Periodic Reporting for period 1 - MaPWave (Designing Many-Particle Wavefunctions in Mesoscopic Quantum Devices)
Reporting period: 2022-08-01 to 2024-07-31
Project Context:
The overarching goal of “MaPWave” is to define the electronic structure and carrier dynamics of 2D semiconductor quantum devices by directly engineering the quantum wavefunctions of the charge carriers.This requires access to the energy- and momentum-dependent quantum states in micro- and nano-scale devices. The plan is to combine state-of-the-art electron spectroscopies with femtosecond time-resolution and nano-scale spatial resolution in order to overcome these challenges and demonstrate that electronic and optoelectronic properties of quantum devices composed of 2D transition metal dichalcogenides (TMDCs) can be engineered at the level of the fundamental electronic wavefunctions.
Overall Objectives:
I. Preparation of electron-hole pair wave function:
The idea is to use the method of stacking the dissimilar TMDCs WS2,MoS2 and WSe2 as a primary approach to engineer the quantum states of 2D semiconductors. The electronic band gaps of these materials are staggered, thereby making it possible to excite a hole in one material while an electron is excited in the other when exposed to a light pulse. Strong Coulomb interactions between these oppositely charged excitations leads to the formation of an interlayer electron-hole pair, which is called an interlayer exciton. These quasiparticles follow the Bose-Einstein quantum statistics such that they can condense into a single quantum state –i.e. a Bose-Einstein condensate. These collective many-body states are highly robust with long lifetimes that make them extremely attractive for both energy harvesting and storage, as well as for quantum information technology where they can be utilized as fault-tolerant qubits. The preparation of the many-body wavefunction associated with such a condensate and obtain quantitative information on electron-hole binding energies, lifetime and density, which dictate the quantum efficiency of the materials.
2. Tuning many-body interactions with superlattices:
Introducing a lattice mismatch via a finite twist angle between stacked 2D semiconductors leads to a moiré superlattice. The long-range potential of such a moiré can be tuned using the twist angle, leading to momentum-shifted replicas of the quantum states with distinct interacting
exciton condensates. Direct measurement of the extent of localization of such superlattice excitons and determine their lifetime depending on the superlattice, which will ultimately widen the scope of potential optoelectronic applications of the materials.
3.Transfermation of electronic properties:
Stacks of TMDCs will be integrated in field-effect device architectures, enabling control of the charge carrier concentration in the materials using an electrostatic gate electrode. Doping the materials with extra electrons leads to the possibility of inducing conducting states that would
induce a semiconductor-to-metal transition. Depending on interaction strength, which is controlled by carrier concentration, temperature and twist angle, the charged excitations around the Fermi level of the doped system could form charge ordered or superconducting states. By inducing and tuning these states, which demonstrates complete quantum control of basic electronic properties and function.
The overarching goal of “MaPWave” is to define the electronic structure and carrier dynamics of 2D semiconductor quantum devices by directly engineering the quantum wavefunctions of the charge carriers.This requires access to the energy- and momentum-dependent quantum states in micro- and nano-scale devices. The plan is to combine state-of-the-art electron spectroscopies with femtosecond time-resolution and nano-scale spatial resolution in order to overcome these challenges and demonstrate that electronic and optoelectronic properties of quantum devices composed of 2D transition metal dichalcogenides (TMDCs) can be engineered at the level of the fundamental electronic wavefunctions.
Overall Objectives:
I. Preparation of electron-hole pair wave function:
The idea is to use the method of stacking the dissimilar TMDCs WS2,MoS2 and WSe2 as a primary approach to engineer the quantum states of 2D semiconductors. The electronic band gaps of these materials are staggered, thereby making it possible to excite a hole in one material while an electron is excited in the other when exposed to a light pulse. Strong Coulomb interactions between these oppositely charged excitations leads to the formation of an interlayer electron-hole pair, which is called an interlayer exciton. These quasiparticles follow the Bose-Einstein quantum statistics such that they can condense into a single quantum state –i.e. a Bose-Einstein condensate. These collective many-body states are highly robust with long lifetimes that make them extremely attractive for both energy harvesting and storage, as well as for quantum information technology where they can be utilized as fault-tolerant qubits. The preparation of the many-body wavefunction associated with such a condensate and obtain quantitative information on electron-hole binding energies, lifetime and density, which dictate the quantum efficiency of the materials.
2. Tuning many-body interactions with superlattices:
Introducing a lattice mismatch via a finite twist angle between stacked 2D semiconductors leads to a moiré superlattice. The long-range potential of such a moiré can be tuned using the twist angle, leading to momentum-shifted replicas of the quantum states with distinct interacting
exciton condensates. Direct measurement of the extent of localization of such superlattice excitons and determine their lifetime depending on the superlattice, which will ultimately widen the scope of potential optoelectronic applications of the materials.
3.Transfermation of electronic properties:
Stacks of TMDCs will be integrated in field-effect device architectures, enabling control of the charge carrier concentration in the materials using an electrostatic gate electrode. Doping the materials with extra electrons leads to the possibility of inducing conducting states that would
induce a semiconductor-to-metal transition. Depending on interaction strength, which is controlled by carrier concentration, temperature and twist angle, the charged excitations around the Fermi level of the doped system could form charge ordered or superconducting states. By inducing and tuning these states, which demonstrates complete quantum control of basic electronic properties and function.
Aiming the above objectives, work has been progressed in the directions of: preparation of the device, optical and electronic properties in terms of photo luminescence and micro-ARPES on prepared gated devices.
Device preparation:
Large monolayer WS2 was exfoliated and transferred to substrate with the following steps: A master tape was prepared by using scotch tape and a large (<2x2mm) bulk crystal was used to prepare the WS2 master tape, and was copied on to a blue tape or nitto tape for the exfoliation. In parallel, a PDMS gel pak of 10mmx50mm was selected and placed on a glass slide, and then cut into pieces of 10mmx2mm. The prepared blue tape was used to exfoliate the materials on the PDMS and scanned through the optical microscope to identify the monolayer flakes (I). The particular piece of the gel pak having a large monolayer was selected to transfer to the substrate (which was plasma cleaned for 6 minutes in presence of oxygen at the power of 50W). The selected gel pack was fixed on the corner of a glass slide and then flipped the slide and mounted on a motorized micromanipulator. The manipulator brought the gel-pak and the substrate into contact at 30 C. The substrate was heated to 60C, then allowed to cool to 30 C and then the manipulator placed away from the gel-pak to yield WS2 flake on the substrate. The WS2 flake was transferred by dry transfer onto the polycarbonate (PC) on polydimethylsiloxane (PDMS) stamp on a glass slide mounted on a motorized micromanipulator. The manipulator brought the stamp and WS2 into contact at 60 C. The substrate was heated to 90C, then allowed to cool to 60C and then the manipulator placed away from the stamp to yield WS2 on stamp (2).
3. hBN flake was exfoliated on the substrate directly. Initially, a BN crystal of < 0.5mmx0.5mm was picked and placed on a scotch tape and prepared a master tape, another scotch tape was used to copy the master tape to prepare a daughter tape. The daughter tape was used to exfoliate at room temperature on Si/SiO2 substrate, which was after oxygen plasma treatment at 50W for 3 minutes of the substrate. The substrate was scanned through the microscope to identify the suitable BN flake. The flake was specified its orientation and picked by the stamp as explained in step 2 at a temperature of 120 C.
4. Graphite flake was exfoliated the same as hBN at a temperature of 110 C, and followed the same transfer process as BN at the temperature of 130 C.
5. The stack of WS2, BN, Graphite was transferred to the patterned substrate. The pattern was prepared by standard photolithography on a Si/SiO2 substrate. The transfer follows step 4 at a temperature of 180 C, which helps to melt the PC and get separated from the PDMS and yields the stack on the patterned substrate.
6. The stack was cleaned with chloroform (ratio), Acetone, and isopropanol for a minute each in a sequence to get rid of the top PC and the residues from tape and PDMS. Following the cleaning, it was annealed at 300 C for 3 hours in an oven.
7. Graphene flake was exfoliated and transferred to another stamp same as graphite (step 4). The picked graphene was aligned and transferred to the stack through the process of step 5.
8. The final stack was cleaned and annealed (step 6) again, yielding to the sample to be measured (figure 1.c)
The device was wire-bonded in a chip carrier and mounted on a custom-made sample plate that allowed in situ electrical connections at the main chamber of the micro-ARPES beamline (SGM4) of ASTRID2 synchrotron. Prepared sample was annealed in ultrahigh vacuum (UHV) at 200°C overnight prior to transfer to the measurement chamber. Measurements were acquired at a sample temperature of around 300 K with a photon energy of 55 eV. A capillary mirror was used to focus the beam down to 4µm spots and the photoemitted electrons were collected by a hemispherical analyzer () mounted in the UHV chamber. ARPES map was taken around the sample area to identify the monolayer TMDC, hBN, graphene top contact, and gold electrode (Figure 1c). These areas were typically around 10 micrometers across, bigger than the beam spot. Angle-resolved photoemission spectra were acquired while the back-gate voltage VG was varied in situ with the graphene grounded and gate floated through a four probe keithley (). During the measurement, the hemispherical analyzer with 2D detector was positioned to acquire spectra in the G-K direction of the WS2 Brillouin zone, and rotated 25 degree (without affecting the sample position and beam spot) to access the K point of the graphene as shown in the inset sketch in figure 1d. This mismatch of 25 degree between the WS2 and graphene K points allows easily distinguishing valence band dispersions without any noise to the individual materials band in the heterostructure.
Achievements: Through the above process, it has been successfully demonstrated the in-operando micro-ARPES of a monolayer WS2 flake in a back gated configuration. It measured the electronic structure of the monolayer WS2 in presence of electric field and hence the flake becomes conductive at certain doping level. Interestingly, it measures the conduction band formation with respect to doping both in the bare and graphene covered WS2 flake. The visualization of conduction band under graphene is a great achievement as per the in-operando ARPES on the mesoscopic material is concern. This achievement leads to trace the charge transfer pathway of the carriers to populate the conduction band of the graphene covered WS2 flake.
Device preparation:
Large monolayer WS2 was exfoliated and transferred to substrate with the following steps: A master tape was prepared by using scotch tape and a large (<2x2mm) bulk crystal was used to prepare the WS2 master tape, and was copied on to a blue tape or nitto tape for the exfoliation. In parallel, a PDMS gel pak of 10mmx50mm was selected and placed on a glass slide, and then cut into pieces of 10mmx2mm. The prepared blue tape was used to exfoliate the materials on the PDMS and scanned through the optical microscope to identify the monolayer flakes (I). The particular piece of the gel pak having a large monolayer was selected to transfer to the substrate (which was plasma cleaned for 6 minutes in presence of oxygen at the power of 50W). The selected gel pack was fixed on the corner of a glass slide and then flipped the slide and mounted on a motorized micromanipulator. The manipulator brought the gel-pak and the substrate into contact at 30 C. The substrate was heated to 60C, then allowed to cool to 30 C and then the manipulator placed away from the gel-pak to yield WS2 flake on the substrate. The WS2 flake was transferred by dry transfer onto the polycarbonate (PC) on polydimethylsiloxane (PDMS) stamp on a glass slide mounted on a motorized micromanipulator. The manipulator brought the stamp and WS2 into contact at 60 C. The substrate was heated to 90C, then allowed to cool to 60C and then the manipulator placed away from the stamp to yield WS2 on stamp (2).
3. hBN flake was exfoliated on the substrate directly. Initially, a BN crystal of < 0.5mmx0.5mm was picked and placed on a scotch tape and prepared a master tape, another scotch tape was used to copy the master tape to prepare a daughter tape. The daughter tape was used to exfoliate at room temperature on Si/SiO2 substrate, which was after oxygen plasma treatment at 50W for 3 minutes of the substrate. The substrate was scanned through the microscope to identify the suitable BN flake. The flake was specified its orientation and picked by the stamp as explained in step 2 at a temperature of 120 C.
4. Graphite flake was exfoliated the same as hBN at a temperature of 110 C, and followed the same transfer process as BN at the temperature of 130 C.
5. The stack of WS2, BN, Graphite was transferred to the patterned substrate. The pattern was prepared by standard photolithography on a Si/SiO2 substrate. The transfer follows step 4 at a temperature of 180 C, which helps to melt the PC and get separated from the PDMS and yields the stack on the patterned substrate.
6. The stack was cleaned with chloroform (ratio), Acetone, and isopropanol for a minute each in a sequence to get rid of the top PC and the residues from tape and PDMS. Following the cleaning, it was annealed at 300 C for 3 hours in an oven.
7. Graphene flake was exfoliated and transferred to another stamp same as graphite (step 4). The picked graphene was aligned and transferred to the stack through the process of step 5.
8. The final stack was cleaned and annealed (step 6) again, yielding to the sample to be measured (figure 1.c)
The device was wire-bonded in a chip carrier and mounted on a custom-made sample plate that allowed in situ electrical connections at the main chamber of the micro-ARPES beamline (SGM4) of ASTRID2 synchrotron. Prepared sample was annealed in ultrahigh vacuum (UHV) at 200°C overnight prior to transfer to the measurement chamber. Measurements were acquired at a sample temperature of around 300 K with a photon energy of 55 eV. A capillary mirror was used to focus the beam down to 4µm spots and the photoemitted electrons were collected by a hemispherical analyzer () mounted in the UHV chamber. ARPES map was taken around the sample area to identify the monolayer TMDC, hBN, graphene top contact, and gold electrode (Figure 1c). These areas were typically around 10 micrometers across, bigger than the beam spot. Angle-resolved photoemission spectra were acquired while the back-gate voltage VG was varied in situ with the graphene grounded and gate floated through a four probe keithley (). During the measurement, the hemispherical analyzer with 2D detector was positioned to acquire spectra in the G-K direction of the WS2 Brillouin zone, and rotated 25 degree (without affecting the sample position and beam spot) to access the K point of the graphene as shown in the inset sketch in figure 1d. This mismatch of 25 degree between the WS2 and graphene K points allows easily distinguishing valence band dispersions without any noise to the individual materials band in the heterostructure.
Achievements: Through the above process, it has been successfully demonstrated the in-operando micro-ARPES of a monolayer WS2 flake in a back gated configuration. It measured the electronic structure of the monolayer WS2 in presence of electric field and hence the flake becomes conductive at certain doping level. Interestingly, it measures the conduction band formation with respect to doping both in the bare and graphene covered WS2 flake. The visualization of conduction band under graphene is a great achievement as per the in-operando ARPES on the mesoscopic material is concern. This achievement leads to trace the charge transfer pathway of the carriers to populate the conduction band of the graphene covered WS2 flake.
Results at each gate voltage follows the doping affect at three different regions of the device. (i) what happens to the graphene top contact, (ii) bare part of WS2 flake (red star in FIG 2b,c), and (iii) graphene covered part of WS2 flake (blue star in FIG 2b,c) upon the doping operations. (i) FIG. 1d shows the in plane momentum KX vs energy (E − EF , where E is the photoelectron energy, and EF is the fermi energy) is the energy momentum dispersion of the graphene at the corner of the BZ (K-point), acquired with both n-, and p-doping (at -6V, 0V, and 8V of VG). The Dirac point energy (ED) shifts from up to down with respect to doping, follows a linear dispersion. In case of p-doping, the graphene Dirac point moves down and appears like a cut at the fermi level above the Dirac point. Whereas, with no doping, the Dirac point of the graphene sets at the fermi level. However, in case of the n-doping, the bands move up in energy and the FL appear below ED. This linear variation of doping dependent band shifting is the direct visualization of electrostatic response of the graphene top contact. Alongside, the carrier density that is extracted from its momentum distribution at each VG shown in Fig.1g. The device was operated from -6V to 12 V of VG, that estimates the maximum density of 5.3×1012/cm2at -6V, follows a constant slope while ndoped. Whereas the maximum density of 3.9×1012/cm2 is extracted at 12V with a nonlinear behavior of density with respect to VG, and observed a saturation after 10V. (ii) In case of bare part of WS2 flake, It is clear that with no doping, the bands are sharp with a spin-orbit splitting of 420 meV, and the K point is 520 meV higher in energy than the Γ-point, confirming a monolayer WS2. After doping with a density of 2.9×1012/cm2, the conduction band appears at the K point near fermi level, leading to a band gap of 2.0 °æ 0.025eV. This visualizes the position of the CB lies at the K-point of the monolayer TMDC and has direct band gap at K-point. The measured band gap is an outcome of the band renormalization due to the doping. The band position of the TMDC follows the electrostatic potential that developed due to the charge transfer (CT) from graphene to the bare part of TMDC flake with respect to the doping. From the FIG. 2a, the valence band maximum of the bare part follows the linear shift from 2eV to -6eV with respect to VG from -4V to 5V that follows the electrostatic potential linearly. After 5V, it starts the nonlinear behavior of the band shifting, leads to the beyond saturation of electron-hole accumulation, and hence formation of the CB takes place near the fermi level at the density of 2×1012/cm2, and VB is nearly 2eV below the fermi level. At the VG > 5V the CB starts populating and become more intense after 7V, following a “V” shape (Fig. 2b, black dots) starting from n- to p-doping with minimum energy at 6V VG. (iii) In case of the covered WS2 (FIG 1f), the bands are less intense as it is the bottom layer where the photoemission intensity is low compared to the top layer. It is clear that the bands of the covered WS2 are more confined and less broadened upon doping compared to the bare part of WS2. The VB moves down from -1.2eV to -2eV while going from -6V to 10V, a small energy change of 0.8meV while populating the conduction band. The shifting of VB is linear all the way up to the appearance of the CB population. The CB starts appearing at the density of 3×1012/cm2 near the FL leading to the band gap of 2.1eV at K point. It is observed that the band gap of the bare part is nearly 120 meV less compare to graphene-covered part of the WS2 flake (Fig 2c). Alike bare part of the flake, the covered part provides direct evidence of free carriers and the extracted EDC peak follows an upward curvature leads to the extraction of effective mass m∗ = (0.355 ± 0.02) × me of CB at the density of 4.2×1012/cm2. The method of probing TMDC bands by encapsulating through the top contact
The asymmetric slope of the carrier density (FIG 1f) between n-, and p-type of doping is due to the response of the WS2 flake to the carriers under the graphene. As the charge transfer from graphene to the WS2 is different for different types of doping, the carrier density appears to be different for n-, and p-doping. In addition, once the doping and the band filling on the WS2 flake saturated, the density on the graphene starts saturating after a density of 3.9×1012/cm2. In case of n-doping, VB of the WS2 flake linearly follows the electrostatic potential with respect to VG, whereas p-doping follows both linear and nonlinear behavior. This difference of linear (< 2×1012/cm2) and nonlinear (> 2×1012/cm2) response of the WS2 flake for different doping type leads to the asymmetric nature of the carrier density on the graphene. The particular linear and nonlinear shifting of the bands in the bare part of the WS2 flake that leads to populate the CB follows its electrostatic potential to the doping upon charge transfer from top graphene to the bare part. Whereas, in the covered part, the VB remains at almost same energy as the charge carriers developed still on graphene, so it does not follow the electrostatic potential. At higher density (n > 3.5×1012/cm2), the CB starts appearing at FL, whereas it starts appearing at a density of 2×1012/cm2 in case of bare part of the flake. Even at the lower density, the charge carriers were developed on the bare part of the flake following an efficient CT from graphene top contact. After saturation of band filling, at the bare part and at higher density, doping becomes efficient on the covered part of the flake, and the VB of both the parts meet at the density of 3.5×1012/cm2 and hence the CB starts appearing. This distinct difference in the band renormalization to populate CB between the bare and covered part of the WS2 flake is unique and is the first demonstration of difference
in CB formation mechanism. The origin of the distinct behaviour across the interface is due to the difference in doping between the bare and covered part of WS2 flake. Alike inhomogeneity of the currents and hence the doping inhomogenity across the measured area on the bare part of WS2 that leads to the broadening of the bands, the covered part provides the uniform doping across the measured spot to achieve the uniform doping with narrow linewidth of both VB and CB. This demonstrates the unique method to provide an uniform dopingnwhile measuring the TMDC through the graphene. Importantly, the band gap of the bare part of the WS2 flake is 120 meV less compared to the covered part of the flake. In addition, the many body effect is also responsible to lower the band gap due to the higher density in case of bare part of the flake. The domination of the interlayer screening over the environmental screening is responsible for the bend renormalisation of 120meV at this density. In the flip side, it is observed that, larger is the doping in case of bare part of TMDC, smaller is the interlayer screening and hence the band gap is shrinking more. In addition, due to higher density, the plasmonic behaviour plays a role to reduce the band gap. On the other hand, smaller is the doping on the TMDC under the graphene, experiences larger internal screening and hence gives rise to 120meV larger in band gap. This is a competition of doping between the bare and covered part of the TMDC including the technical fact of photoemission intensity between the positions. However, it is clear that, at both the positions, CB population starts at different density, and concludes that the band gap renormalization is due to the difference of density between the positions, which includes internal screening due to the doping.
The asymmetric slope of the carrier density (FIG 1f) between n-, and p-type of doping is due to the response of the WS2 flake to the carriers under the graphene. As the charge transfer from graphene to the WS2 is different for different types of doping, the carrier density appears to be different for n-, and p-doping. In addition, once the doping and the band filling on the WS2 flake saturated, the density on the graphene starts saturating after a density of 3.9×1012/cm2. In case of n-doping, VB of the WS2 flake linearly follows the electrostatic potential with respect to VG, whereas p-doping follows both linear and nonlinear behavior. This difference of linear (< 2×1012/cm2) and nonlinear (> 2×1012/cm2) response of the WS2 flake for different doping type leads to the asymmetric nature of the carrier density on the graphene. The particular linear and nonlinear shifting of the bands in the bare part of the WS2 flake that leads to populate the CB follows its electrostatic potential to the doping upon charge transfer from top graphene to the bare part. Whereas, in the covered part, the VB remains at almost same energy as the charge carriers developed still on graphene, so it does not follow the electrostatic potential. At higher density (n > 3.5×1012/cm2), the CB starts appearing at FL, whereas it starts appearing at a density of 2×1012/cm2 in case of bare part of the flake. Even at the lower density, the charge carriers were developed on the bare part of the flake following an efficient CT from graphene top contact. After saturation of band filling, at the bare part and at higher density, doping becomes efficient on the covered part of the flake, and the VB of both the parts meet at the density of 3.5×1012/cm2 and hence the CB starts appearing. This distinct difference in the band renormalization to populate CB between the bare and covered part of the WS2 flake is unique and is the first demonstration of difference
in CB formation mechanism. The origin of the distinct behaviour across the interface is due to the difference in doping between the bare and covered part of WS2 flake. Alike inhomogeneity of the currents and hence the doping inhomogenity across the measured area on the bare part of WS2 that leads to the broadening of the bands, the covered part provides the uniform doping across the measured spot to achieve the uniform doping with narrow linewidth of both VB and CB. This demonstrates the unique method to provide an uniform dopingnwhile measuring the TMDC through the graphene. Importantly, the band gap of the bare part of the WS2 flake is 120 meV less compared to the covered part of the flake. In addition, the many body effect is also responsible to lower the band gap due to the higher density in case of bare part of the flake. The domination of the interlayer screening over the environmental screening is responsible for the bend renormalisation of 120meV at this density. In the flip side, it is observed that, larger is the doping in case of bare part of TMDC, smaller is the interlayer screening and hence the band gap is shrinking more. In addition, due to higher density, the plasmonic behaviour plays a role to reduce the band gap. On the other hand, smaller is the doping on the TMDC under the graphene, experiences larger internal screening and hence gives rise to 120meV larger in band gap. This is a competition of doping between the bare and covered part of the TMDC including the technical fact of photoemission intensity between the positions. However, it is clear that, at both the positions, CB population starts at different density, and concludes that the band gap renormalization is due to the difference of density between the positions, which includes internal screening due to the doping.