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Conduction band offset and polarization effects in InAs nanowire polytype junctions I-Ju Chen, Sebastian Lehmann, Malin Nilsson, Pyry Kivisaari, Heiner Linke, Kimberly A. Dick, and Claes Thelander Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b04211 • Publication Date (Web): 21 Dec 2016 Downloaded from http://pubs.acs.org on December 27, 2016

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Conduction band offset and polarization effects in InAs nanowire polytype junctions I-Ju Chen†*, Sebastian Lehmann†, Malin Nilsson†, Pyry Kivisaari†, Heiner Linke†, Kimberly Dick†,‡, and Claes Thelander†* †Solid State Physics and NanoLund, Lund University, Box 118, S-221 00 Lund, Sweden ‡Center for Analysis and Synthesis, Lund University, Box 124, S-221 00 Lund, Sweden Key Words: Nanowire, InAs, crystal structure, zinc blende, wurtzite, transport ABSTRACT Although zinc-blende (ZB) and wurtzite (WZ) structures differ only in the atomic stacking sequence, mixing of crystal phases can strongly affect the electronic properties, a problem particularly common to bottom up-grown nanostructures. A lack of understanding of the nature of electronic transport at crystal phase junctions thus severely limits our ability to develop functional nanowire devices. In this work we investigated electron transport in InAs nanowires with designed mixing of crystal structures, ZB/WZ/ZB, by temperature-dependent electrical measurements. The WZ inclusion gives rise to an energy barrier in the conduction band. Interpreting the experimental result in terms of thermionic emission and using a drift-diffusion model, we extracted values for the WZ/ZB band offset, 135 ±10 meV, and interface sheet polarization charge density on the order of 10-3 C/m2. The extracted polarization charge density is 1-2 orders of magnitude smaller than previous experimental results, but in good agreement with first principle calculation of spontaneous polarization in WZ InAs. When the WZ length is reduced below 20 nm, an effective barrier lowering is observed, indicating the increasing importance of tunneling transport. Finally, we found that band-bending at ZB/WZ junctions can lead to bound electron states within an enclosed WZ segment of sufficient length, 1

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evidenced by our observation of Coulomb blockade at low temperature. These findings provide critical input for modeling and designing the electronic properties of novel functional devices, such as nanowire transistors, where crystal polytypes are commonly found. TEXT In the search of materials for future high-speed and low-power transistors, much attention has been given to the InGaAs compounds for their high mobility and injection velocity.1-3 Nanowires (NWs) of such materials, obtained by bottom-up growth, are of particular interest owing to the prospects of silicon integration4 and scaling to small channel dimensions.5 However, a well-known problem associated with such nanowires, in particular with those grown using Au-free methods on Si, is that they generally suffer from a high density of stacking defects and polytypism.6-8 In bulk the stable crystal phase of InAs is the zinc blende (ZB), whereas in nanowires the wurtzite (WZ) phase can be more favorable, depending strongly on growth conditions, nanowire diameter and presence of impurities.9 Theoretical calculations predict that WZ has a larger band gap than ZB with an up to 126 meV positive conduction band offset.10,11 However, owing to a complex combination of crystal-, interface- and surface-related effects, there is not yet a clear physical description on how polytypism affects electron transport in such materials. Understanding the WZ-ZB junction properties would be of strong relevance not only for transistor research, but also for the multitude of quantum transport studies employing InAs nanowires on topics such as conductance quantization,12 superconducting weak links,13,14 spin manipulation15and quantum computing16. Electrical characterizations of InAs NWs with crystal phase heterostructures, either having random mixtures of crystal phases17,18 or prepared with clean crystal phases19,20, have indeed revealed that WZ segments introduce significant barriers in the conduction band. A substantially higher resistivity was found for NWs with polytype mixtures compared to either pure ZB or WZ NWs.17 Moreover, the 2


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barrier properties of WZ were further demonstrated in studies on crystal-phase quantum dots, attained by growth of pairs of thin and closely spaced WZ segments in InAs ZB NWs.19,20 A reliable extraction of the crystal phase-related band offset from these electrical measurements is however made more complicated by a significant difference in the carrier concentration between ZB and WZ InAs. As ZB and WZ are grown at different III/V ratio and/or different temperature, background carbon dopant incorporation can occur differently.21 Also, InAs with a native surface oxide has a high concentration of donor-type surface states, which depends strongly on the oxide species22 and nature of the crystal facets.23 A further complication is that the lower symmetry of the WZ crystal phase is expected to give rise to a spontaneous polarization field24 and associated polarization charges at the interface between WZ and ZB. To account for the stronger pinch-off characteristic observed in polytypic WZ/ZB InAs NWs compared to pure ZB NWs, a polarization charge density ≥ 10-2 C/m2, on the same order as in WZ IIInitrides, was proposed by Dayeh et al..18 However, STM studies along WZ/ZB interfaces of cleaned InAs nanowires showed no evidence of polarization charge.23 Off-axis electron holography experiment25 and density functional theory (DFT) calculations24 also suggest much smaller spontaneous polarization in WZ InAs, one and two orders of magnitude lower than in Ref. 18, respectively. The aim of this study is to understand how each of these effects contributes to the conduction band energy profile in InAs NWs and impact the electrical properties. For this purpose, precisely controlled ZB/WZ/ZB heterostructures with five different WZ segment lengths in otherwise identical geometries are grown by metal organic vapor phase epitaxy (MOVPE), where structural changes are induced by changing the group III/V precursor flow ratio26 during growth. Temperature dependent electrical characterization is used to extract electron activation energy barriers for different WZ lengths, gate and bias voltages. Comparisons with numerical simulations allow us to distinguish the respective 3


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effects of carrier concentration, conduction band discontinuity, and polarization charges on the conduction band energy barrier profile. From fitting the data we extract values for the ZB-WZ band offset and polarization charge density, and find that they are consistent with recent theoretical predictions on relatively low spontaneous polarization in WZ InAs. We also observe a clear transition in the dominant transport mechanism from thermionic emission to tunneling at reduced WZ barrier lengths. Finally, in accordance with simulated band diagrams, Coulomb oscillations observed in low temperature electrical measurements reveal that a quantum dot can form in a single WZ segment of sufficient length as a result of interface band-bending. The NWs were grown by low pressure MOVPE on (111)B InAs substrates using Au aerosols with a nominal diameter of 40 nm as seed particles following the vapor liquid solid (VLS) approach27. Control of the InAs crystal phase was here attained by changing the effective group V hydride flow as reported in Ref. 20. For the present study the following conditions were used. An AIXTRON 3x2´´ close coupled showerhead system (CCS) was operated at a pressure of 100 mbar and a total carrier gas flow of 8 slm. After a 10 min annealing step in an AsH3/H2 ambience at a set temperature of 550°C with an AsH3 molar fraction of χ = 2.5x10-3 the temperature was set to 470°C for the NW growth. At a trimethylidium (TMIn) molar fraction of χ = 1.8x10-6 a stem was grown for 240 s with an AsH3 molar fraction of χ = 1.3x10-4 before the actual ZB/WZ/ZB segmented structure was grown with AsH3 molar fractions of χ = 4.5x10-5 and χ = 1.6x10-2 for WZ [0 0 0 1] and ZB [1 1 1] growth, respectively. A total of five samples studied had a step-wise increase in growth time for the enclosed WZ segment of 10, 20, 40, 80, and 160 s, whereas all other segments had a constant growth time of 600 s. The growth was terminated by turning off the TMIn supply and cooling under the same AsH3/H2 ambience as used for the annealing down to 300°C. From transmission electron microscopy (TEM) (Fig. 1a) and electron channeling contrast imaging (ECCI)28,29 using scanning electron microscopy (SEM) (Fig. 1b), the lengths of WZ segments, LWZ, are estimated to be 8 ± 2 nm, 19 ± 3 nm, 45 ± 4 nm, 82 ± 17, and 210 ± 25 for 10, 20, 40, 80, and 160 s growth time, respectively 4


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(imaging details and LWZ statistics are presented in supporting information.) The diameters of the ZB segments were found to be 60 ± 5 nm, which are 0 - 5 % (< 3 nm) wider than corresponding WZ segments. The use of ECCI in SEM to resolve ZB and WZ crystal phases in InAs NWs is discussed more extensively in Ref. 20. The electrical characterization is based on back-gate NW field-effect transistors (Fig. 1c). NWs with different LWZ were deposited onto SiO2/Si samples, where the degenerately n-doped (P) Si substrates act as back-gate under a 200 nm SiO2 insulating layer. Suitable NWs were identified by low-resolution SEM and selected for contact processing. The samples were spin coated with resist (polymethyl methacrylate, PMMA) and electron beam lithography was used to create openings for the NW contacts. The InAs NW contact area was etched in a mixture of (NH4)2Sx and H2O 1:20 for 1 minute at 40oC before a film of 25 nm Ni and 75 nm Au was evaporated onto the sample, which was then lifted off in acetone.

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Figure 1. (a) High resolution TEM image of the position in the InAs NW with the ZB/WZ/ZB

crystal structure sequence, with LWZ ~ 19 nm (b) SEM image of the device with LWZ = 82 nm (bottom). Crystal phase segments resolved by ECCI in the SEM (upper). (c) Schematics of the back-gate field-effect transistor of an InAs NW with ZB/WZ/ZB heterostructure. The electrical characterization was carried out using a variable temperature probe station, in specific ranges of back-gate voltages, -4.25 V < VG < 1 V, bias voltages -100 mV < Vbias < 100 mV, and temperatures 110 K < T < 240 K. Temperature dependent I-Vbias curves (Fig. 2a) were measured as a function of VG. Given the high mobility in InAs, transport of electrons over the heterojunction barrier, which is dominated by thermionic emission for most of the LWZ and barrier range studied here, is the rate-limiting process. For pure ZB devices, n-type carriers are not depleted even with VG = -20 V (supporting information), thus eliminating any important contribution from metal-semiconductor Schottky barriers. Therefore, the current is expected to exhibit a temperature dependence according to the thermionic emission equation30,

=

(

)

,

Eq. 1

with current density J, Richardson’s constant A, elementary charge q, Boltzmann constant kB, and temperature T, for bias voltages greater than kBT/q. The activation energy qΦB is defined as the difference between the conduction band edge at the top of the WZ barrier and the Fermi level Ef (Fig. 2b), and its value at different VG and Vbias can be obtained by fitting the temperature-current relation (Fig. 2c). Eq.1 assumes a Boltzmann distribution, and is therefore only valid for non-degenerate barriers, i.e. when qΦB >>kBT.31 For qΦB > kBT/q. We observe an increase in qΦB with WZ segment length, LWZ, even for LWZ > 82 nm. Whereas tunneling transport can lower the effective energy barrier for thin barriers, it cannot explain the increase of qΦB for longer LWZ. Instead, the length dependence suggests that the relatively lower carrier concentration observed in WZ segments plays an important role in forming the potential barriers. Electrical characterization of single-phase NW segments from the same growth batch shows that the carrier concentration in WZ is an order of magnitude lower than in ZB (supporting information). In an n-n+ junction, the builtin potential can be simply obtained from the carrier concentrations Nn and Nn+ in the n and n+ side, which can be approximated by kBT

for non-degenerate doping. However, for a short WZ

segment, carrier diffusion at the ZB/WZ interface can drastically lower the barrier energy. By solving Poisson’s equation with a surface donor state density in WZ nsurface,WZ an order smaller than in ZB

nsurface,ZB, the simulation results reproduce the increasing trend of qΦB with increasing LWZ (Fig. 3c, d). As there is no intentional doping in the NWs under study, the carrier concentration is attributed to surface states and carbon incorporation, which would be situated at the surface of the NWs. The band diagram (Fig. 3d) reveals that under the assumption of continuous conduction band edge, carrier diffusion at ZB/WZ interface prevents shorter WZ segments from forming a significant potential barrier. The barrier height is therefore sensitive to the WZ segment length and to the relative carrier concentrations across the interface, and thus also to VG.

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Figure 3. (a) Activation energy barrier qΦB at bias Vbias = 0 V extrapolated from qVbias >> kBT. (b) Schematics of band diagrams resulting from the individual effect of I. carrier concentration difference, II. band offset, and III. interfacial polarization charge between ZB and WZ. (c, d) VG dependent qΦB and conduction band minimum simulated with a surface donor state concentration in WZ an order of magnitude lower than in ZB. (e, f) VG dependent qΦ B and conduction band minimum simulated with nsurface,ZB = 1.2x1012 cm-2, nsurface,WZ = 0.9x1011 cm-2, and 135 meV band offset. (g) A filled contour plot of the simulated electrical potential distribution at the cross-section in the middle of a 82 nm WZ barrier at VG = -2V. However, in the experiments a pronounced activation energy was observed even for WZ segments as short as 19 nm (Fig. 3a), which cannot be explained by a carrier concentration difference only. A positive offset of the conduction band minima of InAs WZ relative to ZB was then taken into consideration. Here, parameters including the WZ band gap, conduction band offset, surface donor state density in ZB nsurface,ZB and WZ nsurface,WZ were varied to fit qΦB measured for LWZ = 45, 82, and 9


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210 nm. With the onset of carrier inversion in part of the NW, the measured qΦB starts to saturate at more negative VG, with a maximum value equal to a fraction of the WZ band gap. Taking into consideration a spread in NW diameter and LWZ, a good agreement between the numerical calculation and experimentally measured qΦB is found (Fig. 3e), with a WZ band gap of 345 ± 15 meV , band offset of 135 ± 10 meV, nsurface,ZB = 1.2 ± 0.4 x1012 cm-2, and nsurface,WZ = 0.9 ± 0.1 x1011 cm-2. We find that effects of the small diameter differences between ZB and WZ are negligible relative to the spread in these values. As indicated by the band diagram (Fig. 3f), the band offset effectively reduces the carrier diffusion at the ZB/WZ interface and contributed to the buildup of energy barriers. The effect on qΦB is particularly evident for shorter LWZ and at lower VG. The conduction band edge offset found here is close to that obtained by DFT calculations, 86 - 126 meV.10,11,23 However, in scanning tunneling spectroscopy (STS) measurements carried out on oxide-free ZB and WZ surfaces no offset was observed, attributed to n-type defects.23 The theoretical calculations10 and STS measurements23 also indicate a 36 and 70 meV larger band gap for WZ compared to ZB. The WZ band gap extracted here from the maximum qΦB represent an average over the experimental temperature range, 110240K, and is however smaller than the band gap of ZB InAs measured by photoluminescence32, 397365 meV. It is worth noting that in this study we attribute the temperature dependent current solely to conduction band electron transport. However, the model does not take into account that at the onset of carrier inversion in WZ, tunneling into the valence band is possible, leading to an underestimation of the activation energy qΦB for conduction band electron transport and thus also the band gap. Due to the back-gate geometry of the three-terminal device, the potential distribution inside the NW is not radially symmetric under the influence of VG. When a negative VG is applied, the surface of the NW, especially the side of the NW facing the back-gate, is expected to be much more strongly depleted than the rest (Fig. 3g). As a result, a region in the upper half of the NW will have the

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strongest contribution to the overall conduction. Therefore, in this study, we always used modeled band diagrams and barrier heights near this region when comparing with the experimental results. In the I-Vbias characterization, partial current rectification as shown in Fig. 2a is generally observed. It indicates asymmetry in the energy barrier, which we attribute to polarization effect. In WZ crystals, atomic bonds are commonly distorted from the symmetric tetrahedron.24,33 Therefore, in III-V hexagonal polytypes the center of positive and negative charge do not overlap and results in spontaneous polarization Psp which does not exist in ZB.24,33 Moreover, in heterostructures, strain at the junction can also give rise to piezoelectric polarizations Ppz. The polarization field is related to the polarization charge density σ by δ" = δ#"$% & "%' ( = )*,

Eq.2

An abrupt change in the polarization field at a junction leads to a sheet of polarization charges σ (Fig. 4a). At the two ZB-WZ interfaces, polarization charges of opposite signs form and result in accumulation and depletion of electrons (Fig. 4b), respectively. They create an asymmetric electric potential, which is distinct from the symmetric band diagram induced by band offset and carrier concentration difference. Due to the asymmetric potential, applying a negative (positive) bias near the accumulation (depletion) interface will decrease the electric field and reduce the energy barrier (Fig. 4b). A corresponding reverse bias will increase the field and therefore have a weaker influence on the barrier value.

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Figure 4. (a) Schematics of the device structure and sign of the polarization charge σ and polarization field in WZ PWZ. (b) Band diagrams modeled with inclusion of interfacial polarization charges, at VG = -2 V and Vbias = 0, 100, and -100 mV. (c) Activation energy barrier (qΦ B) measured at Vbias = 100 (blue triangle) and -100 mV (red rectangle) as a function of qΦB extrapolated to zero bias. The best fit (dashed line) is obtained by using a sheet polarization charge density |σ| = 0.33±0.03x10-3 C/m2 at the ZB/WZ interface for this specific device (LWZ = 45 nm). The asymmetry is also evident in the activation energy barrier measured at different bias polarity (Fig. 4c). Simulation of qΦB at Vbias = 100 and -100 mV, obtained by solving Poisson’s and driftdiffusion equations with thermionic emission boundary conditions at ZB/WZ interfaces, enables us to extract a sheet charge density |σ| or |δP| from 0.33 to 0.80 x10-3 C/m2 for five devices. The bias polarity dependence of current and qΦB suggest positive (negative) polarization charge at the top (bottom) ZB/WZ interface (Fig. 4a), causing accumulation (depletion) of electrons. However, the asymmetry is much less pronounced at low carrier concentrations (more negative VG), for which the middle of the WZ segment dominates the barrier formation. We would like to point out that the range of LWZ studied here is on the order of electron mean free paths in InAs NW, therefore the use of drift-diffusion model in the transport simulation will likely lead to overestimation of voltage drop within the barrier and underestimation of voltage drop at the ZB/WZ interface at which the electrons are injected. We also note that due to asymmetric biasing relative to the gate potential, the rectification of current and asymmetry in activation energies can be mildly reduced as the case shown in Fig. 4 or enhanced (supporting information) depending on the choice of biasing and grounding contact. Still, the asymmetry we attribute to a polarization charge can be observed regardless of the choice of biasing contact (supporting information). 12


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Due to the absence of spontaneous polarization in ZB crystals in combination with the small lattice parameter deviation between ZB and WZ34, and thus small piezoelectric field (supporting information), the presence of σ and δP can be explained by spontaneous polarization Psp and/or piezoelectric polarization Ppz induced by external strain. If we attribute the extracted δP solely to Psp in WZ, its absolute value is indeed close to the spontaneous polarization of bulk WZ InAs calculated from first principle24, 10-3 C/m2, and is 1 - 2 orders of magnitude smaller than found in multiple previous experimental studies18,25. However, it is of opposite sign to the calculated value. First principle calculation discloses that the spontaneous polarization of WZ III-V compound is generally governed by the internal cell parameters, especially u which characterizes the length uc of the bond connecting anions and cations parallel to the c-axis for lattice constant c. u in non-nitride III-V WZ is found to be smaller than the ideal tetrahedral value 3/8,24 observed by room temperature X-ray diffraction (XRD) experiments in the case of WZ InAs34. A roughly linear trend between u and spontaneous polarization is found from the calculations, with positive spontaneous polarization Psp for u < 3/8 and negative Psp for u > 3/8. However, the spontaneous polarization value depends on the exact atomic bonds and charge distribution. For WZ binary compounds with small internal parameter deviation from the ideal tetrahedron (u - 3/8), determination of the sign of polarization charge is more difficult24 and a deviation from the linear trend is observed in the theoretical calculation result24,35. Our finding can indicate that for the case of weak spontaneous polarization and small deviation from cubic symmetry, the simple relation between the sign of (u - 3/8) and spontaneous polarization may not hold. On the other hand, if the extracted δP were a result of external strain, it indicates the presence of a strain field on the order of 1 - 3%. The extracted polarization charge is further included in the simulation of the VG dependent qΦB (Fig. 5). It raises the activation energy, which is especially obvious for shorter LWZ. Comparing the simulation and experimental data up-close, a good agreement is found for LWZ = 45, 82, and 210 nm, regardless of the inclusion of polarization charge. However, for LWZ = 8 and 19 nm (at VG close to 0 V) 13


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experimentally measured qΦB is noticeably lower than the calculation. We attribute this discrepancy to tunneling transport that becomes increasingly significant compared to thermionic emission for LWZ + 19 nm at the given measurement temperature, 110 -240 K. For LWZ as short as 8 nm, despite the non-negligible qΦB calculated with parameters inheriting from fitting long LWZ data, no energy barrier is detected, suggesting that electron tunneling is the main contribution to the current.

Figure 5. qΦ B extracted from the experiment (circle) and numerical simulation with |σ| = 0 (solid line) and 0.7x10-3 C/m2 (dashed line) for (a) LWZ = 210, 82, and 45 nm, and (b) 19 and 8 nm. The simulated band diagram in Fig. 3f indicates that due to the crystal phase band offset it is possible to form a shallow quantum dot within a single WZ segment for sufficiently high carrier concentration in WZ. The effect is also illustrated in Fig. 3b when only conduction band offset is considered. For this reason, low temperature (roughly 10 K) electrical characterization was performed on NWs with LWZ = 45, 82, and 210 nm. Indeed we observed that devices with LWZ = 82 and 210 nm frequently showed Coulomb oscillations (Fig. 6 a, b) and Coulomb blockade diamond patterns (Fig. 6 c, d) before pinchoff, whereas the LWZ = 45 nm devices showed no such periodic conductance oscillations (supporting information). These results are consistent with the simulated band diagram wherein a more pronounced potential well is formed for longer WZ segments, having bound states for a specific 14


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Fermi level energy window. The amplitudes of the Coulomb oscillations depend strongly on VG, as is expected for shallow barriers. Gate capacitances Cg of 2.3 and 4.4 aF are extracted for devices with 82 and 210 nm WZ segments, respectively. The scaling of Cg with WZ segment length affirms that the QDs are formed within the WZ segments, and also the presence of a band-offset at both ZB/WZ interface directions.

Figure 6. (a, b) Coulomb oscillations and (c, d) charge stability diagrams (dI/dVbias vs. Vbias and VG) recorded for NWs with LWZ = 82 and 210 nm, respectively In conclusion, the effect of polytypism on the electronic properties of InAs nanowires is studied through temperature dependent electrical characterization. The study is based around designed ZB/WZ/ZB heterostructures with a series of precisely controlled WZ segment lengths. We discern the roles of carrier concentration difference, crystal phase band offset, and interfacial polarization charge in shaping the conduction band profile at various Fermi level positions. We find the carrier concentration in the WZ InAs segments to be an order of magnitude lower than in ZB, providing a strong gate modulation of the WZ conduction band edge. For longer LWZ (LWZ > 45 nm), with sufficiently high nWZ relative to nZB, the conduction band discontinuity (135 ± 10 meV) results in abrupt energy barriers at each ZB/WZ interface, which are sufficient to reduce conductivity and 15


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change depletion behavior at room temperature. Additionally, when nWZ is much lower than nZB, and especially for longer WZ segments, the built-in potential constitutes the main energy barrier centered within the WZ segment. It can create activation energy barrier nearly equal to WZ band gap and severely impede electron transport. On the other hand, the effect of WZ barrier for shorter LWZ (LWZ ≤ 19 nm) is eased due to the combined effect of reduced barrier formation because of carrier diffusion from ZB and the tunneling. We also extract a polarization charge density at ZB/WZ interfaces from the asymmetry of the activation energy with the bias polarity. Given the small value, it does not have a significant effect on the overall activation energy value. However, for crystal structure quantum dots, such as demonstrated in Ref. 19, 20 the asymmetry can have a considerable effect on electron distribution and transport. Nanowires of InAs are today used in a wide range of research topics, but often with an unintentional mix of crystal phases. With these new findings we can better predict, and engineer, the electronic properties, and also improve existing band structure models. ASSOCIATED CONTENT

Supporting Information This material is available free of charge via the Internet at http://pubs.acs.org Additional material includes the statistics of nanowire structure geometry, material parameters and physical models used in the simulation, determinations of carrier concentrations and electron mobility in the pure ZB and WZ segments, the effect of asymmetric biasing on the I-Vbias characteristic, estimate of piezoelectric field at ZB/WZ interface, and gate voltage dependent conductance at 10 K for different LWZ. AUTHOR INFORMATION

Corresponding Author

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*Email: [email protected]; [email protected]

Phone: +46462227740

ACKNOWLEDGMENT The authors thank Rainer Timm and Anders Mikkelsen for helpful discussion and acknowledge financial support from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 336126; the People Programme of the European Union (Marie Curie Actions, FP7-People-2013-ITN) Grant No. n°608153; PhD4Energy; the Swedish Research Council (VR); the Knut and Alice Wallenberg Foundation (KAW); The work received direct financial support from NanoLund. REFERENCES 1. del Alamo, J. A. Nature 2011, 479, 317−323. 2. Ford, A. C.; Ho, J. C.; Chueh, Y.-L.; Tseng, Y.-C.; Fan, Z.; Guo, J.; Bokor, J.; Javey, A. Nano Lett. 2008, 9 ( 1) 360– 365 3. Kim, D.-H.; del Alamo, J. A.; Antoniadis, D. A.; Brar, B. IEEE Int. Electron Devices Meet.

2009, 861–864 4. Svensson, J.; Dey, A. W.; Jacobsson, D.; Wernersson, L.-E. Nano Lett. 2015, 15, 7898 5. Dey, A. W.; Thelander, C.; Lind, E.; Dick, K. A.; Borg, B. M.; Borgström, M.; Nilsson, P.;

Wernersson, L. E. IEEE Electron Device Lett. 2012, 33, 791−793. 6. Martensson, T.; Wagner, J. B.; Hilner, E.; Mikkelsen, A.; Thelander, C.; Stangl, J.;

Ohlsson, B. J.; Gustafsson, A.; Lundgren, E.; Samuelson, L.; Seifert, W. Adv. Mater. 2007, 19, 1801−1806 7. Tomioka, K.; Motohisa, J.; Hara, S.; Fukui, T. Nano Lett. 2008, 8 (10), 3475–3480 8. Pan, D.; Fu, M.; Yu, X.; Wang, X.; Zhu, L.; Nie, S.; Wang, S.; Chen, Q.; Xiong, P.; von

Molnár, S.; Zhao, J. Nano Lett. 2014, 14 (3), 1214–1220 9. Dick, K. A.; Caroff, P.; Bolinsson, J.; Messing, M. E.; Johansson, J.; Deppert, K.;

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555−558. 17


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13. Doh, Y. J.; van Dam, J. A.; Roest, A. L.; Bakkers, E.; Kouwenhoven, L. P.; De Franceschi,

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J.; Marcus, C. M.; et al. Phys. Rev. Lett. 2015, 115, 127001. 15. Csonka, S.; Hofstetter, L.; Freitag, F.; Oberholzer, S.; Schönenberger, C.; Jespersen, T.

S.; Aagesen, M.; Nygård, J. Nano Lett. 2008, 8, 3932−3935. 16. Nadj-Perge, S.; Frolov, S. M.; Bakkers, E. P. A. M.; Kouwenhoven, L. P. Nature 2010,

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Nano Letters

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2844 32. Fang, Z. M.; Ma, K. Y.; Jaw, D. H.; Cohen, R. M.; Stringfellow, G. B. J. Appl. Phys. 1990, 67, 7034– 7039 33. Bauer, B.; Hubmann, J.; Lohr, M.; Reiger, E.; Bougeard, D.; Zweck, J. Appl. Phys. Lett. 2014, 104, 211902 34. Kriegner, D.; Panse, C.; Mandl, B.; Dick, K. A.; Keplinger, M.; Persson, J. M.; Caroff, P.;

Ercolani, D.; Sorba, L.; Bechstedt, F.; Stangl, J.; Bauer, G. Nano Lett. 2011, 11 (4), 1483−1489 35. Wood, C., Jena, D., Eds. Polarization Effects in Semiconductors: From Ab Initio Theory to Device Applications; Springer: New York, 2008

19


Nano Letters

(a)

ZB

WZ

ZB 5 nm

(c)

-

(b)

A

ZB WZ

500ACS nm Paragon Plus Environment VG

+

100 nm

-

+

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Page 20 of 26

ZB

Vbias

Page 21 of 26 (a)

VG (V) 0.25

-24

8 4 0

-4 -100 -50

0

50 100

ln(I / T2)

I (A)

240 K 210 K 180 K 160 K 125 K 110 K

-0.75

-26

-1.75

-28

Vbias (mV)

-50

0

50

Vbias (mV)

(b)

E E

(c) -22

I (nA)

1.0 1 2 3 0.5 4 5 6 7 0.0 8 9 10 -0.5 11 12 13 -1.0 14 15 -100 16 17 18 19 20 f 21 22 c 23

Nano Letters

qFB

100

-2.75 -30

-32

Slope~-qFB

ACS Paragon Plus Environment 4 5

-3.75 6

7

8

9 -1

1000 / T (K )

10

250 200

II. Band offset

Ec ZB WZ

(c) 300

150

ZB

50 0 -4

-3

-2

-1

0

1

I

100

0

VG = -2 V

-4

-3

-2

200

0

1

VG

(f) 300

-3 V 0V

-3 V 0V

200

I

I+II

100

100 0

-1

VG (V)

Ef

Ef

0

-100

-100 8

-2 V

x (mm)

1

VG

(d) 300

Gate VG

210 nm 82 nm 45 nm 19 nm 8 nm

VG (V)

-0.16 V

y (mm)

SiO2

0

I+II

100

0 -1

ZB

150

50

-2

WZ

200

50

-3

ZB

ZB

250

150

-4

Ec (meV)

Vacuum

WZ

(e) 300

210 nm 82 nm 45 nm 19 nm

200

VG (V)

(g)

Ec ZB

250

100

Page 22 of 26 III. Polarization charge

Ec

qB (meV)

210 nm 82 nm 45 nm 19 nm 8 nm

300

Nano Letters I. nWZ < nZB

Ec (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

(b)

qB (meV)

Activation energy qB (meV)

(a)

19

45

82

210 nm

ACS0 Paragon 100 200Plus 300 Environment 400 500 600 700 800 900

z (nm)

8

0

19

45

82

210 nm

100 200 300 400 500 600 700 800 900

z (nm)

b) 100

qB,bias=0

0

qB,bias= 100 mV

-300

-500

c)

160 Forward bias (Vbias= 100 mV)

140

Simulation Reverse bias (Vbias= -100 mV)

120

-200

-400

Ec Ef

-100

E (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Nano Letters

VG = -2 V

Forward bias

qB,bias= -100 mV Reverse bias

-600 -700 0

50


100

150

z (nm)

200

qB, bias (meV)

a)

Page 23 of 26

Simulation qB, bias=0

100 80 60 40 20 0

0

20

40

60

80 100 120 140 160

qB, bias=0 (meV)

qB (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

00

80

60

Nano Letters

b)

300

LWZ = 210 nm

Page 24 of 26

80 80

250 200 150 100

no polarization polarization

100 100

qBq(meV) (meV) B

a)

LWZ = 82 nm

-3

200

LWZ = 8 nm

-20 -4

no polarization polarization

-4

LWZ = 19 nm

-20 0

50 LWZ = 45 nm 0

60 60 40 40 20

-2

-2

-1

0

-1

0

VG (V) -1

0

-4


VG (V)

-3

-3

-2

VG (V)

Page 25 of 26

c)

1.5

dI/dVbias (S)

4

15

LWz=82 nm T=10 K Vbias=0.5 mV

Vbias (mV)

Conductance (S)

a)

1.0

0.5

3.5

10

3

5

2.5

0

2

-5

1.5

1

-10

0.5 -15

0.0

0

-1.4

-1.3

-1.2

-1.1

-1.0

VG (V)

b) 8

-1.6

-1.5

-1.4

LWz=210 nm T=10 K Vbias=0.5 mV

6 4 2

-1.3 -1.2

VG (V)

d)

-1.1

dI/dVbias (nS)

15

8

10

7

5

6 5

0

4

-5

3

-10

2 1

-15

0

-1 9

Vbias (mV)

Conductance (nS)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Nano Letters

0

-0.7

-0.6

-0.5

-0.4

-0.3

-0.65

-0.6

-0.55 -0.5 -0.45

VG (V) ACS Paragon Plus Environment

VG (V)

-0.4

Nano Letters

250

B

qFB (meV)

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

250 200

A

Vbias

+

1

2 300

-

210 nm LWZ 82 nm 210 nm 45 nm 82 nm 19 nm 458 nm nm

300

Page 26 of 26

LWZ ZB WZ ZB

19 nm 8 nm

Ef Ec

200 150

-0.1

qFB 0.0

0.1

0.2

0.3

0.4

150 100

-

0

nWZ < nZB

50 0

+

100 50

-4

-3

-2

VG (V)

-1

VG Band offset

Ec 0 ACS Paragon 1 Plus Environment ZB

WZ

Ec ZB

Polarization charge

Ec ZB

WZ

ZB

ZB

WZ

ZB

Conduction Band Offset and Polarization Effects in ... - ACS Publications

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