Optical NMR from single quantum dots

Solid State Nuclear Magnetic Resonance 11 Ž1998. 49–58

Optical NMR from single quantum dots S.W. Brown ) , T.A. Kennedy, D. Gammon NaÕal Research Laboratory, Washington, DC 20375, USA

Abstract Nuclear magnetic resonance ŽNMR. from constituent Ga and As nuclei was optically detected on excitonic recombination in single GaAs quantum dots formed by interface fluctuations in GaAsrAl 0.3 Ga 0.7 As quantum wells. Orientation of the nuclear spin system by optical pumping causes an Overhauser shift of the excitonic energy levels proportional to the degree of nuclear orientation. NMR was subsequently detected by monitoring changes in the combined Overhauser plus Zeeman splitting of excitons localized in single quantum dots as the RF frequency was swept through a nuclear resonance. The NMR signals originate from ; 10 5 nuclei in the quantum dot—with dimensions of approximately 4 nm = 10 nm = 100 nm—illustrating the extreme sensitivity and spatial resolution of the technique. NMR from such small structures provides a chemically specific probe of the local environment on the nanometer scale. q 1998 Elsevier Science B.V. Keywords: Optical pumping; Overhauser shift; High sensitivity; Quantum dot; GaAs

1. Introduction Mesoscopic systems such as quantum dots and nanocrystals are interesting to study from a theoretical physical or chemical standpoint because they bridge the gap between two extremal limits—the macroscopic regime and the quantum regime. In addition, they exhibit a variety of confinement-related optical and electronic properties useful for opto-electronic device applications. In developing a detailed understanding of the underlying physics governing the properties of these mesoscopic systems, it is helpful to go beyond measurements of ensemble-averaged values to measurements of the properties of individual quantum dots and nanocrystals. Advances in nanocrystal fabrication, in nearfield imaging and in lithographic processing tech-

niques have enabled elegant spectroscopic studies of the optical and electronic properties of single quantum dots and nanocrystals, revealing details of these systems typically obscured by ensemble-averaged measurements w1–3x. Nuclear magnetic resonance ŽNMR. studies of ensembles of nanocrystals have been performed, giving information about the structure of the nanocrystal, including the presence of defects within the nanocrystal w4x and local chemical environments w5x; however, there have been no detailed reports of NMR measurements of single nanocrystals or quantum dots. 1 Extending NMR capabilities to study single nanocrystals or quantum dots can give symmetry, strain and chemical information about the local nuclear environment that could be important in

1

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Corresponding author. NIST, Gaithersburg, MD 20899, USA.

Preliminary results of this work to be published in the Materials Research Society Symposium Series, Fall 1996 Meeting.

0926-2040r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 9 2 6 - 2 0 4 0 Ž 9 7 . 0 0 0 9 5 - 7

S.W. Brown et al.r Solid State Nuclear Magnetic Resonance 11 (1998) 49–58

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understanding details of the optical and electronic properties of the nanostructure. In addition, the single quantum dots can be thought of as nanoprobes, with NMR measurements yielding information about the local environment on the nanometer scale. Conventional NMR, however, requires ; 10 18 spins and has limited spatial resolution; it is, therefore, ill-suited to the study of single nanocrystals or quantum dots. Optical NMR, on the other hand, being limited in principle only by the ability to detect luminescence from specific regions of a sample, has both the sensitivity and spatial discrimination necessary to detect nuclear resonances from single quantum dots w6x. In this work, we present optical NMR spectra from ; 10 5 nuclei within single GaAs quantum dots with dimensions on the order of 4 nm = 10 nm = 100 nm. The spectra were recorded by measuring changes in the Overhauser shift of excitonic energy-level splittings in a single quantum dots as an RF field was swept through resonance frequencies of constituent nuclei. A 69 Ga linewidth of 12 " 2 kHz and a 75As linewidth of 22 " 2 kHz were measured from a specific quantum dot. In addition, frequency shifts on the order of tens of kHz and differences in NMR lineshape were observed from distinct quantum dots. These results —five orders of magnitude more sensitive than previously published optical NMR measurements and 13 orders of magnitude more sensitive than conventional NMR—illustrate the extreme sensitivity of the technique.

2. Background Because this is a novel approach to the optical detection of NMR, we briefly review the Overhauser shift of electronic energy levels and resultant changes under resonant RF excitation. The Overhauser shift is a consequence of the hyperfine coupling between the electronic and nuclear spin systems. The hyperfine interaction can be expressed in the general form: ™

l

™

H hfi ' S P A P I

Ž 1.

where S refers to the electronic spin, I to the nuclear spin, and A is a tensor describing the coupling between the two systems. There are, in general, two

contributions to the hyperfine interaction: a scalar contact term and a dipolar term. For electrons with s-like wavefunctions—as is the case for electrons in the bottom of the conduction band in GaAs—only the scalar contact contribution needs to be considered. Eq. Ž1. can then be expressed in terms of a scalar contact term, A, electron and nuclear raising and lowering operators, Sqry and Iqry, and a term proportional to the electronic Ž S z . and nuclear Ž Iz . spin polarizations along the quantization axis, z. H hfi ' A

ž

1 2

Ž Sq Iyq Sy Iq . q S z Iz

/

Ž 2.

The scalar prefactor A is proportional to the electronic and nuclear gyromagnetic ratios times the probability amplitude of the electron at the nucleus, squared: A'

8p 3

" 2ge g N Ce Ž rN .

2

Ž 3.

The first term in Eq. Ž2., involving mutual electron-nuclear spin flips, describes the dynamic part of the hyperfine interaction responsible for nuclear orientation while the second term describes the static shift of the electronic energy levels. Because the strength of the hyperfine interaction depends on the amplitude of the electron wavefunction at the nucleus, the electron-nuclear spin flip rate is largest in regions of electron localization. Consequently, if a net electronic spin polarization can be optically created in a single quantum dot, over time this polarization can be transferred to the nuclear system and, due to long nuclear spin relaxation times, a large nonequilibrium nuclear polarization can build up in the quantum dot. The second term in Eq. Ž2. gives rise to the Overhauser shift of the electronic energy levels. In general, the hyperfine interaction between a delocalized electron and a single nucleus produces a negligible energy shift. However, large, readily observable Overhauser shifts of electronic energy levels can arise from the interaction of a large number of oriented nuclear spins—in this case created by optical pumping—with an electron. Summing the contributions of all nuclei N within the electronic wave-

S.W. Brown et al.r Solid State Nuclear Magnetic Resonance 11 (1998) 49–58

function Ce , the Overhauser shift of the electron energy levels can be written as: D EOH s

8p 3

" 2ge

Ý

2

Ce Ž rN . g N IN S z

Ž 4.

N

where IN is the spin projection of the particular nucleus. The electron wavefunction in the quantum dot can be expressed as the product of a spatially extended ™ envelope function feŽ R .™and a rapidly varying cell ™ periodic part u 0 Ž™ r ., C Ž R,r™. s feŽ R . u 0 Ž™ r .. Assuming a uniform nuclear polarization, separating the contribution to the Overhauser shift from different nuclear species a , and summing over all nuclei ™ within the envelope function feŽ R ., Eq. Ž4. can be expressed as:

D EOH s

8p 3

" 2ge

žÝ a

g Na² I :a u 0 Ž ra .

2

/

Sz

Ž 5.

where ² I :a is the ensemble-averaged spin polarization of one of the constituent nuclei and < u 0 Ž ra .< 2 is the cell-periodic electron density at the nucleus a w7x. Thus, while individual nuclear contributions to the Overhauser shift depend on the magnitude of the envelope function of the electron—and hence on details of the electron localization—the total contribution to the Overhauser shift for a particular nuclear species depends on the degree of orientation of nuclear spins within the quantum dot, but does not depend to first order on the size of the dot. An important consequence of the optical pumping process is that the Overhauser shift can add to or substract from the Zeeman splitting of the excitonic energy levels depending on the orientation of the nuclear magnetic moments with respect to the external magnetic field. The orientation of the nuclear moments depends upon the electronic spin polarization which, in turn, depends on the polarization of the excitation light through the optical selection rules. In nominally undoped GaAs quantum wells, for near-resonant excitation of the heavy hole valence band to conduction band transition, changing the polarization of the excitation light from sq to sy reverses the electronic spin polarization and consequently the orientation of the nuclear magnetic moments as well. There will be a commensurate polarization dependence in excitonic energy level split-

51

tings as the Overhauser shift enhances or opposes the Zeeman splitting. In describing the evolution of the Overhauser shift under NMR, it is useful to express the Overhauser shift in terms of the nuclear magnetization M z s Ng N ² I :z , where N is the number of nuclear spins. The Overhauser shift from a particular nuclear species can be written:

D EOH s Ga Ma z S z , where Gs

=

8p 3

" 2ge u 0 Ž ra .

2

1 Na

Ž 6.

In measuring changes in the Overhauser shift, therefore, we are measuring the evolution of the z-component of the nuclear magnetization; the system response can then in principle be described by well-developed solid-state NMR theories. However, the system response is complicated by the hyperfine interaction due to the fact that all nuclei do not contribute equally to the Overhauser shift because of the dependence of the hyperfine interaction on the amplitude of the electron wavefunction at the nucleus. Nuclei close to the center of the dot, or near the peak of the envelope function of the electron, will thus give rise to a larger shift of the electron energy levels than nuclei at the edge of the dot, where the amplitude of the envelope function is greatly reduced. Lineshapes are also complicated by optical Knight shifts of the nuclear resonance frequencies. The Knight shift is the nuclear analog of the Overhauser shift, proportional to the time-averaged electronic spin polarization w8x: K s s A² S z : I N

Ž 7.

Because the Knight shift is also proportional to the amplitude of the electron wavefunction, nuclei in different regions of the quantum dot will experience different relative Knight shifts of their resonance frequencies and asymmetric lineshapes can result w9x. Total Knight shifts can also vary from dot to dot, depending on the degree of localization and the time-averaged electronic polarization within the particular dot.

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S.W. Brown et al.r Solid State Nuclear Magnetic Resonance 11 (1998) 49–58

3. Experiment The sample consists of a series of five single, nominally undoped GaAsrAlGaAs quantum wells with widths varying from 3 to 15 nm, grown by MBE under conditions promoting the development of large monolayer-thickness, nanometer-size islands at each interface w10x. The islands are elliptical, with varying degrees of ellipticity and in-plane dimensions on the order of 10–100 nm w1,2,11x. Excitons are localized in all three dimensions in these islands by the quantum well in one dimension and by potential differences arising from monolayer thickness fluctuations in the other two dimensions ŽFig. 1 insert.. Excitons localized in distinct islands will have slightly different recombination energies, depending on details of the local environment; luminescence from such a system will, in general, be inhomogeneously broadened. To observe luminescence from single islands—or quantum dots—small apertures were lithographically created in an opaque aluminum film previously deposited on the sample; these apertures defined both the excitation and collection volume in the sample. Extremely sharp luminescence features corresponding to excitonic recombination from individual quantum dots were spec-

trally resolved when the sample was excited through apertures smaller than 5 m m w1,2,11x. Results are presented in this work for excitons localized in a 4.5-nm quantum well, 2 excited through 1.5 m m apertures. A representative PL spectrum from the sample is shown in Fig. 1. The sample was placed in the bore of a superconducting magnet between a four-turn Helmholz coil capable of generating RF fields as high as 3 G; in this work, the RF field was approximately 0.7 G. The sample temperature was maintained at ; 6 K by continuously flowing cold He gas over the sample. Measurements were taken in a standard backscattering geometry ŽFig. 1 insert., with the magnetic field parallel to the wave vector of the incident and scattered radiation ŽFaraday geometry.. The sample was excited with ; 20 mW of 1.64 eV, circularly polarized light from a Ti:sapphire laser while the vertically polarized component of the luminescence was dispersed by a triple grating spectrometer and detected with a liquid nitrogen-cooled CCD array. The system resolution was ; 30 m eV whereas the spectral resolution—how well we can determine the resonance energies—was on the order of 5 m eV.

4. Results and discussion In Fig. 2, PL from a number of quantum dots is shown for external magnetic fields of 0 T, 1.0 T and 2.5 T. The slight shift of the luminescence to higher energy with increasing magnetic field is attributed to the diamagnetic shift w12x. Polarization-dependent differences in excitonic splittings from single quantum dots are also clearly resolved ŽFig. 2b and c. and are attributed to the Overhauser effect w12x. The polarization dependence of the excitonic splitting can be explained with a simplified Hamiltonian where only the Zeeman interaction and the Overhauser shift are explicitly considered. In this case, the total enFig. 1. Low temperature Ž6 K. PL spectrum from a 4.5-nm quantum well excited through a 1.5 m m aperture. Sharp, discrete luminescence features are attributed to recombination from heavy-hole excitons localized by monolayer interface fluctuations Žright insert. in distinct regions of the sample. The sample was placed between a Helmholz pair Žleft insert.; luminescence was collected in a backscattering geometry, with the excitation parallel to the DC magnetic field ŽFaraday geometry..

2

The bulk GaAs heavy-hole, light-hole valence band degeneracy is lifted due to the confinement in the quantum dots with the light-hole recombination occurring approximately 30 meV higher in energy than the heavy-hole recombination. In this work, we only consider luminescence arising from heavy-hole excitonic recombination.

S.W. Brown et al.r Solid State Nuclear Magnetic Resonance 11 (1998) 49–58

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Ž 8.

oriented nuclear system w7x. Overhauser shifts as large as 100 m eV have been measured in individual quantum dots, corresponding to nuclear polarizations approaching 70%. These large, spectrally-resolved Overhauser shifts provide a convenient way to detect NMR. Under resonant RF excitation, the z-component of the nuclear magnetization is reduced in some fashion; this reduction in magnetization will be reflected in a smaller Overhauser shift which, in turn, can be measured as a change—either an increase or a decrease —in excitonic splitting. To demonstrate the principle of the detection scheme, the excitonic splitting in an external magnetic field of 1.0 T was measured as the RF frequency was swept through the resonance frequencies of all three constituent nuclei within the quantum dot— 69 Ga, 71 Ga, and 75As—at various rates. Resonant RF excitation cancels some degree of nuclear orientation while optical pumping restores the ordering of the nuclear system. The time-averaged nuclear magnetization—measured through the Overhauser shift of the excitonic energy levels—is

The first term, linear in applied magnetic field, describes the Zeeman interaction, with g ) the exciton g-value and m B the Bohr magneton w13x; the second term describes the Overhauser shift of the exciton energy levels arising from orientation of the nuclear system. Depending on the polarization of the incident light Žthrough the optical selection rules., the Overhauser shift will add to or subtract from the Zeeman splitting, leading to differences in the observed excitonic splittings. These effects are shown schematically in Fig. 3 for a particular quantum dot. In Fig. 3a, the sample is excited with sq light and the Overhauser shift adds to the Zeeman splitting, yielding an excitonic splitting of 250 m eV. In Fig. 3b, in contrast, the polarization of the excitation light is reversed and the Overhauser shift opposes the Zeeman splitting, giving a measured excitonic splitting of 100 m eV. In the upper traces in Fig. 2b and c, therefore, the nuclear moments are aligned such that the Overhauser shift serves to increase the measured excitonic splittings while in the lower traces, the nuclear moments are reversed and the Overhauser shift reduces the measured splittings. In GaAs, Overhauser shifts of 135 m eV have been predicted for a fully-

Fig. 3. Žr. Excitonic splitting from a single quantum dot for Ža. sq and Žb. sy excitation in an external magnetic field of 3.0 T. Žl. Schematic diagram of the excitonic energy level splittings including the Zeeman interaction and the Overhauser shift.

Fig. 2. Quantum dot luminescence in external magnetic fields of Ža. 0 T, Žb. 1.0 T, and Žc. 2.5 T. The upper traces in Žb. and Žc. correspond to sq excitation, the lower traces to sy excitation.

ergy splitting for an exciton in an external magnetic field can be expressed as: D Etotal s g )m B Bo q Ý Ga Ma z a

54

S.W. Brown et al.r Solid State Nuclear Magnetic Resonance 11 (1998) 49–58

Fig. 4. Excitonic energy level splittings from a single quantum dot as a function of sweep rate as an RF field was swept from 7 to 14 MHz Ži.e., through the resonance frequencies of all three constituent nuclei: 69 Ga, 71 Ga and 75As.. Žinsert. PL, excited with sq-polarized light, from the quantum dot for RF sweep rates of 0 Hz ŽRF frequency fixed off-resonance at 7 MHz. and 2 Hz. The data were taken in an external magnetic field of 1.0 T.

therefore expected to be a function of RF power and sweep rate as well as optical pumping rates. Typical results are shown in Fig. 4 for a particular quantum dot. For this dot, the measured excitonic splitting

was reduced from 160 to 80 m eV as the RF sweep rate increased from 0 to 2 Hz, remaining constant at higher sweep rates. Luminescence spectra from the dot are shown in Fig. 4 Žinsert. for RF sweep rates of 0 and 2 Hz. These results demonstrate the ability to reduce the Overhauser shift of the energy levels with resonant RF excitation and to directly measure the resultant change in excitonic splittings. The RF frequency was then stepped through the 75 As resonance and the excitonic energy levels were measured as a function of RF frequency; results for a particular quantum dot are shown in Fig. 5. When the RF frequency was close to the 75As resonance frequency—for this dot ; 7.275 MHz—a decrease in the energy of the upper level and an increase in the energy of the lower level were observed. These results arise from a decrease in the Overhauser shift of the excitonic energy levels as the 75As nuclear magnetization is reduced on resonance. Depending on the relative contributions of the Overhauser shift and the Zeeman interaction to the excitonic splitting, NMR signals are recorded as either an increase or a decrease in the measured splitting as the RF frequency is swept through a particular nuclear resonance. For example, in Fig. 6

Fig. 5. Ža. PL, excited with sq-polarized light, from a single quantum dot in an external magnetic field of 1.0 T. Žb. Excitonic energy level splittings from the quantum dot as a transverse RF field was stepped through the 75As NMR resonance frequency at a rate less than 0.5 kHzrmin. The two peaks are labelled l Žleft. and r Žright. for identification.

S.W. Brown et al.r Solid State Nuclear Magnetic Resonance 11 (1998) 49–58

Fig. 6. Changes in excitonic splitting from a single quantum dot Žshown in Fig. 5a. in an external magnetic field of 2.5 T as the RF frequency was stepped through the 75As resonance. The sample was excited with Ža. sq and Žb. sy-polarized light. The solid lines are Lorentzian fits to the data.

the magnitude of the excitonic splitting from a single quantum dot in a magnetic field of 2.5 T is plotted as a function of RF frequency as the frequency was stepped through the 75As resonance at a rate - 0.5 kHzrmin. As shown in the figure, the measured

55

splitting decreased from 225 to 205 m eV for sq excitation and increased from 65 to 85 m eV for sy excitation. NMR from other constituent nuclei within the quantum dot has also been observed. In Fig. 7a and b NMR spectra from 69 Ga and 75As nuclei in the same quantum dot are shown for sq excitation; the magnetic field was 1.0 T. The 75As resonance was centered about a frequency of 7.274 " .001 MHz, while the 69 Ga resonance occurred at a frequency of 10.193 " .001 MHz. Measured changes in excitonic splittings for 75As Ž; 30 m eV. and for 69 Ga Ž; 18 m eV. NMR are in good agreement with their expected 50% and 30% contributions to the total nuclear field, respectively. The data were fit to Lorentzian lineshapes, giving 1.0 T NMR linewidths of 22 " 2 kHz for 75As and 12 " 2 kHz for 69 Ga. The NMR linewidths from this quantum dot are an order of magnitude larger than measured dipolar linewidths in bulk GaAs Ž; 2 kHz. w14x. Quadrupole coupling, power broadening and the hyperfine interaction can all contribute to the measured linewidths. All three constituent nuclei have spin 3r2 and corresponding quadrupole moments. There are, in general, two possible quadrupolar contributions to the NMR linewidth: unresolved first order quadrupole

Fig. 7. NMR spectra from a single quantum dot, excited with sq-polarized light in an external magnetic field of 1.0 T. Ža. 75As NMR; the frequency offset was 7.274 " 0.001 MHz. Žb. 69 Ga NMR; the frequency offset was 10.193 " 0.001 MHz. The solid lines are Lorentzian fits to the data, giving a 75As NMR linewidth of 22 " 2 kHz and a 69 Ga linewidth of 12 " 2 kHz.

56

S.W. Brown et al.r Solid State Nuclear Magnetic Resonance 11 (1998) 49–58

splitting and second-order quadrupole coupling. An inverse relationship between linewidth and magnetic field is expected for second order quadrupolar broadening w15x. However, the 2.5 T 75As linewidth is 22 " 3.5 kHz ŽFig. 6a., compared with the 1.0 T linewidth of 22 " 2 kHz ŽFig. 7a.. Based on the insensitivity of the 75As linewidth to external magnetic field, second-order quadrupole coupling does not seem to be the dominant line-broadening mechanism, though unresolved first-order quadrupole splittings may still contribute to the observed linewidths. The steady-state response of a system under nonsaturated excitation conditions can be described by the expression w16,17x: Mz s Mz 0

2 2 Ž D v . q Ž vyv0 . 2 2 Ž D v . q Ž v y v 0 . q Ž D v . T1X g N2 B12

Ž 9. In this equation, D v is a phenomenological line broadening parameter, g N is the nuclear gyromagnetic ratio, B1 is the strength of the RF field Ž; 0.7 G., and T1X is the nuclear spin relaxation time including effects of optical pumping w17x. The resonant

degree of cancellation of the nuclear magnetization wŽ v y v 0 . s 0x can be estimated from the data. From Eq. Ž8., the measured difference in excitonic splitting for sy and sq excitation ŽFig. 6. –160 m eV—is equal to twice the Overhauser shift. 75As is 50% abundant and these nuclei give rise to approximately half of the observed shift for a given polarization—in this case 40 m eV. The measured changes in the excitonic splitting Ž; 20 m eV. therefore correspond to a resonant reduction in the 75As magnetization of ; 50%. From an examination of Eq. Ž9., cancellation of 50% of the magnetization on resonance implies that Ž D v . 2 s D v T1 g N2 B12 , yielding an RF power-dependent increase in measured linewidth up to 40%. Thus, while potentially important, power broadening is not the dominant line-broadening mechanism in this case. Hyperfine coupling between the nuclei and optically created electrons has been used to explain broader NMR linewidths observed in opticallypumped NMR signals from a GaAs quantum well and the surrounding AlGaAs barrier region when the light was kept on during RF irradiation w18x. A similar broadening was observed in time-sequenced

Fig. 8. Ža. PL spectrum showing a number of quantum dots. Žb. 75As NMR spectra detected on luminescence from the two quantum dots labelled 1 and 2 in Ža.. The data were taken with sq excitation in an external magnetic field of 1.0 T. The solid lines are Lorentzian fits to the data.

S.W. Brown et al.r Solid State Nuclear Magnetic Resonance 11 (1998) 49–58

optical NMR measurements of bulk p-type GaAs w19x; in this case, the 69 Ga linewidth increased from 2 to 6 kHz when the light was kept on during RF irradiation. Based on these observations, the linewidths may indeed originate from hyperfinemediated interactions, with the increased linewidth in NMR from quantum dots arising from stronger hyperfine coupling due to the greater localization in the dot. Finally, frequency shifts on the order of tens of kHz and differences in NMR lineshape have been observed from spectrally distinct quantum dots. In Fig. 8a, luminescence from two quantum dots, labelled one and two, is shown. Note that there is a large difference in the measured optical properties of the two dots. Specifically, a large difference in the ratio of the two peak intensities from each dot is observed corresponding to a large difference in the degree of polarization of the luminescence from the two dots. There is a corresponding difference in the NMR spectra. In Fig. 8b, 75As NMR spectra, detected on quantum dot luminescence labelled one and two in Fig. 8a, show a relative shift in resonance frequency between the two dots of ; 20 kHz. Given the large difference in the degree of polarization of luminescence from the two dots, the optical Knight shift, proportional to the time-averaged electronic spin polarization ŽEq. Ž7.., is the mostprobable origin of the frequency shift w15,20x. Strain w15x and the second-order chemical shift w5,15,20x could also give rise to the observed frequency shift, however. Irrespective of origin, these differences must correspond to variations in the two quantum dot environments. In this case, the observed NMR frequency shifts may reflect differences in the optical properties of the two quantum dots.

5. Conclusions In summary, NMR has been optically detected from constituent nuclei within single GaAs quantum dots by measuring changes in the Overhauser shift of energy level splittings from excitons localized in the dots. The NMR signals originate from approximately 10 5 nuclei within a nanometer-scale volume. NMR spectra from a particular quantum dot were fit to

57

Lorentzian lineshapes, giving a 75As NMR linewidth of 22 " 2 kHz and a 69 Ga linewidth of 12 " 2 kHz, respectively. Finally, a relative shift of ; 20 kHz in the 75As resonance frequency was observed from two distinct quantum dots with different optical properties. The NMR measurements may therefore complement optical studies of quantum dots and could also provide additional information about the system. Based on these optical NMR results, previous single molecule ODMR work w21,22x, and the observation of single-impurity-related luminescence features in a similarly apertured, doped quantum well sample, extension of the technique to the study of single impurities may be possible.

Acknowledgements We would like to acknowledge and thank Al. L. Efros, M. Rosen, B.V. Shanabrook, E.S. Snow and J. Yesinowski for thoughtful and insightful discussions; M. Goldenberg and D.S. Katzer for the growth of the sample; and D. Park and the NRL Nanoprocessing Facility for patterning the material. This work was supported in part by the Office of Naval Research. Work was performed while S.W. Brown was an NRLrNRC post-doctoral associate.

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