Time-Resolved Photoinduced Thermoelectric and Transport Currents

Apr 11, 2012 - Time-Resolved Photoinduced Thermoelectric and Transport Currents in GaAs Nanowires. Leonhard Prechtel,. †. Milan Padilla,. †...
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Letter pubs.acs.org/NanoLett

Time-Resolved Photoinduced Thermoelectric and Transport Currents in GaAs Nanowires Leonhard Prechtel,† Milan Padilla,† Nadine Erhard,† Helmut Karl,‡ Gerhard Abstreiter,† Anna Fontcuberta I Morral,§ and Alexander W. Holleitner*,† †

Walter Schottky Institut and Physik-Department, Technische Universität München, Am Coulombwall 4a, 85748 Garching, Germany Institute of Physics, University of Augsburg, 86135 Augsburg, Germany § Laboratoire des Materiaux Semiconducteurs, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland ‡

S Supporting Information *

ABSTRACT: In order to clarify the temporal interplay of the different photocurrent mechanisms occurring in single GaAs nanowire based circuits, we introduce an on-chip photocurrent pump−probe spectroscopy with a picosecond time resolution. We identify photoinduced thermoelectric, displacement, and carrier lifetime limited currents as well as the transport of photogenerated holes to the electrodes. Moreover, we show that the time-resolved photocurrent spectroscopy can be used to investigate the drift velocity of photogenerated carriers in semiconducting nanowires. Hereby, our results are relevant for nanowire-based optoelectronic and photovoltaic applications. KEYWORDS: Time-resolved optoelectronic nanoscale transport, gallium arsenide nanowires

S

temporal resolution. In our time-resolved measurements, we are able to separate the individual current contributions because of their characteristic time scales and dynamics in GaAs nanowires. Moreover, we explore the drift velocity of the photogenerated holes. Our results may prove useful for the design of nanowire based photodetectors, photoswitches, solar cells, and high-speed transistors. We investigate p-doped GaAs nanowires, which are grown by molecular beam epitaxy (MBE) on a SiO2-covered (111)oriented GaAs substrate (growth rate ∼0.25 Å/s, As4 partial pressure ∼2 × 10−6 mbar, growth temperature ∼630 °C, and rotation speed 7 rpm).18 The nanowires with {110} facets have a length of 20−30 μm. The diameter of the slightly tapered nanowires increases from ∼80 nm at the tip to 180 nm at the bottom. The change in diameter is the result of a slight radial growth rate in parallel to the fast axial growth. The nanowires are p-type doped by adding a silicon flux during growth. For these growth conditions, a free hole concentration of ∼2.8 × 1018 cm−3 is estimated at room temperature.18 The nanowires are mechanically transferred onto a preprocessed sapphire substrate in a random fashion and then contacted in a coplanar stripline circuit by optical lithography (strip width 5 μm, separation 10 μm, metal thickness Ti/Au 10 nm/300 nm). Figure 1a shows an optical microscopy image of such an electrically contacted p-doped GaAs nanowire. As depicted in Figure 1b, a field probe is positioned ∼400 μm from the

canning photocurrent microscopy is a widely used spectroscopy technique to investigate ballistic and diffusive carrier transport and to map the electronic band bending in contacted nanostructures, such as semiconducting nanowires.1−9 The photocurrent generation in single semiconducting nanowires has been explained either by carrier drift due to internal and external electric potentials,2 by carrier diffusion processes,9 or by a photothermoelectric effect.10,11 Recently, numerical simulations highlighted the interplay of the individual contributions of a photothermoelectric current as well as the drift and diffusion of photogenerated electrons and holes in GaAs nanowires.12 However, it has been pointed out that all these optoelectronic effects contribute simultaneously to timeaveraging photocurrent measurements, thereby complicating their analysis.12 Generally, common photocurrent studies are typically limited to time scales exceeding 10 ps13 because available electronic equipment cannot produce and detect faster trigger signals and transients. Furthermore, optoelectronic charge-carrier dynamics are obscured by the response time of the high-frequency circuits. Yet, it is known from optical experiments that carrier relaxation, thermalization, and recombination processes can occur on much faster time scales in semiconducting nanowires.14 We therefore apply a recently developed pump−probe photocurrent spectroscopy based on coplanar stripline circuits to investigate the photocurrent dynamics in single p-doped GaAs nanowires with a picosecond time resolution.15−17 We determine the dynamics of the photothermoelectric current, the displacement current, and the transport of photogenerated holes to the electronic contacts as well as the carrier lifetime limited current with unprecedented © 2012 American Chemical Society

Received: January 20, 2012 Revised: March 16, 2012 Published: April 11, 2012 2337

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Figure 2. Time-integrated photocurrent maps of the GaAs nanowire measured in the stripline circuit. (a) Deconvoluted reflectivity scan. The nanowire cannot be distinguished in this scan. (b) Timeintegrated IPhoto maps for VSD = −5 V, (c) VSD = +5 V, and (d) VSD = 0 V. Black dashed lines indicate the gold striplines. The black dotted lines indicate the orientation of the nanowire in the stripline. (e) Cut along the dotted lines in the maps in (a) to (d). The vertical dashed lines indicate the position of the gold contacts (λ = 780 nm, PPump = 200 μW, Tbath ≈ 296 K).

Figure 1. Device geometry and optoelectronic pump−probe circuit. (a) Optical microscopy image of a GaAs nanowire contacted by the stripline circuit. Scale bar: 10 μm. (b) Schematic on-chip detection geometry. The pump laser pulse is focused on the GaAs nanowire contacted by the stripline circuit. The probe−pulse triggers the sampling circuit. Gold electrodes are depicted in yellow and ionimplanted silicon (Si) in green.

nanowire on a ∼200 nm thick layer of MBE-grown silicon. Prior to the nanowire transfer, the silicon was O+ ion-implanted with energies of 60 and 90 keV at fluences of 2 × 1015 cm−2, respectively, in order to reduce the charge carrier recombination lifetime in the silicon to be below 1 ps.19 Subsequently, the silicon was etched in an HF/HNO3 dip to remain only at the predefined position of the field probe. The circuitry sketched in Figure 1b allows an on-chip pump−probe detection of the time-resolved photocurrent ISampling. To this end, the GaAs nanowire in the stripline circuit is optically excited by a pump pulse from a titanium:sapphire laser, polarized linearly along the nanowire axis, at a wavelength of λ = 780 nm and a pulse duration of ∼160 fs. After the excitation, an electromagnetic pulse starts to travel along the stripline.20 A sampling circuit senses the transient electric field of the traveling pulse at the position of the field probe (Figure 1b). Here, we utilize an Auston switch based on the ionimplanted silicon on the sapphire substrate. The time delay tDelay between the pump and the probe pulse is controlled by a delay stage. Measuring ISampling in the sampling circuit as a function of tDelay yields information on the time-resolved optoelectronic processes in the nanowire with a picosecond time resolution (Supporting Information).15−17,20 First, we perform spatially resolved and time-integrated photocurrent measurements by scanning the pump laser across the nanowire and recording the current IPhoto in the stripline circuit (see Figure 1b). Figure 2a shows a spatially resolved reflectivity map of the sample, which is deconvoluted with a Gaussian-shaped instrument response function with a diameter of 4 μm to improve the spatial resolution. From the reflectivity map, we deduce the position of the metal striplines, which are depicted as dashed black lines in Figure 2b−d. Figure 2b−d shows photocurrent maps of IPhoto for a bias voltage of VSD = −5, +5, and 0 V, respectively. The photocurrent maps are simultaneously acquired with corresponding reflectivity maps. Figure 2e shows the photocurrent IPhoto along the nanowire (indicated by dotted lines in the photocurrent maps in Figure 2b−d). At VSD = 5 V (−5 V), a positive (negative) current IPhoto is generated for excitation of the nanowire with a maximum (minimum) at ∼2 μm from the right contact. At zero bias, a positive (negative) current IPhoto is generated for excitation in the center of the nanowire (close to the right contact). The asymmetry in IPhoto with respect to the left and right contact is

likely due to the fact that the used nanowires have a higher resistivity at the tip than at the bottom with varying Schottky barriers at positions close to the left and right contact.18 In order to identify the different mechanisms contributing to the time-integrated photocurrent, we perform time-resolved photocurrent measurements to investigate the dynamics of the photocurrent as a function of the excitation position along the nanowire. Figures 3a and 3b show time-resolved traces of ISampling for VSD = 5 V and VSD = −5 V, respectively. The nanowire is excited by the pump laser ∼2 μm from the right contact, as indicated by the open black triangle in Figure 2e and the black cross in Figure 2b−d. In Figure 3a, a positive short

Figure 3. Time-resolved ISampling and individual fit function components (black, green, dotted black, and dashed blue lines as discussed in the text). (a, b) ISampling for excitation position 2 μm from the right contact as indicated with an open black triangle in (d) for (a) VSD = +5 V and (b) VSD = −5 V. (c) Area Afirst of the fit function component fitting the first peak as a function of the source drain bias VSD for an excitation position ∼2 μm from the right contact. (d) Area Afirst as a function of the excitation position x. (e, f) ISampling for excitation position 2 μm from the left contact as indicated with a full red triangle in (d) for (e) VSD = +5 V and (f) VSD = −5 V. 2338

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peak with a full width at half-maximum (fwhm) of ∼1.5 ps centered at tDelay ≈ 3 ps is observed for the positive bias voltage VSD = 5 V. Reversing the bias voltage to −5 V results in a negative short peak with the same fwhm at tDelay ≈ 3 ps (Figure 3b). We fit this first peak with a Gaussian function, which is drawn as a green line in Figures 3a and 3b. At this excitation position close to the right contact, the area Afirst of the first peak is approximately linear in VSD, and its sign changes from positive to negative with VSD (Figure 3c). Generally, directly after an optical excitation of a semiconductor the photogenerated charge carriers redistribute in order to decrease local potential differences. This displacement of the charge carriers decreases the electric field F in the illuminated region. In turn, the optoelectronic response can be described by a transient displacement current density jD = εε0 ∂F/∂t

with different Seebeck coefficients S can result in a thermoelectric current:12 IThermo = (S Nanowire − SStripline)ΔT /R

(2)

with R the total resistance of the electrical circuit. Here, the direction of IThermo depends only on the sign of ΔT, since the Seebeck coefficients of GaAs nanowires and metals are independent of the bias voltage. The temperature increase ΔT of similar, but freely suspended, GaAs nanowires has been recently investigated by micro-Raman spectroscopy combined with laser heating.23 Using these results as a reference, we can estimate the average local temperature increase ΔT to be in the order of 12 K in our measurements assuming a continuous wave excitation (Supporting Information). The local temperature increase after pulsed laser heating, however, can be several orders of magnitude higher compared to a continuous wave excitation, and the temperature usually decays exponentially in time after the excitation.24 A strong indication for a thermoelectric current for exciting the nanowire close to the left contact is therefore the observed exponential decay of the first peak in ISampling with τfirst = of 3.5 ± 1.8 ps (Supporting Information). We note that we do not observe an exponentially decaying peak close to the right contact. There, the strong displacement current peak probably covers the photothermoelectric contribution. We now turn back to the time-resolved photocurrent measurements shown in Figure 3a,b for excitation close to the right contact of the nanowire. We show the data in Figure 3a,b again in Figure 4a,b for an extended time-delay range of up

(1)

with ε and ε0 the dielectric constants.21,22 Consistently, a displacement current can be described by the shape of a temporal Gaussian function if the electromagnetic pulse does not experience dispersion while propagating along the coplanar striplines. In Figure 3d, we show the area Afirst of the first peak as a function of the excitation position x along the nanowire for source-drain biases of VSD = 5, 0, and −5 V. In the excitation region close to the right contact (x > 11 μm) the area Afirst changes sign along with VSD. From the Gaussian shape and the observed fwhm of the first peak as well as the voltage dependence of Afirst, we conclude that a displacement current due to nonuniform illumination in combination with an externally applied electric field is generating the first peak at tDelay ≈ 3 ps for an excitation of the nanowire close to the right contact. This interpretation is in agreement with similar timeresolved measurements on carbon nanotubes.16 In the excitation region close to the left contact, we observe also a significant first peak in the time-resolved photocurrent. In Figure 3e,f, we show corresponding time-resolved traces of ISampling at VSD = +5 V and VSD = −5 V at an excitation position on the nanowire 2 μm from the left contact. The excitation position is indicated with a full red triangle in Figures 2e and 3d and with a red cross in Figure 2b,d. Remarkably, at positions close to the left contact of the nanowire, the sign of the first peak is independent of the polarity of the applied bias. We always detect a positive area Afirst for the investigated voltage range (5 μm < x < 11 μm in Figure 3d). We point out that in the time-integrated photocurrent measurements we detect only a negligible signal at these positions (see Figure 2). For excitation positions close to the left contact, we can exclude a displacement current as the dominant optoelectronic process by the following arguments. First, the peak area does not change sign with the applied source-drain bias, and it has no counterpart in the time-integrated photocurrent maps (Figure 2). Second, the first peak decays exponentially (as shown in Figure 3e,f), and it does not have the Gaussian shape usually observed for displacement current peaks (exemplarily shown in Figure 3a,b). Third, the fwhm of 3.5 ± 1.8 ps is considerably larger than for an optical excitation in the center of the nanowire or close to the right contact (fwhm ∼ 1.5 ps). Instead, we explain the first peaks of ISampling at positions close to the left contact by a photothermoelectric current. Generally, a localized laser illumination also results in a local temperature increase, e.g., by charge carrier relaxation via phonon generation.12 A temperature difference ΔT at the interface of two materials

Figure 4. (a) Time-resolved ISampling extended to 2 ns and individual fit function components for the excitation position 2 μm from the right contact as indicated with an open black triangle in (c) at VSD = +5 V. The black, green, dotted black, and dashed blue lines are fit functions as discussed in the text. (b) Same measurement for VSD = −5 V. (c) Area Arec as a function of nanowire position. (d) Velocity of photogenerated holes as a function of VSD for two different nanowire samples (blue and black data points) as determined from the fit function component Ihole. Solid lines are fits with a hole mobility saturation function.

to 2 ns. We observe a steplike increase of ISampling directly after the first peak at ∼3 ps and a slow increase starting ∼20 ps after the first peak. Finally, the signal decays on a slow time scale back to the initial value of ISampling (Figures 4a,b). The sign of these two further photocurrent components depends on the polarity of the applied bias voltage. In turn, we explain them by the combination of a recombination lifetime limited current (Irec) and a transport current of photogenerated holes (Ihole). 2339

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Accordingly, we fit the overall traces of ISampling with the sum of three peak functions: I(t ) = Ifirst + Irec + Ihole

We then measure ISampling as a function of the applied bias voltage VSD. The hole drift velocity vh can be estimated to be v h = dcontact /(t trans − t1st)

(3)

with dcontact the distance to the contact in the direction of the drifting holes and (ttrans − tfirst) the arrival time of the hole peak with respect to the instantaneous displacement current peak at ∼3 ps. In Figure 4d we show vh as a function of VSD for two different nanowire samples (black and blue data points). Our interpretation as a hole drift current is corroborated by the dependence of vh on VSD, and it is in agreement with numerical investigations of bulk GaAs photoswitches conducted by Dunn and Walker.27 Furthermore, our measured values of vh ≈ 8 × 106 cm/s are consistent within typical hole drift velocities in bulk GaAs at high electric fields.28,29 The hole mobility μh(F) in bulk GaAs depends on the electric field, and it can be described as30

The first function Ifirst is associated with the displacement current at ∼3 ps. It can be described by a Gaussian function, as discussed above and depicted in green in Figures 3a,b. The second peak function Irec is associated with the recombination lifetime limited current. It accounts for the steplike increase with a subsequent slow exponential decay: Irec(t ) = I0|e−t / τrec − e−t / τC|

(5)

(4)

According to the theory developed by Auston,20 the response of a photoswitch due to a conductance increase after a pulsed laser excitation follows eq 4, with τrec the recombination lifetime of the optically excited charge carriers and τC a capacitive time-constant governing the rise time of the photoswitch. The corresponding fitting curves are presented as dashed black lines in Figures 3a,b and 4a,b. The third fit function component Ihole is associated with the transport of holes (depicted as a dotted blue line in Figures 3a,b and 4a,b). It accounts for the slow signal increase starting at ∼20 ps with a maximum at 50−100 ps after the first peak. For Ihole we utilize again a fit function as given in eq 4 with τrec as above but a different rise time (Supporting Information). Figure 4c shows the area Arec of the second fit function component Irec as a function of the excitation position x along the nanowire. By comparing Figure 4c with Figure 3d, we can estimate that the area Arec is a factor 103 larger than the area Afirst of the first peak at ∼3 ps. Furthermore, for VSD = ± 5 V the area Arec(x) has the same spatial dependence on x as the time-integrated photocurrent amplitudes IPhoto(x) in Figure 2e. We therefore conclude that the time-integrated photocurrent at VSD = ± 5 V is dominated by a lifetime limited current, which is a photoconductance effect induced by pulsed laser excitation.20 On the basis of this interpretation, we average the obtained values of τrec for the excitation region 10 μm < x < 15 μm to obtain the average charge carrier lifetime τavg = 1510 ± 30 ps. This value is in decent agreement with recent time-resolved photoluminescence measurements on gold-catalyst-free grown GaAs nanowires with values of up to 2.5 ± 0.1 ns.25,26 We point out that in our experiments τavg reflects not only the recombination dynamics of optically excited electrons and holes, but it is modified by the charge transport onto the metal contacts. Thereby, τavg is effectively reduced compared to the recombination lifetime measured in photoluminescence experiments.27 In the region close to the left contact (5 μm < x < 10 μm) and at the right contact (15 μm < x < 20 μm) other processes, such as the photothermoelectric current, influence the dynamics of the fit function component Irec and are therefore not considered for the average charge carrier lifetime τavg. We associate the third fit function component Ihole with the transport of photogenerated holes to the contacts. Experimentally, we do not observe a consistent time shift of the hole transport peak as a function of the excitation position along the nanowire, as has been shown in a time-of-flight analysis for the transport peak of photogenerated electrons in bulk GaAs.15 Instead, we investigate the hole drift velocity and the hole mobility by fixing the excitation position on the nanowire at a distance of ∼6 μm to the left and ∼4 μm to the right contact.

μ h (F) = μ h,0 /(1 + μ h,0 ·F /v h,s)

(6)

with μh,0 the effective hole mobility at zero electric field and vh,s the hole saturation drift velocity.28 The fit in Figure 4d uses eq 6 and vh = μh(F)·|F|. It reproduces the data surprisingly well, given that the hole transport peak has a fwhm of more than a hundred picoseconds and a shift of only tens of picoseconds (Supporting Information). Generally, the time-of-flight analysis presented here can also be used to investigate the mobility of photogenerated holes in nanowires, if the electric field along the nanowire is known (e.g., for a homogeneous doping and ohmic contacts). In the present case, the time-integrated photocurrent data in Figure 2e suggest that the voltage drops across only a short section of the nanowire, which is located close to the right contact. Our data further suggest that the local electric field F is proportional to VSD, i.e., |F| = VSD/l, with l the length of the section. For l < 1 μm, the fitting curves in Figure 4d allow estimating μh,0 to be smaller than 400 cm2/(V s), which is consistent with bulk values. We note, however, that drift-diffusion simulations of nanowires considering the exact morphology are needed to give further insight into the electric field dependent mobility and drift velocity of the photogenerated holes.27 Furthermore, we explain the absence of an electron transport peak in the measurements presented here by a dominant displacement current peak with opposite current direction, effectively covering the electron transport peak. We point out that we obtain similar photocurrent results also on a second nanowire sample. The only difference is the magnitude of the time-integrated and time-resolved photocurrents. The results are even similar for resonant and nonresonant excitation of the nanowire. For instance, we do not find a detectable dependence of the dynamics of the photothermoelectric current on the laser excitation energy. This is an indication that the dynamics of the thermoelectric current is dominated by heat conduction processes and not by relaxation processes via phonon generation. In conclusion, we experimentally identify and separate the individual photocurrent mechanisms in single p-doped GaAs nanowires, which are overlaid and therefore individually not resolvable in time-integrated scanning photocurrent measurements. We identify a displacement current with a fwhm of ∼1.5 ps and a photothermoelectric current with an exponential decay time of ∼3 ps. We show that a recombination lifetime limited current with τavg = 1510 ± 30 ps dominates the time-integrated 2340

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photocurrent. Finally, we uncover the field-dependent transport velocity of photogenerated holes. Our findings may prove essential for nanowire-based photoswitches, high-speed transistors, photodetectors, and solar cells.

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(21) Zhou, X. IEEE J. Quantum Electron. 1996, Vol. QE-32 (9), 1672. (22) Krökel, D.; Grischkowsky, D.; Ketchen, M. B. Appl. Phys. Lett. 1989, 54, 1046. (23) Soini, M.; Zardo, I.; Uccelli, E.; Funk, S.; Koblmüller, G.; Fontcuberta i Morral, A.; Abstreiter, G. Appl. Phys. Lett. 2010, 97, 263107. (24) Shah, J.; Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures; Springer: Berlin, Heidelberg, 1999. (25) Demichel, O.; Heiss, M.; Bleuse, J.; Mariette, H.; Fontcuberta i Morral, A. Appl. Phys. Lett. 2010, 97, 201907. (26) Breuer, S.; Pfüller, C.; Flissikowski, T.; Brandt, O.; Grahn, H. T.; Geelhaar, L.; Riechert, H. Nano Lett. 2011, 11, 1276. (27) Dunn, G. M.; Walker, A. B. J. Appl. Phys. 1996, 79, 7329. (28) Yang, C.-M.; Canoglu, E.; Garmire, E.; Goosen, K. W.; Cinningham, J. E.; Jan, W. Y. IEEE J. Quantum Electron. 1997, 33 (9), 1498. (29) Brennan, K.; Hess, K. J. Appl. Phys. 1986, 59 (3), 964. (30) Hurd, C. M.; McKinnon, W. R. J. Appl. Phys. 1995, 77 (8), 4077.

ASSOCIATED CONTENT

S Supporting Information *

Details on the coplanar stripline circuit, the sample preparation, the bandwidth of the detection scheme, the thermoelectric current, and the hole transport current. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank I. Zardo for fruitful discussions and technical help. We gratefully acknowledge financial support from the DFG, the German excellence initiative via the “Nanosystems Initiative Munich (NIM)”, and the “TUM Institute for Advanced Study”. A.F.i.M. thanks ERC funding through grant UpCon and SNF through proposal no. 137648.

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REFERENCES

(1) Wang, J.; Gudiksen, M. S.; Duan, X.; Cui, Y.; Lieber, C. M. Science 2001, 293, 1455. (2) Ahn, Y.; Dunning, J.; Park, J. Nano Lett. 2005, 5 (7), 1367. (3) Pettersson, H.; Tragardh, J.; Persson, A. I.; Landin, L.; Hessman, D.; Samuelson, L. Nano Lett. 2006, 6 (2), 229. (4) Hayden, O.; Agarwal, R.; Lieber, C. M. Nat. Mater. 2006, 5, 352. (5) Allen, J. E.; Hemesath, E. R.; Lauhon, L. J. Nano Lett. 2009, 9 (5), 1903. (6) Thunich, S.; Prechtel, L.; Spirkoska, D.; Abstreiter, G.; Fontcuberta i Morral, A.; Holleitner, A. W. Appl. Phys. Lett. 2009, 95, 083111. (7) Kim, C. J.; Lee, H.-S.; Cho, Y.-J.; Kang, K.; Jo, M. J. Nano Lett. 2010, 10, 2043. (8) Reimer, M. E.; van Kouwen, M. P.; Barkelid, M.; Hocevar, M.; van Weert, M. H. M.; Kouwenhoven, L. P.; Zwiller, V.; Algra, R. E.; Bakkers, E. P. M.; Björk, M. T.; Schmid, H.; Riel, H. J. Nanophotonics 2011, 5, 053502. (9) Graham, R.; Miller, C.; Oh, E.; Yu, D. Nano Lett. 2011, 11, 717. (10) Cai, J.; Mahan, G. D. Phys. Rev. B 2006, 74, 075201. (11) Fu, D.; Levander, A. X.; Zhang, R.; Ager, J. W., III; Wu, J. Phys. Rev. B 2011, 84, 045205. (12) Fu, D.; Zou, J.; Wang, K.; Zhang, R.; Yu, D.; Wu, J. Nano Lett. 2011, 11 (9), 3809. (13) Gallo, E. M.; Chen, G.; Currie, M.; McGuckin, T.; Prete, P.; Lovergine, N.; Nabet, B.; Spanier, J. E. Appl. Phys. Lett. 2011, 98, 241113. (14) Johnson, J. C.; Knutsen, K. P.; Yan, H.; Law, M.; Zhang, Y.; Yang, P.; Saykally, R. J. Nano Lett. 2004, 4 (2), 197. (15) Prechtel, L.; Manus, S.; Schuh, D.; Wegscheider, W.; Holleitner, A. W. Appl. Phys. Lett. 2010, 26, 261110. (16) Prechtel, L.; Song, L.; Manus, S.; Schuh, D.; Wegscheider, W.; Holleitner, A. W. Nano Lett. 2011, 11, 269. (17) Prechtel, L.; Song, L.; Schuh, D.; Ajayan, P.; Wegscheider, W.; Holleitner, A. W. Nat. Comm. 2012, 3, 646. (18) Dufouleur, J.; Colombo, C.; Garma, T.; Ketterer, B.; Uccelli, E.; Nicotra, M.; Fontcuberta I Morral, A. Nano Lett. 2010, 10, 1734. (19) Doany, F. E.; Grischkowsky, D.; Chi, C.-C. Appl. Phys. Lett. 1987, 50, 460−462. (20) Auston, D. H. IEEE J. Quantum Electron. 1983, 19, 639. 2341

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