentlybeen reported for polar nitride quantum dots [26].
Environment-induced line broadening.
The effect ofthe environment on spectral shifts is twofold. First, hy-perfine coupling between an electron and nuclei inducesthe Overhauser field, which acts as an effective magneticfield in the tens of mT range [27]. Second, a charge dis-tribution in the vicinity of dots induces a local electricfield. However, the effect of nuclear fluctuation on linebroadening is considered to be negligible at least in thepresent samples, because a typical value for a nuclearfield is 10 mT, which corresponds to a spectral shift of0.25 µ eV for GaAs [21]. This is much smaller than theobserved linewidth, which reaches several meV. Thus, thefollowing discussion deals only with the effect of electricfield fluctuation on line broadening.A local electric field has various microscopic origins.A common example of a field source is charge particlestrapped in impurities or defects. However, their densitiesare normally very low in samples grown with molecularbeam epitaxy (MBE, ∼ cm − ). Hence, it is difficultfor the bulk impurities or defects to realize line broad-ening that are comparable to the measured spectra, asalso discussed later. Despite the charging and discharg-ing of trapping centers close to dots, here we propose thefluctuation of charge carriers trapped by the vacuum-semiconductor interface as a field source.The formation of surface states, which trap charge car-riers, is linked to the presence of electronically active de-fects at the vacuum-semiconductor interface [28]. It isknown that the surface state density depends on orien-tations and chemical treatments, and reaches 10 cm − for a naturally oxidized GaAs(100) surface [29]. Chargecarriers are efficiently trapped by the surface states, andinduce a local electric field normal to the surface on av-erage. The phenomenon also serves as the origin of bandbending and Fermi-level pinning [30]. When the sampleis optically excited, some of the photoinjected carriers re-combine with surface charges, and others occupy differ-ent surface states. Consequently, the microscopic chargearrangement changes randomly, which gives rise to fieldfluctuation and spectral broadening through time inte- FIG. 5. (Color online) (a) Calculated Stark shift for a 12-nm-high GaAs quantum box surrounded by an infinite barrier(lines) and a finite barrier (open circles) as a function of avertical field. (b) Monte Carlo simulation for electric fieldsinduced by randomly positioned surface charges with a den-sity of 1 × cm − at a point 60 nm from the charge layer.The red line shows a field strength induced with a uniformcharge sheet. gration. The effect is orientation dependent, and tallerdots become more sensitive to the induced field. Size-dependent Stark coefficients.
Qualitative ex-planation of the measured line broadening is based onthe derivation of Stark coefficients and the simulation offield fluctuation. The Stark shift E S of a single-particlelevel is described by the second-order perturbation of theinteraction Hamiltonian, i.e., E S = (cid:88) n ≥ |(cid:104) ψ | eF z | ψ n (cid:105)| E − E n = ( eF ) (cid:88) n ≥ Z n E − E n , (1)where F is an electric field, E and E n are the singleparticle eigen energies of the ground state and the n thexcited state, respectively, and Z n = |(cid:104) ψ | z | ψ n (cid:105)| is adipole moment along a direction parallel to the field.The above equation demonstrates the size dependenceof Stark shifts, where the dipole moment is proportionalto the confinement length L , the energy denominator isscaled by ( π h / m ) L − , hence the Stark coefficient isenhanced as the fourth power of the effective dot sizealong a built-in field.Figure 5(a) shows the field dependence of spectralshifts calculated for a 12-nm-high GaAs dots. Thelines show the analytic dependence for a model basedon infinite-potential quantum boxes with m ∗ e ( m ∗ h ) =0 .
067 (0 . . Ga . As potential and the effect of valence-band mixing in terms of four-band k · p perturbation.Both models exhibit parabolic dependence, as expected.Enhanced shifts in the finite-potential dot with respect tothe infinite-potential dot arise due to the extended wavefunction. These results imply that an energy shift aslarge as 1 meV, which is a typical linewidth in the mea-sured spectra, requires a field strength of the order of FIG. 6. (Color online) Calculated energy fluctuations due torandomly positioned surface charges with different densitiesof 1 × , × , and 1 × cm − . The experimentallymeasured linewidths are also indicated by the gray points,which are equivalent to the data points shown in Fig. 4.
10 kV/cm, which is expected at a position only ∼ Simulation of field fluctuation.
We evaluate the fieldfluctuation using a Monte Carlo simulation, where anelectric field is induced by randomly positioned chargeparticles in a flat layer. Figure 5(b) shows the fieldstrength distribution at a point 60 nm from the surface(dielectric constant (cid:15) = 13). This condition reproducesthe geometry of our structure. We found that the fieldchanges randomly with different charge arrangements.The statistics yields a mean field strength F of 7 kV/cmand a standard deviation of 1.4 kV/cm for a charge den-sity of 1 × cm − . The validity of this simulation isconfirmed by the agreement between the observed meanstrength and the value predicted for a uniform chargesheet, F z = σ/ π(cid:15)(cid:15) ≈ .
97 kV/cm, where σ denotes acharge density. We performed the simulation for differ-ent values of σ , and found that the magnitude of fieldfluctuation ∆ F is nearly proportional to √ σ .We assume that ∆ F transfers proportionally to linebroadening ∆ E S , i.e.,∆ E S ≈ ∆ F ∂E S ( F ) ∂F (cid:12)(cid:12)(cid:12)(cid:12) F = F = E S ( F ) 2∆ FF . (2)The substitution of Eq. 1 into Eq. 2 yields the line broad-ening dependence on the transition energy of dots, seeSupplementary Discussion for calculation details. Fig-ure 6 compares the experimental linewidths and the cal-culated spectral fluctuation for different charge densities.There is fairly good agreement between the experimentalwidths and calculated broadening when the charge den-sity is of the order of 10 cm − , which is a reasonablevalue [31].Note that the lower bound of the measured linewidthsis limited by our spectrometer resolution, though a pre-vious investigation on similar dot systems using a higher-resolution spectrometer revealed the linewidths as largeas a few tens of µ eV at wavelengths around 1.8 eV [18].Note also that the model curves exceed the measuredlinewidths at low energies. These inconsistent asymp-totes are attributed to the fact that the present modelignored the effect of Coulomb binding. The quantumconfined Stark shifts are associated with the wavefunc-tion separation between electrons and holes. Coulombattraction would inhibit such separation, and suppressenergy shifts. The upper bound of line broadening istherefore roughly limited by the exciton binding ener-gies, which were predicted to be a few tens of meV forGaAs/AlGaAs dots [24]. Conclusions.
Spectral diffusion in the photolumi-nescence of single quantum dots is an interesting phe-nomenon that bridges microscopic random dynamics andmacroscopic optical response. Here we studied morpho-logically controlled GaAs quantum dots grown by dropletepitaxy to understand the source of environmental fluc- tuation, and demonstrated the impact of fluctuating sur-face charges on dot line broadening.From a technological point of view, however, the linebroadening phenomenon is unfavorable for practical ap-plications of quantum dots to photon emitting devices.The present results suggest several ways to engineer spec-tral broadening. First, we expect to suppress line broad-ening by creating dots with a sufficiently low aspect ratiothat are robust as regards a random electric field normalto surface. Second, we expect to achieve narrower spec-tra by embedding dots more deeply in the barrier matrix,where the effect of random charges at the surface wouldbe effectively smoothed out. Line broadening is expectedto decrease with the inverse of the dot-surface distance,see Supplementary Figure 3 for the simulation result. Fi-nally, the use of a substrate with a chemically stable sur-face, such as a gallium terminated (111)A surface [32–34],and/or defect passivation technologies [29, 31, 35] are an-other potential route by which to reduce surface chargefluctuation.This work was partially supported by Grant-in-Aidfrom Japan Society for the Promotion of Science. [1] P. Michler, ed.,
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