Synthesis of Ultra-Thin Superionic Cu 2 Se and New Aspects of the Low-Temperature Crystal Configurations

Superionic conductors offer unique advantages for novel technological devices in various fields, such as energy storage and neuromorphic computing. Above 414 K, Cu 2 Se turns into a well-known superionic conductor via a phase transition, and it is demonstrated to exhibit peculiar electrical and thermoelectric properties in bulk. Here, we report a large-area synthesis of ultra-thin single crystalline Cu 2 Se using the chemical vapor deposition method. We demonstrate that Cu 2 Se crystals exhibit optically and electrically controllable robust phase reconfiguration below 414 K. Moreover, our results show that the mobility of the liquid-like Cu ion vacancies in Cu 2 Se causes macroscopic fluctuations in the Cu ordering. Consequently, phase variations are not dictated by the diffusive motion of the ions but by the local energy minima formed due to the interplay between the extrinsic and the intrinsic material parameters. As a result, long-range ordering of the crystal below 414 K is optically observable at a micrometer scale. Our results show that Cu 2 Se could find applications beyond thermoelectric such as smart optical coatings, optoelectronic switching, and ionic transistors.

a. Schematic of a substrate-engineered device: a MoS2 flake is suspended over a circular hole drilled in the substrate. Metal contacts are used for scanning photocurrent microscopy (SPCM), scanning thermal gate microscopy (SThGM) and I-V measurements. The inset shows a magnification of the area indicated by the dashed yellow square, where Seebeck coefficients of supported and suspended parts are labelled with 1 and 2 , respectively. b. Optical microscope image of a multilayered device over circular holes with indium contacts, marked with grey overlays. Scale bar: 10 µm. In the following we predict that a thermoelectric junction with a Seebeck coefficient difference of tens of µV/K can be fabricated when connecting regions of suspended MoS2 to supported regions. We assume that the Seebeck coefficient in thermal equilibrium is composed of contributions from the energy-dependent diffusion ( ), scattering ( τ ) and the phonon-drag ( ), so that = + + 9,10 . Here, and τ terms can be written from the Mott relation assuming that MoS2 is in the highly conductive state and electrons are the majority carriers: where is the temperature, is the Boltzmann constant, is the electron's charge, is the relaxation time, is the Fermi energy, is the conduction band edge energy, is scattering parameter and is the energy. ( ) is the m-th order Fermi integral 11 . In the 2d limit, is energy independent, thus is zero. term can be estimated from the theory of phonon-drag in semiconductors in the first order as = − where, and are the group velocity and the mean free path of a phonon, is a parameter to modify the electron-phonon interaction strength and ranges from 0 to 1, and is the electron mobility, respectively 10 . Importantly, and are heavily affected by the presence of a substrate 12 which implies that the term gets strongly modified when the MoS2 flake is suspended.
To test this hypothesis, we fabricated substrate-engineered MoS2 devices by mechanical exfoliation and dry transfer 21 of atomically thin MoS2 flakes on substrates (sapphire or oxidized silicon) with prepatterned trenches/holes formed by focused ion beam (FIB). We contacted the flakes with Indium needles [22][23][24] which are suitable for achieving Ohmic contacts to MoS2 25,26 (gold-contacted device measurements are shown in Supporting Information). A typical device is shown in Figure 1b. We then used scanning photocurrent microscopy, to locally heat up the junction with a focused laser beam and to measure the photothermoelectric current that is generated (see Methods for experimental details). Figure 1c shows the greyscale reflection intensity map and the corresponding photocurrent distribution over the device. For the few-layer suspended MoS2 devices we observe a bipolar photoresponse at the junctions between the supported and the suspended part of the crystal. The spatial distribution of the signal agrees well with the finite element analysis simulations, given in the supporting information, and suggests the formation of a thermoelectric junction. When applying a voltage bias to the junction, the photocurrent, changes linearly with bias, while the photoconductance, = − 0 ( , 0 : photocurrent under and 0 mV bias, respectively) stays constant (Figure 1d). Such bias-independent photoconductance is typically an indication for an photothermoelectric nature of the observed signal 22,24,[27][28][29] . Although we propose that the photocurrent in substrate-engineered MoS2 devices is dominated by the photothermal effect (PTE) 30,31 , other possible mechanisms have been reported that may lead to a photovoltaic response. These include (1) strain related effects such as strain modulation of materials properties and flexophotovoltaic effect 13 , and (2) substrate proximity related effects that forms a built-in electric field 32 .
Next, we present experimental evidence for a thermoelectric origin of the observed photocurrent. To this end, we employed scanning thermal gate microscopy (SThGM), where a hot AFM tip heats up the junction locally while the resulting voltage build-up on the devices is recorded (see Methods). Since no laser-illumination of the sample is required in this method, it can be used to ultimately exclude photovoltaic effects. Figure 2 compares SPCM and SThGM maps of the same holes. We observed the same bipolar signals in the suspended regions with both experimental methods. Thanks to its sub-100 nm lateral resolution, SThGM further allows us to observe local variations of the thermovoltage in supported MoS2 that can be attributed to charge puddles induced by local doping via the substrate [33][34][35] . We confirmed that the SThGM signal disappears when no power is dissipated in the probe heater, which rules out parasitic effects induced by the laser used for AFM feedback. Furthermore, SThGM allows us to estimate the magnitude of the local Seebeck coefficient variations. Using the probecalibration data we obtain a value of Δ = 72 ± 10 µV/K (See supporting information). Despite the uncertainties regarding the real sample temperature, the obtained Δ value is very close to the theoretically predicted value. To understand why suspending MoS2 alters its Seebeck coefficient, we first would like to discuss the possibility of strain induced changes in the materials properties. MoS2, like graphene, is nominally compressed when deposited on a substrate [36][37][38][39] . Upon suspending the crystals, the free-standing part either adheres to the sidewalls of the hole and dimples or, bulges. As a result, strain might be present in the free-standing part of the crystal. Strain can affect both the bandgap and the Seebeck coefficient of MoS2. The indirect optical gap is modulated by -110 meV/%-strain for a trilayer MoS2 36,40 . Ab initio studies show a ~10% decrease in the Seebeck coefficient of monolayer MoS2 per 1% tensile strain 41 . To estimate the biaxial strain, we performed atomic force microscopy (AFM) height trace mapping on the samples. Most samples, regardless of the geometry of the hole exhibit slight bulging of a few nanometers. For the MoS2 flakes suspended on the circular holes in the device shown in Figure 3a, the bulge height is ≈ 25 nm. Similar values were measured for other devices. The biaxial strain can then be calculated using an uniformly loaded circular membrane model, and is as low as 0.0025% 42 . Such a small strain on MoS2 is not sufficient to induce a significant change in bandgap or Seebeck coefficient [43][44][45] .
Next, we consider the substrate induced changes on the material properties. The presence or the absence of the substrate can cause enhanced or diminished optical absorption due to the screening effects, Fermi level pinning 46 and charges donated by the substrate 7,47 . More significantly, the doping effect due to the trapped charges at the interface with the substrate can locally gate the MoS2 and modify the number of charge carriers 48 and thus its Seebeck coefficient. To investigate the electrostatic impact of the substrate on the MoS2 membrane, we investigated the surface potential difference (SPD) on devices using Kelvin Probe Force Microscopy (KPFM). SPD can provide an insight on the band bending of the MoS2 due to the substrate effects 49 . Figure 3b-d shows the AFM height trace map and the uncalibrated SPD map of the sample. SPD across the supported and suspended part of the flake is on the order of 50 mV. This shift in the SPD value hints that there is a slight change in the Fermi level of the suspended part with respect to the supported part of the crystal. The same type of charge carriers is dominant on both sides of the junction formed by the suspended and supported parts of the crystal. The band structure formed by such a junction in zero bias cannot be used in separation of photoinduced carriers 50 , however, it can lead to the formation of a thermoelectric junction 11,51 . This is in line with the SThGM measurements. In the remainder of the paper, we aim at controlling the electrostatics that are responsible for the formation of a thermoelectric junction. Charge transport in MoS2 is dominated by electrons due to unintentional doping 52,53 . Modulating the density and the type of free charge carriers can be done by applying a gate voltage to the junction 54 . This significantly modifies the magnitude and the sign of the Seebeck coefficient as demonstrated in previous studies 16,30,31,55 . The Mott relation 56 can be used to model the Seebeck coefficient as a function of : Here, is the temperature, is the Boltzmann constant, is the electron's charge, is the device resistance, is the Fermi energy and is the energy.
Since hole transport is limited due to substrate induced Fermi level pinning on SiO2 supported MoS2 field-effect devices, 46 to observe the sign inversion of the Seebeck coefficient (see the Supporting Information for measurements on device fabricated on SiO2 and Al2O3 coated SiO2) we followed an alternative approach to emulate suspension: we fabricated heterostructure devices where the crystal is partially supported by hexagonal boron nitride (h-BN). h-BN is commonly used to encapsulate twodimensional materials thanks to its hydrophobic and atomically smooth surface. This leads to less unintentional doping due to the interfacial charge trapping and reduced electron scattering 7,57,58 . A ~10 ML MoS2 is placed over a 10 nm thick h-BN crystal to form a double-junction device (see supporting information for a single-junction device formed by a MoS2 flake which is partially placed over a h-BN flake) and indium contacts are placed over the MoS2. The device is on 1 µm thick oxide coated Si substrate where Si is used as the back-gate electrode. Figure 4a shows the optical micrograph of the device and its schematic. The presence of h-BN modifies the SPD by 80 mV -a value very similar to the values we find for suspended devices (see SI) -which is consistent with the relative n-doping by the h-BN substrate 32,57 . We therefore attribute this difference to the Fermi level shift due to the difference in interfacial charge doping by the different substrates.

Figure 4b
shows the SPCM map under zero gate voltage. We observe a bipolar photocurrent signal from the junctions between h-BN and SiO2 supported MoS2. Raman mapping (see the Supporting Information) reveals slight intensity decrease and a small shift of the A 1 peak over the h-BN supported part of the MoS2. This is consistent with the stiffening of the Raman mode due to the higher degree of charged impurities in SiO2 as compared to h-BN 7 . By applying a gate voltage to the device, its resistance can be tuned significantly as free charges are depleted (Figure 4c). Under large positive gate voltages, the I-V characteristic becomes asymmetric. To investigate the dependence of the photocurrent on carrier type and concentration, the laser is held at specific positions on the device as marked in Figure 4d, and the gate is swept from positive to negative voltages with respect to the ground terminal. For positive gate voltages, the magnitude of the photoresponse from both junctions, between h-BN and SiO2 supported MoS2, (points 2 and 3) decrease. When a negative gate voltage is applied, the magnitude of the photoresponse at both junctions increases by almost a factor of two at = −21.5 V. Once this maximum is reached, the amplitude of the photocurrent at both points decreases and has the same value as the photocurrent generated over the MoS2 (point 4) at = −34.5 V.
These observations can be qualitatively explained as follows: at a gate voltage of = −34.5 , the majority charge carrier type in the h-BN supported part changes from electrons to holes. As a consequence, the Seebeck coefficients of MoS2 resting on h-BN and SiO2, respectively, become similar, which leads to ∆ ≈ 0, and curves 2,3 and 4 in Figure 4d cross. The photocurrent signal recorded near the indium contacts (points 1 and 5) decreases non-monotonically with decreasing and reaches zero at = −40 . At this voltage the Seebeck coefficient of MoS2 on SiO2 reaches that of Indium (SIn = + 1.7 µV/K) 59 .
In conclusion we demonstrated that substrate engineering can be used to generate a thermoelectric junction in atomically thin MoS2 devices. Similar strategies can be employed in other low dimensional materials that exhibit large and tunable Seebeck coefficients. This might in particular be promising at low temperature where effects like band-hybridization and Kondo scattering can produce a very strong photothermoelectric effect 9 .

Competing Interests
The Authors declare no Competing Financial or Non-Financial Interests.

Methods
SPCM setup is a commercially available setup from LST Scientific Instruments Ltd. which offers a compact scanning head with easily interchangeable lasers. Two SR-830 Lock-in amplifiers are employed, one for the reflection map and the other for the photocurrent/voltage measurements. In the main text we reported the photocurrent (a measurement of the photovoltage is given in Figure  S2). The incident laser beam is chopped at a certain frequency and focused onto the sample through a 40x objective. The electrical response is collected through gold probes pressed on the electrical contacts of the devices and the signal is amplified by a lock-in amplifier set to the chopping frequency of the laser beam. Although various wavelengths (406, 532, 633 nm) are employed for the measurements, unless otherwise stated we used 532 nm in the experiments reported in the main text (see Figure S3 for SPCM measurements with different wavelengths). All the excitation energies are above the indirect bandgap of the few layer MoS2.
Scanning Thermal Microscopy measurements were performed with a Dimension Icon (Bruker) AFM under ambient conditions. The probe used in the experiments is VITA-DM-GLA-1 made of a palladium heater on a silicon nitride cantilever and tip. The radius is typically in the order of 25-40 nm. The heater is part of a modified Wheatstone bridge and is driven by a combined 91 kHz AC and DC bias, as reported elsewhere. The signal is detected via a SR830 lock-in amplifier and fed in the AFM controller. This signal monitors the probe temperature and thus allows to locally map the thermal conductance of the sample. In this work, the power supplied to the probe gives rise to a 45K excess temperature.
While the probe is scanning the sample, we measure the voltage drop across the device using a low noise preamplifier (SR 560). This voltage is created by the local heating induced by the hot SThM tip. It is then fed also to the AFM controller and recorded simultaneously. In this study, the thermovoltage measurements were performed without modulating the heater power. We note that it is also possible to generate similar maps by varying the heater temperature and detecting thermovoltage via lock-in detection.

Data Availability
Source data available from the corresponding authors upon request.

Theoretical prediction of the substrate-effect induced Seebeck coefficient difference in MoS2
As discussed in the main text, we assume that the Seebeck coefficient S in thermal equilibrium is composed of contributions from the energy-dependent diffusion ( ), scattering ( τ ) and the phonondrag ( ), so that = + + . Here, and τ terms can be written from the Mott relation assuming that MoS2 is in the highly conductive state and electrons are the majority carriers: As mentioned in the main text, τ is zero as is energy independent in the 2d limit. term is composed of constants related to material properties, scattering parameter and the Fermi integral . The scattering parameters of 2d materials are listed in Table   1. 1,2 Here, as discussed in detail in Ref. 1 , = 0 adequately accounts for the acoustic phonon scattering and small deviations of experimental data from the calculated values is due to the other scattering mechanisms. As a result, at the room temperature for suspended MoS2 (10 12 cm -2 ) is about -400 µV/K and for SiO2 supported MoS2 (10 13 cm -2 ) is about -200 µV/K. term can be estimated from the theory of phonon-drag in semiconductors in the first order as = − where, and are the group velocity and the mean free path of a phonon, is a parameter to modify the electron-phonon interaction strength and ranges from 0 to 1, and is the electron mobility, respectively. As the dominant charge carriers are electrons, term has a negative sign. We use the parameters given in Table 2. Based on the values given in the table we obtain 2 = −230 µV/K and = −100 µV/K.
The total = + for suspended and SiO2 supported parts can be calculated by adding both contributions.
= −500 µV/K and 2 = −430 µV/K. Of course, we consider this to be a rough estimate as we ignore charged impurity scattering and strongly screeded Coulomb scattering. Also there are certain errors associated with the measurement of the parameters used for the calculation of the Seebeck coefficients. However, overall, this calculation shows that the substrate induced effect must be present under right experimental conditions.

SPCM map on a gold electrode substrate engineered MoS2 device
Throughout the study we used indium contacted devices thanks to their rapid fabrication. To compare our indium device results, we fabricated gold contacted devices. Figure S1 shows the optical microscope images and corresponding SPCM reflection and photocurrent maps. There is no qualitative difference between the indium contacted devices and gold contacted device in the substrateengineered photocurrent. Despite IV measurement is collected from 0.25 to -0.25 V its rectifying behaviour can be observed. Power dependence of the photocurrent from the substrate engineered junction is also comparable to the one reported in indium contacted devices.  Figure S2 shows an MoS2 device fabricated on trenches drilled on sapphire with different depths. We performed SPVM, AFM and KPFM Measurements. First, AFM measurements show that the crystal is stuck to the bottom of the 100 nm deep trench (Figure S2b). For the rest of the trenches the flake bulges about 10 nm above the surface (Figure S2c). AFM height trace map also reveals a peculiar wrinkle formation over the suspended part of the flake.

Scanning photovoltage microscopy, AFM and KPFM measurements on a parallel trench device
In this measurement we operated the scanning microscope at photovoltage mode. Figure S2d shows the reflection map and the corresponding photovoltage map. The bipolar response is evident with slightly lower positive signal in some of the trenches. This asymmetry can be explained by lower heating of one side of the samples due to the scan direction. One important observation that agrees well with the photothermoelectric photoresponse is that the 100 nm trench shows very small photovoltage as compared to other trenches.

SPCM maps taken at different laser wavelengths and incidence polarization
We used three different wavelengths, 406, 532 and 633 nm, in our experiments all of them which are at an energy larger than the band gap of MoS2. Figure S3 shows the SPCM results collected with different laser wavelengths. Also, polarization dependence of the photocurrent measured at each end of the trench as well as a point over the contact is given in Figure S3f. There is no polarization dependence of the photocurrent. This shows that The effect is not due to built in polarization fields.

Figure S3 a.
Optical microscope image of a two-terminal substrate-engineered MoS2 device with different trench widths. Scale bar is 10 µm. b. SPCM reflection map of the region marked with yellow rectangle in a. c, d and e show photocurrent map taken at different wavelengths. At each run laser power is set to ~40 µW. The measured signal in all three measurements are very close and the overall photocurrent features are the same. f. Incident polarization of the 633 nm laser is rotated and is measured at three different points marked by colored arrows on d, black dots-near contact, red dotsat the positive side and blue dots-at the negative side of the trench. There is no polarization dependence of the measured photocurrent at the three points where photocurrent is measured.

Finite element simulation of a substrate modified thermoelectric junction
To understand how a substrate modified thermoelectric junction would behave depending on how the contacts are configured, we performed finite element analysis simulations using COMSOL Multiphysics. An irregularly shaped crystal is modelled over a substrate with a hole and voltage at a floating terminal is measured with respect to different laser positions. The observed pattern agrees with our measurements. Figure S4 shows the thermoelectric emf generated and temperature distribution maps.

Gate dependent measurements
We performed gate dependent SPCM measurements both on suspended and h-BN supported MoS2 devices. In both cases, we used 1 µm SiO2 coated Si wafers. Si is used as the back gate in both device configurations. We reported the h-BN supported junctions in the main text as devices over holes showed significant change upon application of negative gate bias. Figure S5 shows the degradation of the suspended device. After application of a few volts the device irreversibly shows a contrast change starting from the edges of the hole. We fabricated a long trench with open ends to see if the trapped air within the hole is causing the observed contrast change. However, same contrast change is observed after applying negative gate voltages. We observe that the contrast change starts from near the hole and expands from there. At the moment we are not fully aware of the reasons leading this contrast change. We consider that the release of the adsorbed molecules on the surface of the substrate under large negative gate voltages lead to such degradation. To prevent the sample degradation problem under large negative gate voltages, we coated the substrate surface with 5 nm thick Al2O3 using atomic layer deposition (ALD) method after milling the holes with FIB. Then, the device is fabricated over the ALD coated surface. The device didn't show any sign of degradation and produced pronounced photoresponse. Measurements from the device is given in Figure S6. Although the device exhibits the expected gate dependent response, as discussed in the main text, there is no carrier inversion induced reduction in the photovoltage due to the Fermi level pinning. H-BN supported devices performed better and showed no sign of such a contrast change. Figure S7 shows the reflection and the photocurrent maps reported in the main text and the photocurrent from point 2 and 3 subtracted from point 4, marked on the photocurrent map. Both junctions of the h-BN show almost identical response under gate voltage (point 3 data is multiplied by -1 for viewing convenience). Figure S8 a. Same figure from the main text is copied here for convenience. b. Raman intensity map and the 1 peak shift map is given. c. Gate dependent signal from point 4 is subtracted from the gate dependent data from point 2 (red curve) and point 3 (blue curve). Blue curve is multiplied by -1 for viewing convenience.

Scanning Thermal Microscope Calibration and Seebeck variation estimation
The Scanning Thermal Microscope (SThM) measurements were performed on a commercial Bruker Icon instrument with a VITA-GLA-DM-1 probe. The probe, consisting of the silicon nitride lever with a Pd heater/thermometer has been calibrated on a hot plate to relate the temperature to its electrical resistance. The calibration curves are shown on figure S9. Temperature as a function of electrical resistance As described elsewhere 4,5 , the probe is part of a modified Wheatstone bridge which is balanced at low voltage. During the measurements, we applied a combined AC (91 kHz) and DC bias on the bridge which heats the probe and creates a bridge offset that directly measures the probe heater temperature. For most experiments, we applied 1mW on the probe creating a Δ of 50 ± 2 K, when the probe was far away from the sample.
When the SThM tip is brought into contact with the devices, it locally heats the materials below its apex. While the probe scans the surface, the device open circuit voltage is recorded and amplified via a SR830 voltage preamplifier. This voltage is referred to as the thermovoltage. We excluded any shortcut between the probe and the device as no leakage current could be measured between the probe and both contacts.
The thermovoltage can be written analytically as 6 As shown elsewhere 6,7 , it is possible to deconvolute the Seebeck coefficient from the temperature gradient. This however requires a precise estimation of the temperature gradient and thus the sample temperature rise under the tip, Δ .
As we know the probe temperature far away from the sample (50 ± 2 K) and we monitor its temperature via the Wheatstone bridge, we know that the probe temperature in contact with the sample is 43.8 ± 4 K. The probe cooling occurs because of several heat transfer mechanisms 4,5 (solidsolid conduction, air conduction, water meniscus, …).
For those probes, the Pd heater is however distributed over the whole triangular shaped silicon nitride tip 4,5 . This implies that the tip temperature and probe temperature are different. We turned to finite element modelling (COMSOL Multiphysics) to estimate the tip temperature over the MoS2 suspended and supported sample. Figure S10 shows the overall simulated probe and sample.
We used reported values for the in-plane and out-of-plane MoS2 thermal conductivity as well as for the MoS2-glass interface conductance. Reported values vary greatly in literature [8][9][10][11][12][13][14][15][16] . However, to the best of our knowledge, for a thick sample (>10 layers), the values are on the order of 30 Wm -1 K -1 for the supported in-plane, 60 Wm -1 K -1 for the suspended in-plane and 3 Wm -1 K -1 for the cross-plane conductivities. For the substrate interface conductance, we used 1 MWm -2 K -1 . Using those material parameters, we estimated a ratio between the probe temperature and the tip apex temperature of 4.9. The model also accounts for the tip-sample thermal resistance. This method and model were experimentally confirmed elsewhere 4,5,17 . Taking these into consideration, we obtain a sample temperature rise Δ of 7.4 ± 0.7 K. This gives a Seebeck variation of 72±10 µVK -1 .