Letter pubs.acs.org/NanoLett
Understanding the Impact of Schottky Barriers on the Performance of Narrow Bandgap Nanowire Field Effect Transistors Yanjie Zhao,† Drew Candebat,‡,§ Collin Delker,‡,§ Yunlong Zi,† David Janes,‡,§ Joerg Appenzeller,‡,§ and Chen Yang*,†,∥ †
Department of Physics, Purdue University, West Lafayette, Indiana 47907, United States School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States § Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States ∥ Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States ‡
ABSTRACT: Semiconductor nanowires have been explored as alternative electronic materials for high performance device applications exhibiting low power consumption specs. Electrical transport in III−V nanowire (NW) field-effect transistors (FETs) is frequently governed by Schottky barriers between the source/ drain and the NW channel. Consequently the device performance is greatly impacted by the contacts. Here we present a simple model that explains how ambipolar device characteristics of NW-FETs and in particular the achievable on/ off current ratio can be analyzed to gain a detailed idea of (a) the bandgap of the synthesized NWs and (b) the potential performance of various NW materials. In particular, we compare the model with our own transport measurements on InSb and InAs NW-FETs as well as results published by other groups. The analysis confirms excellent agreement with the predictions of the model, highlighting the potential of our approach to understand novel NW based materials and devices and to bridge material development and device applications. KEYWORDS: Nanowire, III−V, InSb, InAs, narrow bandgap, field-effect transistor, ambipolar, on/off-current ratio, Schottky caling Si based metal−oxide−semiconductor field-effect transistors (MOSFETs) while improving their performance has become increasingly difficult. The search for alternative electronic materials and optimized device structures for future device applications with both higher performance and lower power consumption has attracted the interest of researchers from various disciplines. Semiconductor nanowires (NWs), one of the candidates considered in this context, enable gate-allaround device geometries and offer strong charge confinement. Both aspects help to achieve better electrostatic control and thus allow for aggressive channel length scaling.1 A substantial amount of research has focused on III−V NWs as III−V materials exhibit higher mobilities when compared to Si.2 Yet in comparison with Si and Ge NWs,3 growth of III−V compound NWs with correct stereochemistry is more challenging.4 Consequently, careful characterization, particularly electrical characterization, of the property of the NWs is essential for successful material development. Often the carrier mobility is obtained from NW electrical characterization and considered as a key parameter for benchmarking. Mobility values extracted from NW-FET measurements using the conventional MOSFET model are often found to be orders of magnitudes lower than the bulk values. Several factors are responsible for this. For example, for sufficiently small wire diameters, transport cannot be described by classical equations applied to conventional MOSFETs, and
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© 2012 American Chemical Society
quantum transport needs to be explicitly considered.5 Moreover, contact effects, which can be more pronounced in NWFETs compared to conventional MOSFETs, cannot be easily disentangled from the channel contributions.6 Additionally, scattering events, which determine the mobility, are more complicated. Surface roughness effects amplified by the ultrathin body of the NW can limit the extracted mobility in nonencapsulated device structures.7 Finally, the more pronounced quantum capacitance1 complicates determination of the actual total gate capacitancea key input parameter for the mobility extractionthus affecting the accuracy of the extracted mobility values. Therefore we submit that determining the mobility without addressing the above factors is often not a robust method and the extracted mobility value can be misleading if used to quantitatively determine the quality of NWs synthesized. In this work we propose a simple yet reliable model that focuses on the off-state of a three-terminal device structure to understand the transport in NW-FETs employing a back-gate or overlapping top-gate and metal source/drain (S/D) contacts with Schottky barriers.8 The model establishes a simple relation between the on/off-current ratio of a NW-FET and the Received: July 19, 2012 Revised: September 4, 2012 Published: September 5, 2012 5331
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energy spacing between one-dimensional (1D) subbands resulting from charge confinement due to the small diameter of the wires is substantially larger than kBT, and therefore transport takes place only in the first subband. Under equilibrium conditions, electrons (holes) populate states above the conduction band edge Ec (below the valence band edge Ev) in the channel according to the Fermi distributions in source and drain (as shown schematically in Figure 1a).5 Four different current components contribute to the total current. Specifically, I1 and I2 are electron currents flowing into the conduction band from the source and drain, respectively; I3 and I4 are hole currents flowing into the valence band from the drain and source, respectively. The total current is the sum of these four current components Id = ∑Ii. The calculated Id versus Vgs for different channel materials with various bandgaps is shown in Figure 1b. The ambipolar behavior of the transfer characteristics is clearly visible. In the on-state of the n-branch (at positive gate voltages), the current is carried by electrons in the conduction band; that is, Id ≈ I1 + I2. As gate voltages become negative, the device is turned off since I1 and I2 decrease rapidly. Different from a conventional n-MOSFET where n+-Si is used as S/D and prevents hole injection from the drain into the channel, the lack of a bandgap in the S/D metal contacts allows for hole injection for decreased (more negative) gate voltages, thus I3 and I4 increase. When Efs and Efd are located approximately in the middle of the bandgap Eg, where I1 + I2 = I3 + I4, the device reaches the minimum off-current state. As the gate voltage becomes more negative, I3 and I4 dominate, and the device operates in its pbranch with holes flowing from drain to source through the valence band. The analysis assumes that the device operates at small Vds. Ion of the n-branch is defined as Id at the threshold voltage, which corresponds to the point where Ef coincides with Ec (or Ev for the p-branch). Note that the threshold voltage is the upper end of the exponential regime in the logarithmic transfer characteristics. Ioff denotes the current at minimum off-state as described above. In this case Ion and Ioff can be calculated from the energy integral of the density of states, Fermi velocity, and Fermi distribution in source and drain5 to be:
bandgap of the NW material and reveals the physics of the ambipolar behavior of transfer characteristics for NW-FETs, especially for narrow bandgap III−V materials. The impact of the Schottky barrier at the metal S/D contacts on the ambipolar behavior and on/off-current ratio is included in the simulation explicitly. Tunneling through the Schottky barriers plays a critical role for the device performance observed. Three special scenarios of Fermi level line-ups are discussed, representing cases without significant Schottky barriers and with Schottky barriers for either a conduction band or a valence band. We have chosen InSb and InAs NW-FETs as test cases for our model because of the unique electrical properties of bulk InSb and InAs2 and the detailed NW growth processes developed by us and other groups.9−18 Notably, electrical characteristics reported for InSb NWs19−23 and InAs NWs24−26 are rather different in terms of their ambipolar behavior and on/off-current ratioseven if the same type of metal contact had been used. By using our model that includes the impact of Schottky barrier contacts, different transfer characteristics are explained. We find in particular that including the wire diameter and gate oxide thickness is key to properly describe the tunneling currents through the S/D Schottky barriers. With our approach it is possible to create a universal plot of on/offcurrent ratio versus bandgap that includes our results and values extracted from the literature, which highlights the excellent agreement between our simulation and experiments. Initially, we make the following assumptions for the derivation of the various current components I1 through I4 in Figure 1: (1) Transport in the wire is ballistic; (2) No Schottky barriers are present between metal S/D contacts and the NW channel, and the gate is in full control of the channel; (3) The
Ion ≈ I1 + I2 ≈
Ioff ≈ 2 ×
e2 Vds h
⎛ Eg ⎞ 2e 2 Vds exp⎜ − ⎟ h ⎝ 2kBT ⎠
(1)
(2)
where e is the charge of an electron, h is Planck constant, Eg is the bandgap, kB is Boltzmann constant, and T is the temperature. As device dimensions shrink, the conventional dependences of Id on channel width W, length L, mobility μ, gate voltage Vgs and drain voltage Vds become invalid, and Id needs to be derived from the respective quantum mechanical expressions. The channel width W translates into the number of 1D modes, and the channel length L and mobility μ become irrelevant since no scattering processes occur due to operation in the ballistic regime. Therefore Id of a device in the quantum transport regime only depends on the number of modes (that we assumed to be one in eq 1 and 2), the gate and drain voltages, and the bandgap. Note that the conductance obtained from eq 1 is different from the quantum conductance 2e2/h by a factor of 2 due to the fact that Ion had been defined here at
Figure 1. (a) Schematics of current flow in a NW-FET without Schottky barriers. Efs and Efd are the Fermi levels in the source and drain, respectively. The total current consists of four components: the electron currents I1 and I2 through the conduction band and the hole currents I3 and I4 through the valence band (Id = ∑Ii). The purple solid lines in the source and drain regions display the Fermi distribution of electrons at room temperature. (b) Calculated drain current Id as a function of Vgs for InSb, InAs, and GaSb NW-FETs at small Vds without the inclusion of Schottky barriers. 5332
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threshold voltage instead of the deep-on-state. The factor 2 in front of the right-hand side of eq 2 arises from the fact that both the conduction band and the valence band contribute equally to the total current at minimum Ioff. The factor 2 in the denominator of the exponential term can be attributed to the fact that Efs and Efd are around the middle of the bandgap. Equation 2 implies that, for an ideal NW device operating in the 1D ballistic regime at small Vds, the maximum resistance in the off-state is max R off ≈
⎛ Eg ⎞ h exp⎜ ⎟ 2 4e ⎝ 2kBT ⎠
(3)
Combining eqs 1 and 2, we can derive the on/off-current ratio as: Ion 1 ⎛ Eg ⎞ ≈ exp⎜ ⎟ Ioff 4 ⎝ 2kBT ⎠
(for small Vds)
(4)
While one might think that eq 4 may hold true only under very particular conditions considering the assumptions 1 through 3 from above, in fact eq 4 is a very robust measure for metal contacted devices that DO NOT involve Schottky barriers. Diffusive or ballistic transport conditions in the channel play a minor role since Ion at threshold and Ioff even in the classical case do not depend on mobility. Moreover, the number of modesif transport is not just carried by one as assumed abovemodifies Ion and Ioff simultaneously leaving the Ion/Ioff ratio unaltered. It is for these reasons that in fact eq 4 captures quantitatively the situation in many experimental systems. The only device specific parameter that determines the on/off-current ratio when ignoring the impact of Schottky barriers is thus Eg. Therefore Eg can be directly extracted from the device characteristics if no Schottky barriers need to be considered, which is the case for ultimately scaled devices, as will be discussed below. A smaller Eg therefore leads to an exponentially increasing Ioff (eq 2) and consequentially an exponentially smaller on/off-ratio (eq 4). Next we will extend the model above to include the effect of Schottky barriers quantitatively. The presence of a Schottky barrier for either the conduction or valence band reduces the transmission probability into that band since carriers have to tunnel through an additional barrier. This reduces the current in the on-state and/or off-state. The analysis considers a case where the n-current is suppressed due to Schottky barriers in the conduction band but there is no Schottky barrier in the valence band. For small Vds, the center region of the channel can be considered as exhibiting flat-band conditions, and the potential profile at the Schottky barrier follows a dependence that is described by ϕ(x) = ϕg exp(−x/λ), where ϕg is related to the gate bias, as shown in Figure 2a. The width of the Schottky barrier is found as λ = ((εNW/εox)dNW·dox)1/2, assuming a fully depleted NW body.1 εNW and εox are dielectric constants of the NW body and gate dielectric, respectively. dNW and dox are the diameter of the NW and the gate oxide thickness, respectively. The transmission probability TWKB and the tunneling current ITunnel through the Schottky barrier are calculated using a semiclassical (WKB) approximation.27 Identical Schottky barriers at source and drain are assumed for small enough Vds, and the total transmission coefficient Ttotal = TWKB/(2−TWKB) assumes noncoherent transport. The results of the numerical calculation of ITunnel in comparison with the thermionic emission current ITE for a special case where ϕB =
Figure 2. (a) Band diagram showing the Schottky barrier which is partially blocking the n-current from turning on. The Schottky barrier can be replaced by an effective barrier height ESB. Note that ESB is a function of ϕB, ϕg, λ, and m*. (b) Calculated tunneling current density through the Schottky barrier in comparison with the thermionic emission current density over the barrier, for λ from 0 to 300 nm and ϕB = Eg = ϕg = 0.17 eV. (c) ESB (solid colored lines) as a function of ϕg assuming ϕB = Eg = 0.17 eV (corresponding to the scenario 3 in the later discussion). Dashed line denotes Eg − (ϕB − ϕg). The cross * = Eg − (ϕB − ϕg*) are the minimum off-current points where ESB states. The values of E*SB are indicated by dotted lines.
Eg = ϕg = 0.17 eV and m* = 0.014m0 (InSb) is shown in Figure 2b for various λ. A smaller λ results in an increase of ITunnel due to the shorter tunneling distance required. An effective barrier height ESB can be defined when ITE over this new barrier ESB is identical to the sum of ITunnel and ITE of the original Schottky barrier, as shown in Figure 2a. Note, ESB depends on ϕB, ϕg, λ, and m*. Figure 2c shows the calculated ESB-values as a function of ϕg for InSb with different λ values, assuming ϕB = Eg = 0.17 eV (the scenario 3 in later discussion). The minimum offcurrent state of a device may not occur anymore when Ef in the contact regions coincides with the middle of Eg. Instead, as indicated by the dotted lines in Figure 2c, ESB * = Eg − (ϕB − ϕg*) redefines the minimum off-current: Ioff ≈ 2 ×
⎛ 2E * ⎞ 2e 2 Vds exp⎜ − SB ⎟ h ⎝ 2kBT ⎠
(5)
Although ϕB may be predetermined by the difference between metal work function ϕM and electron affinity χ of the semiconductor, the effective Schottky barrier height E*SB is not. Here we discuss three special scenarios to explain the essential impact of the Schottky barriers on current transport: (1) Ef aligns with Ec, (2) Ef aligns with the middle of Eg, and (3) Ef aligns with Ev. While the actual alignment may differ from the above three scenarios, the discussion of these three cases elucidates how the symmetry of the ambipolar transfer characteristics gets affected for different contact conditions. Figure 3a and 3c show the schematics of transfer characteristics for scenarios 1 and 3, respectively. Due to the presence of Schottky barriers in case 1 for holes, the current in the p-branch 5333
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the bulk value of InSb. Those two distinct observations are indeed consistent with what the model predicts for InSb. A typical room-temperature output characteristic of the n-branch is shown in Figure 4b. The measured curves exhibit a smooth linear region and maximum on-current of a few μA. Unlike output characteristics from other larger bandgap materials, Id cannot be switched off due to the very small bandgap of InSb. Typical transfer and output characteristics of an InAs NWFET are shown in Figure 4c,d. The ambipolar behavior is observed as expected, yet with a more pronounced n-branch. Although the on-current level is similar to the InSb case, Ioff is much lowerin the 10−10 A rangein part due to the larger bandgap of InAs. The measured on/off-ratio ranges from 103 to 104 for most of the devices. Consistent with our expectation of the impact of Schottky barriers for asymmetric transfer characteristics, the experimental on/off-ratio is larger than 240 as predicted using the bulk bandgap value of InAs in eq 4. Fermi level pinning frequently found for InAs to be close or even in the conduction band29 is responsible for the reduced minimum off-current and increase in the inverse subthreshold slope of the p-branch, leading to a larger on/off-ratio and asymmetrical ambipolar behavior. Figure 5 shows our concluding plot for on/off-current ratio vs bandgap for both the ideal case where λ = 0 (solid line) and the extreme Schottky barrier case with a very large λ value (dashed line), assuming scenarios 1 and 3. As the NW-FET size scales down, a thinner diameter, thinner gate oxide and/or high-k dielectric leads to a reduction of λ. Thus Schottky barriers will have significantly less impact on the characteristics, and the transfer characteristics will convert into the ideal case without Schottky barriers, as indicated by the arrow. The same figure also shows extracted data from a number of other publications on InSb NWs: Nilsson et al.,19 Das et al.,20 Wang et al.,21 and Paul et al.22 The extracted on/off-ratio is around 6−11 for both Nilsson and Das casesquite similar to our results. Although we deduce λ-values ranging from 35 to 90 nm, the symmetrical ambipolar behavior suggest consistently scenario 2 (symmetric Schottky barriers) in those devices. Interestingly, Wang and Paul have reported an on/off-ratio of 250−500 and 106, respectively for InSb NWs, substantially larger than what is reported by us here and in refs 19 and 20. In both cases, a very pronounced n-branch is present, and the pbranch is almost entirely absent. In Wang’s case, Cr which has a relatively small work function (ϕM = 4.5 eV) was intentionally chosen as contact metal. According to our model this choice resulted in a scenario 1 where Ef aligns with Ec, and a Schottky barrier close to the value of Eg exists for hole injection into the valence band. In addition, the 150 nm SiO2 gate dielectric used leads to a large λ value of 180 nm (assuming as indicated before a fully depleted NW device). In this case our model predicts an on/off-ratio of around 200−300 consistent with the experimental results. In Paul’s InSb case, the particular device consisted of a 10 nm diameter NW with Ni contacts and a 300 nm SiO2 gate dielectric, which results in λ ∼ 110 nm. The measured 106 on/ off-ratio and the almost nonexistent p-branch from transfer characteristics can only be understood if two assumptions are made: (1) Due to the confinement effect of the ultrathin diameter NW, the bandgap of InSb has been increased to around 0.43 ± 0.03 eV. This seems to be reasonable according to other previous publications.32,33 (2) Ef of Ni contacts aligns with Ec due to Fermi level pinning. Similar to Wang’s case, the
Figure 3. Schematics of transfer characteristics for three scenarios of Schottky contacts: (a) Ef aligns with Ec; (b) Ef aligns with the middle of the bandgap; and (c) Ef aligns with Ev. The presence of Schottky barriers can result in an asymmetrical ambipolar behavior with an increased on/off-current ratio (a and c) or a fairly symmetrical ambipolar behavior with a slightly decreased on/off-current ratio (b). Arrows indicate how a reduction of λ will result in a decreasing impact of the Schottky barriers on the ambipolar behavior and the on/offratioconverting all transfer curves into the ideal case where λ = 0 (dotted line).
for negative gate voltages (p-current) is partially blocked by the barrier, resulting in a larger inverse subthreshold slope in that branch and consequently an asymmetrical ambipolar behavior.28 In addition, Ioff is reduced due to the Schottky barrier (eq 5), while Ion for electrons at positive gate voltages is not affected, thus a larger on/off-current ratio can be expected. Case 3 illustrates the reverse scenario with a Schottky barrier present for electron injection. In scenario 2 shown in Figure 3b, the magnitude of Ioff does not change, while both branches exhibit a larger inverse subthreshold slope. Thus a fairly symmetrical ambipolar behavior and a slightly smaller on/offcurrent ratio are obtained. For all three scenarios, a smaller λ will result in a smaller impact on the ambipolar behavior and the on/off-ratio, as illustrated by the arrows in Figure 3. Note that smaller λ-values are obtained when dox and/or dNW are scaled down. To experimentally verify our proposed model, InSb and InAs NWs were synthesized and fabricated into back-gated FETs. Both microscopy and spectroscopy studies suggest that high quality crystalline structures have been grown successfully with the correct composition.18 The transfer characteristics of an InSb NW-FET at room-temperature in vacuum are shown in Figure 4a. Two distinct features are observed. First, the curves exhibit a fairly symmetrical ambipolar behavior. Second, a small on/off-ratio together with a rather high Ioff at 10−7 A level is clearly visible. An on/off-ratio of approximate 6−10 at small Vds was observed for most of our InSb devices, and the extracted Eg-value of 0.16−0.19 eV using eq 4 is in good agreement with 5334
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Figure 4. Electrical characteristics of back-gated FETs using synthesized InSb NW (a, b) and InAs NW (c, d) at room-temperature. Inset of (a): optical microscopy image of NW-FETs with multiple channel lengths; scale bar: 2 μm. An almost symmetrical ambipolar behavior and an on/offcurrent ratio of around 8 were observed for InSb. An asymmetrical ambipolar behavior and an on/off-current ratio of around 3 × 103 were observed for InAs.
assumption number 2, Fermi level pinning of Ni on InSb, has not been reported so far. A possible alternative scenario involves that In2O3 is present in Paul’s casea byproduct of the InSb synthesis using CVD since similar transfer characteristics with on/off-ratios of 106 have been reported for NW device from this material.34 Besides InSb, on/off-current ratios were also extracted from other types of nanomaterials, including InAs NWs from Jiang et al.,24 single-walled carbon nanotubes (SWNTs) from Javey et al.30 and Ge/Si NWs from Xiang et al.,31 as shown in Figure 5. For InAs, the observed high on/off-ratio of 5 × 102 to 3 × 103 and a strong asymmetric ambipolar behavior in Jiang’s case are very similar to our results, suggesting scenario 1 as discussed above. Two examples that belong to the ultimately scaled case, that is, λ is approaching 0, are Javey’s SWNTs results and Xiang’s Ge NW device characteristics. In Javey’s case, SWNTs of diameter around 1.7 nm and bandgap of 0.5 eV were used as channel material with an 8 nm HfO2 gate dielectric. The large work function metal Pd was chosen for S/D contacts, leading to scenario 3, with λ between 3 and 5 nm. Thus almost completely transparent Schottky barriers lead to rather symmetrical ambipolar characteristics and a calculated on/off-ratio of 4 × 103, which is consistent with the measured 2 × 103 to 5 × 103. In Xiang’s case, the NW-FET consists of a 15 nm Ge NW as channel (with very thin Si passivation layer) and a fully overlapping top gate with a 4 nm HfO2 dielectric. This configuration leads to a λ of less than 7 nm; therefore a very symmetric ambipolar behavior and an on/off-ratio of 5 × 104 to 1.3 × 105 was observed (note the definition of Ion and Ioff here
Figure 5. On/off-current ratio vs bandgap for the ideal case without Schottky barrier or λ = 0 (solid line) and extreme Schottky barrier case (scenarios 1 and 3) where λ is very large (dashed line). The arrow indicates the trend of the on/off-ratio as a result of scaling down of device size. Colored diamonds with error bars present the extracted on/off-ratios from (a) InSb, d ∼ 80 nm, λ ∼ 80 nm, this work; (b) InSb, d ∼ 77 nm, λ ∼ 35 nm, Nilsson et al.;19 (c) InSb, d ∼ 100 nm, λ ∼ 90 nm, Das et al.;20 (d) InSb, d ∼ 50 nm, λ ∼ 180 nm, Wang et al.;21 (e) InSb, d ∼ 10 nm, λ ∼ 110 nm, Paul et al.;22 (f) InAs, d ∼ 20−25 nm, λ ∼ 70 nm, Jiang et al.;24 (g) InAs, d ∼ 30 nm, λ ∼ 50 nm, this work; (h) SWNT, Eg = 0.5 eV, λ ∼ 3−5 nm, Javey et al.30 and (i) Ge, d ∼ 15 nm, λ ∼ 7 nm, Xiang et al.,31 all at room temperature. Note: the bulk bandgaps are used for all NWs except the 10 nm InSb NW in (e) where Eg ≈ 0.43 ± 0.03 eV, and the 50 nm InSb in (d) where Eg ≈ 0.18 eV. The bandgap of SWNT in (h) is quoted from original literature.
large λ-value almost completely blocked the current contribution from the valence band; therefore an on/off-ratio of 106 and a nonexistent p-branch would be obtained. However 5335
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(8) Appenzeller, J.; Knoch, J.; Derycke, V.; Martel, R.; Wind, S.; Avouris, P. Phys. Rev. Lett. 2002, 89 (12), 126801. (9) Caroff, P.; Wagner, J. B.; Dick, K. A.; Nilsson, H. A.; Jeppsson, M.; Deppert, K.; Samuelson, L.; Wallenberg, L. R.; Wernersson, L.-E. Small 2008, 4 (7), 878−882. (10) Ercolani, D.; Rossi, F.; Li, A.; Roddaro, S.; Grillo, V.; Salviati, G.; Beltram, F.; Sorba, L. Nanotechnology 2009, 20 (50), 505605. (11) Vogel, A. T.; de Boor, J.; Wittemann, J. V.; Mensah, S. L.; Werner, P.; Schmidt, V. Cryst. Growth Des. 2011, 11 (5), 1896−1900. (12) Zhang, X. R.; Hao, Y. F.; Meng, G. W.; Zhang, L. D. J. Electrochem. Soc. 2005, 152 (10), C664−C668. (13) Khan, M. I.; Wang, X.; Bozhilov, K. N.; Ozkan, C. S. J. Nanomater. 2008, 698759. (14) Park, H. D.; Prokes, S. M.; Twigg, M. E.; Ding, Y.; Wang, Z. L. J. Cryst. Growth 2007, 304 (2), 399−401. (15) Yang, X.; Wang, G.; Slattery, P.; Zhang, J. Z.; Li, Y. Cryst. Growth Des. 2010, 10 (6), 2479−2482. (16) Vaddiraju, S.; Sunkara, M. K.; Chin, A. H.; Ning, C. Z.; Dholakia, G. R.; Meyyappan, M. J. Phys. Chem. C 2007, 111 (20), 7339−7347. (17) Caroff, P.; Messing, M. E.; Mattias Borg, B.; Dick, K. A.; Deppert, K.; Wernersson, L.-E. Nanotechnology 2009, 20 (49), 495606. (18) Zi, Y.; Zhao, Y.; Candebat, D.; Appenzeller, J.; Yang, C. ChemPhysChem 2012, 13 (10), 2585−2588. (19) Nilsson, H. A.; Caroff, P.; Thelander, C.; Lind, E.; Karlstrom, O.; Wernersson, L.-E. Appl. Phys. Lett. 2010, 96 (15), 153505. (20) Das, S. R.; Delker, C. J.; Zakharov, D.; Chen, Y. P.; Sands, T. D.; Janes, D. B. Appl. Phys. Lett. 2011, 98 (24), 243504. (21) Wang, Y.; Chi, J.; Banerjee, K.; Gruetzmacher, D.; Schaepers, T.; Lu, J. G. J. Mater. Chem. 2011, 21 (8), 2459−2462. (22) Paul, R. K.; Penchev, M.; Zhong, J.; Ozkan, M.; Ghazinejad, M.; Jing, X.; Yengel, E.; Ozkan, C. S. Mater. Chem. Phys. 2010, 121 (3), 397−401. (23) Candebat, D.; Zhao, Y.; Sandow, C.; Koshel, B.; Yang, C.; Appenzeller, J. In InSb nanowire field-effect transistors - Electrical characterization and material analysis; University Park, PA; Device Research Conference (DRC), June 22−24, 2009; pp 13−14. (24) Jiang, X. C.; Xiong, Q. H.; Nam, S.; Qian, F.; Li, Y.; Lieber, C. M. Nano Lett. 2007, 7 (10), 3214−3218. (25) Thelander, C.; Froberg, L. E.; Rehnstedt, C.; Samuelson, L.; Wemersson, L.-E. IEEE Electron Device Lett. 2008, 29 (3), 206−208. (26) Lind, E.; Persson, A. I.; Samuelson, L.; Wernersson, L.-E. Nano Lett. 2006, 6 (9), 1842−1846. (27) Sakurai, J. J.; Tuan, S. F. Modern Quantum Mechanics; AddisonWesley Publishing Company: Upper Saddle River, NJ, 1994. (28) Appenzeller, J.; Radosavljevic, M.; Knoch, J.; Avouris, P. Phys. Rev. Lett. 2004, 92 (4), 048301. (29) Mead, C. A.; Spitzer, W. G. Phys. Rev. Lett. 1963, 10 (11), 471− 472. (30) Javey, A.; Guo, J.; Farmer, D. B.; Wang, Q.; Yenilmez, E.; Gordon, R. G.; Lundstrom, M.; Dai, H. J. Nano Lett. 2004, 4 (7), 1319−1322. (31) Xiang, J.; Lu, W.; Hu, Y. J.; Wu, Y.; Yan, H.; Lieber, C. M. Nature 2006, 441 (7092), 489−493. (32) Khayer, M. A.; Lake, R. K. IEEE Trans. Electron Devices 2008, 55 (11), 2939−2945. (33) Chen, H.; Sun, X.; Lai, K. W. C.; Meyyappan, M.; Xi, N. In Infrared Detection Using an InSb Nanowire; June 2−5, 2009, Traverse City, MI, IEEE Nanotechnology Materials and Devices Conference (NMDC): New York, 2009; pp 212−216. (34) Ju, S.; Ishikawa, F.; Chen, P.; Chang, H.-K.; Zhou, C.; Ha, Y.-g.; Liu, J.; Facchetti, A.; Marks, T. J.; Janes, D. B. Appl. Phys. Lett. 2008, 92 (22), 222105.
is different from that in Xiang’s paper). In both cases, excellent agreement is observed between experimental results and the predictions from eq 4. Collectively the above examples imply the following: (1) A high on/off-current ratio obtained from small bandgap materials such as InSb by using a thick gate dielectric is insufficient to claim its suitability for future device applications since the Schottky barrier contribution, rather than an intrinsic channel property, is responsible for this effect. (2) Scaling device dimensions will always lead to a decreasing λ; consequently the on/off-ratio will ultimately only depend on the bandgap of the channel, and symmetrical ambipolar characteristics will be obtained. (3) For NWs with sufficiently small diameters, the on/off-ratio will increase as a result of the increased bandgap due to confinement effects. This hints toward using narrow bandgap materials for device applications by choosing a proper wire diameter. In conclusion, we presented a simple yet powerful model that captures the current levels in the off-state of a narrow bandgap NW (or tube) that is back-gated or utilizes an overlapping topgate and metal S/D contacts. In our model, the often observed ambipolar behavior is explained as a consequence of injection of electrons and holes into the conduction and valence band, respectively. The on/off-current ratio is shown to be mainly related to the bandgap of the channel material, since the bandgap determines the minimum off-current of the device. Schottky barriers were found to be the cause for different reported on/off-ratios with asymmetrical ambipolar characteristics. By assuming three particular scenarios of Fermi level lineup relative to the conduction and valence band, the impact of Schottky barriers on the on/off-current ratio and the symmetry of the ambipolar behavior has been evaluated through simulation. Comparing experimental results on InSb, InAs, and Ge NWs as well as carbon nanotubes with our calculations shows an excellent agreement and provides performance information for ultimately scaled devices from materials with different bandgaps.
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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 This work is supported by National Science Foundation DMR Grant No. 0847523. REFERENCES
(1) Appenzeller, J.; Knoch, J.; Bjork, M. I.; Riel, H.; Schmid, H.; Riess, W. IEEE Trans. Electron Devices 2008, 55 (11), 2827−2845. (2) Schroder, D. K. Semiconductor Material and Device Characterization; Wiley-IEEE Press: New York, 2006. (3) Lieber, C. M.; Wang, Z. L. MRS Bull. 2007, 32 (2), 99−108. (4) Dick, K. A. Prog. Cryst. Growth Charact. Mater. 2008, 54 (3−4), 138−173. (5) Datta, S. Quantum transport: atom to transistor; Cambridge University Press: New York, 2005. (6) Smith, J. T.; Zhao, Y.; Yang, C.; Appenzeller, J. In Effects of nanoscale contacts to silicon nanowires on contact resistance: Characterization and Modeling; South Bend, IN; Device Research Conference (DRC), June 21−23, 2010; pp 139−140. (7) Ford, A. C.; Ho, J. C.; Chueh, Y.-L.; Tseng, Y.-C.; Fan, Z.; Guo, J.; Bokor, J.; Javey, A. Nano Lett. 2009, 9 (1), 360−365. 5336
dx.doi.org/10.1021/nl302684s | Nano Lett. 2012, 12, 5331−5336
