Characterization of electrostatically defined bottom-heated InAs nanowire quantum dot systems

Conversion of temperature gradients to charge currents in quantum dot systems enables probing various concepts from highly efficient energy harvesting and fundamental thermodynamics to spectroscopic possibilities complementary to conventional bias device characterization. In this work, we present a proof-of-concept study of a device architecture where bottom-gates are capacitively coupled to an InAs nanowire and double function as local joule heaters. The device design combines the ability to heat locally at different locations on the device with the electrostatic definition of various quantum dot and barrier configurations. We demonstrate the versatility of this combined gating- and heating approach by studying, as a function of the heater location and bias, the Seebeck effect across the barrier-free nanowire, fit thermocurrents through quantum dots for thermometry and detect the phonon energy using a serial double quantum dot. The results indicate symmetric heating effects when the device is heated with different gates and we present detection schemes for the electronic and phononic heat transfer contribution across the nanowire. Based on this proof-of-principle work, we propose a variety of future experiments.


Introduction
Thermoelectric (TE) materials enable the conversion of temperature gradients to electricity and are in principle capable of power generation and active cooling, but in practice, however, are often held back by low figure of merits, thus limiting efficiencies [1][2][3]. Nanoscale semiconductor devices, instead of relying on intrinsic material properties, allow engineering of favourable electronic and thermal device properties and thus have led to various concepts for efficient thermal energy harvesting [3][4][5][6].
A conventional two-terminal heat engine consists of a TE device coupled to two thermal reservoirs at different temperatures [7]. The figure of merit of such heat engines scales with the Seebeck coefficient S of the device and the ability to maintain a large temperature difference between reservoirs. Here, nanowires can yield advantages compared to bulk materials in the form of an increased S, and a reduction of the phononic contribution to the thermal conductivity [2,5]. Maximum TE efficiency of a heat engine, however, is expected only when the device acts as perfect energy filter and requires further modification of the electronic structure of the device [1,8,9].
Nanowire-based, heated TE QD devices are commonly built with epitaxially-defined InAs/InP QD structures [18,20,28]. Such epitaxially defined QD systems offer large single-particle energies and symmetric tunnel couplings at the cost of a static barrier structure and complex control over the tunnel couplings [29]. TE devices further require a heater with a large, local heating efficiency, controlled and continuous tunability of the temperature gradient and compatibility with the QD gating technique [30]. In addition to these requirements, symmetric alignment of the heater with the QD system is important for the controlled definition of temperature gradients and a requirement for purely phonon-absorption based three-terminal energy harvesters [28]. Accurate alignment of a side-or top-heater electrode to epitaxially defined QD structures in nanowires remains, however, technically challenging.
In this proof-of-principle work we use thin InAs nanowires, which have been demonstrated to form high quality electrostatically defined QD structures and single particle energies of around 1 meV in sidegated devices [31], with a combined bottom-gate and bottom-heater device architecture. These devices combine the flexibility to form variable barrier and multi-barrier structures [32] with the ability to heat localized at different positions along the nanowire axis, engineering different temperature gradients. Our approach naturally results in a symmetric heating effect of the heaters with respect to electrostatically induced barriers. In the following, we experimentally study the TE effect across the barrier-free nanowire and QDs as well as phonon-assisted transport (PAT) and the TE effect on a double quantum dot (DQD) structure.

Device fabrication
Arrays of 50 nm wide Ti/Au (2/8 nm) gate stripes with a center-to-center distance of 100 nm were defined atop a thermally oxidized silicon substrate by a combination of electron beam lithography (EBL) and thermal evaporation. Next the gate arrays were covered by an 8 nm HfO 2 layer via atomic layer deposition within an EBL exposed high-k window. This allows the following deposition of thin, chemical beam epitaxy grown, wurtzite InAs nanowires (diameter 35-40 nm, grown in (111)B orientation), electrically insulated from the gate stripes, using a micromanipulator. The accurate position of suitable nanowires with respect to the gate arrays were identified in a scanning electron microscope and 600 nm spaced source (S) and drain (D) contacts to the nanowires were designed such that seven gate stripes (g1-g7, counted from S to D) are capacitively coupled to the enclosed nanowire segment. The nanowire contacts halfway overlap with the outer two gates (g1, g7) to allow full control over all enclosed nanowire sections and every third gate stripe (g1, g4, g7) is connectable on both ends and thus can act as local joule heater. In a final iteration of EBL in combination with Ni/Au (25/75 nm) thermal evaporation the nanowire contacts are defined and all active gates are connected to pre-patterned bondpads on the substrate. A tilt-angle SEM image of an exemplary device is shown in figure 1(a).

Measurement details
All measurements were performed in a dilution refrigerator and by fitting Coulomb peaks we find a base electron temperature of 90 ± 5 mK in the absence of heating on the device. Each measurement line has a cold-filtering resistance of 3.26 kΩ and the experimental setup is schematically illustrated in figure 1(a).
Yokogawa GS200 and Yokogawa 7651 voltage sources are used to bias all gates g1-7 (V 1-7 , V 1,4,7 ) and the source contact (V SD ). The current through the nanowire is detected with a HP 34401A voltmeter on the drain side after conversion to a voltage by a Femto DLPCA-200 I/V converter at a gain of 1 nA V −1 and an input impedance of 10 kΩ. We note that in this measurement configuration, electrons traveling from drain to source result in a positive current reading.
To locally heat the nanowire on the left (L), middle (M) or right (R) side, we apply a heating bias dV L/M/R = V 1/4/7 − V 1/4/7 symmetrically around the voltage used to capacitively gate the nanowire (V 1/4/7 + V 1/4/7 )/2 on the two ends of g1, g4 or g7, respectively. This leads to a heating current flow I L/M/R through the gate stripe g1/4/7, which in turn acts as highly localized joule heater to the nanowire device, inducing a temperature gradient. For consistency in notation between all active bottom-gates we in the following denote the average voltage applied to the left/middle/right heater as V 1/4/7 .
For pure thermocurrent (I th ) measurements, we apply an effective, offset adjusted bias V SD = 0 V to the source contact, correcting for an experimental setup based potential offset between the source and drain side. This offset was characterized by minimization of the bias driven current I SD through the nanowire at a point of high conductance (Coulomb peak for QDs in section 3 and triple point for DQDs in section 4) by application of a small bias V SD . We find a bias offset of −21 ± 2 μV which drifts slowly over time and use repeated control measurements throughout the data collection to exclude the possibility of larger shifts. All bias values V SD are adjusted by −21 μV.

Nanowire and heater characterization
As a first step to prepare the device for the formation of QD and DQD structures, the nanowire is tuned to a conductive regime where the presence of unintentional barriers is excluded. Unintentional barriers are observed in the ungated device due to the conduction band roughness and low electron densities in thin InAs nanowires at low temperatures [33,34]. Thus, we apply V 1-7 = 1 V to enhance the nanowire conductivity and measure the resulting I SD − V SD -curve shown in figure 1(b). Observation of ohmic behavior with an overall circuit resistance R ≈ 61 kΩ around V SD = 0 V confirms barrier free transport across the device. Consequently, in the following we always apply 1 V to all gates which are not actively used as either a barrier-or plunger gate.
In the barrier free regime of figure 1(b), we further demonstrate heater functionality by studying the TE effect across the nanowire by heating on the right side and measuring the resulting thermocurrent I th as a function of the heater bias dV R . The results are plotted in figure 1(c) and the short-circuit current indicates a net electron flow from drain to source, as sketched in the lower inset of figure 1(c), with thermocurrents reaching up to I th = 300 pA at dV R = ±200 mV. While a quantitative analysis of the Seebeck effect would require accurate thermometry, we consider the maximum magnitude of the thermocurrent and calculate the corresponding thermo-voltage ΔV th ≈ 15 μV. As is discussed in section 3, at a heater bias of dV R = 200 mV a maximum temperature difference between the left and right device contact of ΔT = |T L − T R | ≈ 0.5-1 K and an average temperature T = (T L − T R )/2 ≈ 2.5 K are realistic, which in turn yields an estimate for the upper bound of the Seebeck coefficient of |S| = |ΔV th /ΔT| I=0 ≈ 15-30 μV K −1 [7,35]. Here, T L and T R denote the electron temperatures on the source and drain side of the device, respectively. This estimate is comparable in magnitude to the Seebeck coefficient observed for InAs nanowire segments of comparable length at 4.2 K [36] and 10 K [37]. Figure 1(c) further yields information regarding heating symmetries. First, I th is symmetric around dV R = 0 and the sign of the heater current has no impact on the heating effect. Second, we independently measure I th as a function of dV L , dV M and dV R , which is shown in the upper inset of figure 1(c). A comparison of heating on the left and right bottom-heater reveals opposite signs of I th but comparable magnitudes, suggesting a symmetric heating effect. In contrast, heating with the middle bottom-heater results in significantly lower I th which indicates near uniform heating of the nanowire with a slightly increased temperature on the source-compared to the drain contact. This is attributed to a slight source and drain asymmetry with respect to g4.

Quantum dot thermoelectrics
Next, we introduce barriers to form a QD, which acts as sharp energy filter and in principle allows for highly efficient TE power conversion [1,8,9,18,19]. Further, in contrast to the barrier-free device configuration, fits to TE based thermocurrent measurements on QDs have in recent years been established as a reliable thermometry method without the need for additional device components [18,20,21,28].
A small negative bias applied to g2 and g4 ( , electrostatically forms barriers in the nanowire conduction band. The resulting QD charge stability diagram as a function of the plunger gate voltage V 3 is shown in figure 2(a) and the corresponding measurement configuration is schematically illustrated in figure 2(b). We note that in the following, we refer to the configuration shown in figure 2(b) as left QD (QD L ) as opposed to a QD formed on the right side (QD R ) between g4 and g6 ( The charge stability diagram in figure 2(a) shows well-defined Coulomb blockade in a sequential tunneling regime and a clear single-particle energy spectrum. Regions of negative differential conductance are attributed to the non-uniform density of states in the quasi one-dimensional nanowire lead segments enclosing the QD. From the Coulomb diamond dimensions a gate lever arm α QD To study the TE effect across the QD, we first identify two consecutive crossings with a ground-to excited-state spacing of more than 1 meV. This choice ensures that for moderate heating only a single QD resonance contributes to thermocurrents.
With the reasonable assumption of conventional odd-even spin filling in our QD, we can then approximate the current through the system at the selected transitions by rate equations for a single spin-degenerate QD resonance [20,38]. We further assume the QD to have an infinite charging energy, be weakly coupled to the reservoirs and neglect co-tunneling effects as well as lifetime and thermal QD level broadening. The QD resonance in our model system can be populated by 0, 1 or 2 electrons. Because of the spin degeneracy expected in experimental systems, every charge state transition can effectively be described by either the 0 → 1 or the 1 → 2 charge state transition of the model system. For an effective 0 → 1 QD charge state transition one then obtains where either a spin up or down electron can enter the QD. In contrast, only an electron with a fixed spin populates the resonance at any given time and thus the tunneling process out of the QD limits the current. Conversely, for an effective 1 → 2 charge state transition the current is described by where the tunneling process into the QD is spin selective but both a spin up or spin down electron can exit the resonance. Therefore, for an effective 1 → 2 charge state transition, the tunneling process into the QD limits the current. In (1) and (2), Γ L/R are the tunnel couplings between the QD level and the source/drain reservoir and e is the elemental charge. Further, is the Fermi-Dirac distribution of the left/right lead at the QD level position (μ QD ) relative to the electrochemical potential of the leads (μ SD ) δE = μ SD − μ QD [20]. The ability to implement a symmetric device bias is included in (3) and k B denotes the Boltzmann constant. We note that (1) and (2) are capable of describing both, bias driven currents I SD and thermocurrents I th [20,38].
The experimentally detected thermocurrent along the red dashed cutline in figure 2(a) for a heating bias dV R = 46 mV is presented in figure 2(c). Each charge state transition gives raise to a characteristic TE signal in a range of several k B T around μ SD where |f L − f R | 0. Positive current peaks corresponds to a net electron flow from the hot to the cold reservoir where the QD resonance is situated above μ SD (illustrated in figure 2(d)). Negative current peaks correspond to electrons traveling from the cold to the hot side when the QD level is tuned energetically below μ SD (see figure 2(e)).
For the thermocurrent signal around δE = 0 the amplitude of the negative current peak exceeds that of the positive current peak. This suggests that current is limited in a configuration where μ QD > μ SD and f L,R < 0.5. Consequently, the resonance is mostly unoccupied and we identify the tunneling process into the QD as spin-selective, thus thermocurrent-limiting, and find an effective 1 → 2 charge state transition, illustrated in figure 2(d). Conversely, for the TE signal around δE ≈ 5 meV transport through a mostly occupied QD level (μ QD < μ SD , f L,R > 0.5) yields a lower thermocurrent amplitude (see figure 2(e)). Here tunneling out of the resonance is the limiting factor and we identify an effective 0 → 1 QD charge state transition. We therefore use (2) and (1) to first fit Coulomb peaks corresponding to the first and second signal in figure 2(c) and obtain the tunnel couplings in table 1.
With knowledge of the tunnel couplings, we fit the data in figure 2(c) for the reservoir temperatures with a combination of (2) and (1), where an offset correcting factor is added to f L/R in (1) to account for the energy gap between the two QD resonances. The fit (solid red line) is in good agreement with the experimental data and yields T L = 0.75 ± 0.01 K and T R = 1.10 ± 0.01 K.
In figures 3(a)-(d) we present thermocurrent measurements as discussed in figure 2(c) as a function of the heater bias dV H for different combinations of heater and QD locations: QD L heated from g2 (a) and g7 (b) and QD R heated from g2 (c) and g7 (d). The results clearly highlight how the TE signals grow wider for increased heater bias and revert polarity due to the temperature gradient reversal when heating is applied on different sides of the device. We further find traces of excited state contributions to the thermocurrent in (b) and (d), which will be addressed briefly in section 5.
To obtain a detailed picture of the heater effect on the device in a QD geometry, we repeat the thermometry fits on figures 3(a)-(d) and the results for the absolute temperature difference ΔT and the average temperature T as a function of dV H are presented in figures 3(e) and (f), respectively. Due to the non-negligible effect of excited states already at low heating bias in figure 3(d) the fit is limited to the TE signal around δE = 0. We note that the quality of the fit results varies with the heating bias. For low heating the TE signal only consists of very few data points and is affected heavily by the offset bias drift. In contrast, for high heating bias excited states begin to contribute to the TE signal lineshape, which is not covered by the fit. Thus, the best agreement between the fit and data is found in a range dV H = [10 . . . 80] mV.
Interestingly, the fit reveals comparable T across all probed heater and QD combinations. In contrast, ΔT coincides only when either QD is heated from the opposite nanowire end and QD L heated from the left (g1) side results in clearly suppressed ΔT. For QD R heated from the right ΔT initially increases steeply before a decrease in slope at dV R ≈ 40 mV occurs.
To understand the temperature dependence on the heating location, consideration of the heat transfer mediating mechanisms across the nanowire is relevant: first, hot electrons diffuse through the nanowire, leading to an electronic heat flow contribution, dependent on the electron conductivity. Second, hot phonons diffuse through the nanowire and via electron-phonon coupling increase the electron temperature along their path. This phononic heat flow contribution is heavily dependent on the coupling between the phonon and electron bath in the system [39] and the phonon mean free path (PMFP). In the barrier-free nanowire configuration in section 2 the electronic thermal resistance is assumed very low as a direct consequence of the high device conductance, leading to an almost uniform nanowire temperature profile [39]. This is changed by the introduction of a QD to the system. The QD drastically decreases the conductance and suppresses electronic heat transfer away from the charge degeneracy points [40,41], while the phononic contribution is expected to remain unaffected by the QD [7,39]. Because the heating power in our symmetric bottom-heater architecture only depends on the magnitude of dV H rather than the heater location or nanowire configuration, T is found to coincide for all tested QD and heater combinations. In contrast, ΔT, which for the TE effect to occur must be present between the nanowire lead segments surrounding the QD, now becomes strongly dependent on the ratio of the electronic to the phononic heat transfer contributions.
The decreased ΔT for heating in close vicinity to the QD as opposed to heating at a larger distance on the opposite device end indicates that (i) phononic heat transfer is an important contribution to the overall heat flow across the nanowire in the presence of a QD and (ii) the coupling strength of the phonon to the electron thermal reservoir and PMFP now strongly influence the magnitude of the temperature difference ΔT. Consequently, the lower ΔT detected for QD L when heated on the left side (and also QD R for high dV R ) compared to heating from the right (left) side is attributed to an increased phonon mediated heat flow across the QD in close vicinity to the heater electrode.

Thermocurrents in double quantum dots
Qualitative insight on the phonon energies and PMFP in the device can be obtained by studying a configuration in which heat transfer from the hot phonon bath to the electron reservoirs is directly converted to a thermocurrent. This is achieved by the formation of a DQD, combining the left and right QD. In DQD structures, thermocurrents of two different origins are experimentally reported in literature: the TE effect [28,42] and PAT [28,[43][44][45][46]. In recent work, we demonstrated that a weakly coupled DQD is ideal for the detection of PAT, while a strong interdot coupling regime favors observation of the TE effect [28].
Consequently, in order to identify both possible thermocurrent effects reliably, we tune the DQD to an intermediate interdot coupling regime where not only characteristically clear finite bias triangles but also avoided-crossing behavior near the triple points (TP) are observed [10]. The resulting charge stability diagram at V SD = 100 μV is shown in figure 4(a). The device configuration, where g2, g4 and g6 (V 2 = −0.14 V, V 4 = 0.04 V, V 6 = −0.23 V) are used to induce barriers, is schematically illustrated in figure 4  Figure 4(c) shows the thermocurrent across the DQD as a function of the plunger gate biases V 3 and V 5 at dV M = 5 mV in a comparable range to (a). Thermocurrent signals are observed around each TP and we identify two separate transport contributions: along the level detuning axis Δ directional electron transport is achieved by lifting electrons from an energetically lower, occupied to a higher, unoccupied level on the other QD via phonon absorption. This PAT process requires the temperature of the phonon bath T ph > T L,R to exceed that of the electronic system [47] and is schematically illustrated in figure 4(d). In addition, we also observe a weak TE effect along , where the DQD effectively behaves like a single QD as sketched in figure 4(e). The polarity of the TE effect indicates T L > T R , which is in line with the observation in section 2 for heating a barrier-free nanowire configuration on g4. A detailed discussion and disentangling of PAT and the TE effect contribution in DQDs is found in [28].
In a regime where PAT occurs, the DQD essentially acts as a sensitive, energy resolved detector for hot phonons [46]-a concept also exploited for the detection of noise [48] and photons [49]. The total extent of the PAT signal along Δ is a measure for double the maximum energy that can be supplied by phonons for electrons to overcome Δ, 2E ph . To estimate E ph , we locate where along Δ the positive and negative current signal drops below 1% of its maximum amplitude (orange dashed lines in figure 4(c)). At dV M = 5 mV this analysis yields a lower bound for E ph = 0.52 ± 0.08 meV.
Next, we test the impact of the heater location on the thermocurrent across the DQD in an expanded plunger gate range for which the charge stability diagram at V SD = 100 μV is shown in figure 5(a). To quantify the phonon energies in the nanowire at the position of the DQD and dependent on the heating location, we extract E ph . The results with heat applied on g1, g4 or g7 as a function of the heating bias are shown in figure 5(e). For heating on g4 (black circles), where most data points are available, we find a clear scaling of E ph with dV M .
A direct comparison at dV H = 40 mV yields an average reduction of E ph by a factor of 0.64 for heating on g1/7 as opposed to applying heat to g4. Further, to obtain similar phonon energies to heating with dV M = 40 mV, a heater bias of dV R = 100 mV is required. We explain the detected reduction in E ph for an increased distance to the heat source d with damping of the phonons by scattering events [50]. In InAs nanowires at room temperature, PMFPs of l ph = 250 ± 40 nm have been reported [51] and are expected to increase at lower temperatures as a result of a reduction in electron-phonon and phonon-phonon scattering [50]. With the assumption of an exponential decay of the phonon energy E ph ∝ e −d/l ph and a heater center-to-center distance of d = 300 nm between g1/7 and g4, we also estimate the PMFP in the nanowire l ph of several hundred nanometers. The estimated PMFP, which is of the same order of magnitude as the bottom-gate spacing, provides additional evidence of an increase in the phononic heat flow across single QDs formed close to the heater electrode discussed in section 3.  In addition to insights on the PMFP, a comparison of figures 5(b)-(d) further reveals that the magnitude and polarity of the TE effect along depends strongly on the choice of the heater location and is more pronounced for side-in contrast to center heating. To illustrate the TE effect more clearly, we extract cutlines along for heating on g1 (red dashed line in figure 5(c)) and g7 (blue dashed line in figure 5(d)). The thermocurrents along these cutlines are shown in figure 5(f) and demonstrate the reversed polarity of the TE signals forming around each TP. From the polarity of I th , we find as expected T L > T R for heating on the left and T R > T L for heating on the right side of the DQD as illustrated in the insets of figure 5(f).
In line with the discussion in [28] we further observe distinct resonances in the thermocurrent signals in figures 5(c) and (d). A comparison of charge stability diagrams measured at V SD = 2 mV (figure 6(a)) and V SD = −2 mV (figure 6(b)) to a corresponding thermocurrent measurement at dV R = 40 mV (figure 6(c)) yields energetically matching resonances. Resonances attributed to transport through the same QD levels are labeled with matching colors across figures 6(a), (b) (dashed lines) and (c) (colored arrows).
The observed thermocurrent resonances can, in line with the detailed description given in [28], be attributed to two separate effects: (i) PAT from a populated ground-to an unpopulated and aligned ground-and excited-state pair in the two QDs or (ii) the TE through aligned (excited-) states in both QDs. While in [28] the observed resonances in the thermocurrent are attributed purely to PAT, we find a polarity reversal of the current upon following certain resonances (labeled by black arrows in figure 6(c)) along . Because a pure PAT process leads to no current polarity reversal along the observed current modulation on the resonance is characteristic for a TE contribution to the thermocurrent on the resonance. The remaining resonances, not indicated with black arrows in figure 6(c), do not exhibit a thermocurrent polarity reversal and are thus the result of a PAT process via excited states. Further details of the origin of thermocurrent resonances in DQDs is given in [28]. Finally, we note that for heating on g4, the thermocurrent resonances are suppressed as a result of the increased background PAT signal magnitude due to the higher T ph and the absence of a clear TE effect for near symmetric heating. Consequently, resonances in the thermocurrent appear more distinct when heat is supplied from g1 or g7.

Conclusion and outlook
We have characterized an InAs nanowire situated on an array of seven bottom-gates, where selected gates are used to locally apply heat to the device. This device architecture not only enables the formation of various barrier and multi-barrier structures, with full control over relevant tunnel couplings, but also allows local heating with a near perfect symmetry with respect to the electrostatically defined barrier configurations. The low-temperature experiments presented here verify the device concept by studying thermocurrents in a plain nanowire configuration, electrostatically defined QDs and a DQD. We find the device to produce high quality bias and thermocurrent data and confirm symmetric heating effects when heating with different gates.
The transition from a barrier-free nanowire to a QD configuration is expected to drastically affect heat flow through the nanowire as a result of the suppressed electronic heat flow contribution [39,41]. We use thermocurrent measurements on QDs situated on different sides of the nanowire to probe the local temperature on the either side of the barriers. By selection of suitable charge transitions on each QD, similar to epitaxially defined QDs [18], simple thermometry is accessible for moderate heating without excited state effects being present. The results indicate the importance of a heater-to-QD distance dependent phononic heat-flow in the InAs nanowire. By using a DQD as an energy selective phonon detector, we find that our heating technique elevates the temperature of the phonon-bath beyond the electronic temperature of the device. Further, the DQD PAT measurements confirm a phonon energy loss for an increased DQD-center distance to the heater, which indicates a PMFP of the order of magnitude of the gate-electrode spacing.
Based on the proof-of-principle work presented in this paper, we suggest in the following a selection of research directions and future experiments for which we believe our combined bottom-gate and heater architecture to be ideally suited.
PAT in single QDs: in figure 3(d) for the charge state transition at δE ≈ 5 meV we observe additional effects to the ground-state TE effect for QD R heated from the right (also QD L heated from the left) as opposed to heating from a larger distance on the leftmost (rightmost) gate. Because ΔT and T are comparable across both measurements, this indicates an origin other than an excited state contribution to the TE effect. The apparent heater-distance dependence suggests a PAT-based effect. In QDs, microwave photon absorption in the contacts reportedly leads to similar signals [52,53] but detection requires either charge sensing [54], a bias V SD [55] or an asymmetric coupling of the microwave-field to the source-and drain reservoirs [56]. As a result of the short PMFP in our nanowire, the phonon-bath could be coupled differently to the source and drain electron reservoirs, but the observed effect warrants further investigation.
Heat flow characterization: the ability to (i) use QDs for electron thermometry, (ii) DQDs for phonon detection, (iii) change the location of the QD and DQDs with respect to the heater position in controlled steps and (iv) control all relevant tunnel couplings sets the stage to study heat flow characteristics and the PMFP in nanowires. This not only allows independent characterization of the electronic and phononic heat transfer across the nanowire but also serves as a test bed for deviations from the Wiedmann-Franz law, which are expected in QD devices and vary with the coupling to the leads [40,[57][58][59][60].
Three-terminal thermal energy harvesting: the PAT process in DQDs essentially converts a heat flow from a hot phonon-bath to the electron-bath to electrical power and thus acts as a three-terminal energy harvester [28,61,62]. Such systems have gained interest in recent years as they allow access to a regime where fluctuations are highly relevant and thermodynamic uncertainty relations are theoretically predicted to result in trade-offs between power, power fluctuations and the efficiency [63,64]. Further, a DQD coupled to a phonon-bath has a predicted functionality as phonon TE transistor and rectifier [65]. Our device architecture offers ideal conditions to study the properties of a DQD thermal energy harvester. P-n hybrid devices: our gate architecture allows (i) fully independent gating of separate nanowire sections and (ii) symmetric heating in the nanowire center. In combination with a small bandgap semiconductor nanowire, such as InSb [66], where through moderate gating either p-or n-type behavior can be induced, a single nanowire p-n thermocouple can be realized. This is possible by heating in the center of two nanowire segments tuned to a p-and n-regime, respectively. Taking this concept further, a serial DQD consisting of a p-and n-type QD can be phonon coupled and via PAT give insight into electron-hole interactions where traditional current spectroscopy is blocked.