Letter pubs.acs.org/NanoLett
Electron Trapping in InP Nanowire FETs with Stacking Faults Jesper Wallentin,*,† Martin Ek,‡ L. Reine Wallenberg,‡ Lars Samuelson,† and Magnus T. Borgström† †
Solid State Physics, Lund University, Box 118, S-221 00, Lund, Sweden Polymer and Materials Chemistry/nCHREM, Lund University, Box 124, S-221 00, Lund, Sweden
‡
S Supporting Information *
ABSTRACT: Semiconductor III−V nanowires are promising components of future electronic and optoelectronic devices, but they typically show a mixed wurtzite-zinc blende crystal structure. Here we show, theoretically and experimentally, that the crystal structure dominates the conductivity in such InP nanowires. Undoped devices show very low conductivities and mobilities. The zincblende segments are quantum wells orthogonal to the current path and our calculations indicate that an electron concentration of up to 4.6 × 1018 cm−3 can be trapped in these. The calculations also show that the room temperature conductivity is controlled by the longest zincblende segment, and that stochastic variations in this length lead to an order of magnitude variation in conductivity. The mobility shows an unexpected decrease for low doping levels, as well as an unusual temperature dependence that bear resemblance with polycrystalline semiconductors. KEYWORDS: Nanowire, FET, crystal structure, electron transport, mobility
T
in Figure 1, is similar to the one suggested by Anderson20 and used by Mott for amorphous semiconductors.21 In this work, we show that the ZB segments trap carriers and thereby control the electron transport in polytypic InP NWs. Previous investigations have suffered from an uncertainty regarding the contact resistance,17 but here we use highly doped NW ends to form low-resistance contacts even to undoped InP NWs. Calculations show that conductivity even at room temperature is controlled by the crystal structure. We used metal−organic vapor phase epitaxy (MOVPE) with trimethyl indium (TMI) and phosphine (PH3) as growth precursors. NWs of 100 nm diameter were grown with highly n-doped ends using hydrogen sulfide (H2S), surrounding a middle segment in which the doping was varied between nominally undoped and highly doped in six steps. The diameter and all growth conditions were kept constant. Hydrogen chloride (HCl) was used to prevent radial growth,22 which could otherwise short-circuit the middle segment. We created NW-FETs using samples from all six doping levels by contacting the ends of the NWs, so that the channel length was defined by the 1.4 μm middle segment. The average resistance for the highest doped devices was 7 kΩ, which gives an upper estimate of the contact resistance for the other devices. The low-resistance contacts assured that the resistance was dominated by the channel and allowed us to characterize low-doped NWs, which is otherwise difficult due to the
he interest in III−V semiconductor nanowires (NWs) for future electronic and optical components1−4 has significantly increased the past decade. These materials offer high electron mobility, superior optical properties, and great flexibility in heterostructure design,5,6 and the demonstration of epitaxial growth on Si substrates7 has shown a path toward integration with mainstream electronics. Although the common III−V materials have the cubic zincblende (ZB) crystal structure in bulk, NWs often exhibit a mix of the ZB and the hexagonal wurtzite (WZ) crystal structures.8 As the NWs grow axially, single-crystalline layers of either ZB or WZ are formed. In InP, this polytypism gives rise to a staggered type II band alignment with the conduction band (CB) in ZB 129 meV below that in WZ.9 The optical characteristics of such polytypic NWs have been thoroughly studied in recent years.10−14 Short ZB segments are crystal phase quantum wells (QWs), and in thin NWs quantum dots are formed that can be single-photon emitters.15 Although III−V NWs are usually polytypic unless the growth conditions are specifically tuned for crystal purity, the electron transport of such polytypic NWs has not been studied in much detail with respect to the crystal structure. The current path is along the NW axis and, unlike 2DEG devices, orthogonal to the confining potential. Recent publications indicate that polytypism can reduce mobility16 and conductivity.17 Our group has recently shown subthreshold slopes only 13% above the theoretical limit, paired with surprisingly low mobilities, in NW-FETs made of polytypic InP NWs.18 The ZB segment lengths, and therefore the quantized energy levels, show a Poisson distribution.19 The resulting band structure, sketched © 2011 American Chemical Society
Received: September 15, 2011 Revised: November 4, 2011 Published: December 7, 2011 151
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The capacitance, Cox, was calculated using a metallic cylinderplane system with compensation factor of 2 for the planar oxide.25 Using the measured mobility and resistivity, the carrier concentrations were evaluated with a Drude model. The lower-doped devices (χH2S < 5.6 × 10−7) showed the expected exponential dependence in the subthreshold region. For χH2S > 5.6 × 10−7 the devices could not be turned off. We found that the hysteresis and subthreshold slopes decreased significantly below 0 °C in the undoped devices, and we measured 117 mV/decade at 237 K. This low value for a simple back-gated device, similarly to optical measurements of InP NWs,26 indicates a low density of surface states which would otherwise screen the channel. In the highest-doped sample (χH2S = 7.1 × 10−6), the gate control was too poor to determine the transconductance, possibly due to a dominant contact resistance. We instead used the Burstein−Moss shift, observed with microphotoluminescence (PL),24,27 to estimate the carrier concentration to 9 × 1018 cm−3. This is about 1 order of magnitude less than H2Sdoped InP NWs grown at comparable conditions but without HCl.24 The measured carrier concentration, n, increased approximately quadratically versus χH2S and was as low as 8.1 × 1013 cm−3 in the undoped NWs. Such high purity InP, corresponding to only 0.9 carriers per device, should be difficult to achieve, especially considering the low growth temperature and memory effects from the highly doped bottom segment. To explain the low carrier concentrations, we propose that the ZB segments act as traps for the electrons, similar to InP quantum dots in GaInP barriers.28 We calculated the bound states in the ZB segments, using coupled finite QWs with typical segment lengths as observed in TEM and found that there was only one bound state in all but the very longest observed segments. While the short, most common ZB segments had bound states around 20−50 meV below the WZ CB edge, the longest observed segment in TEM (6.4 nm) had a calculated binding energy of 90 meV. This agrees well with the results of Bao et al., who theoretically and optically found a bound state at about 80−100 meV, in InP NWs with slightly more ZB than ours.13 Assuming that the DOS per unit volume and energy, ρ(E), is the sum of the DOS of N QWs, each with a single bound state Ei, ρ(E) can be written as:
Figure 1. (a) Low- and high-resolution TEM of an InP NW, scale bar 5 nm. (b) Schematic conduction band, indicating bound states Ei and the Fermi level Ef. (c) Average WZ segment length vs χH2S. (d) Sketch of NW-FET device, where n is the doping in the middle segment. (e) Calculated ZB trap states ρ(0), calculated dopant density, and measured carrier concentration vs χH2S. The highest doped sample was characterized optically rather than electrically. Arrows indicate the results for samples with χH2S = 0 (undoped). The error bars indicate one standard deviation for the 5−20 devices measured per χH2S.
formation of Schottky-like contacts. Hereafter, any doping refers to the middle segment. For methods details, please see the Supporting Information. H2S increases the growth rate of InP NWs significantly,23,24 but HCl removed this effect. Transmission electron microscopy (TEM) revealed that the undoped NWs had a mix of WZ and ZB with short segments lengths, as shown in Figure 1. With increasing H2S molar fraction, χH2S, the share of WZ increased slightly, but the crystals were far from the pure WZ previously observed in InP NWs grown with H2S but without HCl.24 All NW-FETs displayed linear source−drain characteristics, except the undoped (more precisely nonintentionally doped) devices that exhibited slight nonlinearity and hysteresis. By changing χH2S, it was possible to tune the conductivity over more than 5 orders of magnitude. The resistivity in the undoped devices was as high as 460 Ωcm (resistance 0.82 GΩ), showing that HCl completely removed any conductive shell growth. Additionally, all devices except the highest doped showed linear back gate (Vg) dependence above the threshold. We used the transconductance in this region, gm = dI/dVg, to determine the mobility, μ, using the relation gm = μCoxVsd/L2, where Vsd = 10 mV is the source−drain voltage and L is the channel length.
N
ρ(E) =
N
A m m θ(E − Ei) ∑ θ(E − Ei) = 2 ∑ V πℏ2 L πℏ i i
(1)
Here, A and V are the (cross-sectional) area and volume of the channel in the device, m is the ZB effective mass, θ is the step function, and E is the energy measured from the WZ CB edge. We used the distribution of ZB segments as observed in TEM to calculate the total trap state density ρ(0) as a function of χH2S, shown in Figure 1. A single 6.4 nm segment could trap about 200 electrons, which corresponds to a density of 2 × 1016 cm−3 in our devices. The calculated total trap state density was 4.6 × 1018 cm−3 in the undoped NWs, 5 orders of magnitude higher than the measured carrier concentration. Radial quantization and charging energies have been ignored in these 100 nm diameter NWs but should give slightly lower DOS. 152
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doped devices, the measured activation energy Ea at zero gate voltage varied between devices in the range 30 to 45 meV. This agrees with the calculated Ef = −34 meV, assuming Ea = −Ef. The undoped devices did not have measurable conductivity below room T with the gate grounded, due to the low currents and high activation energies, but exhibited similar behavior with a gate voltage around +2 V. Calculations showed that Ef, up to χH2S = 3.3 × 10−8, was determined primarily by the length of the largest ZB segment. Increasing this length from 3 to 10 nm shifted Ef by 50 meV and decreased the conductivity about 1 order of magnitude. Since this length is determined stochastically19 it varies significantly between NWs, possibly explaining the observed large variations in conductivity at low χH2S. This variation is much larger than effects of random placement of few dopants.30 Similar variations has been observed in polytypic InAs NWs.17 Note that the effect of random variations in contact resistance can be ignored in our devices. Even at room temperature the conductivity, as well as the threshold voltage, should be determined by the longest ZB segment, since the deepest ZB bound state was larger than kT. In the higher-doped samples (above χH2S = 3.3 × 10−8), the calculations showed that the longest few segments were filled, giving an averaging effect over the channel length. This could explain the reduced standard deviations observed at these doping levels. For low-power electronics, much shorter channel lengths are desirable. In this case, the effects of random ZB segment lengths are even more severe, since there is very little averaging in short channels. For instance in a 32 nm channel FET, a single 6.4 nm segment could trap electrons corresponding to a density of 9 × 1017 cm−3. The special DOS in these NWs should also affect the subthreshold performance and may contribute to the nearly ideal subthreshold slopes that we have previously observed in these NWs.18 In thin NWs with an additional radial quantization which creates quantum dots from the ZB segments, the NWs could possibly reach the so-called quantum capacitance limit.31 Returning to the temperature-dependent measurements, we found that in both doped (χH2S = 1.5 × 10−7) and undoped (χH2S = 0) devices the activation energy Ea could be reduced (increased) with a positive (negative) gate voltage. Data for an undoped device is shown in Figure 2. The coupling between the channel potential, Φf, and the gate potential, Φg, is determined by the capacitances of the system, and can be written as2
The energy of the carriers should be Fermi distributed, where only a small share of the carriers is above the WZ CB edge and contributes to the conductivity. Similarly to Mott,21 we assume that that the conductivity is thermally activated, σ(Ef, T) ∼ exp(Ef/kT), where Ef is the Fermi level measured from the WZ CB edge. Based on the ρ(E) discussed above, we computed the dopant concentrations, and Ef, which would give the measured conductivities. For the nonintentionally doped NWs we calculated a dopant concentration of 1.3 × 1015 cm−3, comparable to background carrier concentrations previously reported in our system.29 Devices with χH2S = 0 (“undoped”) and 1.5 × 10−7 (“doped”, average device resistance 0.35 MΩ) were investigated in temperature-dependent measurements using liquid helium. The source−drain characteristics of the doped samples were linear down to about 150 K. We found that the conductivity for all devices was thermally activated, as shown in Figure 2. For the
Cox dΦf = dΦg Cox + Csd + Cq
(2)
Here, Cox is the oxide capacitance, Csd is the source and drain capacitance, and Cq is the channel or quantum capacitance. Since Φg = −eVg, and Φf = Efs+Ea where Efs is the constant Fermi level in the contacts, this can be rewritten as
dEa eCox =− dVg Cox + Csd + Cq Figure 2. (a) Arrhenius plot of current for an undoped device at selected gate voltages, Vg. Vsd = 10 mV. (b) Schematic band diagram at zero bias. (c) Activation energy, Ea, vs back gate voltage Vg, for the same device as in panel a. (d) dEa/dVg, derived from the measured values shown in panel c, and the calculated ratio −Cox/(Cox + Csd + Cq).
(3)
In the on-state of the device, Cq ≈ Vq2ρ(Efs − Φf), or Cq ≈ Vq2ρ(−Ea), that is, the channel capacitance is proportional to the density of states. Therefore, the Ea(Vg) dependence can be used to investigate ρ(E). We evaluated Ea(Vg) as well as dEa/ dVg from the gate-sweep measurements. At low gate voltages 2
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Cq should be negligible, and as expected Ea(Vg) shows a linear dependence. We found from a linear fit in this region that Cox/ (Cox + Csd) ≈ 0.6 for the exhibited undoped device. Thus, this is a reasonably well-behaved long-channel NW-FET. The steeply decreased slope toward higher Vg between Ea of 50 and 100 meV in Figure 2c, observed in both undoped and doped devices, suggests an increase in ρ around the ZB states. We calculated Cq and dEa/dVg, based on ρ(E), and found a reasonable agreement between measurements and calculations as shown in Figure 2d. The calculations, which ignore broadening of ρ(E) due to the finite temperature, show stepwise changes in capacitance at the bound states of the longest ZB segments. Note that the position of these steps depends on the stochastically determined length of the longest ZB segments, as discussed above. The agreement is less satisfying for low activation energies, possibly because other sources of temperature dependence in the conductance become significant. The measurement of low activation energies is also rather difficult. Doped devices (χH2S = 1.5 × 10−7) showed similar behavior, but shifted to lower Vg. Finally we discuss the mobility, which exhibited a maximum versus χH2S as shown in Figure 3. The reduced mobility in
this temperature it decreased. This is also unexpected since phonon scattering typically dominates in low-doped InP, giving an increased mobility at lower T. Our undoped InP devices showed mobilities which are almost 2 orders of magnitude lower than bulk values, similarly to polytypic InAs NWs.17 NWs from the same batch have shown similar mobilities using omega wrap gates.18 Assuming a thermal velocity of 3.9 × 107 cm/s, the average scattering length in the undoped NWs can be estimated to 3 nm, which is comparable to the average WZ segment length and much less than the NW diameters. This suggests that the crystal structure limits the mobility in our low to medium-doped samples, which is in line with previous indications.16,33 At χH2S = 1.9 × 10−6, where the mobility starts to decrease toward higher doping, the average distance between dopants is comparable to the WZ segment length and it is plausible that impurity scattering dominates. However, it is unclear why the mobility was so much lower in the undoped NWs compared with the doped ones, since the WZ segment length was only 15% shorter. The capacitance can depend on the carrier concentration, which can lead to an underestimate of the mobility for low doping levels,25 but in the linear region the carrier concentration should be too high for such effects. We note that the highest mobility was reached at χH2S = 5.6 × 10−7, where the calculated dopant density is close to the density of trapped electrons. Therefore we argue that the scattering is due to trapped electrons, rather than the crystal defects themselves, and that the dopant ions in the doped NWs partially neutralize these charges. A full model of the mobility in polytypic NWs is beyond the scope of this communication. The threshold voltage decreased linearly versus T with a proportionality constant of around 5 mV/K for the undoped and 10−13 mV/K for the doped (χH2S = 1.5 × 10−7) samples. Typically, Vth decreases linearly in n-MOSFETs with a slope of about 1 mV/K.34 Due to the higher Vth, some doped devices changed from normally on to normally off at low T. Below 150 K, the already low mobility in the undoped devices decreased further. We found a reasonable fit with an activated mobility as used by Davis and Mott,21 (μ ∼ exp(−Ea/kT)), where Ea ≈ 10 meV. In the doped samples, the source−drain measurements became increasingly nonlinear below 150 K. We speculate that at low temperature the transport becomes dominated by tunneling through the thin WZ barriers. At 4.2 K, we observed signs of Coloumb blockade, similar to InAs NWs.16 Although the patterns were quite stable over time, they showed large variation between devices. This is not surprising, since the channels contained hundreds of coupled QWs with randomly varying thickness. In conclusion, we have shown that the ZB segments in polytypic InP NWs act as traps for carriers, and our calculations indicate that the length of the longest ZB segment determines the conductivity. We probed the DOS by measuring the activation energies as function of gate voltage and found reasonable agreement with calculations based on TEM data. In line with the trap model, the mobility is better described by models for noncrystalline materials than for bulk semiconductors. Our results demonstrate that the crystal structure dominates the electron transport in polytypic InP NWs even at room temperature.
Figure 3. (a) Mobility vs χH2S, calculated from the transconductance. The mobility in the highest doped sample, indicated with a red square, was calculated using the carrier concentration measured optically. (b) Source−drain current vs Vg at selected temperatures for an undoped NW-FET (the same device as in Figure 2). (c) Mobility and threshold voltage vs T, for the same device as in (b).
highly doped InP is associated with impurity scattering.32 However, the drop in mobility at low doping levels is unexpected since the impurity scattering should decrease as observed in bulk InP.32 The doped samples (χH2S = 1.5 × 10−7) showed a constant mobility at all temperatures. The undoped samples showed a constant mobility above 150 K, while below
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ASSOCIATED CONTENT S Supporting Information * Methods details, growth rate measurements, TEM statistics, electrical measurements, and conductance and transconductance. 154
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(23) Borgström, M. T.; Wallentin, J.; Heurlin, M.; Fält, S.; Wickert, P.; Leene, J.; Magnusson, M. H.; Deppert, K.; Samuelson, L. IEEE J. Sel. Top. Quantum Electron. 2011, 17 (4), 1050−1061. (24) Wallentin, J.; Mergenthaler, K.; Ek, M.; Wallenberg, L. R.; Samuelson, L.; Deppert, K.; Pistol, M. E.; Borgström, M. T. Nano Lett. 2011, 11 (6), 2286−2290. (25) Khanal, D. R.; Wu, J. Nano Lett. 2007, 7 (9), 2778−2783. (26) Munch, S.; Reitzenstein, S.; Borgström, M.; Thelander, C.; Samuelson, L.; Worschech, L.; Forchel, A. Nanotechnology 2010, 21 (10), 105711. (27) Bugajski, M.; Lewandowski, W. J. Appl. Phys. 1985, 57 (2), 521− 530. (28) Hessman, D.; Persson, J.; Pistol, M. E.; Pryor, C.; Samuelson, L. Phys. Rev. B 2001, 64 (23), 233308. (29) Ramvall, P.; Carlsson, N.; Omling, P.; Samuelson, L.; Seifert, W.; Stolze, M.; Wang, Q. Appl. Phys. Lett. 1996, 68 (8), 1111−1113. (30) Seoane, N.; Martinez, A.; Brown, A. R.; Barker, J. R.; Asenov, A. IEEE Trans. Electron Devices 2009, 56 (7), 1388−1395. (31) Knoch, J.; Riess, W.; Appenzeller, J. IEEE Electron. Device Lett. 2008, 29 (4), 372−374. (32) Anderson, D. A.; Apsley, N.; Davies, P.; Giles, P. L. J. Appl. Phys. 1985, 58 (8), 3059−3067. (33) Stiles, M. D.; Hamann, D. R. Phys. Rev. B 1990, 41 (8), 5280. (34) Chen, H. H.; Tseng, S. H.; Gong, J. Solid-State Electron. 1998, 42 (10), 1799−1805.
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]. ACKNOWLEDGMENTS We thank Claes Thelander, Kristian Storm, Dan Hessman and Andreas Wacker for fruitful discussions. This work was performed within the Nanometer Structure Consortium at Lund University (nmC@LU) and was supported by the Swedish Research Council, by the Swedish Foundation for Strategic Research, and by the EU program AMON-RA (214814). This report is based on a project which was funded by E.ON AG as part of the E.ON International Research Initiative.
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