Abrupt p-n junction using ionic gating at zero-bias in bilayer graphene

TL;DR

This paper demonstrates a novel method to create abrupt p-n junctions in bilayer graphene using ionic gating at zero bias, revealing enhanced photothermoelectric effects and potential for large-area optoelectronic devices.

Contribution

The authors introduce a new technique combining electrostatic and electrolytic gating to form abrupt p-n junctions in bilayer graphene without bias, enabling improved optoelectronic properties.

Findings

Presence of two Dirac peaks confirms p-n junction formation.

Photovoltage increases at lower temperatures, indicating supercollision scattering.

Six-fold photovoltage pattern suggests hot electron photothermoelectric effect.

Abstract

Graphene is a promising candidate for optoelectronic applications. In this report, a double gated bilayer graphene FET has been made using a combination of electrostatic and electrolytic gating in order to form an abrupt p-n junction. The presence of two Dirac peaks in the gating curve of the fabricated device confirms the formation of a p-n junction. At low temperatures, when the electrolyte is frozen intentionally, the photovoltage exhibits a six-fold pattern indicative of the hot electron induced photothermoelectric effect that has also been seen in graphene p-n junctions made using metallic gates. We have observed that the photovoltage increases with decreasing temperature indicating a dominant role of supercollision scattering. Our technique can also be extended to other 2D materials and to finer features that will lead to p-n junctions which span a large area, like a superlattice, that can generate a larger photoresponse. Our work creating abrupt p-n junctions is distinct from previous works that use a source-drain bias voltage with a single ionic gate creating a spatially graded p-n junction.

Tables

Table 1. Table 1: Comparison of reports of formation of p-n junction in graphene and related 2-D materials

Reference	Material Used	Study
Zhang et. al. [28]	MoS2	Spatially graded p-n junction with bias dependent barrier height using ionic liquid
Chakraborty et. al. [27]	Bilayer Graphene	Spatially graded p-n junction with bias dependent barrier height using solid polymer electrolyte
He et. al. [26]	Graphene (CVD)	p-n-p junction using ionic liquid and electrostatic back gate. Junction is abrupt but each region is a few millimetres wide and spatial control of the geometry is not possible.
Our Work	Bilayer graphene	Hybrid gating (combination of electrostatic and electrolytic gating) using ionic liquid, formation of abrupt junction and photoresponse study.

Equations

$$PV(V_{BG},V_{TG})=[S(n_{BG})-S(n_{TG})]\Delta T$$

$$S=\frac{{\pi }^2{k}_B^{2}T}{3e}\frac{d(lnR)}{dn}\frac{dn}{dE}$$

$$PV=f_{PV1}(V_{BG})-f_{PV2}(V_{BG}+\eta (V_{TG}))$$

$$q_{1}=\Big{[}\frac{A_{2}\epsilon_{a}\epsilon_{b}}{a\epsilon_{b}+b\epsilon_{a}}+\frac{\epsilon_{a}}{a}\left(A_{1}+A_{3}\right)\Big{]}v_{1}+\Big{[}-\frac{\epsilon_{a}}{a}\left(A_{1}+A_{3}\right)\Big{]}v_{2}+\Big{[}-\frac{A_{2}\epsilon_{a}\epsilon_{b}}{a\epsilon_{b}+b\epsilon_{a}}\Big{]}v_{3}$$

$$q_{2}=\Big{[}-\frac{\epsilon_{a}}{a}\left(A_{1}+A_{3}\right)\Big{]}v_{1}+\Big{[}\left(\frac{A_{3}\epsilon_{b}}{b}+\frac{\epsilon_{a}}{a}\left(A_{1}+A_{3}\right)\right)\Big{]}v_{2}+\Big{[}-\frac{A_{3}\epsilon_{b}}{b}\Big{]}v_{3}$$

$$q_{3}=\Big{[}-\frac{A_{2}\epsilon_{a}\epsilon_{b}}{a\epsilon_{b}+b\epsilon_{a}}\Big{]}v_{1}+\Big{[}-\frac{A_{3}\epsilon_{b}}{b}\Big{]}v_{2}+\Big{[}\frac{A_{2}\epsilon_{a}\epsilon_{b}}{a\epsilon_{b}+b\epsilon_{a}}+\frac{A_{3}\epsilon_{b}}{b}\Big{]}v_{3}$$

$$C_{12}=\frac{\epsilon_{a}}{a}\Bigg{[}\frac{1}{f\left(a\epsilon_{b}+b\epsilon_{a}\right)}\left(A_{1}a\epsilon_{b}+A_{1}b\epsilon_{a}+A_{2}a\epsilon_{b}+A_{3}a\epsilon_{b}+A_{3}b\epsilon_{a}\right)\Bigg{]}$$

$$PV(V_{BG},V_{TG})=f_{PV1}(V_{BG})-f_{PV2}(V_{BG}+\eta (V_{TG}))$$

Full text

Introduction

Graphene [1] has unique optical [2, 3, 4] and electronic [5] properties which has made it a promising material for optoelectronic devices such as photodetectors. The creation of p-n junctions with tunable chemical potentials allows the transduction of light into electrical signals. In conventional electrostatic gating, a metallic gate separated by a dielectric is used. The maximum carrier density, typically $5\times 10^{12}$ $\textrm{cm}^{-2}$ for silicon dioxide, is limited by the breakdown strength of the dielectric.

Electrolytic gating [6] is an alternate technique that has the advantage of large achievable carrier densities, $\sim 4\times 10^{13}$ $\textrm{cm}^{-2}$. This is limited by the leakage current through the electrolyte  [7]. The large capacitance is a result of the formation of an interfacial electrical double layer [8] with a thickness of $\sim 1$ nm. Electrolytic gating has been used for tuning the carrier density in various semiconductors such as organic polymers [9], carbon nanotubes [10], and superconductors  [11, 12]. Other non-tunable techniques for large doping density include chemical doping [13, 14], exposure to electron beams [15] or light[16, 17], incorporating dopant atoms in the lattice [18, 19] and other growth techniques [20]. Graphene can be electrolytically gated using different types of electrolytes such as aqueous solutions of salts [21], solid polymer electrolytes of lithium or potassium salts in a polymer matrix [6], ionic liquids [22] and their gels [23]. Electrolytic gating has been used previously in order to explore properties such as superconductivity in MoS2 [24]. The achievement of large carrier density is important for the study of properties of graphene below the Bloch-Grüneisen temperature [25]. The added advantage of this technique is that the ionic liquids have larger optical transmission compared to a metallic top gate.

In this article, we demonstrate the formation of a p-n junction in graphene using a combination of electrostatic and electrolytic gating at zero bias. Part of the graphene is covered with a protective layer of hydrogen silsesquioxane (HSQ) resist which prevents the electrolytic top gate from influencing the entire graphene region. Creating p-n junctions at zero bias using electrolyte gates is scalable and has not been done before. Graphene p-n junctions have previously been created using metallic gates and with electrolytic gating by putting ionic liquid drop on millimetre sized CVD graphene [26] and by applying a drain-source bias comparable with the gate voltage [27]. Using the existing non-zero bias technique, an abrupt p-n junction is difficult to realize. With our technique, we can create an abrupt profile which is important for optoelectronic applications. Further, we have independent control of the source drain bias voltage and p-n junction barrier height and using a zero bias is possible. Table 1 summarizes work related to the formation of p-n junction by various techniques and establishes novel aspect of our work. Figure 1 shows a comparison of the abrupt p-n junction profile that we have formed and compared it to previous reports that use a source–drain bias voltage to create a gradual junction using electrolytic gating.

To demonstrate the p-n junction we measure the gating curve and observe two Dirac peaks. We also study the electrical properties of the p-n junction and the photoresponse as a function of the junction barrier height and temperature. We find that the photoresponse is dominated by the photothermoelectric effect, characterized by a sixfold pattern in the photovoltage, similar to the results obtained with electrostatic dual gates [29]. The photovoltage increases as the temperature decreases which is indicative of hot electron thermalization by disorder assisted supercollisions [30].

Experiment

Graphene flakes identified with visual contrast and Raman spectroscopy (Supplementary Section I) were mechanically exfoliated on Si/SiO2 (300 nm) chips and metallization with titanium (7 nm) and gold (85 nm) is done using standard electron beam lithography. The ionic liquid reacts with electrodes made from chromium and gold and this limits the metals that can be used. A large in-plane electrode is made in the vicinity of graphene to serve as the top gate electrode.

In order to mask the graphene to protect it from the ionic liquid, we have tried partial coverage with polymethylmethacrelate (PMMA) resist, with overexposed PMMA, and HSQ resist. We found that PMMA tended to dissolve in the ionic liquid over time and LiClO4 in a PEO matrix was not sufficiently optically transparent (Supplementary Section II). Multiple electrodes are present on each of the regions so that the the electrical properties can be separately measured and we can verify that the resist protects graphene from ionic gating. We have used a thick (500 nm) HSQ protective layer patterned with a dose of 350 $\mu$C/cm2. We have also fabricated devices completely covered with HSQ in order to verify that they are not affected by the ionic top gate (Supplementary Section III).

An optical image of the device used and the measurement scheme is shown in Figure 2. Measurements are performed in an optical cryostat with simultaneous measurement of the resistance and photovoltage.

Ionic liquids [31] are salts that are liquid at room temperature, are transparent and stable. We have used the ionic liquid EMI-Im (also called EMI-TFSI). Its glass transition temperature [32]is 175 K and melting point [33] is 258 K. Below the freezing point, the ions in ionic liquid are immobilized and do not respond to externally applied fields. Our measurements are conducted above (273 K) and below (30 - 150 K) the freezing point. Changing the voltage applied to the ionic gate at $T\leq 150\>\text{K}$ is done by cycling the temperature. Ionic liquids are hygroscopic [34] and their electrical properties are degraded by water absorption. Dehydration is usually done by heating in vacuum or by freeze drying [35]. Our measurements are performed in an optical cryostat, and the device is initially cooled to around 30 K in vacuum, leading to removal of water.

We have noticed that it is necessary to put a very small amount of ionic liquid so that the size of the droplet is small. When the ionic liquid drop covers a large area, the back gate capacitance increases, similar to the effect seen by Xia et al. [36]. We have estimated that the effective increase in back gate capacitance is by factor of $\sim$ 7 for a drop size of $\sim 1$ mm2 (Supplementary Section IV). Besides this, a large ionic liquid drop can touch the aluminium wire bonds with which it reacts. We use a 25 $\mu m$ wire-bonder wire to wick a small amount of the ionic liquid and put in on the graphene device. The HSQ surface, in contrast with overexposed PMMA tends to repel the ionic liquid and this can be an added factor in the ionic liquid preferentially covering only the exposed parts of graphene. The refractive index of the ionic liquid and HSQ are nearly identical ($\sim 1.5$) so that a surface of uniform refractive index is presented to the incident light (Supplementary Figure S5).

We have also monitored the current through the top gate using a sourcemeter to find the usable electrical limits of the top gate voltage (Supplementary Section V). A top gate voltage of $\pm 2.5$ V results in a current less than 1 nA. This current does not change if we turn on the laser illumination, indicating an absence of photochemical reactions. After applying a top gate voltage of 4 V, we have observed that the Ti/Au electrodes directly under the ionic liquid were corroded and the ones protected by HSQ were intact, further indicating that HSQ is able to effectively shield the underlying material from the ionic liquid (Supplementary Figure S5).

Figure 2 shows resistance measurements at 280 K as a function of the two gates for each of the exposed and masked region separately. The region which is exposed to the ionic liquid shows gating with both the top and back gates. We have calculated the ionic gate capacitance using the back gate capacitance of 11.5 $nF/cm^{2}$ and the capacitance ratio $\eta=C_{TG}/C_{BG}\sim 90$; this gives the ionic gate capacitance $C_{TG}=1\mu F/cm^{2}$. We observe that the resistance of the region of the flake which is masked by HSQ remains unaffected by the top gate. All subsequent measurements are done across the p-n junction.

The variation of the resistance across the p-n junction at 273 K for all values of $|V_{TG}|\leq 0.8$ V and $V_{BG}\leq 25$ V is shown in Supplementary Section VI and indicates the formation of p-n junction at room temperature. Similar electrical measurements performed at 120 K are shown in Figure 3. These consist of four regions corresponding to p-n, n-p, n-n and p-p doping. The dotted lines indicate the charge neutrality peaks of the two regions and the polarity of the exposed and covered regions is indicated. The maximum carrier density was determined by using the known value of the ionic gate capacitance and the maximum gate voltage applied and it is found to be $7\times 10^{12}$ cm*-2*.

To change the top gate voltage, the device was first warmed to 273 K and the top gate voltage is adjusted and allowed to stabilize for 30 minutes before the device is cooled down to 120K. The photovoltage generated at 120 K at the p-n junction is given in Figure 3 along with line slices of the data for given values of the top gate voltage. The data has been acquired by repeated warming and cooling for each value of the top gate voltage. The junction is robust and does not show any thermal cycling effects (Supplementary Section IX).

The plot of the photovoltage at the junction shown in Figure 3(b) as a function of the top and back gate voltages exhibits a six-fold pattern. The photovoltage is zero along the lines $n_{TG}=0$, $n_{BG}=0$ and $n_{TG}=n_{BG}$ and alternatively positive and negative on either side ($n_{TG}$ and $n_{BG}$ are the carrier densities in the region exposed to the ionic liquid and covered with HSQ respectively). This manifests itself as two intersections of the photoresponse curve with zero when measuring the photovoltage as a function of the each gate, a shown in Figure 3(c). The conventional mechanism of photoresponse generation in semiconductors is the generation of an electron hole pair due to the the absorption of a photon and their separation under the influence of a built-in electric field such as that arising at a p-n junction. This is referred to as the photovoltaic effect and the net photoresponse depends on the magnitude and direction of band bending.

We schematically illustrate in Figure 4 that the photovoltaic effect cannot explain the multiple polarity reversals that are exhibited by the p-n junction. Along the highlighted line shown in Figure 4 with a constant value of $V_{BG}$, the charge density in the region covered with HSQ remains constant. Along this line, only the Fermi level of the exposed region changes. This change is monotonic and the photoresponse will only change sign once by going through zero at the flat band condition at point 2. However, the experimentally measured photoresponse data goes through zero twice, at point 2 and point 4, and therefore cannot be explained by the photovoltaic effect.

The photothermoelectric effect is consistent with our observations of a six-fold pattern. Under the effect of light illumination, the temperature at the p-n junction increases and the temperature at the source and drain contacts remains at the bath temperature. The difference in carrier densities on either side of the junction leads to different Seebeck coefficients in the two regions. This results in a net photo-induced voltage developing across the device.

The multiple polarity reversals arise because of the functional form of the Seebeck coefficient’s dependence on the charge density, illustrated in Figure 4. The Seebeck coefficient is positive for hole doping and negative for electron doping. It is an odd function and goes through a maximum before decreasing at large carrier densities. For a given value of the Seebeck coefficient of the covered region influenced by the back gate, there are two distinct carrier densities where Seebeck coefficient of the exposed top-gated region will be equal to that of back gated region, resulting in a zero photovoltage. Along the highlighted line Figure 4, the sign and magnitude of the Seebeck coefficient and the photovoltage at five distinct points is highlighted.

The photovoltage is given by difference in the Seebeck coefficients in the two regions:

[TABLE]

and the Mott relation relates the Seebeck coefficient and the charge density:

[TABLE]

For bilayer graphene [27], $n=-sign(E_{F})\alpha[\gamma_{1}|E_{F}|+E_{F}^{2}]$ and $dn/dE=-\sqrt{\alpha^{2}\gamma^{2}+4|n|\alpha}$, where $n<0$($n>0$) for electron (hole) doping, $\alpha=(\pi(\hbar v_{f})^{2})^{-1}$, and the inter-layer hopping energy $\gamma_{1}\sim 390$ meV. The resistance data is fitted to the form $R=L/W(e\mu)^{-1}\frac{1}{\sqrt{n^{2}+n_{0}^{2}}}$, from which we get $d(lnR)/dn=\frac{-n}{n^{2}+n_{0}^{2}}$.

We can estimate the value of the Seebeck coefficient from the experimental data. The photovoltage arising form the photothermoelectric can be written as a linear combination of two functions that depend on the doping level in each region, similar to equation 1:

[TABLE]

where $\eta=C_{TG}/C_{BG}$ and we treat the functions $f_{PVi}$ as unknowns and estimate them from the experimental data using two dimensional Fourier transforms (Supplementary Section VII), similar to the approach taken by Gabor et. al. [29]. The function $f_{PV2}$ has been plotted in Figure 5(a) as a function of the carrier density. For the photothermoelectric effect, the function is related to the Seebeck coefficient as $f_{PVi}=S\Delta T$ (S is the Seebeck coefficient and $\Delta T$ the temperature increase). The experimental value is compared to the theoretical result obtained using the Mott relation, equation 2 and is shown in Figure 5(b).

The temperature increase is estimated from the experimental data as $\Delta T=f_{PV}/S=50$ mK. This is smaller than the expected temperature increase of $\sim 1K$ that would be expected from the electronic thermal conductivity of graphene [37] of $\sim 2-5$ W/m/K, also obtainable from the the Wiedemann-Franz relation. This difference is because the temperature increase of the electronic subsystems obtained through the heat balance equation [30] is strongly dependent on the cooling length. We have also neglected any light absorption in the ionic liquid and the effective optical power reaching the device and the corresponding temperature increase could be lower.

Photovoltage measurements at temperatures ranging from 30 K to 150 K have also been performed. The normalized photovoltage magnitude at different top gate voltages has been plotted in Figure 6(a). The photovoltage increases with decreasing temperature. The photovoltage rises rapidly below 90 K and in this range, the product of photovoltage and temperature is constant, indicating that the photovoltage is inversely proportional to temperature (Supplementary Section X). The photo-responsivities we have obtained range from 100 mV/W at 273 K to 600 mV/W at 30 K. Increase in the photovoltage at lower temperatures indicates an increase in the cooling length, implying that the cooling rate increases with temperature. This is similar to the trend observed [38] in monolayer graphene where this has been attributed to disorder mediated supercollisions [30, 39, 40] as the dominant electronic thermalization mechanism.

In conclusion, we have achieved the formation of an abrupt p-n junction in graphene using a combination of electrostatic and electrolytic gating using HSQ as a protective mask. This technique is scalable and the fabrication of an array of p-n junctions, such as a superlattice [41], can be realized by the narrow features that can be lithographically patterned using HSQ. The combination of larger optical transparency of ionic liquids and the potential for larger carrier densities make this an interesting system for optoelectronic studies.

Acknowledgements

We acknowledge funding from the Department of Atomic Energy, the Department of Science and Technology (Swarnajayanti Fellowship for M.M.D) of the Government of India and ITC-PAC Grant No. FA5209-15-P-0092.

Author contributions statement

S.G. and A.J. performed the experiments. The manuscript was written by S.G., A.J. and M.M.D. All authors discussed the results and commented on the manuscript.

Additional Information

Competing financial interests The authors declare no competing financial interests.

I Raman spectrum of graphene

Figure S1 shows the Raman spectrum of the bilayer graphene flake presented in the main text measured with an excitation wavelength of 532 nm.

II Optical Transparency of LiClO4/PEO

We tried using a PEO/LiClO4 solid electrolyte but found that it was not optically transparent. Though it has been used before for optical measurements \citesuppDas2008B, it is difficult to apply it locally so that it is uniform and does not contact the back gate.

III Ionic Gate screening by HSQ and PMMA

In order to verify whether HSQ is able to effectively mask the ionic liquid, we fabricated a graphene device which was completely covered with HSQ. The measured resistance as a function of both the top gate and back gate separately is given in Figure S3.

Even though the device is fully covered with HSQ, Figure S3(b) shows that the change in the top gate voltage causes the resistance to change slightly. This change is small and indicative of a low capacitance. On plotting the gating curves of the top gate and back gate on the same scale (Figure S3(c)), it can be seen that the change in the resistance because of the top gate is comparable to that due to the back gate. This indicates that the capacitance between the electrolytic top gate and graphene is smaller than what would be expected from a few nanometres thick Debye layer and that the high capacitance due to the electrolyte has been suppressed.

We also made another device using PMMA overexposed at a dose of 10000 $\mu C/cm^{2}$ which completely covers the graphene flake. The gating curves for this device are shown in Figure S4. The resistance changes with the top gate and the slope $dG/dV_{TG}$ is more than that of the back gate. However, the magnitude of the change is small compared to that of the back gate. It is possible that there are small areas within PMMA that the ionic liquid can percolate through and affect graphene.

We also applied large top gate voltages ($\sim 4.5$ V) to the bilayer graphene device that is presented in the main text. This caused corrosion of the electrodes. From the optical image given in Figure S5, we find that the electrodes covered by the HSQ are unaffected, once again indicating that the HSQ is an effective mask for the ionic liquid.

IV Capacitance variation with area of ionic liquid

Ignoring the quantum capacitance by treating the graphene as a metal, we model the device as a system of conductors as shown in Figure S6. The back gate, graphene and top gate are denoted by $1$, $2$ and $3$ and they overlap vertically with overlap areas $A_{i}$ as indicated.

Neglecting fringing fields, we can write the capacitance matrix relating the charge on each conductor $Q_{i}$ to its potential $V_{i}$ as:

[TABLE]

[TABLE]

[TABLE]

The effective capacitance per unit area between the back gate and graphene with the top gate at a fixed potential is $C_{12}=q_{1}/v/f$ with $v_{1}=v,v_{2}=v_{3}=0$ with $f$ as the area on conductor 2 on which charge accumulates ($f\approx A_{1}+A_{3}$).

[TABLE]

From the device geometry, we estimate the capacitance with $\epsilon_{a}=3.9\epsilon_{0}$, $\epsilon_{b}=16.5\epsilon_{0}$  \citesuppHuang2011B, $A_{1}=(425\>\mu\textrm{m})^{2}$, $A_{3}=(80\>\mu\textrm{m})^{2}$, $b=1$ nm, $a=300$ nm, $f=(425\>\mu\textrm{m})^{2}$.

Figure S7 gives the factor of increase in the back gate capacitance as a function of the ionic liquid drop dimension.

V Ionic top gate leakage current

We have measured the leakage current of the ionic liquid by monitoring the current drawn by the top gate. The current is less than 1 nA till $V_{TG}=4$ V. However, we saw an abrupt change in the device resistance at around 3.5 V

VI Electrical characterization of p-n junction at room temperature

Figure S9 shows the resistance and corresponding photovoltage at 273 K as a function of both the top and back gates.

VII Fourier Transform Analysis

If $z(x,y)=f(ax+b)$, $Fz(k_{x},k_{y})=Ff(k_{x}/a)\delta(ak_{y}-bk_{x})$, where $Fz$ and $Ff$ are the Fourier transforms of $z$ and $f$ respectively and $k=1/x$,

Accordingly, if the photovoltage $PV$ is given by:

[TABLE]

The Fourier transform of $f_{PV1}$ lies along the $1/V_{BG}$ axis and $f_{PV2}$ lies along the $1/V_{TG}=\eta(1/V_{BG})$ axis. The values of $f_{PVi}$, $i=1,2$ are found by masking with a Gaussian and taking the inverse transform.

Since, for the data at 120K, acquisition of the photovoltage at each top gate voltage involves heating and cooling, the data is sampled coarsely at intervals of 0.1 V, with 17 points ranging from -0.8 V to 0.8 V, we have only shown the function form of $f_{PV2}$ in the main text.

VIII Measurement Circuit

Light of wavelength 635 nm modulated at 145 Hz is focused on the junction using a microscope objective. A current of 50 nA at 550 Hz is applied across the source and drain to measure the resistance. Two lock-in amplifiers, at 145 Hz and 550 Hz are used to measure the photovoltage and the resistance respectively. (see Figure 1(a) in the main text).

IX Thermal cycling stability

We have verified that the p-n junction formed using the technique demonstrated in the paper is not affected by thermal cycling. We have measured both the resistance and photovoltage with before and after 15 thermal cycles between measurements taken at the same top gate voltage. Figures S10, S11 and S12 show plots of resistance taken at three different temperatures – 30, 60 and 120 K for different top gate voltages. The two plots are plotted in blue and green and there are 15 thermal cycling between them. All plots show both forward and backward sweeps of the gate voltage so that hysteresis, if present, can be identified. At all three temperatures, the gating curves overlap indicating that the p-n junction created is immune to thermal cycling effects.

Similarly, the photovoltage has also been measured at 30 K and 60 K and is shown in Figures S13 and S14 , with 15 thermal cycling events between the curves. Here, the difference between the two measurement st is more pronounced. However, the trend is clearly the same. Each thermal cycling event takes a significant amount of time – nearly 4 hours – including the time we wait for the sample to stabilize. During this time, any position change of the sample due to thermal drift in the sample stage, or any long- term drift in the z-position of microscope objective that is used to focus light – even by a few microns - will result in a change in the intensity and position of light illumination. This can account for the changes we have observe in the photovoltage cycling events shown below.

We noticed a decrease in the top gate capacitance during the first heating and cooling cycle where it decreased from $90\,C_{BG}$ to $40\,C_{BG}$ ($C_{BG}$: back gate capacitance) and subsequently remained stable over the course of measurements which involved more than 50 thermal cycles.

X Temperature Dependence

In Figure S15, we have plotted the product of the photovoltage and temperature as a function of the back gate voltage for different top gate voltages. Since the 30 K and 60 K curves overlap, the photovoltage $PV\propto 1/T$ in this temperature range.