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Electrically tunable, sustainable, and erasable broadband light absorption in graphene sandwiched in Al2O3 oxides

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Abstract

Graphene has been used as an electrically tunable material for switchable devices. A large area fabrication of Al-doped ZnO/Al2O3/graphene/Al2O3/gold/silicon device was enabled by a spin-processible hydrophilic mono-layer graphene oxide. The graphene was obtained directly from graphene oxide during the atomic layer deposition without other extra steps. A significant shift of Raman frequency up to 360 cm−1 was observed from graphene in the fabricated device, indicating a structural change in graphene. The absorption from the device was tunable with a negative voltage applied on the Al-doped ZnO side. The generated absorption change was sustainable when the voltage was off and erasable when a positive voltage was applied. The sustainability of tuned optical property in the graphene under investigation can lead to a design of device with less power consumption and many other applications.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Graphene is a two dimensional (2D) material with atomic-thick layer of carbons in 2D hexagonal structure [1,2]. Light absorption in graphene has been intensively studied [3–15] as it is a fundamental physical phenomenon for applications in detector [15], solar energy [16,17], biosensing [18], optical imaging [8] and etc. A perfect absorption (i.e. total light absorption) has been studied in two- or three-layer dielectric materials or dielectric/metallic materials [19]. The realization of perfect absorption is based on the selection of dielectric constant of materials for the phase matching of the destructive interference. Optical materials with tunable optical properties (e.g. phase-change materials) have been used to meet the phase matching condition for the perfect absorption [20–23]. In contrast to the optical properties of noble metals that cannot be tuned or changed, the permittivity of transparent conductive oxides, such as Al-doped ZnO and indium tin oxide, is tunable [24–28]. Their optical properties can be adjusted via doping or tuned electrically through carrier accumulation and depletion, providing great advantages for designing tunable photonic devices or realizing perfect absorption [24–28]. However, the tuning of the optical properties in transparent conductive oxides needs a strong electric field that can cause the voltage breakage across the spacer [24,28].

It is known that the optical property of gated graphene can be tuned [4–9,13]. The use of graphene as an electrode has led to an electrically switchable device for electromagnetic wave absorption [9]. However the voltage induced property change cannot be sustained when the voltage is off. Single layer graphene has a universal absorption of 2.29% [4,11]. If graphene is sandwiched between oxides [29], it can be used to store trapped charges that change the Fermi level of graphene [4–9,13].

In this paper, large area multiple-layer device with graphene sandwiched between Al2O3 oxides was fabricated through spin-coating of mono-layer graphene oxide and atomic layer deposition of oxides. The tunability, sustainability and erase-ability of the fabricated optical device were primarily studied through experiments.

2. Experiments and simulations

The large area of samples was enabled by spin-processible hydrophilic mono-layer graphene oxide that was used as received from the vendor (Cheap Tubes Inc.) without further purifications. The mono-layer graphene oxide was dispersed in DI water without surfactant. Both Al-dope ZnO (AZO) and Al2O3 layers were deposited by atomic layer deposition (ALD) using an Ensure Scientific 9200 ALD system. Reaction precursors, including Trimethylaluminum [(CH3)3Al, TMA] and Diethylzinc [(C2H5)2Zn, DEZ], were respectively used as Al and Zn sources, while H2O vapor was used as an oxidant. Ultrahigh purity nitrogen was used as the purging gas with a flow rate of 20 sccm. The process pressure was about 10−1 Torr and the substrate temperature was maintained at 250 °C during deposition. The device design is shown schematically in Fig. 1(a). Before ALD deposition, the Au-coated n-type Si substrates were cleaned by acetone and alcohol, rinsed by deionized (DI) water, and dried with flowing nitrogen gas. Then 20-nm Al2O3 layer was deposited at 250 °C by ALD. As soon as the Al2O3/Au/Si was taken out of ALD chamber and cooled down to room temperature, the mono-layer graphene oxide was deposited by spin coating at 800 rpm using the graphene suspension of 2 mg/ml. Then the wafer with graphene oxide/Al2O3/Au/Si was loaded into ALD chamber for 3 nm Al2O3 deposition at 250 °C followed by growing a top layer of 100 nm AZO in the same chamber. The AZO layer contains 4% Al dopants. Two devices with stacks of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon and with stacks of 100-nm AZO/5-nm Al2O3/gold/silicon were fabricated. Silver pastes were used for bonding gold wires to the device with one wire bonded on AZO and the other on silicon, for the purpose of electrical and optical characterization. The current-voltage (IV) measurement was carried out to select good samples for further electrical and optical characterizations.

 figure: Fig. 1

Fig. 1 (a) Schematic of multiple-layer film device where gold, 20-nm Al2O3, graphene, 3-nm Al2O3, 100 nm AZO were stacked on n-type silicon. (b) SEM of cleaved cross-section of fabricated device as designed in (a).

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Raman spectrum was measured using an Almega XR confocal Raman spectrometer from Thermo Electron. It was excited by a 532 nm laser. FT-IR was measured using a Nicolet 6700 Fourier transform infrared (FTIR) spectrometer from Thermo Electron. The attached Continuum Infrared Microscope was used for reflection measurement. Multi-frequency capacitance measurement and current/voltage measurement were performed using Keysight B1500A Semiconductor Device Analyzer. Scanning Electron Microscope (SEM) was measured using Hitachi SEM S-4800-I equipped with IXRF Iridium Ultra Microanalysis. SEM of cleaved cross section of AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon is shown in Fig. 1(b).

The simulation was performed using MIT Electromagnetic Eq. Propagation (MEEP) simulation tool [30] through parallel simulations in Simpetus Electromagnetic Simulation Platform in Amazon Web Services (AWS). A unit length of 100 nm and a resolution of 200 were used in the simulations.

3. Results

Figure 2(a) shows a Raman spectrum from the graphene oxide used in the device. D and G peaks are labelled in the figure and they are the characteristic features of graphene oxide. During the ALD process, the graphene oxide became graphene in the device with a stack of AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon. At 250 °C, the dangling oxide group of the graphen oxide was not only reduced but also used by ALD precursor to form Al2O3. The nucleation of Al2O3 started most possibly at the defect sites of mono-layer graphene [29] as explained by the Raman spectrum in Fig. 2(b). Due to the photoluminescence of defects in AZO [31], the confocal Raman cannot detect any signals from graphene if measured from the surface. On the cross-section of the device, a strong peak at 520 cm−1 and a weak 2D mode from graphene were observed as shown in the red line in Fig. 2(b), when the laser spot was close to the silicon layer. The blue line in Fig. 2(b) is the Raman spectrum taken from the cross-section of device when the laser spot was close to the graphene and AZO. The rising band towards 2900 cm−1 is due to the photoluminescence of defects in AZO [31]. D, G and 2D modes of graphene were identified in the Fig [32–35]. The weak D mode and strong 2D peak in Fig. 2 indicate that the explored sample is indeed graphene (not graphene oxide) [32–35]. The broad peak under D mode might be due to different types of defects. The sharp peak under 2D mode in Raman spectrum in Fig. 2(b) also indicates mono-layer graphene instead of multiple-layer graphene. The device prepared by spin-coating of graphene oxide with 3500 rpm also shows the sharp 2D peak, indicating that the device prepared by 800 rpm in this study is actually composed of physically separated layers of monolayer graphene material.

 figure: Fig. 2

Fig. 2 (a) Raman spectrum from graphene oxide drop-coated on Si wafer. (b) Raman spectrum measured from the cross-section of AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon device. The blue line (referring to the primary axis) was measured at a spot close to AZO and graphene and the red line (referring to the secondary axis) was measured at a location close to silicon on the cross-section.

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Raman peak shift in graphene due to the isotope effect was previously observed [36]. Here we also observed a significant peak shift in graphene as shown in Fig. 2(b). The D, G and 2D modes are near 1100, at 1560 and 2330 cm−1, respectively, in the proposed graphene sandwiched in Al2O3 oxides, compared to 1350, 1583 and 2690 cm−1 in free-standing graphene [32–35]. The peak was shifted by 250, 23, and 360 cm−1 for D, G and 2D modes, respectively. The shifting percentage in G mode in proposed sandwiched graphene structure is relatively small with respect to others, probably due to the fact that it is originated from the opposite vibration of neighboring lattice and such small vibration has a small effect from the defect or Al2O3 [35]. D mode has a large effect from the defects and 2D mode has a large effect from Al2O3 due to the breathy-like vibration from six carbons in a hexagon and two vibrations involving the hexagons from two different unit-cells [35]. Considering Al atoms at the defect sites of graphene, an effective mass will change the D-mode Raman frequency ν = 1350 cm−1 to a new frequency ν` = 1147 cm−1 following the Eq. (1) [37]:

v`=v(mc×mc)/(mc+mc)(mAl×mc)/(mAl+mc)
where mAl and mC are the atomic mass of Al and C, respectively. For 2D mode, Raman frequency ν = 2690 cm−1 will be shifted to a new frequency ν` = 2286 cm−1 and ν` = 2374 cm−1 if considering the effective masses of (mAl, mC) and (mAl-O average, mC), respectively. The average of 2286 and 2374 cm−1 is 2330 cm−1, in a good agreement with the measured 2D peak at 2330 cm−1.

The reflection from 100-nm AZO/Al2O3/gold/silicon with a different Al2O3 thickness of 5, 23, 100 and 380 nm, respectively, was simulated and shown in Fig. 3(a). The Drude–Lorentz oscillator model in Eq. (2) was used in the simulation for AZO:

ε(ω)=εbωp2ω2+iΓpω+f1ω12ω12ω2iΓ1ω
where εb is the background permittivity, ωp is the unscreened plasma frequency, Γp is the carrier relaxation rate, and f1 is the strength of the Lorentz oscillator at the center frequency ω1 with the relaxation Γ1.

 figure: Fig. 3

Fig. 3 (a) Simulated reflection spectra from 100-nm AZO/Al2O3/gold/silicon with a different Al2O3 thickness of 5, 23, 100 and 380 nm, respectively. (b) measured reflection from a device of 100-nm AZO/5-nm Al2O3/gold/silicon (blue) and from a device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon (red).

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Figure 3(b) shows measured reflections from 100-nm AZO/5-nm Al2O3/gold/silicon (blue) and from 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon (red). The measured reflections show a dip. Starting from the parameters εb=3.358, ωp=1.45 eV, Γp=0.139 eV, f1=0.701 eV,ω1=2.253 eV and Γ1=0.688 eV that were obtained from ellipsometer measurement [38], the parameters in Eq. (2) was adjusted so that the simulated reflection from 100-nm AZO/5-nm Al2O3/gold/silicon in Fig. 3(a) has the almost same dip wavelength and the same dip depth (relative to the reflection at 3200 nm) as the measured reflection in Fig. 3(b). Usually the change of ωp will shift the dip wavelength and an increase of Γp will decrease the reflection. The simulated reflection from 100-nm AZO/23-nm Al2O3/gold/silicon has almost same dip wavelength as the measured reflection from AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon in Fig. 3(b) while the dip depth is different due to the presence of graphene in the sample. The simulated reflection dip has been red-shifted and deepened by increasing the Al2O3 spacer thickness. Further increasing of the spacer thickness to 380 nm can lead to perfect absorption at the dip wavelength.

Through the comparison of the simulated and measured reflection, the parameters in the Eq. (2) were obtained as follows: εb=4.0, ωp=1.1 eV, Γp=0.139 eV, f1=0.54 eV, ω1=2.253 eV and Γ1=0.108 eV.

When a negative voltage was applied to the AZO side in the device, the reflection decreased. Figure 4(a) shows the measured (R-2V-R0)/R0 where R-2V and R0 are the measured reflection under the voltage −2V and original (0V) for the device of 100-nm AZO/5-nm Al2O3/gold/silicon (purple line) and the device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon (light-blue line). Because of gold film in the device, there is no transmission (T = 0). Absorption is related to the reflection by A = 1-R-T = 1-R. The measured reflection changes can be understood by the absorption changes. The carrier accumulation effect on the absorption of AZO/5-nm Al2O3/gold/silicon stack was calculated through Poisson’s Eq. (3):

d2ϕ(x)dx2=ρ(x)εAZOqεAZONd{eqϕ(x)/(kBT)1}
where εAZO is the static dielectric constant of AZO ( = 8𝜖𝑜 [28]), Φ(x) is the potential in the AZO as a function of depth x from the surface, q is the electron charge, ρ(x) is the charge density, Nd is the bulk carrier concentration of AZO at 0 V (Nd = 3.34 × 1026 m−3 for the plasma frequency of 1.1 eV), KB is the Boltzmann Constant and temperature T = 273.15 K. A surface potential of 0.0597 V [24,28] was used in the Poisson Eq. (3) for v = −2 V. Using the Poisson’s Eq. (3), the carrier concentration as a function of depth x was calculated and the complex refractive index n + i k was calculated assuming that ωp is changed with the carrier concentration while other parameters in Eq. (2) were constant. From the imaginary part (k) of the refractive index, the absorption coefficient α was obtained by α = 4πk/λ. The simulated absorption changes (squares in Fig. 4(a)) approximately match to the measured one (purple line in Fig. 4(a)) at wavelengths of 1720, 2070, 2500, 2810, 3800, 6498, 11510 and 14226 nm.

 figure: Fig. 4

Fig. 4 (a) Measured (solid lines) and simulated (dashed line and squares) (R-2V-R0)/R0 for devices with and without graphene: i.e. 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon and 100-nm AZO/5-nm Al2O3/gold/silicon, respectively. (b) measured (RV-R0)/R0 from a device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon when a voltage sequence was applied to the AZO side of the device. The reason for a feature at 5793 is unknown. If the graphene is crumpled due to the trapped charges, plasmonic resonances will appear in mid-infrared [39].

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However, the measured (R-2V-R0)/R0 from the device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon could not be explained by only considering the AZO carrier accumulation effect. Furthermore, the reflection change was sustained when the voltage was off as shown in Fig. 4(b). Thus a mechanism beyond AZO-induced absoprtion change was further considered. On the other hand, the Fermin level in graphene can be changed by the stored charges in graphene. Thus the interband and intraband transitions of graphene were carefully considered in the simulation of (R-2V-R0)/R0 for the sample containing graphene, together with a resonance term related to excitonic effect or structural resonance as presented in Eq. (4) [40,41]:

A(ω)=4πc(EFe2π×γ(ω)2+γ2+e28[tanh(ω+2EFΓ)+tanh(ω2EFΓ)]+resonanceterm)
where γ is the intraband transition broadening,Γ is the interband transition broadening, EF is the Fermi level, e is the electron charge, and e2c = 1/137 is the universal absorption parameter of graphene. We set KBT=0.023538 eV (KB is the Boltzmann Constant and T = 273.15 K). The resonance term is mathematically similar to the Fano model used for excitonic effect [11,42,43]. The parameters of γ, Γ can vary with the Fermi level of graphene [11,41,43,44]. Γ = 4KBT [11,40] was used at 0 V while Γ = 2KBT, γ= 1.6 KBT, and EF = 0.042 eV for −2 V. The simulated (R-2V-R0)/R0 as shown in a dashed red line in Fig. 4(a) fits the measured data.

Figure 4(b) shows the details of measured (RV-R0)/R0 for the device of AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon during the states when the graphene charges are trapped, sustained and erased. R0 is the reflection from the sample at the original 0V state. The solid red line shows (RV-R0)/R0 when the AZO side was initially applied with −2 V voltage. The reflection keeps dropping while the −2V voltage is applied (e.g. for a few minutes). 5 minutes later, the reflection change became very small. The solid blue line is the measured (RV-R0)/R0 from the sample after we waited for 20 minutes. Such a time-dependent reflection changes in the proposed device can be understood as follows. Initially at −2 V, charges were tunneled through the 3-nm Al2O3 spacer. Thus the amount of carrier accumulation at the interface of AZO and 3-nm Al2O3 was small as the charge was tunneled to graphene side. Then the amount of carrier accumulation increases when the sample was continuously illuminated by the FTIR light source, the alignment laser and building lights (The light absorption produced charges were confirmed later in Fig. 5 using a solar simulator). Because the measurement took three minutes, continuous light absorption occurred even the building light was off. Finally an equilibrium can be reached among the light absorption produced charges, the carrier accumulation at the interface and trapped charges at graphene.

 figure: Fig. 5

Fig. 5 (a) Capacitance-voltage characterization at 10 kHz for the device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon. Arrows indicate the sweep directions. Inset is the schematic of two capacitors in series across the 3-nm and 20-nm Al2O3, respectively. (b) Measured negative open-circuit voltages as a function of solar powers when the device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon was illuminated by a solar simulator.

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After the AZO side of the sample was biased at −2 V for 20 minutes, we then changed the voltage to 0 V and switched off the power supply to the sample (i.e. open circuit). The dashed light-green line in Fig. 4(b) is the reflection at 0 V for 0 minutes, that is very close to the solid red line (−2 V for 0 minute) as the trapped charges was sustained even when the power was off and the accumulated carriers in AZO was released. With increased times, the reflection drops as seen in spectra in dashed light-blue line and dark-blue dash-dot line in Fig. 4(b), for 2 minutes and 4 minutes, respectively. After 6 minutes as seen in Fig. 4(b), the reflection at 0 V (in dashed purple line) is almost the same as the one at −2 V for 20 minutes as the charges were accumulated in AZO. The multimeter read 0.09 V after the sample was in open circuit for 6 minutes due to absorption induced charge accumulation from the building light, alignment laser and FTIR light source. When the voltage at AZO side was switched to + 2.02 V, the charge carriers in AZO was depleted. The reflection (in solid black line) went almost back to the original state between 1700 and 7700 nm, indicating that the charge trapped in graphene was almost erased. There is a dip around 3878 nm in reflection after the sample was switched to 2.02 V and the reflection is less than the original state between 7700 and 15000 nm, indicating a possibility that there is ionic migration during the gating process.

Therefore we observed that the charges trapped in graphene and induced optical changes were sustainable for a long time without any power consumption, and these trapped charges can be erased with a reversed bias. The sustainability of optical property in the proposed graphene structure will lead to optical devices, such as optical switch, with less power consumption [40].

4. Discussion

From Fig. 3(a), we learned from the simulation that the wavelength of the reflection dip increased when the spacer thickness increased. If the spacer thickness is the same, an increase of refractive index in spacer will also shift the dip to a larger wavelength due to the increased optical pass length of nd (where n is refractive index and d is the thickness) [45]. The formation of space charge layer in graphene has increased the dielectric constant of Al2O3 in a graphene-embedded gate dielectric [29]. When more charges were trapped in graphene in our device, the wavelength of the reflection dip shifted from 2207nm in solid red line in Fig. 4(b) to 2521 nm in solid light-blue line. On the other hand, the reflection from the device also shifted when the negative voltage was off as seen from Fig. 4(b). Thus the amount of carriers in AZO also played a role in the change of nd.

The trapped charges in graphene in AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon were observed by capacitance-voltage measurement. Figure 5(a) shows the capacitance-voltage characterizations of AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon at a frequency of 10 kHz. The inset in Fig. 5(a) shows a schematic of two capacitors in series cross 3-nm Al2O3 and 20-nm Al2O3, respectively. The capacitor across 3-nm Al2O3 can be considered to be dynamic where charges were accumulated (or depleted) at the AZO/Al2O3 interface, and induced charges were tunneled through 3-nm Al2O3 and trapped in graphene. The trapped charges in graphene can be calculated as C3nm •δVhyster/e, where C3nm is the static capacitor across the 3-nm Al2O3 layer, δVhyster is hysteresis voltage and e is the charge of electron. The δVhys equals 0.3 V as read from Fig. 5(a) near −2 V at 10 kHz. The trapped charges in graphene was calculated to be 7.27 × 1012 and trapped charge density in graphene was 4.98 × 1012 /cm−2.

The carrier change in AZO during the illumination was further confirmed in open-circuit photovoltaic voltage measurement when the proposed AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon device was illuminated by a solar simulator. Figure 5(b) shows the open-circuit voltage as a function of solar powers. A negative voltage was generated on the AZO side. The absolute value of the voltage increases with the increased solar powers. At the solar power of 14 W, −0.21 V was obtained at the AZO side. Further measurement in FTIR reflection has been performed. After a reflection measurement, the sample was covered by a black foil thus setting the sample in dark for two minutes and removing the photocarrier effect. The reflection before the sample covering and after removing the covering shows 1% change above 3300 nm, which is much smaller than the reflection change in two minutes in Fig. 4(b).

5. Summary

In summary, graphene has been obtained from graphene oxide during the atomic layer deposition of Al2O3, as confirmed by Raman spectrum. Large area of graphene has been sandwiched between Al2O3 in AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon through spin-coating of mono-layer graphene oxide. Raman spectrum has indicated a structural change in graphene sandwiched between Al2O3. The optical measurements have revealed that the absorption (as measured by reflection) in graphene is tunable with a biasing voltage and the induced absorption change is sustained when the voltage is off. Such a change has been erased by an external voltage. The sustainability of changes of optical property in graphene will lead to optical devices with less power consumption and many other applications.

Funding

National Science Foundation (NSF) (1661842, 1661749)

Acknowledgment

We thank Dr. Jose Perez for a discussion of Raman spectrum.

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of multiple-layer film device where gold, 20-nm Al2O3, graphene, 3-nm Al2O3, 100 nm AZO were stacked on n-type silicon. (b) SEM of cleaved cross-section of fabricated device as designed in (a).
Fig. 2
Fig. 2 (a) Raman spectrum from graphene oxide drop-coated on Si wafer. (b) Raman spectrum measured from the cross-section of AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon device. The blue line (referring to the primary axis) was measured at a spot close to AZO and graphene and the red line (referring to the secondary axis) was measured at a location close to silicon on the cross-section.
Fig. 3
Fig. 3 (a) Simulated reflection spectra from 100-nm AZO/Al2O3/gold/silicon with a different Al2O3 thickness of 5, 23, 100 and 380 nm, respectively. (b) measured reflection from a device of 100-nm AZO/5-nm Al2O3/gold/silicon (blue) and from a device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon (red).
Fig. 4
Fig. 4 (a) Measured (solid lines) and simulated (dashed line and squares) (R-2V-R0)/R0 for devices with and without graphene: i.e. 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon and 100-nm AZO/5-nm Al2O3/gold/silicon, respectively. (b) measured (RV-R0)/R0 from a device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon when a voltage sequence was applied to the AZO side of the device. The reason for a feature at 5793 is unknown. If the graphene is crumpled due to the trapped charges, plasmonic resonances will appear in mid-infrared [39].
Fig. 5
Fig. 5 (a) Capacitance-voltage characterization at 10 kHz for the device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon. Arrows indicate the sweep directions. Inset is the schematic of two capacitors in series across the 3-nm and 20-nm Al2O3, respectively. (b) Measured negative open-circuit voltages as a function of solar powers when the device of 100-nm AZO/3-nm Al2O3/graphene/20-nm Al2O3/gold/silicon was illuminated by a solar simulator.

Equations (4)

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v`=v ( m c × m c )/( m c + m c ) ( m Al × m c )/( m Al + m c )
ε(ω)= ε b ω p 2 ω 2 +i Γ p ω + f 1 ω 1 2 ω 1 2 ω 2 i Γ 1 ω
d 2 ϕ(x) d x 2 = ρ(x) ε AZO q ε AZO N d { e q ϕ(x)/ ( k B T) 1 }
A(ω)= 4π c ( E F e 2 π × γ (ω) 2 + γ 2 + e 2 8 [ tanh( ω+2 E F Γ )+tanh( ω2 E F Γ ) ] +resonance term )
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