Locating environmental charge impurities with confluent laser spectroscopy of multiple quantum dots
M. Hauck, F. Seilmeier, S. E. Beavan, A. Badolato, P. M. Petroff, A. Högele
LLocating environmental charge impurities with confluent laser spectroscopy ofmultiple quantum dots
M. Hauck , F. Seilmeier , S. E. Beavan , A. Badolato , P. M. Petroff , and A. H¨ogele Fakult¨at f¨ur Physik, Munich Quantum Center and Center for NanoScience (CeNS),Ludwig-Maximilians-Universit¨at M¨unchen, 80539 M¨unchen, Germany Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA and Materials Department, University of California, Santa Barbara, California 93106, USA (Dated: August 26, 2018)We used resonant laser spectroscopy of multiple confocal InGaAs quantum dots to spatially locatecharge fluctuators in the surrounding semiconductor matrix. By mapping out the resonance con-dition between a narrow-band laser and the neutral exciton transitions of individual dots in a fieldeffect device, we identified spectral discontinuities as arising from charging and discharging eventsthat take place within the volume adjacent to the quantum dots. Our analysis suggests that residualcarbon dopants are a major source of charge-fluctuating traps in quantum dot heterostructures.
I. INTRODUCTION
The exciton transitions in self-assembled InGaAs quan-tum dots (QDs) are elementary to potential applica-tions in quantum information processing [1] and quan-tum cryptography [2]. For quantum cryptography pro-tocols, QDs can be used to generate indistinguishablesingle photons [3, 4] with high repetition rates [5], orto produce entangled photon pairs on demand [6]. Inaddition, efficient all-optical spin manipulation schemescharacteristic to QDs [7] can be exploited for spintron-ics applications [8]. Recent developments in spin-photoninterfacing can also be used to reversibly transfer qubitsbetween light and QD states [9, 10] and place QDs along-side the nitrogen-vacancy center in diamond [11] as a po-tential solid-state building block for practical quantumdevices. All these experiments ubiquitously rely on awell defined and stable resonance condition between theexciton transition and the laser fields.In current QD devices, however, the fidelity of suchprotocols is limited by spectral fluctuations. Early res-onant experiments identified spectral diffusion as a pri-mary limitation to the temporal stability of the resonancecondition [12]. More recent studies of resonance fluores-cence [13, 14] and its dynamics [15] found that the mainsource of resonance instability is the charge noise dueto fluctuations in the electrostatic environment, whichis detrimental to the quality of single photons that canbe generated in QD devices [16–18]. Recent work on re-lated device heterostructures has identified charge trapsat the GaAs/AlGaAs superlattice (SL) interface as a ma-jor source of spectral diffusion [19], and similar effectshave also been observed in devices without a SL [20].In this work, we investigate the resonance condition for anumber of QDs in a field-effect device, and find that spec-tral jumps are caused by charge fluctuations occurring inthe semiconductor volume surrounding the QDs, and arenot purely an interface effect. Using the gate-voltage de-pendence combined with the magnitude of the spectralfluctuations, we identify the likely source of these chargetraps as residual carbon impurities, and the individual impurity sites can be located more precisely when theirinfluence can be observed in more than one QD spectrum.Such spectroscopic studies could be used in the first in-stance as a highly sensitive measure of semiconductorpurity, and secondly to adjust the growth methods andheterostructure design so as to reduce the detrimentalcharge-noise in QD devices.
II. EXPERIMENTAL DETAILS
The self-assembled InGaAs QDs studied here weregrown by molecular beam epitaxy (MBE) [21] with sub-sequent annealing, and have emission energies around1 . n + doped GaAs layer (thickness 20 nm, doping concentra-tion 4 · cm − ) which forms the back electrode. The‘top’ side of the QD-layer is covered first by a 30 nmthick GaAs capping layer, and then with an additionalAlGaAs/GaAs SL of 116 nm thickness. A 5 nm NiCrlayer was evaporated on top of the SL to form the secondelectrode.The energy levels of individual QDs were investigatedwith photoluminescence (PL) [23] and differential trans-mission (DT) [24] spectroscopy in a confocal microscopesetup shown schematically in Figure 1(a). The samplehad a QD density such that there were typically 10 − ∼ µ m diameter. Out of this small ensemble,individual QDs were spectrally selected for PL and DTmeasurements. By applying a gate voltage V G betweenthe top gate and the back contact, the energy levels of aQD shift relative to the Fermi energy E F , allowing con-trol over the number of electrons that occupy the dot[22]. Figure 1(b) represents a typical QD PL chargingdiagram as a function of V G , showing the neutral exciton(X ) and the negatively charged exciton (X − ) emissionresonances, respectively [23].The neutral exciton transition was investigated in finer a r X i v : . [ c ond - m a t . m e s - h a ll ] O c t -600 En e r g y p v e V b -500 -4001.27461.27451.2744 -800 -600 -400 -200 01.2651.2701.275 GatepvoltagepvmVb En e r g y p v e V b Laservresonant/nonresonantb 4KTransmissionsignalSpectrometervab N o r m a li z e d p c o n t r a s t voltagescan vbbvcbvdb X X X laserscan GatepvoltagepvmVb
FIG. 1: (a) Setup for spectroscopy of a single quantum dot at4.2 K. For resonant excitation, the transmission is measuredby a photodiode underneath the sample. Photoluminescenceis measured using a spectrometer. (b) Photoluminescencecharging diagram of a quantum dot (QD1) with character-istic X and X − stability plateaus. (c) High resolution DTspectroscopy of the X stability plateau for the same dot asin (b). In addition to the linear Stark shift, there are sev-eral abrupt changes in the exciton resonance energies as thegate voltage is varied. (d) Normalized DT spectra along thedashed lines shown in (c). detail for a number of QDs using DT spectroscopy, withthe polarization of the excitation laser chosen so as toexcite just one of the two exchange-interaction split res-onances [12]. Examples of DT spectra are shown in Fig-ure 1(d). The calculated lifetime-limited linewidth of theX transition is ∼ . µ eV, however the transition is fur-ther broadened due to charge fluctuations in the solidstate matrix surrounding the QD [12, 15]. For chargefluctuations that occur on a time scale much faster thanthe measurement integration times (typically ∼ ± µ eV [12, 15].For a significant fraction of QDs, the linear relationshipbetween the exciton resonance energy and the appliedgate voltage is interrupted by several distinct jumps. Anexample of this effect is apparent in Figure 1(c). The en-ergy dispersion gradient is consistent across the X tran-sition plateau, however there are discontinuities in energyobserved at specific values of V G . With increasing V G , thetransition energy jumps to lower values by an amount in the range of 7 to 38 µ eV. Such spectral discontinu-ities could be caused by similar environmental charge-fluctuations which give rise to exciton line-broadening.However, the spectral jumps studied here in more de-tail occur at specific gate voltages, and correspond tolarger resonance-energy shifts in the QD transition. Re-cently, the work of Houel et al. [19] attributed thesespectral jumps to discrete charging of potential-traps lo-cated at the interface to the SL. Our analysis detailedbelow suggests the presence of additional potential-trapsin the surrounding GaAs matrix. III. MODELLING & DISCUSSION
The exciton resonance energy E of a QD is shifted byan electric field F through the quantum confined Starkeffect: E = E − p · F + β · F (1)where E is the unperturbed exciton resonance energy, p = p ˆ z is the static dipole moment of the exciton transi-tion, and β is the polarizability [25]. This relation quan-tifies how an applied electric field can be used to shiftthe exciton resonance deterministically, and also encom-passes the mechanism through which charge fluctuationsin the solid-state matrix surrounding the QD can perturbthe resonance [19].An applied gate voltage V G generates an electric field F = − ( V G − V S ) l ˆ z , where l is the distance between the n + layer and the top surface electrode, and V S = 0 .
62 V isthe Schottky barrier potential [25]. The axial polariz-ability β z along the growth direction has been measuredfor similar dots as ≈ − . µ eV/(kV/cm) [25]. For theX transition, which occurs with | V G + V S | in the range0 . − . p canbe determined from the gradient of the X transition en-ergy versus gate voltage V G as p = ( ∂E/∂V G ) · l . Valuesof p are typically e × . e is the elemen-tary charge) for the strongly confining QDs surveyed inthis work [25]. In the QD plane, there is no permanentdipole moment, however the larger geometric extent ofthe dot in this direction implies a much larger lateralpolarizability of the order of β xy ≈ − µ eV/(kV/cm) [26]. Therefore, charge fluctuations in the vicinity of aQD can perturb the exciton resonance by coupling to thepermanent dipole moment in the ˆ z -direction, or throughthe polarizability in the lateral plane.The magnitude of the exciton resonance-energy shiftcaused by a single unit charge q placed near the dot canbe determined with a simple electrostatic model of theheterostructure depicted in Figure 2(c). A QD excitonis represented as a dipole oriented along the ˆ z -axis, posi-tioned between two electrodes. A charge-trapping site islocated at an arbitrary distance from the dot, describedby position vector r . Upon occupation of such a trapping l a t e r a l g c oo r d i n a t e g H n m G f=fQf8f zgcoordinategHnmGf =f Qf 8f 4f 6f5f4f SL q = f q q q q q q Qf q =f q + pCBVBf Q5 55 =75 En e r g y E F S ili c o n g i m p u r i t y g l e v e l C a r b o n g i m p u r i t y g l e v e l q tunnellinggatthegFermienergy tunnellinggatQDHGgsubbandCB VB + HaGHbG HeG HcG _ + r =75 b a c k g g a t e t o p g g a t e excitondipole z q HdG QDHGg=.gsubband z (nm) f Q5 55 =75 Impurityglevelsgforz q g=g45..46gnm SL tunnellinggbarrier cappingglayerQDlayer t o p g g a t e b a c k g g a t e zgcoordinategHnmGzgcoordinategHnmGzgcoordinategHnmG q q6ff q5ff q4ffq=.QQq=.Qfq=.=8 En e r g y g H e V G GategvoltagegHmVG
FIG. 2: (a) Conduction and valence band edges in the heterostructure device. E F is the Fermi level, and SL labels thesuperlattice region, which is scaled down for better visibility of the regions of interest. The QDs are located at z = 25 nm.(b) Impurity charging processes that could give rise to the observed energy jumps in the X resonances; an electron-tunnellingresonance between a silicon impurity and the back gate (left), or a hole-tunnelling resonance between a carbon dopant and asubband in the 2DHG that forms at the interface to the SL (right). (c) The electrostatic model of the heterostructure. Theexciton energy is perturbed by an added charge q (here shown to be positive). The effect of the conducting back- and top-gatelayers are included to first order in the form of image charges of opposite parity to q (here negative). (d) The resonancecondition at the valence band edge between the carbon impurity level and the n = 1 subband of the 2DHG. The range of V G over which the resonance-jumps are observed implies that the carbon sites must be located within the z q = 45 −
46 nmregion. (e) Positions of added charge q that result in specific values of energy shift ∆ E . The contour lines are labelled withthe value of ∆ E in µ eV, where the orange-red lines are solutions for q = + e , and the green-blue lines correspond to q = − e .The grey lines of constant z indicate the regions where there are tunnel resonances for either the silicon or carbon impuritysites. It is important to note that only the carbon impurities exhibit an overlap between the tunnel-resonance V G range andthe Stark-shift ∆ E range, and that this region of overlap is not at the interface to the SL. potential, the change in the static electric field, ∆ F , atthe QD position is approximated as:∆ F = 14 π(cid:15) (cid:15) r (cid:18) q | r | ˆ r + − q | r m | ˆ r m + − q | r m | ˆ r m (cid:19) , (2)where q is a unit charge equal to either ± e , (cid:15) is the per-mittivity, (cid:15) r is the dielectric constant of the surroundingGaAs matrix, and ˆ r = r / | r | . The first term in the brack-ets arises from the impurity charge q . The response ofthe freely-moving charges in the electrodes to the alteredcharge environment is included (to first order) as secondand third terms in the form of image charges m and m , located behind the back gate and top electrode at r m and r m respectively [see Figure 2(c)].Combining equations 1 and 2, the energy shift is ob-tained as a function of the position and parity of theadded charge. As an example, Figure 2(e) shows the pos-sible positions for added charges of either ± e that wouldinduce a step-change in exciton energy in the range of −
10 to − µ eV, calculated for the QD1 in Figure 1with p = e × .
208 nm. At large axial distances, the en-ergy jumps could be caused by either a negative chargeappearing below the dot, or a positive charge appearingabove the dot, i.e. the observed charging events producean electric field which opposes the externally-controlled field. In the lateral plane, the addition of either paritycharge could induce such an energy shift. Aside from themagnitude of the energy jumps, their gate voltage depen-dence is also central to identifying the charge impuritylocation. Since the spectral jumps occur at specific gatevoltages, this suggests that the individual trap sites aretuned through tunnel-resonances with charge reservoirsas V G is varied.On the lower side of the dot, the most likely sourceof the electron-trapping sites are the silicon (Si) donordopants. The n + back-gate consists of heavily Si-dopedGaAs, and previous studies have shown that Si atomsdiffuse during the growth process up to several tens ofnm along the growth direction of the sample [27]. Theenergy level associated with the Si donor-electron lies E Si = 5 . V G -controlled tunneling mechanismis a resonance with the Fermi level in the back gate [seeFigure 2(b)]. A Si impurity site with z in the range0 .
85 to 1 . −
600 to −
400 mV. However, a change of − e at this loca-tion would induce a QD resonance-energy shift less than7 µ eV [see Figure 2(c)]. Such an energy shift is barelyresolvable within the X linewidth, and indeed all theobserved discontinuities investigated here have a largerchange in energy. Therefore, we can exclude Si impuri-ties as the origin for the observed spectral jumps.In the region above the QD layer, carbon (C) atomsare the likely source of hole-trapping sites. There is in-evitably a residual background C-doping in any MBEgrown device, and the concentration is known to be onthe order of 10 cm − for our sample. The C acceptoratoms have an energy level E C = 26 meV above the va-lence band [29]. The V G -controlled tunneling resonancein this case involves a sub-band in the two-dimensionalhole gas (2DHG) that forms at the interface to the Al-GaAs/GaAs SL [depicted in Figure 2(b)]. The energy ofthe n th -subband in the 2DHG is given by [30]: E n hole = E gap + E − c n (cid:20) ( e (cid:126) ) m F (cid:21) / , (3)where E gap denotes the GaAs bandgap energy, E = e ( V G − V S ) /z is the valence band energy at the po-sition of the 2DHG, c n is the n th Airy coefficient approx-imated by c n ≈ (cid:2) π ( n − ) (cid:3) , and the effective mass m = 0 .
57 [31]. The carbon charge-trap energy as well as E as a function of V G are shown in Figure 2(d), iden-tifying resonance conditions in the V G range from − −
400 mV for a carbon atom with z in the intervalof 45 −
46 nm. These z -boundaries are depicted in Fig-ure 2(e) to highlight the fact that a charge of + e locatedwithin this z -slice can indeed induce energy shifts up to-60 µ eV. This location of the charge traps is well withinin the GaAs capping layer and does not coincide with theinterface to the SL [19]. Remarkably, however, our resultsare consistent with the observation that an increase of theseparation between the QD layer and the SL is sufficientto inhibit spectral jumps in the plateau of X and favorthe narrowing of the exciton resonance [19]. The dis-placement of the SL to larger values of z implies a changein the resonance condition between the C-impurity leveland the lowest 2DHG sub-band through z in Equa-tion 3 such that carbon impurity sites would effectivelybe depopulated at gate voltages characteristic of the X stability regime. A. Impurity-site charging dynamics
The spectra of the X transition for the dots surveyedin the course of this work exhibited in general a morecomplex structure than would be expected from the sim-plistic model described above. The model explains themajority of spectral jumps, where the QD transition en-ergy changes abruptly from one value to a lower onewithin a V G span of 5 to 10 mV. This overlap in gate volt-age of the QD energies corresponding to charged and un-charged impurity states is indicative of the rate at whichhole-tunnelling occurs between the impurity site and the2DHG. A fast tunnelling process yields a small overlapin V G and vice versa, analogous to the overlaps observed -600 -500 -400 Gate voltage (mV) E n e r g y ( e V ) -600 -500 -400 E n e r g y ( e V ) Gate Voltage (mV) -600 -500 -4001.27441.27451.2746 E n e r g y ( e V ) Gate voltage (mV) (b)(c) P nr = 0.002 nWP nr = 2 nW P nr = 0.0 W (a) FIG. 3: X stability plateaus of the QD1 recorded in DTwith an additional non-resonant laser at (a) zero, (b) low( P nr = 0 .
002 nW) and (c) high ( P nr = 2 nW) power. (b)The non-resonant laser at 850 nm photo-generates charge car-riers in the wetting layer which yield reduced spectral jumps(indicated by white arrows) due to partial saturation of thecharge-trap impurities. (c) At high non-resonant laser pow-ers the charge impurities are fully saturated and the plateauis free of spectral discontinuities. Additionally, the accumu-lation of photoinduced holes at the superlattice results in ashift of the stability plateau (indicated by the red arrow) dueto a partial screening of the gate voltage. in PL charging diagrams of QDs in samples with dif-ferent thicknesses of the tunneling barrier between theQD and the Fermi reservoir and correspondingly differ-ent electron tunneling rates. In addition to the ‘sharp’transitions in the charge state of the impurity site, weobserve in our DT data instances where an impurity-sitecoexists in both charged and uncharged configurationsover an extended gate voltage range of 50 to 100 mV. Anexample of such a coexistence can be seen in Figures 1(c)and 3(a) for V G between −
480 mV and −
400 mV. Thisbehavior is inexplicable within the modelling frameworkdeveloped above. A refined model should take into ac-count not only resonant tunneling between the impuritysite and the 2DHG, but also dynamic charge capture pro-cesses that occur in the presence of an optically generatedcharge reservoir [20].To qualitatively understand the impurity site charg-ing dynamics, we adopt the rate-equation formalism ofRef. [20] to determine the time averaged steady-state oc-cupation of the impurity site N i as: N i = 11 + γ e /γ c , (4)where γ c and γ e denote the rates at which a hole is cap-tured in, or escapes from, the impurity trap respectively.In the simple case that was modelled above, γ e (cid:29) γ c when the impurity site is energetically higher than the n = 1 subband of the 2DHG, and N i →
0. Conversely,when the gate voltage is tuned such that the impuritysite is below the lowest 2DHG subband, then γ e (cid:28) γ c ,and N i →
1. However, the capture rate γ c can also beinfluenced by the excitation of charge carriers in the QD.Previous investigations have shown that the tunnellingrate of holes from a QD is significantly enhanced as itis tuned through resonances with energy levels in the2DHG [32]. It is possible therefore, for holes to tunnelfrom the QD to an n > n = 1 state of the 2DHG. TheseQD–DHG resonances effectively enhance γ c such that itbecomes comparable to γ e (determined only by the va-lence band properties), and therefore it becomes feasiblefor the impurity-site to be partially occupied over an ex-tended V G range, despite not being resonant itself withthe 2DHG state. The QD–2DHG resonances observedin similar heterostructures were measured to occur overa range of ≈
100 mV in V G [32], in agreement with the V G span in which we observe intermediate values of N i .We can further dynamically perturb the charge envi-ronment of the system with the use of non-resonant op-tical excitation [19]. In addition to the resonant laser,the output of an 850 nm laser diode is directed onto thesample, which excites electron-hole pairs in the wettinglayer. The effect of this additional charge-carrier gener-ation on the QD charge sensing phenomena is two-fold,firstly altering the electrostatic response of the QD, andsecondly directly influencing N i . The first of these ef-fects is due to a build up of holes in the 2DEG, whichare generated in the wetting layer, but due to the energy-gradient across the heterostructure, tend to relax intothe 2DHG. This accumulation of positive charge at theinterface to the SL has the effect of partially screeningthe dot from the externally applied field (causing thewell known energy shift of the exciton plateau [33]) aswell as screening the QD from the impurity charge. Con-sequently the spectral jumps decrease monotonically inmagnitude with increased non-resonant laser power (seeFig. 3). The effectiveness of the screening depends on thecharge density of the 2DHG, and therefore is determinedby the laser power. In the limit of high charge density,we can modify the electrostatic model to include the re-sponse of the 2DHG in the form of an additional mirrorcharge. With this modification, an energy jump in theQD spectra of 30 µ eV in the absence of non-resonant lightis reduced to just 16 µ eV. In addition to this electrostatic -40-200-60-40-200 -600 -500 -400-40-200 E n e r g y s h i f t ( µ e V ) Gate voltage (mV)
QD1QD2
QD3 (a)(b) 25 nm55 nm46 nmz SL
QD 1
CLaser focusQD 2 QD 3
FIG. 4: (a) Plateau of the neutral exciton for three differentquantum dots. The linear Stark shift is subtracted for clarity.All three quantum dots are situated within one common laserspot (inset lowest panel). QD 1 shows three distinct jumpsin the exciton dispersion, QD2 has two and QD3 features onediscontinuity. QD1 and QD2 have one jump in common whichis at a gate voltage of -485 mV and for QD1 and QD3 a jointdiscontinuity at -526 mV is observed. (b) 3D-model of thethree quantum dots with corresponding impurities assumingthat only carbon states participate. This is only one possibleconfiguration as the angles ϕ between the quantum dots andimpurity cannot be determined. Impurities are red and thequantum dots are grey. shielding, the second effect of non-resonant excitation isthe direct influence on N i [20]. The capture rate γ c isincreased with P pump , and beyond a certain saturationpower N i →
1, despite the impurity trap not being en-ergetically favorable compared to the n = 1 level of the2DHG. This dynamic saturation effect can be observedin Figure 3(c). B. Single impurity sensed with multiple QDs
The transverse location of an impurity site cannot bepinpointed with just one QD sensor, however further con-straints can be obtained by using multiple QDs within theimpurity vicinity. The absorption spectra of three differ-ent QDs (labelled as QD1 to QD3) within a commonfocal spot (of ≈ µ m in diameter) are shown in Figure4(a), with the background linear Stark shift subtractedfor clarity. It can be seen that there are concurrent spec-tral jumps occurring for two different QDs at the samegate voltage V G , which are likely caused by one singleimpurity. For the spectral-jumps which only occur in asingle spectrum we assume the charge-trapping sites aretoo far away from the alternate dots for the spectral ef-fects to be resolved.As a specific example of the charge sensing capabil-ity, we determine the location of the impurity site thatcauses jumps in the spectra of QD1 and QD3. The z -position of the charge impurity is calculated (using V G = 528 . ± z q = 46 . ± . E = 12 ± µ eV, while for QD2 the energy change is∆ E = 38 ± µ eV. The measured dipole moments foreach of these dots ( p = e × .
180 nm and e × .
208 nmfor QD1 and QD3, respectively) determine the transverselocation of the impurity site as 29 . ± . . ± . IV. CONCLUSION
In summary, we have identified the cause of spectraljumps in the neutral exciton transitions of QDs as be- ing due to charging of carbon impurity sites. Our re-sults suggest these impurities are located in the semicon-ductor region surrounding the QD layer. This is furtherre-enforced by measuring the spectral signatures of thecharge trapping concurrently for more than one QD. De-spite the fact that the charge trapping sites are not them-selves at the interface, our analysis suggests that movingthe SL interface further from the dot layer would stillimprove the exciton resonance stability, by shifting thetunnel resonances to different gate voltages.
V. ACKNOWLEDGMENTS
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