Quantitative Measurement of the Electron and Hole Mobility−Lifetime

NANO LETTERS

Quantitative Measurement of the Electron and Hole Mobility−Lifetime Products in Semiconductor Nanowires

2006 Vol. 6, No. 5 948-952

Yi Gu,† John P. Romankiewicz,† John K. David, Jessica L. Lensch, and Lincoln J. Lauhon* Department of Materials Science and Engineering and Materials Research Center, Northwestern UniVersity, EVanston, Illinois 60208 Received December 30, 2005; Revised Manuscript Received March 2, 2006

ABSTRACT The mobility−lifetime products (µτ) for electrons and holes in CdS nanowires were quantitatively determined by scanning photocurrent microscopy of devices with ohmic contacts. Ohmic contacts were fabricated by ion bombardment of the contact regions. By analyzing the spatial profiles of the local photoconductivity maps, we determined that electron transport (µeτe ≈ 5 × 10-7 cm2/V) was more efficient than hole transport (µhτh ≈ 10-7 cm2/V). The results demonstrate that photocurrent mapping can provide quantitative insight into intrinsic carrier transport properties of semiconductor nanostructures.

One-dimensional (1D) nanomaterials in general1 and semiconductor nanowires in particular2 are promising building blocks for high-performance nanoscale devices. Their promise derives in part from expectations of exceptional or unique optical and electronic properties, including intrinsic polarization sensitivity,3 low-threshold lasing,4-6 and enhanced mobility.7,8 In the context of such expectations, quantitative measurements of nanowire properties are desirable to confirm and quantify the advantageous characteristics of these new materials. Furthermore, the optimization of material and device processing requires the measurement of reliable figures of merit. The field-effect mobility, µFE, is an important figure of merit for field-effect transistors,9 but in nanowire devices µFE is typically based on an estimated gate capacitance,10,11 which in turn depends on the device geometry and the density of surface states at the semiconductor-insulator interface.9 Consequently, µFE is best understood as an extrinsic quantity12 that, although a useful metric of device performance, cannot be used generically to quantify and optimize intrinsic nanowire properties. Clearly, quantitative metrics of carrier transport that derive from intrinsic material properties, and not the contacts or device geometry, will facilitate the development of the materials and technology. In particular, one would like to be able to directly determine the effects of surface passivation on carrier transport. Here we report the quantitative determination of the mobility-lifetime product, µτ, for both electrons and holes in CdS nanowires grown by the vapor-liquid-solid (VLS) * Corresponding author. E-mail: [email protected]. † The authors contributed equally to this work. 10.1021/nl052576y CCC: $33.50 Published on Web 04/01/2006

© 2006 American Chemical Society

method. µτ, with units of cm2/V, represents the average carrier drift length per unit field and is an important figure of merit for charge-collecting devices including photodetectors13,14 and photovoltaics.15 Mobility-lifetime values were determined in a number of CdS nanowire devices by analyzing the spatial variations in the photoconductivity as measured by scanning photocurrent microscopy (SPCM).16-19 Electron transport (average µeτe ≈ 5 × 10-7 cm2/V) was found to be more efficient than hole transport (average µhτh ≈ 10-7 cm2/V), consistent with the larger mobility of electrons in bulk CdS.9 Although devices with at least one ohmic contact were necessary to measure µτ for both electrons and holes, the measured values do not depend on the nature of the contact, emphasizing that µτ is intrinsic to the nanowire. Comparison of µτ with bulk mobility values and measured nanowire photoluminescence lifetimes suggests that surface recombination limits carrier collection in nanowire photodetectors. On the basis of our findings, we propose that SPCM can be used to quantitatively assess the effect of surface passivation schemes on charge transport in semiconductor nanowires. Nanowire synthesis and device fabrication procedures were the same as those reported previously19 with the exception of an important advance that allowed the selective fabrication of ohmic or Schottky contacts. CdS nanowires with ∼50 nm diameters were grown with gold nanocatalyst particles and thermal chemical vapor deposition of a single-source precursor. The metal electrodes of two- and four-terminal nanowire devices were defined by electron beam lithography, metal evaporation, and liftoff. As described previously,19 Ti metal

Figure 1. (a) Procedure for fabricating ohmic contacts. Contact regions are defined on resist coated nanowires (i) by e-beam lithography (ii) and exposed to Ar ion bombardment (iii) prior to metal deposition (iv), resulting in ohmic contacts (v). Devices with one ohmic and one Schottky contact can also be produced by ion bombarding only one contact. (b) Current-voltage curves for nanowire devices with different contacts. The solid blue line was measured on an ohmically contacted NW. After bombardment of the entire NW, it became much more conductive (red dotted line). The green dashed line was measured on a NW with one ohmic and one Schottky contact.

deposition on HF-etched CdS nanowires generally resulted in the formation of Schottky contacts. Ohmic contacts, however, are a prerequisite to the independent measurement of µeτe and µhτh as will be shown below. For the present study, ohmic Ti-CdS contacts were formed by bombarding the contact regions with Ar ions (the bias used for bombardment is 500 V) prior to Ti evaporation (Figure 1a). Ion bombardment increases the electron concentration in CdS greatly20,21 by generating sulfur vacancies,22 which act as donors, leading to a narrowing of the Schottky barrier and a linear current versus voltage characteristic in nanowire devices (Figure 1b). If only one of the two contacts is subjected to ion bombardment, then a rectifying Schottky diode results (Figure 1b). To verify that an increase in carrier concentration is responsible for the effect, ohmically contacted nanowires were exposed to Ar ion bombardment after device fabrication, resulting in a three orders-of-magnitude increase in conductivity (Figure 1b). Four terminal voltage versus current measurements on a number of devices allowed the separation of the nanowire resistance from the contact resistance, and atomic force microscope topographic imaging enabled the determination of nanowire resistivities. The resistivity of the nanowires ranges from 200 to 800 Ω‚cm, Nano Lett., Vol. 6, No. 5, 2006

which is typical of semiconducting CdS,23 and the contact resistances of ∼1 GΩ were significantly less than nanowire resistances of ∼5-10 GΩ for devices 4-12 µm in length. The back-gate response of the nanowires indicated n-type conductivity; space-charge-limited current was observed at moderate biases for devices measured in the dark, consistent with ohmic contacts to very resistive material. SPCM measurements on nanowire and nanotube devices with Schottky contacts have been reported previously by our group and others.16-19 For this study, a scanning confocal microscope was used to illuminate ∼50-nm-diameter nanowire devices (Figure 2a) with light from a chopped Ar+ laser (λ ) 457 nm) focused to a diffraction-limited spot (∼400 nm). All measurements were conducted at room temperature. A bias was applied between the two electrodes, and the photocurrent was collected as a function of the beam position (Figure 2b). The relative position of the beam and electrodes was determined by simultaneously recording the reflected light from the sample; the metal electrodes have a higher reflectivity than the SiO2/Si substrate. For the ohmically contacted device of Figure 2a, a peak was observed in the local photocurrent images at all biases. The position of the peak varied monotonically with bias (Figure 2b), in contrast to previous SPCM measurements on Schottky-contact devices.16-19 From the bias dependence of the photocurrent, and the fact that the steady-state current is proportional to the number of charge carriers reaching the electrodes, we can conclude that (1) the field produced by the electrodes separates photogenerated charge carriers and (2) some of these carriers reach the electrodes before recombining. The photocurrent peak always occurs closer to the negatively biased electrode, indicating that hole transport and/or collection is less efficient than electron transport and/or collection, as will be discussed in some detail below. One-dimensional photocurrent profiles were extracted from the SPCM images for quantitative analysis of the carrier collection efficiency versus injection position. Figure 3a presents the photocurrent at 1 V bias as a function of the beam position, which shows a peak shifted toward the hole collector (right electrode). As the carrier injection point is moved away from the peak in either direction, the number of collected charge carriers (photocurrent) is observed to decrease exponentially with distinct slopes on either side of the peak. One can understand both the occurrence of a photocurrent peak as well as the exponential decrease by considering the continuity equation in the context of onedimensional drift-diffusion. As the injection point is moved to the left in Figure 3a, the number of holes reaching the hole collector decreases exponentially. This implies a finite probability of recombination per unit distance; that is, there is some well-defined average distance, Lh, that a hole moves prior to recombining. As the injection point is moved to the right, the number of electrons reaching the electron collector decreases exponentially, but at a different rate as shown by the distinct slope of the photocurrent profile. Fitting the left (right) side of the photocurrent profile using I ) Io exp(((x - d)/Lh(e)) gives the average drift/diffusion length Lh(e) of holes(electrons), where d is the peak position and the positive 949

Figure 2. SPCM imaging of a CdS nanowire device with two ohmic contacts at the top and bottom. (a) Atomic force microscope topographic image of CdS nanowire and electrodes. The electrode width is 1 µm, and the device length is 11 µm. (b) Sequence of SPCM images with the top electrode biased as indicated. The peak photocurrent, whether positive or negative, is always shifted towards the hole collector. The peak shift saturates for |V|> 2.5 V.

Figure 3. Determination of µτ from photocurrent profiles of devices with ohmic contacts. (a) Photocurrent profile along the NW with the left electrode at 1.0 V bias. The inner edges of the left and right electrodes are at 0 and 11 µm, respectively. The dashed red and solid blue lines are exponential fits to the photocurrent versus distance that determine Lh and Le, respectively. Inset: photocurrent profiles at 1, 2, and 3 V bias are shown in red, green, and blue, respectively. The slopes do not change appreciably. The units are the same as those in the larger figure. (b) µeτe (blue) and µhτh (red) values derived from five devices. The error bars correspond to the range of µτ values determined at several applied biases for a given device. Devices 3-5 were fabricated from different sections of the same nanowire.

sign corresponds to holes. The drift/diffusion length of electrons (Le ) 1.47 µm) exceeds that of holes (Lh ) 0.65 µm), in accord with bulk mobility values for CdS (µe ≈ 300 cm2/V‚s, µh ≈ 50 cm2/V‚s). The total current is limited by the individual electron and hole currents because the continuity equation requires that the electron current at the positive electrode equals the hole current at the negative electrode; that is, Jtot ) - Je| + ) Jh| -.24 It follows that there exists a 950

carrier injection position for which the total current is maximized, specifically, where Jtot changes from being limited by Jh to being limited by Je. The maximum photocurrent position shifts toward the hole collector (negatively biased electrode) with increasing bias (Figure 2b), again indicating that hole collection is the limiting factor in the total charge collection process; while the increased electric field enhances both electron and hole collection, the higher electron mobility implies that the differential increase in electron concentration at the electron collector is greater than the differential increase in hole concentration at the hole collector. In equilibrium, the position of maximum photoresponse then shifts toward the hole collector.25 Further analysis of the photocurrent profiles at different bias conditions (Figure 3a inset) provides additional quantitative insight into the nature of electron and hole transport in the device. As the bias increases, the peak shifts toward the hole collector, but the slopes on either side of the peak do not change appreciably. Because the two slopes are determined by the average lengths that electrons and holes move before recombining, and this length is not influenced by the applied bias, we can conclude that both electron and hole transport between the optical generation region and the contacts are diffusive in nature.26 We may therefore equate Lh(e) with the one-dimensional diffusion length (Dh(e)τh(e)*)1/2, where D and τ* are the diffusion coefficient and effective lifetime, respectively.27 The dominance of diffusion currents outside the optical generation region is a consequence of strong space-charge effects in this resistive material. Briefly, large fields near the optical generation region push electrons and holes away from this region so that they can then diffuse to their respective collectors. Thorough validation of this picture requires simultaneous solution of the continuity equation and the Poisson equation with a spatially dependent carrier lifetime, which is beyond the scope of this work. We can state that outside the generation region, the electric field is smaller than the diffusion field28 kBT/eL as indicated by the constant slopes in the photocurrent profiles. Taking a diffusion length of L ≈ 1 µm at room temperature, for example, we estimate that the electric field is less than 0.026 V/µm. This is smaller than the average applied field of ∼0.1 Nano Lett., Vol. 6, No. 5, 2006

V/µm (1 V over 10 µm), consistent with an increased local potential drop near the optical generation region. The extraction of quantitative diffusion lengths enables us to use the Einstein relation, µ ) (q/kBT)D, to determine the mobility-lifetime product as µτ* ) (q/kBT)L2. µτ*, with units of cm2/V, is the average length a carrier moves per unit field, and is therefore an important figure of merit for charge collecting devices; µτ* is directly proportional to the quantum yield13 and the conversion efficiency15 in photodetectors and solar cells, respectively. Taking Lh(e) from the current profiles, and rearranging units, gives µeτe* ) 83 µm/ (V/µm) for electrons and µhτh* ) 16 µm/(V/µm) for holes. In an applied field of ε ) 1000 V/cm (0.1 V/µm), for example, a photogenerated electron will drift an average distance of L ) µτε ) 8.3 µm before recombining. If the contact spacing is less than this distance, then the majority of photogenerated electrons will be collected.29 Photoconductivity profile analysis for additional CdS nanowire devices gave a range of mobility-lifetime products shown in Figure 3b. µeτe* is consistently larger than µhτh* for a given nanowire, which supports our interpretation of the photocurrent profiles. In addition, the nanowire values are comparable to literature values for bulk CdS of 1.6 ( 0.3 × 10-7 cm2/V (ref 30) and 6.2 × 10-8 cm2/V (ref 31) for electrons and holes, respectively. Variations in the measured values could be due to variations in nanowire morphology or surface state density; this is an area that warrants additional systematic study and comparison with structural characterization. When the measured µτ* values exceed those of bulk material, it is not because of an increased mobility, which is unlikely due to surface scattering, but rather an increased effective carrier lifetime, even though the nanowire surface will also decrease electron and hole lifetimes. Indeed, the room-temperature photoluminescence decay time (τPL) in unbiased nanowires is ∼50 ps, indicating highly efficient nonradiative recombination.32 For comparison, we can estimate the carrier recombination time in the biased devices by dividing the measured mobility-lifetime product by typical bulk electron and hole mobilities of µe ) 300 cm2/ V‚s and µh ) 50 cm2/V‚s, respectively. Assuming that the bulk mobilities represent upper bounds, the lower bounds on the effective lifetimes are 0.6 ns and 0.8 ns for electrons and holes, respectively. This significant enhancement in carrier lifetime, and therefore the diffusion length, L ) (Dτ*)1/2, is a straightforward consequence of the separation of electrons and holes by the applied field; the lack of opposite charge carriers outside the generation region reduces the rate of both radiative and nonradiative recombination. In solar cells and photodetectors, both built-in and applied fields are used to minimize such recombination and maximize collection. SPCM measurements on additional nanowire devices with one ohmic contact and one Schottky contact were performed to confirm that µτ* is a property of the nanowire and not the device and to validate our explanation of the increased effective lifetime. Reverse-bias saturation was observed consistently when a negative voltage was applied to the Nano Lett., Vol. 6, No. 5, 2006

Figure 4. Photocurrent images and profiles for a NW device with one ohmic (left) and one Schottky (right) contact. (a) Photoconductivity images with the Schottky diode under reverse bias (+7, +3 V) and forward bias (-0.5, -3 V). Under reverse bias, the photocurrent peak is pinned to the negative electrode. Under forward bias, the photocurrent peak shifts with bias. Partially transparent schematic electrodes are shown so that the SPCM signal may be compared with the electrode position. The images are 3.5 × 0.5 µm2. (b) Photocurrent profiles under reverse (blue) and forward (green) bias. The solid green line is an exponential fit to the photocurrent at forward bias to determine the hole drift/diffusion length.

Schottky contact of a Schottky-ohmic device (Figure 1b). As we noted previously with near-field scanning photocurrent microscopy (NSPM),19 the photocurrent profile near a reverse-biased nanowire Schottky diode is not affected by the applied bias (Figure 4a). Because the collection region is the sum of the space-charge region, which is biasdependent, and the diffusion length, which is not,33 the collection region is determined by the diffusion length of holes.34 The beam width precludes a quantitative extraction of the Lh from these data, but from the photocurrent profiles Lh is on the order of 100 nm (Figure 4b), indicative of a greatly reduced hole effective lifetime due to increased recombination with photogenerated electrons.35. The presence of photogenerated electrons is consistent with the assertion that the space-charge region does not extend significantly beyond the electrode. In contrast, when the Schottky contact is forward-biased, the photocurrent profile once again evolves with bias and is much broader (Figure 4b), giving an Lh of 0.2 µm and a µhτh* of 1.5 × 10-8 cm2/V. The longer diffusion length and higher collected current are consistent with the increased effective lifetime when electrons and holes are spatially separated, and the µhτh* value is comparable to that measured for the ohmically contacted devices. We expect that extensions of the measurements and analysis described here will contribute to the development and optimization of new nanoscale device technologies based on 1D materials. As mentioned previously, the performance 951

of photodetectors3,36,37 and photovoltaics38-40 is limited by the efficiency of electron-hole separation and carrier collection, both of which can be assessed quantitatively through the measurement of µτ that we have demonstrated. The spatial mapping of µτ could prove particularly useful in the analysis of hybrid inorganic-organic photovoltaics, which may exhibit spatial inhomogeneities that depend on processing conditions. More generally, the measurement can be used to quantify the effects of surface functionalization and/or passivation schemes aimed at improving charge carrier transport/collection efficiency in nanowire optoelectronic devices including light-emitting diodes. In future work, selfconsistent modeling of the excess carrier concentrations and internal potentials will help us to achieve the full potential of these promising SPCM measurements. Acknowledgment. This work was supported by Northwestern University and the MRSEC program of the National Science Foundation (DMR-0076097) at the Materials Research Center of Northwestern University through seed funding. Use of the NIFTI facility of the NUANCE Center at Northwestern University is gratefully acknowledged. J.L.L. acknowledges the support of a National Science Foundation Graduate Research Fellowship, and J.P.R. acknowledges support from a Murphy Society Undergraduate Research Grant in Nanoscale Engineering. Time-resolved photoluminescence data were provided by Prof. L. M. Smith, University of Cincinnati. References (1) Xia, Y. N.; Yang, P. D.; Sun, Y. G.; Wu, Y. Y.; Mayers, B.; Gates, B.; Yin, Y. D.; Kim, F.; Yan, Y. Q. AdV. Mater. 2003, 15, 353. (2) Lieber, C. M. Sci. Am. 2001, 285, 58. (3) Wang, J. F.; Gudiksen, M. S.; Duan, X. F.; Cui, Y.; Lieber, C. M. Science 2001, 293, 1455. (4) Huang, M. H.; Mao, S.; Feick, H.; Yan, H. Q.; Wu, Y. Y.; Kind, H.; Weber, E.; Russo, R.; Yang, P. D. Science 2001, 292, 1897. (5) Mao, S. S. Int. J. Nanotechnol. 2004, 1, 42. (6) Gradecak, S.; Qian, F.; Li, Y.; Park, H. G.; Lieber, C. M. Appl. Phys. Lett. 2005, 87, 173111. (7) Sakaki, H. Jpn. J. Appl. Phys. 1980, 19, L735. (8) Lu, W.; Xiang, J.; Timko, B. P.; Wu, Y.; Lieber, C. M. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10046. (9) Sze, S. M. Physics of Semiconductor DeVices, 2nd ed.; Wiley: New York, 1981. (10) Martel, R.; Schmidt, T.; Shea, H. R.; Hertel, T.; Avouris, P. Appl. Phys. Lett. 1998, 73, 2447. (11) Wang, D. W.; Wang, Q.; Javey, A.; Tu, R.; Dai, H. J.; Kim, H.; McIntyre, P. C.; Krishnamohan, T.; Saraswat, K. C. Appl. Phys. Lett. 2003, 83, 2432. (12) Zheng, G. F.; Lu, W.; Jin, S.; Lieber, C. M. AdV. Mater. 2004, 16, 1890. (13) Caputo, D.; de Cesare, G.; Tucci, M. Sens. Actuators, A 2001, 88, 139. (14) Galluzzi, F. J. Phys. D: Appl. Phys. 1985, 18, 685. (15) Beck, N.; Wyrsch, N.; Hof, C.; Shah, A. J. Appl. Phys. 1996, 79, 9361.

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(16) Ahn, Y.; Dunning, J.; Park, J. Nano Lett. 2005, 5, 1367. (17) Balasubramanian, K.; Burghard, M.; Kern, K.; Scolari, M.; Mews, A. Nano Lett. 2005, 5, 507. (18) Balasubramanian, K.; Fan, Y. W.; Burghard, M.; Kern, K.; Friedrich, M.; Wannek, U.; Mews, A. Appl. Phys. Lett. 2004, 84, 2400. (19) Gu, Y.; Kwak, E. S.; Lensch, J. L.; Allen, J. E.; Odom, T. W.; Lauhon, L. J. Appl. Phys. Lett. 2005, 87, 043111. (20) Kroger, F. A.; Diemer, G.; Klasens, H. A. Phys. ReV. 1956, 103, 279. (21) Muscheid, W. M. B. a. W. Ann. Phys. 1954, 15, 82. (22) Look, D. C. J. Appl. Phys. 1974, 45, 492. (23) The resistivities of ion bombarded nanowires, in contrast, were typically 0.1-1 Ω‚cm and n-type as determined by the gate response. (24) For injection points away from the maximum, initially unequal currents produce charge accumulation that brings the entire device into equilibrium. Note that the present analysis for resistive material is very different from that of minority carrier photoconduction at low injection. In the present case, the excess carrier concentration is much larger than the equilibrium electron concentration, leading to pure hole and electron currents at respective electrodes. In the minority carrier low injection limit, carriers do not need to reach the electrodes to contribute to the photoconductivity. (25) Another possibility is that the change in the band bending (and thus potential barriers) adjacent to the contacts might increasingly hinder the collection of holes with increasing bias. However, the linear current-voltage characteristics under uniform illumination suggest that the contact effects are negligible in the carrier collection process. (26) Velocity saturation is also excluded because photocurrent versus voltage curves do not saturate. (27) For pure drift, the corresponding length would be L ) µετ, where ε is the electric field. (28) Gopinath, A. J. Phys. D: Appl. Phys. 1970, 3, 467. (29) The photogenerated carriers in the devices we measured do not move as far because the carrier transport is dominated by diffusion, not drift, outside the generation region. For devices under uniform illumination, both drift and diffusion will occur throughout the device. (30) Weber, C.; Becker, U.; Renner, R.; Klingshirn, C. Z. Phys. B: Condens. Matter 1988, 72, 379. (31) Stephens, R. B. Phys. ReV. B 1984, 29, 3283. (32) For comparison, typical radiative lifetimes in bulk CdS are from 1.4 ns (ref 30) to 4 ns (ref 31). Near band-edge luminescence was studied with femtosecond laser excitation and detected with a fast microchannel plate phototube. (33) The diffusion length depends on the recombination rate, which can be influenced by the bias, however. (34) It is important to note that, in contrast to carbon nanotude devices studied with SPCM, we are asserting that the depletion region lies underneath the contact and does not extend significantly into the nanowire for the bias ranges studied. (35) This diffusion length is consistent with the spatial profile of the photocurrent from the NSPM study on Schottky devices in ref 19. Using the higher resolution of NSPM compared to SPCM with a confocal microscope, we determine a minority carrier diffusion length of ∼110 nm. (36) Kind, H.; Yan, H. Q.; Messer, B.; Law, M.; Yang, P. D. AdV. Mater. 2002, 14, 158. (37) Hsu, C. L.; Chang, S. J.; Lin, Y. R.; Li, P. C.; Lin, T. S.; Tsai, S. Y.; Lu, T. H.; Chen, I. C. Chem. Phys. Lett. 2005, 416, 75. (38) Baxter, J. B.; Aydil, E. S. Appl. Phys. Lett. 2005, 86, 053114. (39) Kang, Y. M.; Park, N. G.; Kim, D. Appl. Phys. Lett. 2005, 86, 113101. (40) Law, M.; Greene, L. E.; Johnson, J. C.; Saykally, R.; Yang, P. D. Nat. Mater. 2005, 4, 455.

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Nano Lett., Vol. 6, No. 5, 2006