Complete thermoelectric benchmarking of individual InSb ... · Complete thermoelectric benchmarking of individual InSb nanowires by combined micro-Raman and electric transport analysis

Complete thermoelectric benchmarking of individual

InSb nanowires by combined micro-Raman and electric

transport analysis

Sara Yazji1,2, Eric A. Hoffman1,2, Daniele Ercolani3, Francesco Rossella3, Alessandro Pitanti3, Alessandro

Cavalli1, Stefano Roddaro3, Gerhard Abstreiter1,2, Lucia Sorba3, and Ilaria Zardo1,4 ( )

Nano Res., Just Accepted Manuscript • DOI: 10.1007/s12274-015-0906-8 http://www.thenanoresearch.com on Oct. 9, 2015 © Tsinghua University Press 2015

Just Accepted This is a “Just Accepted” manuscript, which has been examined by the peer‐review process and has been accepted for publication. A “Just Accepted” manuscript is published online shortly after its acceptance, which is prior to technical editing and formatting and author proofing. Tsinghua University Press (TUP) provides “Just Accepted” as an optional and free service which allows authors to make their results available to the research community as soon as possible after acceptance. After a manuscript has been technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Please note that technical editing may introduce minor changes to the manuscript text and/or graphics which may affect the content, and all legal disclaimers that apply to the journal pertain. In no event shall TUP be held responsible for errors or consequences arising from the use of any information contained in these “Just Accepted” manuscripts. To cite this manuscript please use its Digital Object Identifier (DOI®), which is identical for all formats of publication.

Nano Research DOI 10.1007/s12274‐015‐0906‐8

www.theNanoResearch.com∣www.Springer.com/journal/12274 | Nano Research

2Nano Res.

Complete thermoelectric benchmarking of

individual InSb nanowires by combined

micro-Raman and electric transport analysis

Sara Yazji1,2, Eric A. Hoffman1,2, Daniele Ercolani3,

Francesco Rossella3, Alessandro Pitanti3,

Alessandro Cavalli1, Stefano Roddaro3, Gerhard

Abstreiter1,2, Lucia Sorba3, and Ilaria Zardo1,4,*

1Walter Schottky Institut & Physik Department,

Technische Universität München, D-85748 Garching,

Germany, 2Institute for Advanced Study, Technische

Universität München, D-85748 Garching, Germany, 3NEST, Istituto Nanoscienze-CNR and Scuola Normale

Superiore, I-56127 Pisa, Italy, 4Applied Physics,

Photonics & Semiconductor Nanophysics, Eindhoven

University of Technology, MB 5600 Eindhoven, The

Netherlands

We show a new method for the complete thermoelectric

characterization and figure of merit calculation of single nanowires,

based on combined spatially resolved µ-Raman spectroscopy and

electrical measurements. We apply the new method to Se-doped InSb

nanowires.


3 Nano Res.

Complete thermoelectric benchmarking of individual InSb nanowires by combined micro-Raman and electric transport analysis Sara Yazji1,2, Eric A. Hoffman1,2, Daniele Ercolani3, Francesco Rossella3, Alessandro Pitanti3, Alessandro Cavalli1, Stefano Roddaro3, Gerhard Abstreiter1,2, Lucia Sorba3, and Ilaria Zardo1,4( )

1 Walter Schottky Institut & Physik Department, Technische Universität München, D-85748, Garching, Germany 2 Institute for Advanced Study, Technische Universität München, D-85748 Garching, Germany 3 NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy 4 Applied Physics, Photonics & Semiconductor Nanophysics, Eindhoven University of Technology, MB 5600 Eindhoven, The

Netherlands

Received: day month year Revised: day month year Accepted: day month year (automatically inserted by the publisher)

© Tsinghua University Press and Springer‐Verlag Berlin Heidelberg 2014

KEYWORDS Thermoelectric, thermoelectric figure of merit, Raman spectroscopy, field‐effect transistor measurements, nanowire, InSb

ABSTRACT Nanowires are ideal nanostructures for exploring the effects on thermoelectric behavior of low‐dimensionality and thermal conductivity suppression. However, it is challenging to accurately measure temperature gradients and heat flow in such systems. Here, using combined spatially‐resolved Raman spectroscopy and transport measurements, we show it is possible to determine all the thermoelectric properties of single Se‐doped InSb nanowires and to quantify the ZT figure of merit. The measured laser‐induced heating in the nanowires and the associated electrical response are well‐described by a one‐dimensional heat equation model. Our method allows the determination of thermal contact resistances at the source and drain electrodes of the nanowire, which is found to be negligible in our system. The measured thermoelectric parameters of InSb nanowires are compared with those obtained by field‐effect transistor Seebeck measurements, and are found to be in a very good agreement.

Nano Research DOI (automatically inserted by the publisher)Research Article


4Nano Res.

Address correspondence to Ilaria Zardo, [email protected]

1 Introduction High efficiency heat‐electricity conversion can have a major impact on energy production and enable new self‐powered device applications. The figure of merit ZT=σS2T/κ (where σ, S, and κ are the electrical conductivity, the Seebeck coefficient, and the thermal conductivity, respectively) relates the physical properties of a material with its efficiency as a power generator or heat pump. After the predicted enhancement of the ZT value for materials at the nanoscale [1,2], a large number of materials with ZT>1 at room temperature were discovered [3,4], even if a competitive material with ZT>3 has not been developed yet. ZT~3 or higher is required to use thermoelectric devices as an efficient alternative to mechanical heat engines both for power generation, waste‐heat harvesting, and refrigeration [5,6]. To the best of our knowledge, the highest reached ZT value is 2.6 at 923 K, realized in SnSe single crystals measured along the b axis of the room‐temperature orthorhombic unit cell [7]. In order to give a complete determination of the thermoelectric properties of a material, σ, S and κ need to be measured on the same structure under the same conditions. For systems at the nanoscale, this is experimentally very challenging. For nanowires (NWs), κ was often measured using either suspended SiNx membranes [8‐10] or via local laser heating and Raman spectroscopy [11,12]. The Seebeck coefficient or the power factor σS2 can instead be measured using devices with metallic resistive thermometers, designed in several geometries [13‐16]. A significant effort has been devoted to engineering measurement platforms that allow a complete determination of the thermoelectric properties of individual NWs. At present, many measurements on NWs have been carried out with suspended resistive thermometers similar to the ones described in Reference [17], which require very complex nanofabrication processes. Furthermore, an open issue is the determination of the thermal contact resistance RC between the NW and the thermometers [18].

In this work, we present a new effective method for the determination of the thermoelectric properties and figure of merit of single NWs, based on combined spatially‐resolved Raman spectroscopy and transport measurements. Our approach reduces the impact of thermal contact resistances, which have proven to be problematic in alternative architectures [19]. In our case, they can be directly estimated from measurements and are found to be smaller than the NW thermal resistance. In addition, the method is in principle fully compatible with the field‐effect control of the carrier density in the nanostructure, which has been recently recognized to be very important in the investigation of fundamental properties of nanostructured thermoelectric materials [15]. The temperature gradient ∆T necessary for thermoelectric measurements is provided by the excitation laser, which acts also as thermometer. Raman spectroscopy is used to determine the local temperature rise along the NW. Transport and Raman measurements, together with a simple 1D heating model, allow the determination of the parameters needed for the calculation of the ZT together with the estimate of the thermal contact resistance RC. We apply this novel method to individual Se‐doped InSb NWs, which are expected to be the most promising candidates for thermoelectric application among III‐V semiconductors: InSb NWs with diameter of ~10 nm are for instance expected to have ZT ~ 6 at 300 K [20]. In general, InSb is a narrow band gap semiconductor (0.18 eV) with small effective mass at room temperature and high carrier mobility. In the past, thermoelectric properties of bulk InSb have been widely investigated. The thermal conductivity of bulk InSb has been measured in the broad temperature range from 2 K to 773 K [21‐27] and the room temperature thermal conductivity was found to be ~17 W/mK [24,25,28]. The complete thermoelectric properties investigation of intrinsic bulk InSb has been done between 100 °C and 500 °C, and the average value of the ZT parameter was found to be 0.42 (10‐3) K‐1 [22]. More recently for a Te‐doped


5 Nano Res.

InSb single crystal a ZT value of 0.6 at 637 K was measured [29]. InSb NWs with small diameters (~5 nm) have shown properties of the Luttinger liquid both from thermopower [30] and thermal conductivity [31] studies. Thermopower and electrical measurements on unintentionally n‐doped NWs with larger diameters (~43 nm) showed lower Seebeck coefficient but larger electrical conductivity than pure bulk InSb crystals [32]. A recent study on the phonon dispersion of 54 nm diameter InSb(111) NWs showed a reduced sound speed compared to the bulk, that was attributed to a 35% reduction of the C44 elastic constant, opening new scenarios for the determination of possible causes for the thermal conductivity reduction in NWs [33]. The complete thermoelectric figure of merit of single Sb‐enriched n‐type InSb NWs has been recently measured as a function of growth parameters, with a suspended microdevice [34]. A large suppression of the thermal conductivity with respect to bulk InSb was found (~3 times smaller), but the measured Seebeck coefficient was smaller with respect to the value measured for single crystal InSb [29], resulting in a lower ZT (between 0.002 and 0.006 at room temperature). Here, we obtained values of ZT for Se‐doped InSb NWs ranging from 0.014 to 0.025 at room temperature, which is slightly larger than previous findings in Sb‐enriched InSb NWs, though still lower that the ZT of Te‐doped bulk single crystals. 2 Results and discussion We developed a new method for the investigation the thermoelectric figure of merit of nanostructured materials, consisting in combined spatially‐resolved Raman spectroscopy and transport measurements. In the frame of this work we determine the figure of merit of several single Se‐doped InSb NWs (ESM1 in the Electronic Supplementary Material (ESM)). The measured electron density by field‐effect is 5x1017 electrons/cm3. In order to estimate the thermoelectric figure of merit ZT=σS2T/κ of a system, we need to determine its thermal conductivity κ, Seebeck coefficient S, and electrical conductivity σ. In the past, the thermal conductivity of semiconductor NWs was already estimated using laser heating and Raman spectroscopy [11,12]. By employing combined

spatially resolved Raman spectroscopy and transport measurements we are able to measure S and σ with a simple method, as it will be discussed in the following. The excitation laser employed for Raman spectroscopy is moved along the NW heating it locally, and thus generating the necessary temperature gradient ΔT between the ends of the NW, which is suspended between two metallic stripes that act as heat sinks. In addition, two top contacts are deposited at the NW ends, allowing electrical measurements. At each position of the laser, the Raman spectrum and the current‐voltage (I‐V) characteristic are recorded simultaneously. Through the I‐V curves, σ as well as the thermovoltage (i.e. the open‐circuit voltage VOC) ‐ and therefore the Seebeck coefficient ‐ can be evaluated. The temperature profile along the NW is determined by Raman spectroscopy using the linear relation between the shift Δν of the TO phonon frequency and the increase in temperature caused by the laser heating [35‐36]. Scans along the NWs are performed for several laser powers, i.e. several temperature profiles are measured. A sketch of the device employed for our measurements is shown in Figure 1.

Figure 1 Schematic of the device and of the scattering geometry used for Raman spectroscopy. The InSb nanowire is suspended between two gold stripes evaporated on a SiO2/Si substrate, and clamped with two top contacts. A voltage is applied at one end of the nanowire, and the current is measured through a low-noise current amplifier. The Raman scattering configuration is also shown, together with the nanowire geometry. The entire device is located on a xy piezo stage. In Table 1 we report the geometrical characteristics of the NWs investigated with the combined Raman spectroscopy and electrical measurement method. LS,D indicated the part of the InSb NW between source and drain contact, while Lthermal is the suspended part of the NW over the separation


6Nano Res.

between the lower gold stripes. Both lengths are shown in Figure 2 (a). We want to point out here that the investigated nanowire diameter range is far above the theoretical one for which a significant improvement of the ZT is expected [20]. However, Table 1 Geometrical parameters of the investigated Se-doped InSb NWs as estimated from SEM images

Nanowire Diameter (nm) LS,D (µm)1 Lthermal (µm)2

A 145 2.200 1.560

B 150 2.240 1.880

C 150 2.340 1.870

D 195 2.410 1.940 the method described in the present manuscript can be easily applicable to thinner nanowires, since it involves standard nanowire‐based devices fabrication processes. Results obtained by the combined Raman and open‐circuit Seebeck measurements, were also compared with measurements based on NW field‐effect transistors [15]. As discussed further in the following, these results were found particularly useful to assess the impact of the laser excitation on the thermoelectric response of the NWs. To this aim, we have fabricated devices implementing a buried heating scheme that allows driving both a large thermal bias (up to temperature gradients of ~8 K/μm along the NW) and a strong field‐effect modulation of electrical conductance on the nanostructure. With respect to the previous method, this approach suffers from the fact that it does not allow the estimation of the thermal conductance. However, on the other hand, it allows the precise mapping of the evolution of the Seebeck coefficient S as a function of the gate‐controlled electrical conductivity σ in the desired temperature range. 2.1 Laser heating and Raman spectroscopy The combination of laser heating and Raman spectroscopy has already proven to be effective for the determination of the thermal conductivity of 1 LS,D indicated the part of the InSb NW between source and drain contact. 2 L thermal is the suspended part of the NW over the separation between the lower gold stripes. Both lengths are shown in Figure 2 (a).

NWs [11,12]. The measurement principle is based on the determination of the local temperature from the shift of the phonon frequencies registered via Raman spectroscopy. The excitation laser itself produces a local rise in temperature, which reflects on the creation of a temperature gradient ∆T between the ends of the NW. ∆T is evaluated by fitting the temperature profile with a 1D heat equation, which includes laser heating. We observe a difference in the magnitude of the temperature gradient at the NW ends, which we attribute to a difference in the thermal contact resistances. We measured the Raman spectra of Se‐doped InSb NWs in backscattering configuration, and in the geometry illustrated in Figure 1. The excitation polarization εi and detection polarization εs are selected parallel to the NW axis z, corresponding to the [‐111] direction. In this geometry, the Raman spectra present the transversal optical mode (TO) at ~179 cm‐1, which is the allowed mode from the selection rules, and the forbidden longitudinal LO mode at 210 cm‐1 with lower intensity [37]. The shift Δν of the TO mode caused by laser heating was used to determine the local temperature rise as a function of the laser position xL. We assumed the same linear coefficient between Δν and local temperature rise (with respect to ambient temperature) Trise measured for bulk InSb, i.e. Δν/Trise=‐0.016 cm‐1/K [35] in analogy to the experimental observation on Si NWs [38]. Furthermore, for the nanowire diameters investigated here, we can reasonably assume the bulk relation. However, when using the shift of the optical phonons for the determination of the local temperature rise, particular care has to be taken in excluding possible additional shifts not caused by laser heating. For example, depending on the doping level, optical phonon modes could be superimposed to phonon‐plasmon modes. In our experiments, this can be excluded since the doping level we adopted is low [39]. Alternatively, laser irradiation causes the local lattice expansion, with a possible consequent strain distribution in the surroundings [40,41], which appears as an additional shift of the phonon mode. In this respect, we believe that the strain can be neglected under the experimental conditions we used, i.e. cw laser with relatively low laser power. Indeed, shorter pulsed laser typically induces a much stronger stress wave [40]. Furthermore, a strain distribution broadens the FWHM of the phonon lines, while we


7 Nano Res.

measured FWHM comparable with those temperature dependent reported for bulk InSb [36]. Nevertheless, we cannot exclude the presence of a homogenous strain at the point of excitation source. A typical temperature profile obtained is shown in Figure 2(b) (open black diamonds) for the NW shown in the SEM image in Figure 2(a) at a fixed laser power (135 μW, corresponding to a power density of 24 kW/cm2) together with the spatially resolved Raman shifts (filled blue diamonds).

Figure 2 (a) Scanning electron micrograph of one of the investigated Se-doped NW, with 150 nm diameter (device C). The NW is suspended between two gold contacts; the two top contacts are visible. LS,D and the thermal length (L thermal) are indicated with arrows. The scale bar is 1 µm. (b) Shift of the TO frequency (filled blue diamonds) and local temperature rise (open black diamonds) as a function of the laser position along the NW, for 135 µW laser power. (c) Values of the open circuit voltage VOC (open black squares), short circuit current ISC (open red circles), and conductance G (open green diamonds) extracted from the I-V characteristic curves measured as a function of the laser position. The I-V measurements were collected simultaneously with the Raman spectra relative to (b). Solid lines are fit of the 1D heating model to the experimental data. Dashed lines are guides to the eyes. The spectra were collected every 250 nm along the NW. We collected two spectra (180 seconds of integration per spectrum) for each laser position, which were then averaged. Errors on temperatures are calculated propagating the error on Raman

shifts, which were estimated as the maximum error on Lorentzian fit to the Raman spectra, and we considered 0.05 cm‐1. It has to be noted that the temperature deduced by Raman spectroscopy is associated with the thermal vibrations of the crystal lattice (lattice temperature). At room temperature, phonons and electrons are well coupled. On the time scale of our measurements, the two systems are in thermal equilibrium and Raman spectroscopy is also a valid electron thermometer. 2.2 Measurements, 1D heating model and data analysis The novelty of the measurement technique developed in this work with respect to Reference [12] is that it allows the determination of all the thermoelectric parameters necessary to quantify the figure of merit of an individual NW. So far this could only be demonstrated using architectures based on suspended micro‐heater membranes [17], which are technically more challenging and are affected by critical issues in terms of thermal contact resistances [42]. To access the Seebeck coefficient S = Vth/ΔT, we need to measure the thermovoltage Vth of our system. One possible way is to measure directly the open‐circuit voltage VOC at the NW ends via a high impedance voltage amplifier, while heating the NW with the laser. However, in this way we do not have simultaneous information on the changes of the electrical conductivity. We therefore decided to extract VOC from I‐V characteristics recorded varying the position of the laser on the NW. Therefore we applied an external bias V and recorded the current I with a low noise current amplifier. The applied bias was kept always below 10 mV to avoid additional Joule heating (see ESM2 for details). Without applying a thermal gradient (laser off), for good ohmic contacts we expect V (I = 0) = 0. When the laser is on, ΔT ≠ 0 and the open circuit thermovoltage appears, as well as the short circuit thermocurrent ISC. From the linear fit to the I‐V curves, we can extract VOC, ISC, and the conductance G as a function of the laser position along the NW. At every laser position, we averaged six I‐V curves. As an example, the position dependent I‐V curves and Raman spectra relative to Figure 2 are shown in Figure S2 of the ESM. For comparison, we show the spatially resolved


8Nano Res.

thermovoltages measured both from the I‐V curves and with open circuit conditions in Figure S3 of the ESM. In Figure 2(c) a typical trend of VOC, ISC, and G is shown for one of the Se‐doped InSb NW (C) at a fixed laser power. The laser position was varied moving from the source to the drain contact along the same NW shown in Figure 2(a), collecting simultaneously the Raman spectra from which the temperature profile in Figure 2(b) was extracted. VOC (ISC) first shows an increase (decrease) then a decrease (increase) as a function of laser position, approaching zero approximately when the local temperature rise reaches the maximum, and changing sign going ahead along the NW. This is exactly in agreement with our expectations: the temperature difference at the contacts ΔT is higher when the laser is close to one of the contacts and goes to zero in the middle of the NW ‐ where the local temperature rise is maximum ‐ reversing its sign throughout the other contact. The local temperature profile generated from the laser heating is also reflected in the behavior of the conductance G. It has minima at the NW ends (lowest temperature) and a maximum approximately at the NW center (highest temperature). Similar behavior of the electrical conductivity σ with temperature was obtained by independent electrical measurements (see Figure S4 of ESM). Temperature data obtained by Raman spectroscopy together with VOC and ISC data were analyzed using a 1D heating model including Gaussian heating source, as described in the following. Due to the fact that the electrical contacts have a much larger mass and much higher thermal conductivity than the NW, we treat the contacts as ideal heat sinks that remain at room temperature TRT. The NW temperature, TNW, increases under illumination by the Raman excitation laser positioned at xL. The laser Gaussian beam profile dissipates its power non‐uniformly along the NW generating a local temperature rise T(x) = TNW(x)‐ TRT. At the same time, heat is dissipated by convection from the NW into the surrounding atmosphere at a rate κairT(x), where κair is the thermal conductance to air per unit length. Altogether, the 1D heat equation including laser heating and convective cooling is

,2w

2)Lx2(xexp

π

2

wabsP

-T(x)airκ=2dx

T(x)2d κA ⎥

⎦

⎤⎢⎣

⎡ −− (1)

where the rightmost term describes the Gaussian laser beam profile centered at xL and having a beam waist w. The Gaussian is normalized so that the total integrated power is Pabs=aP, where a is the NW absorption coefficient and P is the laser power. A is the cross sectional area of the NW. This second‐order differential equation requires two boundary conditions. These boundary conditions are related to the contact resistances at the source/drain as discussed in the ESM5. The NW cross sectional area A and the laser beam waist is calculated from the measured FWHM, while the absorbed power Pabs was estimated via ab initio finite difference simulations performed with MEEP software [12,43]. In Figure 2(b) and 2(c) we show as solid lines an example of the fit to the experimental data obtained for one NW using a global fit procedure, namely using the same parameters for all the data set and changing only the laser power. The agreement between data point and the model is quite good. From the fitting of the Raman temperature rise with the 1D heat equation, the values of the temperature difference between the contacts ΔT has been calculated (see ESM5), and therefore we could estimate the Seebeck coefficient. The experimental data were also analyzed via individual fitting procedure, which showed consistent results (see Figure S6 in the ESM5). More details about the fitting procedures are reported in the ESM5. In Figure 3 we show the obtained electrical conductivities σ (panel (a)), Seebeck coefficients S (panel (b)), thermal conductivities κ (panel (c)), and the thermal contact resistances RCS,D (panel (d)) for the investigated Se‐doped InSb NWs. Each NW is indicated with a different symbol. In panel (a) we show with the filled symbols the maximum electrical conductivities extrapolated from the power dependence of the σ (σmax), that were calculated from the position dependent measurements (see Figure S7 in ESM5 for the details). With the half‐filled symbols we indicate the dark electrical conductivities as measured in absence of laser excitation. The dashed line indicates the σ value measured for Te‐doped InSb bulk single crystal [29]. The shaded grey area indicates the range of electrical conductivities measured for Sb‐doped InSb NWs from Reference [34]. The values of σmax are very similar compared


9 Nano Res.

with previous measurements on Sb‐enriched NWs [34]. We want to point out here that the difference between σmax and the dark electrical conductivities can possibly be explained by an effective annealing provided by the laser, which increases the conductivity. Indeed, measurements performed after laser illumination with laser off (data not shown) exhibit a persistent increased σ with respect to the one obtained before laser exposure. We observe negative Seebeck coefficients, as expected for n‐type semiconductors. The S absolute value of Se‐doped InSb NWs is generally larger than what reported so far for Sb‐enriched InSb NWs [34], but in average lower than the Seebeck coefficient measured for Te‐doped InSb bulk [29]. The thermal conductivities (Figure 3(c)) are comparable with the intrinsic InSb bulk value [22] therefore larger than the thermal conductivity measured for InSb NWs in Reference [34]. This

could be due to the clean crystalline structure of the investigated NWs, together with the fact that in the investigated NW diameter range a strong effect of boundary scattering is not expected since the phonon mean free path at 300 K is ~84 nm [40]. An evaluation of the diameter dependence of thermal conductivity is presented in the ESM6. The fitted value for κair ranges from 0.09 to 0.18 W/mK (data not shown) and it is, therefore, much smaller than the NW thermal conductivities. In Figure 3(d) we show the parameter values calculated from the fitting for the thermal contact resistances at source and drain, RCS,D. For each NW we obtain RCS≠RCD, that explains the asymmetric shape of the Raman temperature profile (see Figure 2(b)). It is important to note that the NW thermal resistances are ~3 to 40 times larger than the contact thermal resistances, which thus have a minor effect.

Figure 3 (a) The electrical conductivity σ of different investigated single Se-doped InSb NWs plotted as a function of their diameter. Filled symbols indicate the maximum σ extrapolated from the power dependence of σ (σmax), that were calculated from the position dependent measurements. The half-filled symbols indicate the dark electrical conductivities derived by transport measurements. (b) The Seebeck coefficient S of the different investigated Se-doped InSb NWs plotted as a function of their diameter. Patterned grey area indicates the results obtained with field-effect transistor measurements on NWs of the same growth batch. (c) The thermal conductivity κ of the different investigated Se-doped InSb NWs plotted as a function of their diameter. (d) The thermal contact resistances for source (S, filled symbols) and drain (D, empty symbols) as a function of NW diameter. The values of the different parameters obtained from the same NW are represented always with the same symbol (indicated in the legend). The bulk values of the different parameters are marked as dashed lines for Te-doped single crystal in (a) and (b) [29], and intrinsic bulk in (c) [22]. The range of values obtained by NWs from Reference [34] is marked as shaded grey areas. More interestingly, the obtained values are ~2 orders of magnitude lower than the measured thermal contact resistances for similar nanostructures on SiNx membranes, given by point contacts [19]. This

is clearly an important advantage of the method here described, and the large difference is likely due to the more standard and reliable contacting


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procedures can be used in our case. We remind here that top contacts are realized using standard lithography, chemical passivation, and choosing the most suitable metal for contacts. On the contrary, focused ion beam or electron beam induced deposition (as in the case of membrane devices) restricts the number of metallic contact materials, and allows a much more limited control of the interfaces. Therefore, our method provides much better electrical and thermal contacts with respect to the membrane devices. As discussed in the next section, since the NWs are subject to a focused laser excitation, it is important to assess the impact of photo‐excited carriers in the described measurement procedure. To this end we also performed a measurement of the conductivity and Seebeck coefficient by an all electrical field‐effect measurements on the same Se‐doped InSb NW as‐grown sample investigated with the combined Raman‐transport method. 2.3 S and σ determined by field‐effect transistor measurements Since the excitation laser has energy far above the InSb bandgap, one issue that needs to be considered is the presence of other possible mechanisms that can generate current in semiconductors exposed to illumination. Spatially resolved photocurrent measurements have been extensively used to investigate carrier transport in NWs, nanotubes and thin films [45‐54]. In addition to thermoelectric effect, light exposure can generate built‐in electric field responsible for electron‐hole separation, which can diffuse or drift to the electric contacts. Recently, electro‐thermodynamic modeling of semiconductor NWs under local injection of non‐equilibrium carriers has shown the interplay of the different effects, and predicted photocurrent profiles for different types of electrical contacts [55]. Time‐resolved scanning photocurrent measurements on GaAs and InAs NWs, carbon nanotubes, and graphene have been used to resolve the different temporal contributions to the photocurrent at the picosecond time scale [48,49,52,53]. In order to understand the role of possible photo‐excited charge carriers, independent field‐effect transistor measurements of electrical conductivity and Seebeck coefficient of individual Se‐doped InSb NWs were performed, indicating consistent findings with the results from the

combined Raman spectroscopy and transport measurements. This is a strong evidence that, even if present, the photovoltaic effect in our measurements is negligible with respect to thermal effects. Furthermore, the temperature dependence of the electrical conductivity as measured from all‐electrical measurements (shown in Figure S4 of the ESM) is comparable with the behavior observed with combined Raman and electrical measurement (Figure 2(c)), indicating that the sample response is dominated by thermal effects. Figure 4(a) shows one of the NW field‐effect transistors (FETs) devices. Se‐doped InSb NWs from the same growth batch used for Raman measurements were drop‐casted over a SiO2/Si substrate and source and drain electrodes were fabricated at a relative distance of 1.1 μm. The multicontact arrangement visible in Figure 4(a) allows to operate the electrodes both as electrical leads and resistive thermometers, sampling temperatures TS and TD at the two ends of the FET and the thermal bias ΔT = TD − TS. Operation details and performance of the heating scheme, together with precise information on the measurement procedure, have been presented elsewhere [15,16]. The direct measurement of TS and TD, together with the large ΔT attainable, allow us to determine the precise mapping of S(σ,T) in the explored temperature range for ΔT ranging from a minimum of ≈0.6 K to a maximum of ≈8.5 K. In Figure 4(b) we report the S vs σ curves obtained for five different temperatures above 300 K. The device was thermalized at temperature of 295 K, then the local heater was voltage biased to establish along the NW the temperature difference indicated in parenthesis in Figure 4(b). S exhibits a monotonic dependence on T for every given value of σ, and the T‐dependence of S is linear in first approximation (although this is more evident in the S/T vs σ curves reported in Figure S11 of the ESM). The corresponding power factor S2σ is plotted as function of σ in Figure 4(c).


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Figure 4 Field-effect Seebeck measurements of individual Se-doped InSb NWs. (a) Scanning electron micrograph of one of the investigated devices. The NW is deposited onto a 300 nm-thick SiO2 layer grown on top of n-doped bulk silicon substrate, which acts as a back-gate. A buried heater (H+, H-) is adopted to induce temperature gradients up to 8 K/μm along the NW axis. Four-terminals Ti/Au electrodes are fabricated at the hot and cold sides of the nanostructure, allowing the AC electrical detection of the temperature difference established between the NW ends and, simultaneously, the DC measurement of the I-V characteristic. The measurement set-up, whose DC part is sketched in the overlay, allows the field-effect control of the resistance R and of the Seebeck coefficient S. (b) S vs electrical conductivity, σ, at different temperatures above 300 K. The corresponding temperature differences between the hot and cold end of the NW are reported in brackets. The values of S are extracted by the measurement of R and of the thermovoltage Vth for applied back-gate voltages in the range (0,+10 V). (c) Power factor S2σ as a function of σ at different temperatures. We highlight that the results obtained using the two different methods very nicely match. In both cases we have measured individual Se‐doped InSb

NWs with diameters around 180 nm coming from the same growth batch. From the comparison of the data reported in Figure 3 and Figures 4(b)‐(c), the emerging scenario is that NWs exhibit Seebeck coefficient S in the range 150‐250 μV/K for temperatures above 300 K, while the power factor S2σ exceeds 0.3 mW/(mK2) with σ > 80 S/cm. As an additional assessment of the impact of photo‐excitation effects, we also aimed to separate the temporal contribution of the thermocurrent and photocurrent via frequency dependent measurements modulating the laser with an optical chopper. The chopper frequency dependent measurements are shown in Figure S13 of the ESM. We observed a significant variation on the measured photocurrent starting from ~3 kHz chopping frequency up to ~6 kHz, depending on the laser position along the NW. This means that the main contribution to the photocurrent is due to mechanism happening in the time scale of ~300 μs. Since photocurrent is expected to have a shorter time scale than thermal mechanism [51], we believe that the measured current is driven by thermal effects. Finally, in ESM9 we present an estimation of the photo‐ and thermally‐driven contributions to the electrical conductivity, which also points toward a prevalent thermal effect. 2.4 ZT analysis From the fitting of the electrical data and of the temperature profiles, we can estimate the thermal conductivity κ and the Seebeck coefficient S of our Se‐doped InSb NWs. The two quantities together with the electrical conductivity measured from the I‐V characteristic curves provide the thermoelectric figure of merit ZT. We extracted the ZT value at zero laser power by extrapolating from the power dependence of the maximum ZT measured along the NWs. Details of the figure of merit calculation are described in the ESM5. The obtained results for the investigated NWs are summarized in Figure 5.


12Nano Res.

Figure 5 Figure of merit ZT for the Se-doped InSb NWs at zero laser power. Each symbol indicates a different NW. The ZT bulk single crystal value for Te-doped InSb [29] is marked as a dashed line and the range of values obtained by NWs from Reference [34] is marked as shaded grey area. For comparison, we show the ZT value obtained for Te‐doped InSb bulk single crystal at room temperature [29] as a dashed line, and the range of values measured for two Sb‐doped InSb NWs from Reference [34] marked as shaded grey area. For Se‐doped InSb NWs with diameters between 130 and 195 nm we find ZT values between 0.014 and 0.025 at room temperature. These values are larger than the values reported for Sb‐enriched InSb NWs, with similar diameters [34] and are the highest ever reported for InSb NWs, to the best of our knowledge. In our case, the larger Seebeck coefficients compensate the smaller suppression of the thermal conductivity with respect to Reference [34]. We can attribute this enhancement of ZT to a higher electronic mobility with respect to Reference [34]. Measured Seebeck values are however still lower than those reported for single crystal InSb for similar values of σ [29]. In turn, this leads to the currently smaller ZT. We attribute this effect to un‐optimal doping in the current InSb nanostructures. 3 Conclusion In conclusion, we showed a new method for the complete benchmark of the thermoelectric properties of individual semiconductor NWs and, in particular, Se‐doped InSb NWs. Combined laser heating, Raman spectroscopy and simple electrical measurements allow the determination of the NW thermoelectric figure of merit ZT, together with the

estimate of the thermal contact resistances at the NW‐source/drain contacts. The temperature and electrical data are well described by 1D heating model, which includes Gaussian heat source. Comparison with field‐effect transistor Seebeck measurements shows a good agreement between the obtained results, confirming the validity of the proposed method. Measured ZT values are, to the best of our knowledge, the best reported so far on single InSb NWs. 4 Methods 4.1 Nanowire growth Au‐assisted Se‐doped InSb NWs are grown by chemical beam epitaxy on InAs (111)B substrates, with a InSb length of ~4.5 μm and diameters in the range ~50‐200 nm. Morphology, structure and growth protocol of the NWs are presented in detail in the ESM1. 4.2 Device fabrication and electronic setup Several parallel gold stripes with 100 nm thickness (10/90 nm of Ti/Au), 2 μm width, and ~2 μm separation were fabricated via optical lithography and metal evaporation on a SiO2/Si substrate. The InSb NWs were dropcasted on the device and the wires suspended between two gold stripes were identified using optical imaging. Subsequently, the top contacts were fabricated using electron beam lithography and evaporating 10/120 nm of Ti/Au. The gold stripes were connected to the electronic setup. The bias was supplied using a DC voltage source, and the current was measured via a low‐noise current preamplifier. 4.3 Raman setup We used the 676.4 nm line (EL = 1.83 eV) of a tunable Ar+‐Kr+ laser, focused through a 100x objective with 0.95 numerical aperture, both as excitation energy for Raman spectroscopy and as local heater of the NW. The Gaussian spot size of the laser has a full width at half maximum (FWHM) of ~840 nm. For each NW we selected the laser power in order to avoid local Sb segregation and structural modification of the NW (see ESM10) [36,56]. The Raman spectra were collected by an XY Dilor triple spectrometer equipped with a Si


13 Nano Res.

multichannel charged couple detector, with a resolution of ~1cm‐1. The device was placed on a xy piezo stage with a precision of 10 nm, which allowed spatially resolved measurements. 4.4 Field effect transistor measurements In our case we have addressed the thermoelectric response of the NWs for over 40 temperature values between 86 K and 360 K (see ESM7 for the full dataset presentation and analysis). Large thermovoltage values in excess of 1 mV have been induced in devices comprising a single InSb NW as the active element, and these values were modulated by a field effect. From the back‐gate dependence of the conductance we can extract the standard field effect electron mobility μe,FE value. However, this value is known to be underestimated since it is strongly affected by surface states and gate hysteresis effects. To bypass this problem we provided an independent estimate of the “Seebeck” electron mobility μe,S based on the dependence of the S vs σ curves on electron scattering times (see ESM11) [15]. Acknowledgements We thank M Bichler and H Riedl for excellent experimental help. We acknowledge financial support by the Deutsche Forschungsgemeinschaft via the Excellence Cluster “Nanosytems Initiative Munich” and the TUM Institute for Advanced Study. F.R. acknowledges financial support from the Italian MIUR through the FIRB ‐ “Futuro in Ricerca” project BFR13NEA4 “UltraNano”.

Electronic Supplementary Material: Supplementary material (Description of nanowire synthesis, example of I‐V curves and Raman spectra, comparison with short circuit measurements, temperature dependence of electrical conductivity, details on fitting procedure and on figure of merit evaluation, thermal conductivity diameter dependence, full field‐effect transistor measurements, frequency dependent thermocurrent measurements, photo‐and thermally driven electrical conductivity, laser induced Sb precipitation, and mobility calculation) is available in the online

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Electronic Supplementary Material

Complete thermoelectric benchmarking of individual InSb nanowires by combined micro-Raman and electric transport analysis Sara Yazji1,2, Eric A. Hoffman1,2, Daniele Ercolani3, Francesco Rossella3, Alessandro Pitanti3, Alessandro Cavalli1, Stefano Roddaro3, Gerhard Abstreiter1,2, Lucia Sorba3, and Ilaria Zardo1,4( )

1 Walter Schottky Institut & Physik Department, Technische Universität München, D-85748, Garching, Germany 2 Institute for Advanced Study, Technische Universität München, D-85748 Garching, Germany 3 NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy

4 Applied Physics, Photonics & Semiconductor Nanophysics, Eindhoven University of Technology, MB 5600 Eindhoven, The

Netherlands

Supporting information to DOI 10.1007/s12274-****-****-* (automatically inserted by the publisher)

ESM1‐Nanowire synthesis

All Se‐doped InSb NW growths were performed by Au‐assisted CBE in a Riber Compact 21 system. The system employs pressure control in the metalorganic (MO) lines to determine precursor fluxes during the sample growth. The precursors involved in the NW growth are tri‐methyl indium (TMIn), tertiarybutyl arsine (TBAs), tert‐dimethylaminoantimony (TDMASb) and DiTertiaryButylSelenide (DTBSe), the latter being used as selenium source for n‐type doping. A nominally 0.5 nm–thick Au film was first deposited on (111)B InAs wafers by thermal evaporation. Before the growth was initiated, the samples were heated at 560±5 °C under TBAs flow for 20 min in order to dewet the Au film into nanoparticles and to remove the surface oxide from the InAs substrate. Se‐doped InAs stems were grown at a temperature of 430±5 °C for 90 mins with MO line pressures of 0.3, 1 and 0.6 Torr for TMIn, TBAs, and DTBSe, respectively. The temperature was then lowered to 410 °C and InSb segments were grown for 120 mins with MO line pressures of 0.4, 0.7 and 0.6 Torr for TMI, TDMASb and DTBSe, respectively. In order to reduce the lateral growth, the temperature was increased up to 445±5 °C and the InSb segments were grown for another 270 mins. A first demonstration of InSb growth using InAs stems has been showed in Reference

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[S1] with MOVPE technique. The good morphology and excellent yield of the Se‐doped InSb NWs is demonstrated in Figure S1, where 45o tilted SEM micrograph of the sample is shown.

The investigated InSb NWs have zincblende crystal structure [S2], a length of ~4.5 mm and a wide diameter distribution in the 80‐200 nm range.

Figure S1 45o tilted SEM micrograph of the as-grown Se-doped InSb NWs.

ESM2‐Position dependent I‐V curves and Raman spectra

At each position of the laser, the Raman spectrum and the current‐voltage (I‐V) characteristic are recorded simultaneously. The measurements were performed every 250 nm along the NW. We collected two Raman spectra (180 seconds of integration per spectrum) for each laser position, which were then averaged, and we averaged six I‐V curves. As mentioned in the main text, bias was kept below 10 mV in order to avoid additional Joule heating. Indeed, considering the upper bound voltage of 10 mV, and the nanowire with lower dark electrical resistance (NW D, ~5kW), we obtain the maximum Joule heating of ~20 (10‐3) μW. Considering the results obtained for the absorbed power inside the nanowire, the lowest power absorbed among the investigated nanowire is ~27μW, therefore 3 order of magnitudes higher than the Joule heating. The position dependent I‐V curves and Raman spectra relative to Figure 2 of the main text are shown in Figure S2, together with a titled SEM image of nanowire C with lower magnification than Figure 2(a) of the main text.

Address correspondence to Ilaria Zardo, [email protected]

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Figure S2 (a) Tilted SEM image of the Se-doped nanowire C, where also gold stripes and top contacts are well visible. (b)

Position dependent I-V curves for NW Cat 135 µW laser power (PL). For every position six I-V curves are shown. (c) Waterfall

plot of Raman spectra collected from the same NW at the same laser power as in (b) for different positions along the NW. Spectra

are shifted vertically for clarity. The dashed line is a guide for the eyes. The shift of the TO mode is clearly visible. Same color in

(b) and (c) indicates simultaneous measurements corresponding to the same position along the NW.

ESM3‐Thermovoltage measurements

In the following, we show the comparison of the thermovoltages measured both from direct open circuit measurements and from the I‐V curves. The measurement configurations are shown in Figure S3(a) and (b). In one case (Figure S3(a)) the open circuit thermovoltage (I=0) is measured via a high‐impedance (1 TΩ) differential voltage preamplifier connected to the NW ends. In the second case (Figure S3(b)) a bias V is supplied at one end of the NW and the current I is measured through the current preamplifier at the other extremity. The thermovoltage is extrapolated from the I‐V characteristic curves taking the voltage value at zero current V(I = 0). The comparison between the two different spatially resolved thermovoltage measurements is shown in Figure S3(c) for 45 μW laser power (corresponding to a power density of ~8 kW/cm2).

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Figure S3 Schematic of the two measurement configurations. The scanning electron micrograph is relative to one of the two

measured Se-doped InSb NWs (circle in (c)). The white bar corresponds to 1 µm, and the red circle represents the laser spot. (a)

Open circuit configuration for thermovoltage measurement. VOC is measured via a voltage preamplifier. (b) Configuration for I-V

measurements. A bias V is applied at one end of the NW, and the current I is measured via a current preamplifier at the other NW

end. The thermovoltage is the bias value for which I = 0. (c) Thermovoltage as a function of the laser position along the NW in the

measurements configurations shown in (a) (black squares) and (b) (red circles). The laser power density is fixed at 45 µW.

ESM4‐Temperature dependence of the InSb NWs electrical conductivity

In Figure S4 we show the electrical conductivity as a function of temperature as measured from the all‐electrical method at zero gate voltage (see ESM7 for the measurement details). σ increases with temperature in agreement with the measurements performed with laser heating (see Figure 2 of the main text for comparison).

Figure S4 Electrical conductivity σ of an individual Se-doped InSb NW as a function of temperature T as measured from the

all-electrical method. Different symbols refer to different thermal cycles.

ESM5‐Details on fitting procedure and on figure of merit evaluation

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We use the 1D heat equation to model the laser heating and resulting heat flow through the NW by including a Gaussian driving term and a convective dissipation term. In this model, the temperature, T, is the local temperature rise (relative to room temperature), and varies as a function of position, x, along the NW. The static diffusion equation is an inhomogeneous ordinary differential equation of the form

,0)()(exp1)(dA 2

2

2

2

=−⎥⎦

⎤⎢⎣

⎡ −−+ xT

wxx

wP

dxxT

airLabs κ

πκ (S1)

where κ is the conductivity of the NW (in W/mK), A is the cross‐sectional area of the NW, Pabs is the absorbed laser power, xL is the position of the laser, w=500 nm is the laser beam waist, and κair is the heat convection to the atmosphere per unit length (in W/mK). The second terms represents the normalized Guassian profile of the laser beam. The NW diameter as well as the thermal length are estimated from the SEM images. We approximated the NW cross section A to a hexagon. Pabs is calculated from ab initio finite difference simulations, using MEEP software. In our simulation, we inserted several relevant information of the investigated system (material of the nanowire and of the substrate, NW diameter, distance from the substrate z, laser wavelength and its FWHM). The estimated absorbed power is calculated keeping all the mentioned details into account. Several simulations were performed in order to find values of the resolution, simulation area, perfect matching layers that produces converging values of the absorption. Error on absorbed power is estimated calculating the absorption in the entire NW diameter and z range given by their errors. Then we evaluated the maximum deviation from the value calculated for the mean diameter and z, and gave it as the error on absorption. From our simulation on absorbed power we found a range of relative errors between 2% and 5% that is therefore comparable or smaller than relative error on temperatures. The absorption uncertainty contributes less than the measurement error when determining the fit parameters for a single laser power, and it is negligible in the global fit procedure. The solution to the above differential equation is

1 2( ) ( )mx mxT x C e C e D x−= + + , (S2)

Where m2=κair/κA, the coefficients C1 and C2 are independent of x, and D(x) is the particular integral satisfying the laser driving term. D is given by,

2( /2) 2 2( ) ( )2( ) 2( )( ) .

4 2 2L L

mwm x x m x xL Le x x mw x x mwD x P e Erf e Erf

m A w wκ− − −

⎛ ⎞⎛ ⎞ ⎛ ⎞− − − +⎜ ⎟= −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠ (S3)

Here Erf is the error function. The coefficients C1 and C2 are determined by the two boundary conditions based on the thermal contact resistances RCS and RCD at the semiconductor‐metal interfaces at the respective source and drain ends of the NW. The temperature drop across an interface is equal to its contact resistance times the heat flow through that interface. The change in temperature at the source/drain end of the NW

)2/(, LTT DS m= is related to the thermal contact resistance RCS,D according to DSC

DSDS QRT ,

.

,, = , where

DSQ ,

. is the associated heat current from NW to contact. According to Fourier’s law, the magnitude of

heat flux is dxdTAQ /.

κ= . Therefore, Fourier’s law and RCS,D dictate the following boundary conditions

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, ,,

CS D S D

S D

dTT R Adx

κ= , (S4)

where the derivative is evaluated at x=‐L/2 and x=+L/2. If the NW is perfectly heat sunk to the leads, then RCS,D=0. This is of course an unlikely situation; a contact resistance at semiconductor‐metal interfaces is unavoidable. Indeed thermal contact resistance has been observed in carbon nanotube [S3] and Si based NW devices [S4]. The primary benefit of these boundary conditions, as opposed to assigning TS,D from data alone, is that RCS,D are independent of laser power, thereby reducing the number of unknown parameters when fitting data. The temperature rise at the left and right ends of the NW are

/2( / 2) ( / 2)C C

S Sx L

dTT L R Q L R Adx

κ=−

− = − = , (S5)

/2( / 2) ( / 2)C C

D Dx L

dTT L R Q L R Adx

κ=

= = . (S6)

These two equations can be used to find

/2 /2

1

( ) ( / 2) ( / 2) ( ) ( / 2) ( / 2)

( )( ) ( )( )

CCmL C mL C SD

S D

mL C C mL C CS D S D

RRe R D L D L e R D L D Lm m

Ce R R e R R

ρ ρ ρ ρ

ρ ρ ρ ρ

−

−

⎛ ⎞⎛ ⎞′ ′− + − + − − −⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠=+ + − − −

(S7)

And

/2 /2

2

( ) ( / 2) ( / 2) ( ) ( / 2) ( / 2)

( )( ) ( )( )

CCmL C mL C SD

S D

mL C C mL C CS D S D

RRe R D L D L e R D L D Lm m

Ce R R e R R

ρ ρ ρ ρ

ρ ρ ρ ρ

−

−

⎛ ⎞⎛ ⎞′ ′− + + + − − −⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠=+ + − − −

. (S8)

In Figure S5(a) we show an example of the fit to a Raman temperature profile. The required fit parameters are κ, κair, and the two contact resistances RCS,D . The electronic data and the Raman temperature profiles were fitted with a simultaneous parametric fit. VOC data is included in the parametric fit while the redundant ISC data is not, so that the electronic data does not outweigh the temperature data during the fitting procedure. The fit to VOC and ISC is shown in Figure S5(b). The model predicts the temperature profile along the NW for every position of the laser, as shown in Figure S5(c). The temperature difference at the NW ends is the temperature gradient ΔT, that is used for thermoelectric characterization. From the predicted temperature profiles it is possible to calculate the temperature gradients ΔT at the NW ends as a function of the laser position along the NW. An example of position dependent ΔT is shown in Figure S5(d). From the ΔT calculation and the VOC data, the Seebeck coefficients can be estimated. From the fitting it is also possible to estimate the temperature at the source and drain TS,D.

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Figure S5 (a) Example of the fitting (solid line) of a temperature profile obtained via Raman spectroscopy (open diamonds) at a

fixed laser power, using the 1D hat equation. (b) Fits (solid lines) of the VOC (black squares) and ISC (red circles) data points as a

function of the position of the laser along the NW. Transport data and temperature rises shown in (a) are recorded simultaneously.

(c) Temperature profiles predicted by the model, for different positions of the laser along the NW, indicated by the arrows. (d)

Calculated temperature gradient ΔT between the NW ends as a function of the position along the NW. All the calculation and data

sets shown are relative to the same NW (sample C) and laser power (135 µW).

For each NW, we performed measurements at several laser powers. The fit parameters can be evaluated either via a global or an individual fitting procedure, namely using the same parameters for all the measurement sets, changing only the laser power, or changing the four parameters for each measurement set. The results of the two different fitting procedures are shown in Figure S6. We can see a general agreement between individual and global fit parameters.

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Figure S6 Thermal conductivities κ and Seebeck coefficients S obtained from the fitting to the Raman temperature profiles and

transport data with the 1D heat equation, for NW C. Symbols represent the results of the individual fitting, while dashed lines are

the result of the global fitting. Empty symbols indicate measurements performed at the end of the power series, as a control.

The electrical conductivities were estimated using the equation:

,Lσ =

RA,S D (S9)

where LS,D is the length of the NW between source and drain contact, and we assumed homogeneous charge distribution. LS,D is also estimated from the SEM images of the NWs. NW diameters, thermal and electrical lengths are summarized in Table 1. As shown in Figure 2(c), σ follows the behavior of the temperature profile measured with Raman spectroscopy. The maximum values of sigma σmax have a linear dependence on the laser power. An example of the power dependence of σmax is shown in Figure S7. The values extrapolated at zero laser power are reported in Figure 3(a) of the main text.

Figure S7 Power dependence of σmax, extrapolated from the position dependent measurement of σ (NW C). The solid line is a linear

fit to the data.

For each InSb NW, we calculated ZT at every laser power as a function of the laser position along the NW, using the position‐dependent electrical conductivities, and S and κ obtained from the global fitting. Figure S8(a) displays the position dependent ZT for one NW at different laser powers (NW C). The observed variation of ZT along the NW is caused by the different temperatures induced by the laser beam, including the T‐dependence of Z. Figure S8(b) shows the maximum ZT values (ZTmax) as a function of laser power,

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extracted from the position dependent ZT curves. ZTmax increases linearly with laser power, and this agrees with the observation that the electrical conductivity is linear in temperature and therefore linear in laser power. Since an ideal thermoelectric measurement is performed with an infinitely small temperature gradient, fitting the ZTmax values with a straight line, we could extrapolate the room temperature ZT value at zero laser power. It has to be notice that the obtained ZT value is a lower bound of the NW ZT, because the electrical contact resistance decreases the measured electrical conductivity and the resulting ZT value.

Figure S8 (a) Position dependent calculation of ZT, for different powers (indicated by different colors) (NW C). Error bars are not

shown for clarity. (b) ZTmax as a function of laser power.

ESM6‐Thermal conductivity diameter dependence

If we consider a simple model where the dependence of the thermal conductivity κ on diameter d is given by the reduction of the phonon mean free path due to the nanowire dimensions, we can write the following relation for κ(d):

0 0κ(d) = κ d / (d +l ) , (S10)

with l0 phonon mean free path and κ0 thermal conductivity of the bulk. Considering l0 = 84 nm [S5] and κ0=17 W/mK, we obtain the result indicated with the black dashed‐dotted line in Figure S9. Alternatively, we can model κ(d) with an exponential behavior, as shown for other semiconductor materials [S6]:

0 0κ(d) = κ [1 - exp(-l / d)] , (S11)

which is depicted with the continuous grey line in Figure S9.

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Figure S9 Thermal conductivities of the investigated nanowires (indicated with different symbols) as a function of diameter. Black

dashed-dotted line and grey line and are the calculated κ(d) with equation (S10) and (S11) respectively. Red line is a fit to the data

with equation S(11). In the investigated diameter range, we obtain a similar dependence of κ on d for both models as expected. In both cases, in the investigated diameter range, the thermal conductivity varies only for a few percent, as experimentally observed (less than 10%). In particular, equation (S11) reproduces already quite well the measured values. However, the calculated thermal conductivity is lower than the measured one. This can be explained with an over estimation of the phonon mean free path l0. Indeed, if we perform a fit to the data with equation (S11) leaving l0 as free parameter (solid red line), we find l0 = 69 ± 23 nm. Please, notice that the relatively large error can be easily explained by the reduced amount of data points and to the reduced diameter range. A smaller phonon mean free path for our Se‐doped nanowires compared to the bulk value can be due to the presence of the injected doping carriers. Performing a fit to the data with equation (S10) (line not shown for clarity) we find an even smaller phonon mean free path, l0 ~ 17 nm. In any case, a reduction of l0 with respect to bulk explains qualitatively the observed behavior. ESM7‐Thermoelectric properties of individual Se‐doped InSb NWs in the temperature range from 80 K to 360 K

The all‐electrical method used to determine the thermoelectric properties of individual Se‐doped InSb NWs allowed us to drive thermal bias up to 7.7 K/μm along the NW and a strong field‐effect modulation of electric conductance, achieving precise maps of S vs gate‐controlled conductivity, σ, in a wide temperature range. Figures S10 and S11 report the results of the full Seebeck analysis of the whole data set obtained measuring two different devices in different cooldown, exploring the space of the parameters within the back‐gate interval VBG = (‐14 V,+30 V), induced thermal bias ΔT = (0.6 K, 8.5 K) and temperature T ~ (86 K, 356 K) for a total of more than 20 different temperatures. The S(R,T) curves are reported in Figure S10 for resistances between 5 kΩ and 100 kΩ. Figure S11 reports the Seebeck coefficient, the power factor and the S/T curves as function of the electrical conductivity σ, for the same dataset of Figure S10.

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Figure S10 Results of the Seebeck analysis of the whole data set measured applying a backgate voltage VBG in the range from -14

V to +30 V, at more than 40 different temperatures between ~86 K and ~356 K (selected curves are shown). (a) 3D plot of the

S(R,T) curves. (b) S(R) curves. The arrow indicates the direction of increasing T. Overall, the absolute value of S increases for

increasing temperature (resistance) at given resistance (temperature), as expected. The curves exhibiting the lowest values of R

belong to dataset measured at high temperature applying the highest VBG voltages.

We want to point out here, that we experimentally estimated a series contact resistance < 1 kΩ in the main range of temperature and back‐gate voltage used in this work. For simplicity and since field effect transistor measurements were used as a cross‐check of the main results obtained by the other method presented here, we neglected the contact resistance in our analysis. However, this affects the reported electrical conductivity ‐ and thus the power factor but not the Seebeck coefficient ‐ by an underestimate that can reach ～12% in the case of the highest temperature and applied gate voltage (lowest resistance) but drops rapidly well below 10% as the measured resistance exceeds 10 kΩ.

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Figure S11 Results of the Seebeck analysis of the full dataset measured at different temperatures from 86.3 K to 355.8 K. (a) S

curves as function of the electrical conductivity σ. (b) Power factor S2σ versus σ. (c) S/T vs σ curves.

ESM8‐Frequency dependent thermocurrent measurements.

It is crucial to understand whether the main contribution to the measured electrical conductivity in our system is due to a thermoelectric rather than a photovoltaic effect, since the excitation laser has energy far above the InSb bandgap. In the past five years, there was an increasing tendency in interpreting the measured illumination‐induced electrical current as a result of the photo‐thermoelectric effect, generated by the laser induced local heating. Observation on VO2 NWs [S7], MoS2 monolayers [S8], single‐walled carbon nanotubes films [S9‐S10], and on the junction between single and bi‐layer graphene [S11] suggest that the conduction in these systems is not dominated by built‐in fields at the Schottky barriers (even if they are present) which are generally ascribed to be responsible of photocurrent generation at metal‐semiconductor interface [S12]. In our system, Schottky barriers do not play a role as well, since the I‐V characteristic curves show ohmic behavior of the metal‐semiconductor contact (see Figure S12). On

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MoS2 film qualitatively similar photoresponse to above and sub‐bandgap illumination was measured, supporting the hypothesis of a photo‐thermoelectric current [S8].

Figure S12 Example of typical I-V characteristic curves of two different InSb NWs indicated with different symbols.

In order to investigate the nature of the observed photo‐induced current, we performed spatially resolved measurements modulating the laser frequency with a mechanical chopper. The measurements were performed up to 6 kHz, with 500 nm step size. No significant changes are visible up to 3 kHz (see Figure S13 (a)). Between 3 kHz and 6 kHz (Figure S13 (b)) we observe a change in the absolute value of the current depending on the position along the NW, i.e. the current is significantly reduced in the vicinity of the contacts. Laser power was kept fixed at 113 μW. Our finding is in agreement with frequency dependent measurements on GaAs NWs reported in reference [S13], where no chopper frequency dependence of the photocurrent was observed. In that case, the photocurrent was excited using excitation energy above bandgap but low laser power density and, therefore, no significant thermal current is expected.

Figure S13 Photothermocurrent as a function of position along the InSb NW for chopper frequencies from 0 to 3 kHz (a) and for

selected frequencies (b) (NW D).

ESM9‐Photo‐and thermally driven electrical conductivity

We can write the electrical conductivity in semiconductors as:

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,e h e h e e h hn e n eσ σ σ μ μ= + = + (S12)

where ne(h) is the electrons (holes) concentration, μe(h) is the electrons (holes) mobility, and e is the electron charge. Generally, in semiconductors the mobility decreases with increasing temperature. In Figure 2(c) we show that electrical conductance increases with temperature. An increase of σ with T means that the decrease in μ is compensated by an increase of the charge carriers that in our case is generated both from temperature and photo‐excitation of charges. In order to understand what is the dominant effect between temperature and photo‐excitation, we estimated the density of charge carriers excited by the incident photons (nph) and by temperature (ni(T)) in the simplest case of intrinsic InSb. In first approximation we can assume that each photon excites an electron‐hole pair, i.e. nph =(number of photons/s)xτ/V, where V is the volume of the nanowire illuminated by the laser excitation, and τ is the relaxation time of the excited electrons, given by τ = μm*/e with m* electrons effective mass. The number of photons per second is given by the absorbed power in the system Pabs divided by the photon energy Eph, where Eph =hc/λ, with h Planck constant, c light speed, and λ incident wavelength. For λ = 676.4 nm we have Eph =2.94 10‐19 J. Pabs is calculated with finite difference simulations, as described in ESM5. V can be approximated with a parallelepiped, which is given by the side of the hexagonal cross section of the nanowire times the laser penetration depth times the laser FWHM. We have V~2.2x10‐15 cm3. ni(T) for intrinsic semiconductor is given by:

3/2( ) exp( / 2 ),i e h C V g Bn T n n N N T E k T= = − (S13)

where 2( ) 2(2 * / )C V BN m k T hπ= is the effective density of states in the conduction (valence) band and m* is

the effective mass of the conduction (valence) band [S14]. Both carriers excited by photons and by temperature contribute to the electrical conductivity σtot(T):

,( ) ( ) ( ) ( )( ( ) ( )) ( ) ( )tot ph e h ph e h e e h hT T T n T T T e n T e n T eσ σ σ μ μ μ μ= + = + + + , (S14)

where σph(T) and σe,h(T) are the electrical conductivity generated by charge carriers excited by photons and temperature, respectively. In Figure S14 we show the calculated σtot(T), σph(T), and σe,h(T).

Figure S14 σtot(T) as a function on temperature T as calculated from Equation S(14) (blue line), together with the calculated σph(T),

(red line) and σe,h(T) (black line) using ni(T) from Equation (S13). For σph(T) we used nph =2.3x1016 electrons/cm3, estimated from

the calculation of Pabs for nanowire B measured with a laser power of 68 µW.

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The charge mobilities are taken from Reference [S15]: μe(T) = 7.7x104(T/300)‐5/3 cm2/Vs, and μh ~ 850(T/300)‐1.95 cm2/Vs. We used nph ~2.3x1016 electrons/cm3 calculated for nanowire B measured with a laser power of 68 μW. Since nph does not change with temperature, σph(T) decreases for increasing T. On the contrary σe,h(T) increases with T. However, in the considered conditions σtot(T) is not monotonic as experimentally observed. This means that either nph is overestimated (meaning that not all the incident photons creates an electron‐hole pair that is separated by the bias), or ni(T) is underestimated. The overestimation of nph is evident from the large values of the calculated σ. For larger nph (i.e. at highest laser powers), the effect is more pronounced. The approximation we made to intrinsic bulk InSb is neglecting the doping electrons, and therefore is a first indication that ni(T) is underestimated. In conclusion, if σph(T) is dominant, the increase of electrical conductivity under laser illumination we observe experimentally is not reproduced. However, at high temperature the thermocurrent contribution is in any case bigger than the photocurrent one. ESM10‐Laser induced Sb precipitation

For GaAs NWs it has been shown that laser heating can lead to local structural modifications that affect irreversibly the thermal properties of the NW [S16]. Also in the case of InSb NWs, laser heating can produce Sb precipitation, as shown in Figure S15 for an undoped InSb NW, at a laser power of 360 μW (corresponding to a power density of ~65 kW/cm2). Together with the InSb TO peak at ~180 cm‐1, two peaks due to the scattering from Sb at ~114 cm‐1 and ~150 cm‐1 are clearly distinguishable [S17]. This means that the laser induces important effects related to a temperature increase and can strongly affect the nanostructure. The threshold power density at which structural modifications occur depends on the properties of the NW (i.e. thermal conductivity) and sample geometry. Therefore, for measurements involving laser heating it is crucial to accurately choose the laser power in order to avoid any structural modification of the NWs.

Figure S15 Raman spectrum collected from the middle part of a suspended undoped InSb NW, in the same scattering

configuration as illustrated in Figure 1 in the manuscript. The laser power is 360 µW. The two peaks arising from Sb precipitation

are evident.

ESM11‐Electron mobility: field‐effect method vs Seebeck analysis

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Figure S16(a) shows the source‐drain current as a function of the backgate voltage at low temperature (bottom panel) and the related field‐effect mobility (top panel) calculated as:

2

,e FEg DS g

L dIc V dV

μ = (S15)

where L = 1.1 μm is the distance between source and drain electrodes and Cg ≈ 120 aF is the gate capacitance calculated as Cg = 2πεSiO2L/arccosh[(dSiO2+r)/r] with r radius of the NW, εSiO2 = 3.4 (10‐11) F/m and dSiO2 = 285 nm dielectric constant and thickness of the SiO2 layer, respectively. Separate and independent determination of the electron mobility is achieved from the analysis of the S/T vs σ curves. With respect to the standard field‐effect method based on the assumption of a given value for the gate capacitance, the Seebeck analysis is likely more reliable since it bypasses the screening effects associate to the NW surface potential landscape. Indeed, it provides mobility values significantly higher than the field‐effect method [S18]. Figure S16(b) reports the S/T vs σ curve measured at the same temperature of the curve reported in Figure S16(a) and the fitting curve calculated according to:

1/32

2 2 2 *2/3 2/3

2

31 /

3 3F

B B

E

eS k k mT e E

π

π σ μ σσ

⎛ ⎞⎜ ⎟⎜ ⎟∂⎛ ⎞ ⎝ ⎠= − = −⎜ ⎟∂⎝ ⎠ h

(S16)

his is derived assuming the case of degenerate semiconductors in the low temperature limit so that the

conductivity can be expressed as 22 ( ) ( ) ( )

3 ee fE g E E dE n em E

σ τ μ μ∂⎡ ⎤= − ≈⎢ ⎥∂⎣ ⎦∫ , while the energy is E =

(h2/2m*)(3π2n)2/3 = (h2/2m*)(3π2σ/μe)2/3 and thus σ(E) = μen(E) = (2m/h)3/2(μe/3π2)E3/2, using the value m*(InSb) = 0.014me. In particular, we notice that the approximations nicely apply to the data set measured at T ~ 100 K in the high band‐filling regime i.e. for large electrical conductivity.

Figure S16 (a) drain-source current as a function of the backgate voltage at low temperature (bottom panel) and calculated field-effect mobility (top panel); the maximum of the curve corresponds to a mobility value of ≈ 2200 cm2/Vs. (b) S/T curve as a function of σ and related fit to Eq. (S16), providing an independent estimate of the electron mobility which is not affected by surface charge dynamics. The fitting parameter µe,S = 20000±3000 cm2/Vs is almost one order of magnitude higher with respect to its field-effect counterpart.

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