Controlled Ambipolar Doping and Gate Voltage Dependent Carrier

Oct 15, 2012 - length of 1 μm.8 The infrared light conversion capability of PbS. NW based .... were carried out in a Janis optical cryostat with temp...
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Letter pubs.acs.org/NanoLett

Controlled Ambipolar Doping and Gate Voltage Dependent Carrier Diffusion Length in Lead Sulfide Nanowires Yiming Yang,† Jiao Li,†,‡ Hengkui Wu,†,∥ Eunsoon Oh,§ and Dong Yu*,† †

Department of Physics, University of California, Davis, California 95616, United States Department of Physics, Nanjing University, China § Department of Physics, Chungnam National University, Korea ‡

S Supporting Information *

ABSTRACT: We report a simple, controlled doping method for achieving n-type, intrinsic, and p-type lead sulfide (PbS) nanowires (NWs) grown by chemical vapor deposition without introducing any impurities. A wide range of carrier concentrations is realized by adjusting the ratio between the Pb and S precursors. The field effect electron mobility of n-type PbS NWs is up to 660 cm2/(V s) at room temperature, in agreement with a long minority carrier diffusion length measured by scanning photocurrent microscopy (SPCM). Interestingly, we have observed a strong dependence of minority carrier diffusion length on gate voltage, which can be understood by considering a carrier concentration dependent recombination lifetime. The demonstrated ambipolar doping of high quality PbS NWs opens up exciting avenues for their applications in photodetectors and photovoltaics. KEYWORDS: Nanowires, lead sulfide, doping, field effect transistors, scanning photocurrent microscopy, carrier diffusion length length of 1 μm.8 The infrared light conversion capability of PbS NW based photovoltaic devices has also been demonstrated.9 Realizing PbS NW p−n junctions can further enhance the power conversion efficiency and photodetector sensitivity. To our knowledge, there has been no report on n-type PbS NWs to date. It has been shown that an excess Pb atom produces one free electron, and an excess S atom produces one free hole, although it is unknown whether the defects are vacancy type or interstitial type.10 The composition of bulk PbS crystals can be varied by annealing in the presence of S vapor. Both carrier type and concentration are dependent on S vapor pressure and equilibrium temperature. This dependence is nicely summarized in a useful thermodynamic pressure−temperature− composition diagram in ref 10. At 1000 K, the carrier concentration changes from 8 × 1018 cm−3 (n-type) to 5 × 1018 cm−3 (p-type) as the S vapor pressure increases by 8 orders of magnitude. At 1300 K, a change by 2 orders of magnitude in S vapor pressure results in a similar change in carrier concentration. This relationship provides a guide for doping PbS NWs as well. However, the small dimension of PbS NWs creates new challenges. For example, the annealing temperature is limited by the volatility of the NWs. We observed that NWs evaporated within minutes when the temperature was above 500 °C during postgrowth annealing,

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ontrolled doping of semiconductors is essential for realizing functional electronic devices. Most commonly, doping is achieved by intentionally incorporating impurities (dopants) into an extremely pure (intrinsic) semiconductor. Additionally, compound semiconductors can also be doped by a slight deviation from stoichiometry, such as by interstitial atoms and vacancies. Such defects often occur naturally, leading to unintentional doping. Important examples include pyrite and topological insulators, where nonstoichiometric doping convolutes the intrinsic properties and is detrimental to their potential applications. In this Letter, we demonstrate a simple, controlled ambipolar doping of lead sulfide (PbS) nanowires (NWs) without introducing dopants, by careful tuning of the Pb:S atomic ratio. PbS is an earth-abundant semiconductor with a direct bandgap of 0.41 eV. With a high infrared absorption coefficient and high carrier mobility, PbS has been intensely investigated for application as infrared photodetectors. Thanks to a large Bohr exciton radius (20 nm), PbS nanocrystals exhibit strong quantum confinement effects which can tune the bandgap to optimize solar energy conversion.1 Recently, multiple exciton generation (MEG) has also been observed in lead salt nanocrystals.2,3 However, charge transport in the nanocrystal thin films may suffer from inefficient hopping between nanocrystals.4,5 PbS NWs with continuous charge transport channels may further improve the performance of photodetectors and photovoltaic devices. NWs composed of lead salts have been synthesized by a vapor deposition method.6,7 Previously, we have measured mobilities up to 50 cm2/(V s) in p-type PbS NWs and a minority carrier (electron) diffusion © 2012 American Chemical Society

Received: September 4, 2012 Revised: October 5, 2012 Published: October 15, 2012 5890

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presumably because of their small sizes. Below 500 °C, the diffusion of Pb and S may be too slow to achieve uniform doping, according to our earlier experimental efforts. Here, we report a simple and robust method for ambipolar doping of PbS NWs. PbS NWs are grown through chemical vapor deposition using PbCl2 and S powders as precursors. By adjusting the ratio of the two precursors, we can precisely and reproducibly control the doping type and concentration of the as-grown PbS NWs. With this method, we have grown highquality n-type PbS NWs, evidenced by high carrier mobility and long carrier diffusion length. PbS NWs were synthesized via a chemical-vapor-deposition method in a tube furnace (Lindberg Blue M). Si wafers (⟨100⟩ doped with B, 1−25 Ω cm, test grade) coated by 400 nm thermal oxide were purchased from University Wafer. Ti thin films with a typical thickness of 200 nm were deposited on the SiO2 coated Si substrates by e-beam evaporation (CHA e-beam evaporator). In a typical growth, a Ti coated substrate was placed 5 cm downstream from the center at around 600 °C, while PbCl2 (99.999%, Alfa Aesar) and S (99.9999%, Alfa Aesar) powders were placed at the center and initially outside the heating zone, respectively (Figure 1a). After evacuating the

After development, the substrate was dipped into a 6:1 buffered HF for 3 s to remove surface oxide. Subsequently, 75 nm Cr/75 nm Au was deposited by electron beam evaporation. Figure 2b

Figure 2. Electrical characteristics of PbS NW FETs. (a,c,e) I−V curves as a function of Vg for NWs grown with the precursor mass ratio k = 3, 1, and 1/3, respectively. (b,d,f) Conductance at Vb = 0.1 V as Vg sweeps at a rate of 2.5 V/s. (b) Inset: SEM image of a typical device. (d) Inset: band diagram at different Vg. (f) Inset: linear plot of gate dependence for NWs grown at k = 1/3. Figure 1. (a) Schematic of tube furnace setup for growing PbS NWs. (b) SEM image of as-grown PbS NWs at k = 2. (c) XRD pattern of PbS NWs.

inset shows a SEM image of a typical device. Current−voltage (I−V) curves were measured through a current preamplifier (DL Instruments, model 1211) and a NI data acquisition system. Scanning photocurrent microscopy (SPCM) measurements were performed using a home-built setup based upon an Olympus microscope. Briefly, a 532 nm CW laser was focused by a 100× N.A. 0.95 objective lens to a Gaussian beam with full width at half-maximum (fwhm) of 450 nm. The focused beam was raster scanned on a planar device by a pair of mirrors mounted on a galvanometer, while both the reflection and the photocurrent were simultaneously recorded to produce a spatial map of photocurrent. A more detailed description of our SPCM setup can be found elsewhere.8 Low temperature measurements were carried out in a Janis optical cryostat with temperature measured by a Si diode. High-density PbS NWs are grown on Ti thin films without using H2 following a previously developed recipe.9 Figure 1b shows a SEM image of as-grown PbS NWs. The NWs are uniformly distributed over a relatively large area (5 cm × 1 cm) with a high density. The diameters of NWs range from 50 to

system to a base pressure of 15 mTorr, a 150 sccm N2 (99.999%) flow was maintained while the furnace temperature was ramped to 630 °C at 60 °C/min. Immediately after the peak temperature was reached, S was transferred into the heating zone, where the temperature was measured to be around 450 °C. After 30 min, the furnace was cooled down to room temperature over approximately 3 h. Scanning electron microscopy (SEM) imaging was performed using a Hitachi S-4100 FE-SEM microscope. X-ray diffraction (XRD) was conducted on a Siemens D-500 X-ray powder diffractometer. For fabricating field effect transistors (FETs) incorporating single PbS NWs, we first transferred NWs onto a 300 nm SiO2 covered, highly doped p-type Si substrate (purchased from University Wafer) by gently pressing an as-grown sample against the device substrate. Electrical contacts were then defined using an FEI 430 NanoSem system. 5891

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100 nm, and the length is up to tens of μm, consistent with our previous report.9 To grow NWs with various doping concentration, the mass ratio of the PbCl2 and S powders (k = mPbCl2: mS) is set to 3:1, 2:1, 1:1, and 1:3, respectively. Here, one “part” equals to 30 mg. For example, in a 3:1 growth, we used 90 mg of PbCl2 and 30 mg of S. The density and morphology of the as-grown NWs remain the same as we change the mass ratio k between 1/3 to 3. However, if k is out of this range, the NW density decreases dramatically, and the NW distribution also becomes nonuniform. XRD data of samples grown at different ratios all exhibit PbS rock salt crystal structures. A representative XRD pattern of n-type NWs is shown in Figure 1c. XRD data of p-type NWs have been shown previously.9 As-grown PbS NWs are then transferred to a SiO2 covered Si substrate and are electrically connected by Cr/Au electrodes using standard e-beam lithography. Figure 2 demonstrates the electrical characterization of representative single PbS NW FETs. As we vary the precursor mass ratio k from 3 to 1 to 1/3, the gate dependence clearly indicates n-type, ambipolar, and ptype conduction, respectively. I−V curves and gate dependence data for a k = 2 sample are consistent with this trend and can be found in Figure S1 of the Supporting Information. Multiple samples grown in different batches are tested, and the correlation between the precursor ratio k and doping concentration is reproducible. I−V curves are linear for both n-type and p-type NWs (Figure 2a,e), and four-probe measurements of these devices confirm that the contact resistance is always below 5% of the NW resistance. Zero gate voltage (Vg = 0 V) resistance in the n-type (p-type) NW devices reaches 16 (400) kΩ, corresponding to a resistivity of 1 (30) mΩ·cm, respectively. These values are comparable to the room-temperature resistivity in bulk PbS crystals, ranging from 1 to 10 mΩ·cm, depending on sample preparation.10 At k = 1, resistance is greatly increased to 50 MΩ at Vg = 0 V. In addition, I−V curves are nonlinear under positive Vg, and the current saturates as the magnitude of bias voltage (Vb) is above 0.1 V (Figure 2c). This current saturation diminishes under negative Vg, and I−V curves become linear. The current saturation at high |Vb| under positive Vg can be understood by considering two back-to-back diodes caused by the contact barrier in the lightly doped NWs. Nearly linear I−V curves at negative Vg indicate smaller hole contact barrier in this device (see band diagram in Figure 2d inset). The high electron contact barrier is further supported in the low measured field effect electron mobility at positive Vg as seen in Figure 2d. From the gate dependence, field effect mobilities and carrier concentrations in 22 devices are extracted and summarized in Figure 3. The carrier concentration at Vg = 0 V changes from 1019 cm−3 (n-type) to 1018 cm−3 (p-type), as k is varied from 3 to 1/3 (Figure 3a). At k = 1, nearly intrinsic PbS NWs are achieved with a hole concentration as low as 1017 cm−3. The field effect mobility also strongly depends on k (Figure 3b). The p-type PbS NWs grown at k = 1/3 exhibit mobilities of 15−140 cm2/(V s), similar to the values published previously.8 The mobility measured in n-type PbS NWs grown at k = 2 and 3 reaches 230−660 cm2/(V s), comparable to the value reported in bulk PbS crystals. The mobility of the n-type PbS NWs appears to be significantly higher than that of the p-type and intrinsic NWs. In contrast, similar electron and hole mobilities have been observed in bulk PbS crystals.10 The origin of this discrepancy is not clear but is likely caused by hole scattering at the surface of the NWs. Though the data are not

Figure 3. Carrier concentration (a) and mobility (b) measured in 22 PbS devices as a function of precursor ratio k. Blue (red) data points indicate p-type (n-type) doping. Negative carrier concentration in part a represents p-type doping. (b) Inset: logarithmic plot of carrier mobility vs carrier concentration.

conclusive, carrier mobility also seems to decrease with decreasing carrier concentration (Figure 3b inset). We attribute this relation to two possible reasons: (1) the contact barrier in low carrier concentration NW devices (k = 1) may reduce the measured field effect mobility; (2) carrier transport in NWs with low carrier concentration may suffer from scattering by unfilled surface states, while such carrier scattering is greatly suppressed when these surface states are filled at high carrier concentration. The strong correlation between the carrier concentration and the precursor ratio clearly indicates that PbS NWs can be doped by controlling the stoichiometry without the need of introducing impurities. As the growth temperature is much higher than the melting point of the precursors, we observe that both PbCl2 and S powders completely evaporate within a few minutes. During this nonequilibrium growth, larger precursor amounts lead to a higher vapor pressure of the precursor. The high PbCl2 (S) vapor pressure leads to an excess of Pb (S) atoms and n-type (p-type) PbS NWs, respectively. To significantly vary the doping concentration of bulk PbS at our growth temperature (600 °C), the S vapor pressure has to change by several orders of magnitude.10 In contrast, we have observed a large change in carrier concentration for our NWs by varying the precursor ratio by only about 1 order of magnitude (from k = 1/3 to 3). The stoichiometry of the NWs is likely more sensitive to the vapor pressure change because of the growth mechanism of these NWs. The NWs are most likely grown by a vapor−liquid−solid (VLS) mechanism according to previous reports,6,7 where the Pb and S atoms are dissolved in the liquid catalytic droplet and precipitate into solid PbS NWs after reaching saturation. The Pb:S atomic ratio in the liquid droplet should be more sensitive to the S vapor pressure, compared with annealing the PbS crystal in S vapor. The high diffusion constant of Pb and S atoms in the liquid droplet should lead to uniform doping. An alternative mechanism is through surface doping, where the Pb (S) atoms from the vapor diffuse into the NW from the sidewall and result in n-type (ptype) doping. This mechanism is unlikely because of the low diffusion constant in solid PbS. We then investigate PbS NWs of different carrier types with SPCM. SPCM has been used to characterize local band structure and charge drift/diffusion in NWs grown by vapor deposition8,11−21 and colloidal nanostructures.22,23 In SPCM, electrons and holes are locally injected by a focused laser beam and diffuse/drift along the NWs (Figure 4a inset). These carriers contribute to photocurrent if they can reach the 5892

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of photocurrent decay lD is not likely due to the depletion width near the contact, which is much smaller than the measured lD. Thus, we attribute the extension of the photocurrent to carrier diffusion. Limited by the length of the NW, the 3.9 μm value may be an underestimation of the actual diffusion length. The increase in diffusion length in n-type devices is consistent with the higher mobility exhibited by those devices. We can calculate the carrier recombination lifetime from the measured diffusion length using the equation τ = qlD2/ μkBT. We estimate τ = 10 ns for both n-type and p-type devices, using the majority carrier mobility measured from gate dependence. If the minority carrier mobility is lower than that of the majority carriers, the actual lifetime should be longer than this estimated value. The carrier lifetime has been reported to be 63 μs in intrinsic bulk PbS26 and is much shorter in highly doped PbS. The carrier lifetime in NWs may be further reduced by surface recombination.27 Interestingly, we have observed that the carrier diffusion length strongly depends on gate voltage, as demonstrated in the following two cases: (1) n-type NW device with one Schottky junction; (2) ambipolar NW device. 1. N-Type NW Device with One Schottky Junction (Figure 5). Some of our NW FETs show asymmetric and nonlinear I−V curves, presumably due to Schottky contact barriers (Figure 5b). These asymmetric Schottky devices seem to be caused by the occasional imperfect device fabrication process. We can take advantage of these Schottky devices to

Figure 4. Photocurrent line scans along the NWs and SPCM images at Vg = Vb = 0 V of n-type (a,b) and p-type (c,d) PbS NW FETs. Purple areas indicate the position of contacts. The peak laser intensity is 440 W/cm2 at 532 nm, with a fwhm of 450 nm obtained from photocurrent line scan perpendicular to the NW. The blue curves in a and c are the exponential fitting to extract the photocurrent decay length.

contacts before charge recombination occurs. In the absence of an electric field in the NW, SPCM allows for the measurement of the minority carrier diffusion length, lD = (Dτ)1/2, where D = μkBT/q is the minority carrier diffusion coefficient, q is electron charge, kB is Boltzmann constant, T is temperature, and τ is the carrier lifetime.24 From lD measured by SPCM and the mobility μ extracted from the gate dependence, the carrier recombination lifetime τ can be estimated. The recombination lifetime can also be obtained from ultrafast spectroscopy; however, with SPCM, one can measure the carrier lifetime in an individual NW as a function of carrier density modulated by gate voltage, which is challenging for ultrafast spectroscopy. Our PbS NW FETs exhibit a sensitive and fast photoresponse. The photocurrent rises/drops within 20 μs (limited by instrument response time) upon turning on/off laser illumination, respectively (data not shown here but similar to the one in ref 8). No persistent photocurrent is observed after illumination is turned off, as observed previously.8 The fast photoresponse indicates the surface is free of slow charge traps. We compare SPCM results for n-type and p-type NWs in Figure 4. Photocurrent spots of opposite signs are observed near the contacts at Vb = 0 V, consistent with upward (downward) band bending toward Cr contacts in n-type (ptype) NW devices, respectively (band diagrams shown in Figure 4). The photocurrent is attributed to the charge separation by the band bending at the contacts.11 We estimate the charge separation efficiency ηcc = I/qF = 5.6% from the peak photocurrent of 4 nA, where photon flux F is calculated by integrating the Gaussian shaped laser intensity over the NW.25 The photocurrent as a function of distance from the electrode (x) can be fitted by an exponential function (I = I0exp(−x/lD), giving lD = 3.9 (1.3) μm for the n-type (p-type) NW device, respectively (Figure 4a,c). The characteristic length

Figure 5. (a) Zero-bias photocurrent line scans along the NW as a function of Vg in an n-type NW device with one Schottky contact at laser intensity of 440 W/cm2. Blue areas indicate the position of contacts. Band diagrams are shown on the right. (b) I−V curves of the same device. Inset: peak photocurrent vs Vg. (c) Solid squares are the minority carrier diffusion length lD extracted from the exponential fitting of photocurrent decay in part a as a function of Vg. The red curve shows the best fitting by lD = A/(Vg − Vt)1/2 for Vg > −20 V with A = 4.7 μm·V1/2 and Vt = −15 V. The blue curve shows the calculated carrier diffusion length considering the photoinjected carriers. 5893

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more precisely measure the long carrier diffusion length, as the photocurrent is dominated by only one of the electrodes, and its decay length will be less affected by the finite length of the NWs. Using these devices, we have explored how gate voltage affects band bending and charge diffusion. As clearly seen in Figure 5a, photocurrent is dominated by the Schottky contact at the right electrode in this n-type NW device. Photocurrent spots are seen on both sides of the right electrode, as electrons can travel through the NW underneath the electrode to reach the left electrode. The photocurrent has a much higher magnitude (up to 60 nA) compared to the nearly ohmic contact devices in Figure 4 (4 nA at the same laser intensity), as the larger band bending induces a more efficient charge separation. As we apply a positive Vg, the peak photocurrent increases and saturates at around 60 nA, while a negative Vg decreases the peak photocurrent by a factor of 2 (Figure 5b inset), consistent with a reduced band bending (band diagrams in Figure 5a). The photocurrent saturation at positive Vg indicates that photocurrent is likely limited by the injected photon flux and cannot be increased further by band bending. Indeed, we estimate a close-to-unity (84%) charge separation efficiency from the peak photocurrent of 60 nA. The photocurrent data can be fit very well by the exponential form, as evidenced by the linearity of the curves in a semilog plot in Figure S2. The photocurrent decay length strongly depends on Vg, increasing from 0.39 to 5.7 μm as Vg changes from 50 V to −50 V (Figure 5c). Assuming constant minority carrier mobility, we estimate a change in carrier lifetime by a factor of 200. This is expected since the recombination lifetime is inversely proportional to the carrier concentration. The net transition rate of photoinduced holes in n-type semiconductors is U = Rec(np − ni2) = Δp/τp, where Rec is the recombination coefficient, the total electron density n = n0 + Δn is the sum of dark electron density n0 and photoinjected electron density Δn, ni is the intrinsic electron density, and τp is the hole lifetime.28 When Vg > − 20 V, the dark electron density is much higher than that injected and, approximately, τp = 1/Rec n0; that is., the recombination lifetime is inversely proportional to the dark electron density and hence gate voltage. In this Vg range, the minority carrier (hole) diffusion length can be fit nicely by lD = A/(Vg − Vt)1/2, assuming a linear relation between dark electron density and gate voltage: n0 = C(Vg − Vt), where C is the gate induced carrier density per volt, and Vt is the gate threshold (Figure 5c). When Vg < − 20 V, the dark electron density is much lower than that injected and, approximately, τp = 1/Rec Δn; that is, the recombination lifetime is almost independent of dark electron density or gate voltage. This diffusion length saturation at Vg < −20 V can be seen clearly in Figure 5c. More quantitatively, the diffusion length can be calculated by an asymptotic form lD = (μkBT/[qRec(n0 + Δn)])1/2, which is in excellent agreement with experimental data (blue curve in Figure 5c).29 To best fit Figure 5c, we have used the following values Δn = 4 × 1017 cm−3, Rec = 4 × 10−12 cm3/s, and μ = 20 cm2/(V s) in the calculation. 2. Ambipolar NW Device (Figure 6). A FET device incorporating a NW grown at k = 1 shows an almost symmetric gate dependence for electron and hole conduction (Figure 6a), from which electron and hole mobilities are extracted to be μe = μh = 6 cm2/(V s). At Vg = 0 V, current saturates at high bias (Figure 6a inset), indicating the energy barrier at contacts. The asymmetry in the I−V curve may be caused by the doping concentration gradient along the NW axis (see next paragraph). Zero-bias photocurrent profiles along the NW exhibit broad

Figure 6. (a) Conductance vs Vg for an ambipolar NW device at Vb = 0.2 V. Inset: I−V curve at Vg = 0 V. (b) Zero-bias photocurrent line scan along the NW axis as a function of Vg. Blue areas indicate the positions of electrodes. Arrows indicate photocurrent peak positions. The band diagrams are shown on the right. (c) The ratio of electron and hole transport lengths vs Vg. Upper inset: peak position vs Vg. The error bar is estimated from the broadening of the photocurrent peak in b. Lower inset: band diagram with charge transport direction. The top axis shows carrier concentration estimated from the gate dependence. (d) Photocurrent line scans at Vg = 30 V as a function of Vb for the same device. Peak laser intensity is 440 W/cm2 for b and 220 W/cm2 for d.

peaks, and the peak position shifts from one contact to the other as Vg changes from 40 V to −40 V (Figure 6b). The photocurrent peak shift is most pronounced when the carrier density is low (0 V < Vg < 10 V) (Figure 6c upper inset). At higher magnitudes of Vg, the photocurrent peak is shifted very close to the contacts and appears to be a shoulder of a second photocurrent peak at contact. The magnitude of this photocurrent peak at the contact increases with increasing |Vg| and is caused by band bending (see band diagrams at different gate voltages in Figure 6b). The positive zero-bias photocurrent induced by photoinjection near the center of the NW indicates an internal electric field along the NW, which separates the injected carriers and results in the observed photocurrent. This internal electric field is most likely caused by a doping concentration gradient. During the NW growth, the precursor ratio is expected to change slightly over time, leading to a spatially varying Pb:S atomic ratio and thus a doping concentration gradient along the NW. While the slight doping variation can be ignored in heavily doped NWs, it can significantly alter the Fermi level in lightly doped NWs. At zero bias, an internal electric field is thus developed to align the Fermi level along the NW (see band diagrams in Figure 6). We estimate the built-in potential (Vbi) induced by the doping concentration gradient by conducting bias-dependent SPCM (Figure 6d). The photocurrent is almost completely quenched when Vb is between −80 mV and −120 mV, when the external bias balances Vbi and leads to a flat band. Taking Vbi = 100 mV, we can extract the ratio of the electron concentrations at the left and right contacts to be nL/nR = exp(qVbi/kBT) ≅ 50. 5894

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After understanding the origin of the zero-bias positive photocurrent peak, we will now discuss the photocurrent peak shift by gate voltage. We attribute the photocurrent peak shift to a change in carrier transport length with gate voltage. As the built-in field (Vbi/L ∼ 10 mV/μm) is comparable to the diffusion field (kT/qlD ∼ 10 mV/μm), carrier transport is driven by a combination of drift and diffusion. As demonstrated earlier, the electron (hole) transport length, le (lh), is a function of carrier concentration and hence Vg. As Vg decreases from 40 to 5 V (n-type), the minority carrier (hole) transport length lh increases, as evidenced by slower decay on the left side of the photocurrent peak (Figure 6b). The photocurrent peak position is determined by the ratio between le and lh. Photocurrent is maximized when the photoinduced electrons and holes reach opposite contacts at equal probability,13 or le/lh = xp/(L − xp), where xp is the distance from the photocurrent peak position to the electron collecting contact on the left and L is the channel length, as labeled in Figure 6c inset. As Vg decreases from 40 to 5 V, lh (le) becomes longer (shorter), and the photocurrent peak shifts toward the electron collector. As Vg decreases further below 5 V, the NW is eventually turned from n-type to p-type when Vg is below 5 V, and holes switch from minority carriers to majority carriers. Thus lh is longer than le when Vg < 5 V, and the photocurrent peak moves from being close to the hole collector on the right to being close to the electron collector on the left. The ratio of le/lh calculated from the photocurrent peak positions decreases by about 2 orders of magnitude as Vg decreases from 40 V to −40 V (Figure 6c). As shown in the previous two cases, carrier diffusion length, or carrier transport length in the second case, is strongly dependent on the applied gate voltage in PbS NWs. Though carrier diffusion length has been measured previously in CdS,13 ZnO,15 GaAs,18 and Si NWs,12,17,27 to our knowledge, there has been no report on how gate voltage affects carrier diffusion length. This is likely because CdS and ZnO NWs do not show strong gate dependence, and carrier recombination seems to be dominated by surface recombination in GaAs and Si NWs. If the carrier recombination is dominated by traps and described by Shockley−Read−Hall statistics, the lifetime is inversely proportional to the trap density and is not expected to depend on the doping concentration. The observed long minority carrier diffusion length and strong gate dependence of carrier lifetime indicate that carrier recombination in PbS NWs is not likely dominated by surface recombination and may be instead mainly through the direct band-to-band transition as in bulk. Further investigation such as diameter-dependent diffusion length is necessary to clarify on the recombination mechanism. Lastly, we will briefly present our low temperature conduction measurements of n-type PbS NW devices grown at k = 3. I−V curves remain linear up to 80 K (Figure 7a), indicating vanishingly small contact barriers. The conductance increases from 30 μS at room temperature to 85 μS at 80 K as shown in Figure 7b, in agreement with bulk PbS10 and previous measurements in PbS NWs.30 The reduction in resistivity at low temperature is mainly caused by an enhanced mobility, due to the suppression of phonon scattering and smaller effective mass. We have observed electron mobility as high as 2800 cm2/ (V s) at low temperature (Figure 7b inset). The detailed low temperature transport behavior of PbS NWs is beyond the scope of this Letter and will be investigated more in the future. In summary, we have successfully synthesized high quality ntype, p-type, and intrinsic PbS NWs by adjusting the ratio

Figure 7. (a) I−V curves at various temperatures for an n-type PbS NW device with k = 3. (b) Conductance as a function of temperature. Inset: conductance as Vg sweeps at 2.5 V/s at 160 K.

between Pb and S precursors. The n-type PbS NWs exhibit an electron mobility as high as 660 cm2/(V s) at room temperature and a minority carrier diffusion length up to 3.9 μm at zero gate voltage. The simple, robust, and controlled ambipolar doping and the demonstrated excellent optoelectronic performance of these PbS NWs should promote exciting applications in solar cells and sensitive photodetectors. For example, axial NW p−n junctions may be achieved by adjusting the precursor ratio during the NW growth. Furthermore, we have demonstrated a significant increase of diffusion length with decreasing carrier concentration. In an n-type NW device with one Schottky junction, we have observed an increase in carrier diffusion length from 0.39 to 5.7 μm as Vg is decreased from 50 to −50 V, corresponding to a drastic increase in carrier recombination lifetime by more than 2 orders of magnitude. In an ambipolar NW device, the photocurrent peak position shifts from the hole-collecting contact to the electron-collecting contact, as the NW is turned from n-type to p-type by gate voltage. The strong correlation between carrier density and diffusion length indicates that carrier recombination in PbS NWs may not be greatly influenced by the surface trap states. This finding also provides a method to control the carrier diffusion length by tuning carrier concentration in PbS NWs and may be useful for their optoelectronic applications. For example, higher carrier concentration (thus shorter lifetime) may be preferred in fast photodetectors and lower carrier concentration (thus longer lifetime) in photovoltaic devices based upon PbS NWs.

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ASSOCIATED CONTENT

S Supporting Information *

Electrical characteristics of n-type PbS NWs grown at the precursor mass ratio k = 2 and semilog plot of photocurrent line scans for the n-type PbS NW device with one Schottky contact. 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]. Present Address ∥

Phonone Inc., Santa Clara, California, United States.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.C. Davis Startup fund. We thank R. Graham for useful scientific discussions. E.O. 5895

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(30) Lau, Y. K. A.; Chernak, D. J.; Bierman, M. J.; Jin, S. J. Mater. Chem. 2009, 19, 934.

acknowledges the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (Grant No. 2011-0011883). Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

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REFERENCES

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dx.doi.org/10.1021/nl303294k | Nano Lett. 2012, 12, 5890−5896