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Bipolar Photothermoelectric Effect Across Energy Filters in Single Nanowires Steven Limpert, Adam Matthew Burke, I-Ju Chen, Nicklas Anttu, Sebastian Lehmann, Sofia Fahlvik, Stephen Bremner, Gavin J. Conibeer, Claes Thelander, Mats-Erik Pistol, and Heiner Linke Nano Lett., Just Accepted Manuscript • Publication Date (Web): 09 Jun 2017 Downloaded from http://pubs.acs.org on June 9, 2017
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Bipolar Photothermoelectric Effect Across Energy Filters in Single Nanowires Steven Limpert1,2*, Adam Burke1, I-Ju Chen1, Nicklas Anttu1, Sebastian Lehmann1, Sofia Fahlvik1, Stephen Bremner2, Gavin Conibeer2, Claes Thelander1, Mats-Erik Pistol1 and Heiner Linke1* 1
NanoLund and Solid State Physics, Lund University, Box 118, 22100 Lund, Sweden
2
School of Photovoltaic and Renewable Energy Engineering, University of New South Wales, 2052 Sydney, Australia *
email:
[email protected],
[email protected] ABSTRACT: The photothermoelectric (PTE) effect uses non-uniform absorption of light to produce a voltage via the Seebeck effect and is of interest for optical sensing and solar-to-electric energy conversion. However, the utility of PTE devices reported to date has been limited by the need to use a tightly focused laser spot to achieve the required, non-uniform illumination and by their dependence upon the Seebeck coefficients of the constituent materials, which exhibit limited tunability and, generally, low values. Here, we use InAs/InP heterostructure nanowires to overcome these limitations: firstly, we use naturally occurring absorption “hot spots” at wave mode maxima within the nanowire to achieve sharp boundaries between heated and unheated sub-wavelength regions of high and low absorption, allowing us to use global illumination; secondly, we employ carrier energyfiltering heterostructures to achieve a high Seebeck coefficient that is tunable by heterostructure design. Using these methods, we demonstrate PTE voltages of hundreds of mV at room temperature from a globally illuminated nanowire device. Furthermore, we find PTE currents and voltages that change polarity as a function of the wavelength of illumination due to spatial shifting of sub-wavelength absorption hot spots. These results indicate the feasibility of designing new types of PTE-based photodetectors, photothermoelectrics and hot-carrier solar cells using nanowires. KEYWORDS: photothermoelectric effect, heterostructure nanowires, III-V, hot carriers, photodetectors In the photothermoelectric (PTE) effect, non-uniform absorption of light in a device or material induces a temperature differential, ∆T, that drives a current and produces a voltage via the Seebeck effect. The PTE effect is of interest for optical sensing and for solarto-electric energy conversion, and has been investigated in nanoscale and low-dimensional systems such as nanowires1–4 and 2D materials.5–16 PTE voltages are given by the product of the difference of the Seebeck coefficients of the hot and cold materials and ∆T, and can range from microvolts4 up to hundreds of millivolts.14 Two different types of PTE effects are commonly reported, distinguished by whether a temperature gradient is present in the lattice or only in the carriers (see Supporting Information for more information). The lattice-gradient PTE effect is akin to conventional thermoelectrics, with the carriers assumed to be at the same temperature as the local
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lattice temperature.4 In contrast, in the carrier-gradient PTE effect, the temperature gradient is present between the hot, non-equilibrium, photogenerated carriers present in regions of light absorption and the lattice-temperature carriers present in regions of no absorption, and the lattice remains at a uniform temperature throughout the device.8,9 The carrier-gradient PTE has the significant advantage that much higher ∆T – and thus a much higher PTE voltage – can potentially be achieved, because heat conduction in the lattice does not contribute to temperature equilibration. In this sense, the carrier-gradient PTE also has significant advantages over conventional thermoelectrics where phonon-driven heat flow represents a serious limitation. In this work, we report results of the carrier-gradient type. The performance of PTE devices reported to date has been limited by the need to use a focused laser spot to achieve the required, non-uniform illumination.1–16 Using this method, the diffraction-limited illumination area is relatively large (on the order of the wavelength) and the Airy-disc distributed illumination intensity is uneven. This makes it difficult to achieve sharp boundaries between illuminated/unilluminated regions, limiting the achievable temperature gradients. Furthermore, a focusing optic is required, restricting the usefulness of the PTE effect for sensing and imaging. In this work, we demonstrate the combination of three means to overcome the above-mentioned limitations. Firstly, we illuminate a semiconductor nanowire (Fig. 1a) globally (eliminating the need for a focusing optic) and employ the naturally occurring absorption “hot spots” that are present at wave mode maxima within a nanowire to photogenerate hot electron-hole pairs within sub-wavelength volumes of the device. This achieves sharp edges between heated and unheated regions. Secondly, we employ axial heterostructures as energy filters for electrons – a demonstrated means to enhance thermoelectric performance17–23 (see Supporting Information for more information) – to achieve Seebeck coefficients (S) up to the order of 2 mV/K, much larger than those of typical bulk materials (on the order of S = ±10 and ±100 µV/K in metals and semiconductors, respectively). Thirdly, we make use of the fact that the temperature of photogenerated electrons in illuminated nanowires has been observed to be as much as 190 K higher than that of the lattice,24 likely due to reduced electron-phonon coupling in nanowires. This allows us to establish ∆T between hot, photogenerated carriers and cold, nonphotogenerated carriers estimated to be more than 100 K across a single thermionic energy filter of a few 10 nm width. Combining the large S of a heterostructure energy filter with this high ∆T, we obtain large PTE voltage signals up to 368 ± 5 mV at room temperature and under global illumination. Furthermore, we demonstrate a novel functionality for a photodetector: the ability to electronically distinguish between two different bandwidths of light, or to “see” colors without the use of optical elements, due to the difference in their photoresponse polarity. This is possible because the location of hot spots in the nanowire depends on the wavelength, such that the PTE current and voltage controllably change sign as a function of the wavelength of illumination. The basic mechanism and key innovations of our approach are illustrated in Figures 1b and 1d. The PTE mechanism in our devices relies upon (i) spatially localized volumes of strong and weak light absorption within a single semiconductor nanowire occurring due to the wave nature of light, and (ii) the use of a carrier-energy filter, realized using an axial heterostructure, positioned between regions of strong and weak light absorption. Electronhole pairs are photogenerated predominantly in the regions of strong absorption and there
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establish a local non-equilibrium carrier temperature that is much higher than the lattice temperature.24 This temperature increase occurs because photogenerated electrons quickly (within about a ps) distribute their excess kinetic energy among themselves, whereas thermalization with the lattice is much slower.25 As the transmission spectrum of the carrier-energy filter defines the S of the system (see Supporting Information for more information), the PTE performance of the system can be tuned by varying the energy spectrum transmitted by the heterostructure, for example, by using a thermionic barrier (Figure 1d) instead of a quantum dot (Figure 1b). Materials and Methods. We realized InAs/InP nanowire heterostructures using Auparticle seeded chemical beam epitaxy (CBE)26 (Figure 1a), then transferred the nanowires to an SiO2 substrate equipped with a back gate, and ohmically contacted individual nanowires using electron beam lithography followed by sulfur passivation27 and metal evaporation. Structural nanowire characterization details are presented in the Supporting Information and reveal WZ InAs and InP segments and atomically sharp interfaces. InAs segments were degenerately n-type due to a combination of a surface-related electron accumulation and carbon doping from CBE precursors.28,29 Based on diameter-dependent mobility data from similar InAs NWs30, we expect electron mobilities of ~104 cm2V-1s-1, corresponding to a resistance of about 10 kΩ for a 400 nm long InAs segment. Both types of energy filters used (a single barrier and a double barrier, forming a quantum dot) were grown into the same nanowires (Figure 1a), and contacts were placed around the filter of interest in different devices. Specifically, we fabricated two groups of devices. In one set, a double-barrier quantum dot was centered between a pair of electric source-drain contacts (Figures 1b and 1c); in the other, a single thermionic barrier (Figures 1d and 1e). Devices were electrically characterized in the dark and under illumination under vacuum in a variable-temperature, cryogen-free, micromanipulated probe station with optical fiber access. The illumination source was a supercontinuum laser coupled into a monochromator to control wavelength and bandwidth.
Figure 1. Devices and illustration of device operation at short-circuit. (a) High-angle annular dark field scanning transmission electron micrograph of a single nanowire featuring axial heterostructures. InAs and InP regions are false colored purple and yellow, respectively, as a guide to the eye. Visible are the Au seed particle (far left), a quantum dot defined by a double-barrier InP heterostructure, and a single, thermionic InP barrier. (b) Illustration showing idealized physics of operation of the double-barrier device. The red region indicates
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the ideal situation where light is tightly confined (and thus absorbed) within the right InAs segment due to either a photonic resonance within the nanowire or a plasmonic resonance at the right nanowire/contact interface. Hot electron-hole pairs are photogenerated in the region of light-absorption. The electrons present in the left InAs segment due to unintentional carbon doping are at lattice temperature. Electron quasi-Fermi levels at the contacts are indicated by red lines. (c) SEM image of a double-barrier device. A green rectangle highlights the electrically active region of the device, an idealized band diagram of which is shown in (b). (d,e) Corresponding idealized band diagram and SEM image, respectively, of a single-barrier device. The InAs/InP system was chosen because InAs has high electron mobility (ensuring long carrier mean free paths) and a narrow band gap of EG = 0.39 eV,31,32 (corresponding to light with wavelength λG = 3180 nm) which ensures that the majority of absorbed visible and near-infrared photon energy is converted into photogenerated carrier heat. InP is a suitable barrier material because of its large conduction and valence band offsets with InAs (0.6 eV and 0.4 eV, respectively).26 The valence band offset serves to block photogenerated hole transport, ensuring that ambipolar transport of photogenerated carriers is inhibited, and the large conduction band offset enables a large S, related to the average energy of electrons transmitted by the heterostructure (see Supporting Information for more information).17–23 Finally, the InAs/InP system can be grown with atomically sharp interfaces and ultra-thin layers in nanowires. Results and Discussion. First, we show by electromagnetic wave modelling that optical absorption in a globally illuminated, Au-contacted, lateral nanowire is spatially nonuniform, that the location of strong absorption hot spots is wavelength-dependent, and that these hot spots can be moved from one side of an axial heterostructure to the other by changing the wavelength of illumination. For our modelling, we use the COMSOL Multiphysics wave optics module, a finite-element method software that solves Maxwell’s equations. We present calculations of the normalized absorption rate density, G, within a contacted heterostructure InAs/InP nanowire (Fig. 2a) with a geometry approximating that of the device for which experimental results will be shown in Figure 3. The results from this model show that the electric field magnitude, and correspondingly, the absorption, is nonuniform within the wire and that the maxima of the optical modes within the nanowire into which the light couples spatially shift as the wavelength of light changes (Fig. 2b). The explanation for this result is that the solution to the wave equation depends upon the wavenumber and the complex permittivity of the material, which are wavelengthdependent parameters. By comparison of the results for the contacted wire to the results for uncontacted wires (presented in the Supporting Information), it is apparent that the contacts significantly alter the spatial distribution of the electric field magnitude and correspondingly, the absorption, within the nanowire. This is because they break the optical symmetry of the system and introduce the opportunity for plasmonic resonances to be excited at the nanowire/contact interfaces. At wavelengths less than 700 nm, the field is concentrated within the wire in photonic hot spots similar to those present in uncontacted wires (see Supporting Information), but which do not exhibit symmetry about the middle point of the nanowire because the optical symmetry of the system has been broken by the contacts. Such hot spots can be asymmetrically or symmetrically located with respect to the double-barrier (Fig. 2b, λ = 520 nm, 540 nm and 560 nm). At wavelengths greater than 700
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nm, the field is concentrated at the nanowire/contact interfaces in plasmonic resonances (Fig. 2b, λ = 770 nm) necessitating a logarithmic scale to create a visually interpretable plot. The role of the plasmonic resonances at the nanowire/contact interfaces is to concentrate the electric field into a small volume of the nanowire directly adjacent to the contacts, leading to strong absorption and electron-hole pair generation in this region. When asymmetrically distributed, this local generation of electron-hole pairs can drive a PTE effect in the same manner as an asymmetrically distributed photonic absorption hot spot. To quantify the asymmetry of absorption that occurs on either side of the doublebarrier heterostructure in the electrically active region of the device, we separately calculate GL and GR, the absorption which occurs in the 356 nm long segment to the left and in the 418 nm long region to the right of the double-barrier, respectively (Fig. 2b). From this, we compute the percentage of absorption that occurs to the right of the double barrier: GR/(GL+GR) (Fig. 2c). The presence of several broad wavelength regions where the majority of light absorption is alternatingly to the right, then to the the left of the double-barrier energy filter indicates that one can expect reversals of the sign of the carrier temperature gradient across the double-barrier energy filter, and thus of sign of the PTE voltage generated by the filter, with changing wavelength of illumination. As these broad reversals occur at wavelengths greater than 700 nm, they are attributed to variation in the strength of the plasmonic resonances at the left and right nanowire-contact interfaces. While reversals over narrow wavelength regions are indicated to be present between λ = 500, 520 nm and 540 nm in the photonic hot spot regime, and around λ = 1000 nm and 1360 nm in the plasmonic regime, we were not able to observe these narrow bandwidth reversals experimentally as the bandwidth of our light was broader than the bandwidth over which the reversals are predicted to occur. Importantly, as both the contacted double-barrier and the contacted thermionic barrier are optically asymmetric structures (Figures 1c,e), they can both exhibit asymmetric absorption.
Figure 2. Electromagnetic wave modelling. (a) Model of InAs/InP heterostructure nanowire including contacts with geometry approximating that of the experimental device for which results are presented in Figure 3, with measurement circuit indicated. The wire length is taken to be 1.558 µm as measured by SEM, the wire diameter is taken to be 53 nm, and the wire segment lengths are taken to be (from right to left) 356 nm, 4.5 nm, 17 nm, 4.5 nm, 266 nm, 35 nm and 876 nm as determined from averages of growth batch wires inspected by TEM (see Supporting Information for more information). The contacts are 200 nm wide, 100 nm high, 1450 nm long, and there is 400 nm between their inner edges.
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Finally, they exhibit a vertical offset determined from SEM imaging of the device and have been truncated, their non-nanowire-perpendicular components being excluded to constrain the simulation domain. (b) Geometry of contacted nanowire, showing volumes over which the absorption rate density is integrated to compute GL and GR, the amounts of absorption that occurs on the left and right, respectively, of the double barrier heterostructure. Below this, cross-sections of the normalized absorption rate density, G, along the widest point of the contacted nanowire in (a) are presented for randomly polarized light of wavelengths as indicated. (c) Percentage of light absorption that occurs to the right of the double barrier heterostructure: GR/(GL+GR). The red and blue color overlays highlight wavelength regions where the majority of absorption occurs to the right and left of the double barrier heterostructure, respectively. Next, we demonstrate by experiment that the predicted absorption non-uniformity relative to the position of the energy filter can be exploited to drive bipolar, photothermoelectric currents. A double-barrier device (Figure 1b,c) was cooled to 6 K and a -20 V gate voltage was applied to the substrate in order to access the device’s fully depleted regime (see Figure S7 in SI for conductance curve). Under these conditions, the unilluminated device behaved as an insulator (Fig. 3a – black curve). On the other hand, under illumination with narrowband light (Gaussian with 35 nm full width at half maximum), current-voltage curves clearly show the generation of PTE currents and voltages with a direction (sign) that depends on wavelength (Fig. 3a – colored curves). The observed sign changes can be explained by the wavelength-dependent position of dominant light absorption and carrier heating in the nanowire expected from the modeling in Fig. 2c. This can be seen by comparing Fig. 2c to a measurement of current voltage curves as a function of wavelength (Fig. 3b): the four wavelength regions of alternating absorption asymmetry (Fig. 2c) correspond to the four wavelength regions of alternating PTE effect sign (Fig. 3b). At the positions where the open-circuit voltage, Voc, reverses sign, there is no PTE power production and the current-voltage curve exhibits purely photoconductive behavior. One such example is shown in Fig. 3a (green curve). In these situations, we expect that there is equal absorption of light on either side of the double barrier, consistent with the model. Some differences exist between the modelling results and experimental results. We attribute these to 1) differences between model and the precise experiment geometry, 2) wavelength-dependent photogenerated carrier collection probabilities, and 3) an experimental light source of finite bandwidth. We did not observe any photocurrent or photovoltage in illuminated plain InAs nanowires, emphasizing the role of the energy-filter heterostructure in generating the PTE. We also rule out unintentional Schottky contacts as the origin of the observed photocurrent based on the linearity of the plain InAs dark current-voltage curves (presented in the Supporting Information) and the consistency of our process for making ohmic contact to InAs nanowires.27 Furthermore, we rule out gate-induced Schottky contacts as the origin of the observed photocurrent collection for three reasons. Firstly, the double-barrier is not transmissive to holes. Therefore, a hole must be collected at the contact on the side of its generation and an electron at the contact on the opposite side for a current to be measured. Secondly, if gate-induced Schottky barriers at the contacts were essential for the operation of the device, the thermionic barrier device would not work at room temperature with no gate voltage applied (Figure 4). Finally, due to the photogenerated electrons in the conduction band, the electron concentration in the device will increase from the dark, depleted case and the band structure will flatten, minimizing band bending at the contacts.
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Figure 3. Current-voltage (I-V) curves of a double-barrier device at 6 K with a -20 V gate voltage applied to the substrate (a) I-V curves measured in the dark (black) and under narrowband illumination centered at 650 nm (blue), 700 nm (green) and 750 nm (red) illumination. (b) I-V curves as a function of wavelength measured in steps of 0.01 µm. The curves selected for (a) are indicated by dashed lines and colored arrows. The white region separating positive (blue) and negative (red) current indicates the wavelength-dependent value of Voc, which changes sign multiple times. The PTE performance of the device depends on the nature of the energy filter, and the PTE voltage performance of the device can be improved by replacing the double-barrier structure by a thermionic barrier (Fig. 1d, e), which has a higher S. This is because S of an energy filter scales with the average kinetic energy of carriers transmitted by filter, and the thermionic barrier allows transport only at energies above the barrier, far from the electron quasi-Fermi level. In contrast, the double-barrier allows transport through many quantized energy levels below the barrier edge, which are present in the InAs quantum dot between the double-barriers and which are at energies nearer to the electron quasi-Fermi level. Additionally, because of these low-energy quantized energy levels, the double-barrier device allows large bias induced currents of background and cooled photogenerated carriers to flow in the wrong direction for electrical power generation. For this reason, it was necessary to operate the double-barrier device at 6 K and in it’s depletion region to observe electrical power generation: to eliminate the large bias-induced current of background carriers. In contrast to the double-barrier, the more resistive thermionic barrier allows observation of electrical power generation at room temperature. The dark current-voltage current of the single barrier device (Figure 4a) exhibits the characteristic symmetric and exponentially increasing shape of thermionic emission over a barrier. Under illumination, the device produces electrical power (Figure 4b) and exhibits a PTE current of -13.3 ± 0.2 pA, a PTE voltage of 368 ± 5 mV, and a fill-factor of 27.5 ± 0.4 %.
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Figure 4. Current-voltage curves of the single-barrier device shown in Fig. 1 d, e. (a) Dark current-voltage curve at room temperature with no gate voltage applied. The symmetric, exponentially increasing current with voltage is characteristic of thermionic devices. (b) Illuminated (Gaussian with 720 nm peak and 141 nm full width at half maximum) currentvoltage curve at room temperature with no gate voltage applied. The device produces electrical power and exhibits a photothermocurrent of -13.3 ± 0.2 pA, a photothermovoltage of 368 mV ± 5 mV, and a fill-factor of 27.5 ± 0.4 %. The measured high value of the PTE voltage can be explained in terms of the high Seebeck coefficient of a thermionic barrier, given by21
2.
(1)
Our system has a barrier height of 0.60 eV and a background, non-photogenerated electron temperature of 300 K, giving a Seebeck coefficient of about 2.2 mV/K. Dividing the measured voltage by the Seebeck coefficient, a carrier ∆T across the barrier of 170 K can be estimated. This result is consistent with a recent report in which steady-state carrier temperatures up to 190 K above a 310 K lattice temperature were measured in continuouswave illuminated III-V semiconductor nanowires of about 50 nm diameter, and tentatively attributed to reduced electron-phonon coupling in thin nanowires.24 The observed wavelength dependent photocurrent amounts to a new functionality for photodetectors: the ability to electronically differentiate between two different bandwidths of light due to the difference in their photoresponse polarity and therefore, without the need for additional optical elements such as filters or dispersive gratings. In Fig. 5, we demonstrate a single-nanowire, thermionic barrier device responding to alternating pulses of 1.0 µm and 0.6 µm light with PTE currents of negative and positive 1 pA, respectively, at room temperature. This novel effect could potentially enable the
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development of new pulsed optical communication technologies or wavelengthdifferentiating sensors.
Figure 5. A single-barrier device operated as a color-sensitive photodetector at room temperature, detecting pulses of alternating wavelengths of light. When the device is illuminated by 1.0 µm (0.6 µm) light, a short-circuit current of -1 (+1) pA is detected. We foresee several avenues to improving the photodetection mechanism reported here. Specifically, structures could be investigated in which absorption location is engineered by controlling the length of the nanowire or by placing plasmonic optical antennas adjacent to the nanowire. Efforts to increase power conversion efficiency will focus upon increasing the fill factor and increasing the external quantum efficiency. For example, light in-coupling may be able to be improved by moving from single nanowires to arrays of nanowires.33–36 It is worth pointing out that PTE devices are thermodynamically equivalent37 to hotcarrier solar cells,38,39 a means to exceed the Shockley-Queisser limit,40 and a pathway to high-efficiency third generation solar energy conversion.41 The high open-circuit voltage observed here is a promising step in this direction, motivating future work to explore practical and theoretical efficiency limits of such hot-carrier devices. Supporting Information. The supporting information contains information about photothermoelectric effects, carrier energy filtering and the Seebeck coefficient, nanowire structural characterization, the COMSOL wave optics model, the I-V curves of pure InAs wires, the measured power of the narrowband light, and a conductance curve of the double-barrier device. Acknowledgements. This work was supported by NanoLund, by Energimyndigheten (award no. 38331-1), and by the Swedish Research Council (project no. 2014-5490). SL acknowledges support from the Solander Fellowship, the UNSW University International Postgraduate Award and the UNSW School of Photovoltaic and Renewable Energy Engineering. AMB had support from the Swedish Research Council grant 2015-00619 and Marie Sklodowska Curie Actions, Cofund, Project INCA 600398. IC acknowledges support from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7-People-2013-ITN) under REA grant agreement no. 608153, PhD4Energy.
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