Hong LipersName, Alex W. ContrymanpersName, Xiaofeng QianpersName, Sina Moeini ArdakanipersName, Yongji GongpersName, Xingli WangpersName, Jeffrey M. WeissepersName, Chi Hwan LeepersName, Jiheng ZhaopersName, Pulickel M. AjayanpersName, Ju LipersName, Hari C. ManoharanpersName, Xiaolin ZhengpersName (2015date). “Optoelectronic crystal of artificial atoms in strain-textured molybdenum disulphide.” Nature Communicationstitle·j.
Object of study — monolayer MoS 2term strained into an array of artificial atomsterm·dom over a nanoconeterm substrate
Research question — whether spatially patterned strain in monolayer MoS 2term realises an optoelectronic crystal of artificial atomsterm·dom
Contribution — two-dimensionalterm·dom semiconductors with spatially textured band gapsterm·dom as a new class of materials
phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | exciton funnelling to strain maxima in strain-textured monolayer MoS2 — “Here we realize and confirm this ‘artificial atom' concept via capillary-pressure-induced nanoindentation of monolayer molybdenum disulphide from a tailored nanopattern, and demonstrate that a synthetic superlattice of these building blocks forms an optoelectronic crystal capable of broadband light absorption and efficient funnelling of photogenerated excitons to points of maximum strain at the artificial-atom nuclei.” | |
| claim-type | existence — “Here we realize and confirm this ‘artificial atom' concept via capillary-pressure-induced nanoindentation of monolayer molybdenum disulphide from a tailored nanopattern, and demonstrate that a synthetic superlattice of these building blocks forms an optoelectronic crystal capable of broadband light absorption and efficient funnelling of photogenerated excitons to points of maximum strain at the artificial-atom nuclei.” | |
| method — evidence | — “In the following, we apply spatially modulated biaxial tensile strain in monolayer MoS 2 using a patterned nanocone substrate to realize the optoelectronic crystal consisting of ‘artificial atoms.'” | |
| object of study — evidence | — “In the following, we apply spatially modulated biaxial tensile strain in monolayer MoS 2 using a patterned nanocone substrate to realize the optoelectronic crystal consisting of ‘artificial atoms.'” | |
| research question — evidence | — “In the following, we apply spatially modulated biaxial tensile strain in monolayer MoS 2 using a patterned nanocone substrate to realize the optoelectronic crystal consisting of ‘artificial atoms.'” | |
| contribution — evidence | — “Such two-dimensional semiconductors with spatially textured band gaps represent a new class of materials, which may find applications in next-generation optoelectronics or photovoltaics.” | |
| mechanism | exciton funnelling The strain-induced potential funnels photogenerated excitons from larger to smaller band gap regions, broadening absorption and concentrating photocarriers. — “This electronic potential funnels photogenerated excitons from larger band gap regions into smaller band gap regions, resulting in potential broader spectrum light absorption and more efficient photocarrier concentration.” | mechanisms[0] |
| mechanism | capillary nanoindentation Evaporating ethylene glycol generates a capillary force that pulls the MoS 2 sheet onto the nanocones. — “The evaporation of ethylene glycol that fills the gap between the MoS 2 and nanocones generates capillary force that pulls down the MoS 2 sheet, causing it to conform to the topography of the nanocones and accomplishing the nanoindentation.” | mechanisms[1] |
| sense | nucleus - the nanocone apex, where strain is highest and the band gap smallest — “Since the band gap decreases with increasing tensile strain, the nanocone apex marks the ‘nucleus' of the ‘artificial atom'.” | senses[0] |
| relation | MoS 2 —same-as→ molybdenum disulphide — ( ) — “Here we focus on monolayer molybdenum disulphide (MoS 2 ), a direct band gap semiconductor that shows promise for applications in photonics and optoelectronics due to its extraordinary physical properties” — “monolayer molybdenum disulphide (MoS 2 )” | concept_edges[0] |
| weight | MoS 2 —same-as→ molybdenum disulphide — 0.95 — “Here we focus on monolayer molybdenum disulphide (MoS 2 ), a direct band gap semiconductor that shows promise for applications in photonics and optoelectronics due to its extraordinary physical properties” | concept_edges[0] |
| relation | 2D —same-as→ two-dimensional — ( ) — “Straining two-dimensional (2D) materials 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 with a spatially varying ‘designer' strain can lead to new artificial materials with exotic properties.” — “Straining two-dimensional (2D) materials” | concept_edges[1] |
| weight | 2D —same-as→ two-dimensional — 0.95 — “Straining two-dimensional (2D) materials 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 with a spatially varying ‘designer' strain can lead to new artificial materials with exotic properties.” | concept_edges[1] |
| relation | OBG —same-as→ optical band gap — ( ) — “For instance, uniaxial strain has been shown to modulate the electronic structure 5 , 6 , 7 and reduce the optical band gap (OBG) of monolayer MoS 2 up to 100 meV 6 .” — “reduce the optical band gap (OBG)” | concept_edges[2] |
| weight | OBG —same-as→ optical band gap — 0.95 — “For instance, uniaxial strain has been shown to modulate the electronic structure 5 , 6 , 7 and reduce the optical band gap (OBG) of monolayer MoS 2 up to 100 meV 6 .” | concept_edges[2] |
| relation | QBG —same-as→ quasiparticle band gap — ( ) — “It has been calculated that indenting monolayer MoS 2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG).” — “the local quasiparticle band gap (QBG)” | concept_edges[3] |
| weight | QBG —same-as→ quasiparticle band gap — 0.95 — “It has been calculated that indenting monolayer MoS 2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG).” | concept_edges[3] |
| relation | AFM —same-as→ atomic force microscopy — ( ) — “The clearly visible wrinkles between nanocones ( Fig. 1c ) indicate the presence of deformation and strain in the MoS 2 sheet, which is also verified by atomic force microscopy (AFM; Fig. 1d ).” — “atomic force microscopy (AFM; Fig. 1d )” | concept_edges[4] |
| weight | AFM —same-as→ atomic force microscopy — 0.95 — “The clearly visible wrinkles between nanocones ( Fig. 1c ) indicate the presence of deformation and strain in the MoS 2 sheet, which is also verified by atomic force microscopy (AFM; Fig. 1d ).” | concept_edges[4] |
| relation | STM —same-as→ scanning tunnelling microscopy — ( ) — “A scanning tunnelling microscopy (STM) topograph ( Fig. 1e ) shows the details of a single MoS 2 artificial-atom element.” — “A scanning tunnelling microscopy (STM) topograph” | concept_edges[5] |
| weight | STM —same-as→ scanning tunnelling microscopy — 0.95 — “A scanning tunnelling microscopy (STM) topograph ( Fig. 1e ) shows the details of a single MoS 2 artificial-atom element.” | concept_edges[5] |
| effect direction | tensile strain —causes→ quasiparticle band gap — reduces — “It has been calculated that indenting monolayer MoS 2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG).” — “a tensile strain field that reduces the local quasiparticle band gap” | concept_edges[6] |
| relation | tensile strain —causes→ quasiparticle band gap — reduces — “It has been calculated that indenting monolayer MoS 2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG).” — “creates a tensile strain field that reduces the local quasiparticle band gap” | concept_edges[6] |
| weight | tensile strain —causes→ quasiparticle band gap — 0.85 — “It has been calculated that indenting monolayer MoS 2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG).” | concept_edges[6] |
| effect direction | tensile strain —causes→ band gap — reduces — “Since the band gap decreases with increasing tensile strain, the nanocone apex marks the ‘nucleus' of the ‘artificial atom'.” — “the band gap decreases with increasing tensile strain” | concept_edges[7] |
| relation | tensile strain —causes→ band gap — decreases with increasing — “Since the band gap decreases with increasing tensile strain, the nanocone apex marks the ‘nucleus' of the ‘artificial atom'.” — “the band gap decreases with increasing tensile strain” | concept_edges[7] |
| weight | tensile strain —causes→ band gap — 0.85 — “Since the band gap decreases with increasing tensile strain, the nanocone apex marks the ‘nucleus' of the ‘artificial atom'.” | concept_edges[7] |
| relation | STM/STS —contrasted-with→ optical measurements — compared with — “These strains are much higher than the maximum of ∼0.6% measured by Raman spectroscopy, which can be explained by the inherently atomic scale measurement of STM/STS compared with the optical measurements, which average over the finite laser beam size (∼450 nm).” — “the inherently atomic scale measurement of STM/STS compared with the optical measurements” | concept_edges[8] |
| weight | STM/STS —contrasted-with→ optical measurements — 0.8 — “These strains are much higher than the maximum of ∼0.6% measured by Raman spectroscopy, which can be explained by the inherently atomic scale measurement of STM/STS compared with the optical measurements, which average over the finite laser beam size (∼450 nm).” | concept_edges[8] |
| replication | original | |
| limitation | The 3% strain is a lower bound computed for biaxial strain; uniaxial strain in local areas would need larger magnitudes. — “This is the lower bound as larger strain magnitude is necessary to achieve the observed band gap modulation if the strain is uniaxial, which could exist in local areas due to the imperfect geometry of the nanocones.” | limitations[0] |
| limitation | Raman/PL measurements are optically averaged and dominated by points with a direct transition. — “However, because the Raman/PL measurements are optically averaged, they are dominated by the majority of the points within the laser beam that have direct transition as evidenced by the high PL efficiency.” | limitations[1] |
| limitation | Spin-orbit coupling was left out of the Raman calculations. — “The spin-orbit coupling was not included.” | limitations[2] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | The A exciton PL peak intensity more than doubles in the most strained MoS 2. — “Finally and significantly, the A exciton peak intensity is more than doubled in the most strained-MoS 2 ( Fig. 3a ), and the intensity increase is highly reproducible over the scanned region ( Fig. 3c ).” | content_tags.findings[0] |
| finding | Local atomic strain approaches 3%. — “This result provides confirmation that the local atomic strain is approaching the unprecedentedly high value of 3%.” | content_tags.findings[1] |
| finding | STS shows over 20% modulation of the quasiparticle band gap. — “From the STS measurements, a modulation of over 20% in the QBG is directly observed.” | content_tags.findings[2] |
| finding | The engineered optical band gap extends absorption from 677 nm to 905 nm. — “This engineered OBG enables a broadband light absorption by increasing the absorption bandwidth from 677 nm (unstrained-MoS 2 ) to 905 nm (most strained-MoS 2 ), which covers the entire visible wavelength and most intensive wavelengths of the solar spectrum.” | content_tags.findings[3] |
| finding | Oscillator-strength change is too small to explain the PL enhancement. — “First, according to our exciton calculations (see Discussion below), the change of the oscillator strength on elastic strain is relatively small (∼6% increase under 1% biaxial strain), which cannot explain the observed >100% PL intensity enhancement.” | content_tags.findings[4] |
| quantity | −0.11 eV per 1% — — “The A exciton peak exhibits a linear redshift rate of −0.11 eV per 1% of biaxial tensile strain (dashed purple line in Fig. 4e , also in good agreement with other calculations 1 , 4 ).” | content_tags.quantities[0] |
| quantity | ∼2% — — “The calculations 8 furthermore reveal a direct-to-indirect gap transition at ∼2% biaxial tensile strain, resulting in an increased drop of ∼−0.24 eV per % of the (now indirect) gap with strain ( Fig. 4e , dotted cyan line).” | content_tags.quantities[1] |
| quantity | ∼0.5 eV — — “The measurements also confirm a remarkably large exciton binding energy of ∼0.5 eV, only recently verified to be a general feature of dichalcogenides 36 .” | content_tags.quantities[2] |
| variable | tensile strain — “It has been calculated that indenting monolayer MoS 2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG).” | content_tags.variables[0] |
| definition | optical measurements — “These strains are much higher than the maximum of ∼0.6% measured by Raman spectroscopy, which can be explained by the inherently atomic scale measurement of STM/STS compared with the optical measurements, which average over the finite laser beam size (∼450 nm).” | content_tags.definitions[0] |
| key-terms | molybdenum disulphide, artificial atom, exciton funnel, biaxial tensile strain, nanocones, band gap, photoluminescence, Raman spectroscopy, scanning tunnelling spectroscopy |
| concept | MoS 2 — molybdenum disulphide — “Here we focus on monolayer molybdenum disulphide (MoS 2 ), a direct band gap semiconductor that shows promise for applications in photonics and optoelectronics due to its extraordinary physical properties” | concepts[0] |
| concept | molybdenum disulphide — a direct band gap semiconductor that shows promise for applications in photonics and optoelectronics — “Here we focus on monolayer molybdenum disulphide (MoS 2 ), a direct band gap semiconductor that shows promise for applications in photonics and optoelectronics due to its extraordinary physical properties” | concepts[1] |
| concept | 2D — two-dimensional — “Straining two-dimensional (2D) materials 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 with a spatially varying ‘designer' strain can lead to new artificial materials with exotic properties.” | concepts[2] |
| concept | two-dimensional — not defined in this paper's own words; atomically thin, of a single or few atomic layers — “Straining two-dimensional (2D) materials 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 with a spatially varying ‘designer' strain can lead to new artificial materials with exotic properties.” | concepts[3] |
| concept | atomic force microscopy — not defined in this paper's own words; the probe technique used to verify the deformation of the MoS 2 sheet — “The clearly visible wrinkles between nanocones ( Fig. 1c ) indicate the presence of deformation and strain in the MoS 2 sheet, which is also verified by atomic force microscopy (AFM; Fig. 1d ).” | concepts[4] |
| concept | scanning tunnelling microscopy — not defined in this paper's own words; the technique imaging a single artificial-atom element at atomic scale — “A scanning tunnelling microscopy (STM) topograph ( Fig. 1e ) shows the details of a single MoS 2 artificial-atom element.” | concepts[5] |
| concept | OBG — optical band gap — “For instance, uniaxial strain has been shown to modulate the electronic structure 5 , 6 , 7 and reduce the optical band gap (OBG) of monolayer MoS 2 up to 100 meV 6 .” | concepts[6] |
| concept | optical band gap — not defined in this paper's own words; the band gap seen in optical (PL) measurements, lower than the quasiparticle gap by the exciton binding energy — “For instance, uniaxial strain has been shown to modulate the electronic structure 5 , 6 , 7 and reduce the optical band gap (OBG) of monolayer MoS 2 up to 100 meV 6 .” | concepts[7] |
| concept | QBG — quasiparticle band gap — “It has been calculated that indenting monolayer MoS 2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG).” | concepts[8] |
| concept | quasiparticle band gap — not defined in this paper's own words; the electronic band gap measured locally by tunnelling spectroscopy — “It has been calculated that indenting monolayer MoS 2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG).” | concepts[9] |
| concept | tensile strain — not defined in this paper's own words; stretching deformation of the MoS 2 sheet, highest at the nanocone tips — “It has been calculated that indenting monolayer MoS 2 creates a tensile strain field that reduces the local quasiparticle band gap (QBG).” | concepts[10] |
| concept | artificial atom — not defined in this paper's own words; a point of peak strain whose strain-induced potential mimics the Coulomb potential of a mesoscopic atom — “The resulting modified electronic potential falls off inversely with distance from the indentation, playing the role of an effective electronic potential centred on a mesoscopic ‘artificial atom' 8 .” | concepts[11] |
| concept | exciton funnel effect — not defined in this paper's own words; drift of photogenerated excitons down the strain-graded band gap to the points of maximum strain — “Therefore, we rule out alternate factors discussed above and attribute the anomalous enhanced PL intensity to the novel 2D exciton funnel effect 8 .” | concepts[12] |
| concept | PL — photoluminescence — “However, the indirect band gap of few-layer MoS 2 prevents the distinctive photoluminescence (PL) intensity enhancement expected from the exciton funnelling process from being directly observed 23 .” | concepts[13] |
| concept | AFM — atomic force microscopy — “The clearly visible wrinkles between nanocones ( Fig. 1c ) indicate the presence of deformation and strain in the MoS 2 sheet, which is also verified by atomic force microscopy (AFM; Fig. 1d ).” | concepts[14] |
| concept | STM — scanning tunnelling microscopy — “A scanning tunnelling microscopy (STM) topograph ( Fig. 1e ) shows the details of a single MoS 2 artificial-atom element.” | concepts[15] |
| concept | STS — Scanning tunnelling spectroscopy — “Scanning tunnelling spectroscopy (STS) is performed in different regions of the area shown, and representative d I/ d V tunnel spectra for unstrained-MoS 2 , less strained-MoS 2 , and most strained-MoS 2 are shown in Fig. 4b .” | concepts[16] |
| concept | STM/STS — not defined in this paper's own words; the local tunnelling measurements, which resolve strain at atomic scale — “These strains are much higher than the maximum of ∼0.6% measured by Raman spectroscopy, which can be explained by the inherently atomic scale measurement of STM/STS compared with the optical measurements, which average over the finite laser beam size (∼450 nm).” | concepts[17] |
| concept | optical measurements — average over the finite laser beam size — “These strains are much higher than the maximum of ∼0.6% measured by Raman spectroscopy, which can be explained by the inherently atomic scale measurement of STM/STS compared with the optical measurements, which average over the finite laser beam size (∼450 nm).” | concepts[18] |
| concept | nanoindentation — not defined in this paper's own words; pressing the MoS 2 sheet onto the nanocones so it conforms to them and is strained — “The evaporation of ethylene glycol that fills the gap between the MoS 2 and nanocones generates capillary force that pulls down the MoS 2 sheet, causing it to conform to the topography of the nanocones and accomplishing the nanoindentation.” | concepts[19] |
| concept | nanocones — not defined in this paper's own words; the patterned SiO 2 cones whose tips set the strain maxima — “The evaporation of ethylene glycol that fills the gap between the MoS 2 and nanocones generates capillary force that pulls down the MoS 2 sheet, causing it to conform to the topography of the nanocones and accomplishing the nanoindentation.” | concepts[20] |
| concept | nanosphere lithography — not defined in this paper's own words; the method used to assemble the SiO 2 nanocones — “The as-grown MoS 2 sheet ( Supplementary Fig. 1 ) is transferred onto the SiO 2 nanocones ( Fig. 1b ) assembled using nanosphere lithography 24 , 25 ( Supplementary Fig. 2 ).” | concepts[21] |
| concept | exciton binding energy — not defined in this paper's own words; the energy separating the quasiparticle and optical band gaps, about 0.5 eV here — “The measurements also confirm a remarkably large exciton binding energy of ∼0.5 eV, only recently verified to be a general feature of dichalcogenides 36 .” | concepts[22] |
| concept | direct-to-indirect gap transition — not defined in this paper's own words; the change of MoS 2 from a direct to an indirect gap at about 2% biaxial strain — “The calculations 8 furthermore reveal a direct-to-indirect gap transition at ∼2% biaxial tensile strain, resulting in an increased drop of ∼−0.24 eV per % of the (now indirect) gap with strain ( Fig. 4e , dotted cyan line).” | concepts[23] |
| concept | band gap — not defined in this paper's own words; the energy gap of the semiconductor, tuned here by strain — “Since the band gap decreases with increasing tensile strain, the nanocone apex marks the ‘nucleus' of the ‘artificial atom'.” | concepts[24] |
Full text — tagged
Optoelectronic crystal of artificial atomsterm·dom in strain-textured molybdenum disulphideterm Abstract The isolation of the two-dimensionalterm·dom semiconductor molybdenum disulphideterm introduced a new optically active material possessing a band gapterm·dom that can be facilely tuned via elastic strain. As an atomically thin membrane with exceptional strength, monolayer molybdenum disulphideterm subjected to biaxial strain can embed wide band gapterm·dom variations overlapping the visible light spectrum, with calculations showing the modified electronic potential emanating from point-induced tensile strainterm·dom perturbations mimics the Coulomb potential in a mesoscopic atom. Here we realize and confirm this ‘artificial atomterm·dom' concept via capillary-pressure-induced nanoindentationterm·mth of monolayer molybdenum disulphideterm from a tailored nanopattern, and demonstrate that a synthetic superlattice of these building blocks forms an optoelectronic crystal capable of broadband light absorption and efficient funnelling of photogenerated excitons to points of maximum strain at the artificial-atom nuclei. Such two-dimensionalterm·dom semiconductors with spatially textured band gapsterm·dom represent a new class of materials, which may find applications in next-generation optoelectronics or photovoltaics.
Straining two-dimensionalterm·dom (2Dterm·dom) materials 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 with a spatially varying ‘designer' strain can lead to new artificial materials with exotic properties. Assembling such tuned artificial materials in condensed matter is an emerging field and has employed tools such as atomic manipulation 9 and lithographic techniques 10 . Here we focus on monolayer molybdenum disulphideterm (MoS 2term ), a direct band gapterm·dom semiconductor that shows promise for applications in photonics and optoelectronics due to its extraordinary physical properties 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 . Elastic strain offers a novel and exciting opportunity to tune the band gapterm·dom of monolayer MoS 2term (refs 1 , 2 , 3 , 4 ) since it can sustain very high elastic strain before rupturing compared with its bulk counterpart 19 , 20 . For instance, uniaxial strain has been shown to modulate the electronic structure 5 , 6 , 7 and reduce the optical band gapterm·dom (OBGterm·dom) of monolayer MoS 2term up to 100 meV 6 .
Besides pushing the magnitude of the strain, the ability to apply a spatially controllable strain is even more crucial because it enables the realization of a graded band gapterm·dom semiconductor eagerly sought for wider photonic, optoelectronic and photovoltaic applications 21 , 22 . It has been calculated that indenting monolayer MoS 2term creates a tensile strainterm·dom field that reduces the local quasiparticle band gapterm·dom (QBGterm·dom). The resulting modified electronic potential falls off inversely with distance from the indentation, playing the role of an effective electronic potential centred on a mesoscopic ‘artificial atomterm·dom' 8 . This electronic potential funnels photogenerated excitons from larger band gapterm·dom regions into smaller band gapterm·dom regions, resulting in potential broader spectrum light absorption and more efficient photocarrier concentration. The exciton funnelterm·key concept has been successfully employed to interpret the OBGterm·dom of wrinkled few-layer MoS 2term . However, the indirect band gapterm·dom of few-layer MoS 2term prevents the distinctive photoluminescenceterm·key (PLterm·mth) intensity enhancement expected from the exciton funnelling process from being directly observed 23 . Assembly of the aforementioned artificial atomsterm·dom would result in a large-area functional ‘artificial crystal.' Currently there exists no fundamental proof-of-principle of this idea, neither at the single ‘artificial atomterm·dom' level nor at a more practical macroscopic scale.
In the following, we apply spatially modulated biaxial tensile strainterm·key in monolayer MoS 2term using a patterned nanoconeterm substrate to realize the optoelectronic crystal consisting of ‘artificial atomsterm·dom.' MoS 2term on top of the nanoconesterm experiences high strain, which gradually decreases from the tip to the perimeter of the nanoconesterm ( Fig. 1a ). Since the band gapterm·dom decreases with increasing tensile strainterm·dom, the nanoconeterm apex marks the ‘nucleus' of the ‘artificial atomterm·dom'. The strain profile has been optimized for maximum exciton solar funnel collection by controlling the geometry and dimensions of the nanoconesterm.
Assembly of an artificial-atom crystal via spatially patterned biaxial strain within a monolayer of MoS 2term . ( a ) Schematic of strained MoS 2term indented by SiO 2 nanoconesterm, where the regions on the tips of nanoconesterm exhibit highest tensile strainterm·dom while the areas between nanoconesterm are less strained. The MoS 2term energy band gapterm·dom inversely tracks the strain profile and becomes spatially modulated, forming ‘artificial atomsterm·dom' at the points of peak strain where the strain-induced potential mimics the Coulomb potential around ions in a crystal. ( b ) Cross-sectional scanning electron microscopy (SEM) image of the nanoconeterm substrate. Dotted lines label the SiO 2 /p++ Si and SiO 2 /vacuum boundaries. Solid curve delineates the nanoconeterm shape. Scale bar is 500 nm. ( c ) Tilted false-colour SEM image of the 2Dterm·dom strained MoS 2term crystal defined by the nanoconeterm array. Scale bar is 500 nm. ( d ) AFMterm·mth topography of the 2Dterm·dom MoS 2term strain crystal. Scale bar is 1 μm. ( e ) STMterm·mth topography of a single ‘artificial atomterm·dom' building block within the crystal. Scale bar is 100 nm.
Results Creation of the artificial-atom crystal in strain-textured MoS 2term The as-grown MoS 2term sheet ( Supplementary Fig. 1 ) is transferred onto the SiO 2 nanoconesterm ( Fig. 1b ) assembled using nanosphere lithographyterm·mth 24 , 25 ( Supplementary Fig. 2 ). The as-transferred MoS 2term is soaked in ethylene glycol to remove the trapped air bubbles and optimize the strain ( Supplementary Fig. 3b ). The evaporation of ethylene glycol that fills the gap between the MoS 2term and nanoconesterm generates capillary force that pulls down the MoS 2term sheet, causing it to conform to the topography of the nanoconesterm and accomplishing the nanoindentationterm·mth. The clearly visible wrinkles between nanoconesterm ( Fig. 1c ) indicate the presence of deformation and strain in the MoS 2term sheet, which is also verified by atomic force microscopyterm·mth (AFMterm·mth; Fig. 1d ). A scanning tunnelling microscopyterm·mth (STMterm·mth) topograph ( Fig. 1e ) shows the details of a single MoS 2term artificial-atom element. We note that a similar attempt for templating strain has been carried out in graphene with limited strain magnitude due to a not-yet optimized process 25 , 26 .
Scanning Raman spectroscopyterm·key of the artificial-atom crystal The spatially varying strain distribution is verified by micro-Raman spectroscopy. Figure 2a shows the typical Raman spectra of the most strained-MoS 2 (on tip of nanoconesterm), less strained-MoS 2 (between nanoconesterm) and unstrained-MoS 2 (on flat SiO 2 surface) [ Supplementary Fig. 4 ]. The unstrained-MoS 2 has the typical Raman spectrum of monolayer MoS 2term with two dominant peaks at 385.6 ( ) and 404.9 cm −1 ( A 1g ) 27 , 28 . The strained MoS 2term samples show significant redshifts for both and A 1g peaks: 0.8 and 0.3 cm −1 for less strained-MoS 2 , and 2.4 and 0.6 cm −1 for most strained-MoS 2 . From an overall fit to the redshift magnitudes and the unstrained values, we estimate that (0.230±0.035)% and (0.565±0.025)% biaxial tensile strainsterm·key are sampled on average by the 450-nm diameter laser beam in less strained-MoS 2 and most strained-MoS 2 according to our theoretical calculation discussed later. The Raman mappings of the ( Fig. 2b ) and A 1g ( Fig. 2c ) peak frequencies show that the periodically varying strain is consistent over the entire scanned artificial crystal (25 μm 2 ). The darker (lower frequency) and brighter (higher frequency) colours ( Fig. 2b,c ) indicate that tensile strainterm·dom is highest on the tips of nanoconesterm—at ‘artificial atomterm·dom' nuclei—and gradually decreases to a minimum towards the perimeters of the nanoconesterm.
Scanning Raman spectroscopyterm·key of the MoS 2term strain crystal. ( a ) Raman spectra of most strained-MoS 2 , less strained-MoS 2 and unstrained-MoS 2 . Symbols are measurement data; curves are fitting data. Inset: schematic atomic displacement of the in-plane and out-of-plane A 1g modes. ( b , c ) Scanning Raman spectroscopic maps plotting ( b ) peak frequency and ( c ) A 1g peak frequency of strain-textured MoS 2term on the nanoconeterm substrate. Scale bars are 1 μm.
Scanning PLterm·mth spectroscopy of the artificial-atom crystal The effect of strain on the OBGterm·dom of MoS 2term strain crystal is examined by micro-PL spectroscopy. Figure 3a compares the representative PLterm·mth spectra of the most strained-MoS 2 , less strained-MoS 2 , and unstrained-MoS 2 , where the strong PLterm·mth peaks arise from the direct band gapterm·dom emissions in monolayer MoS 2term . First, unstrained-MoS 2 shows a typical PLterm·mth spectrum of monolayer MoS 2term with a principal peak at 1.83 eV (A exciton) and a minor peak at 1.95 eV (B exciton) 11 . Second, the strained MoS 2term clearly exhibits redshift of the A exciton energy: 18 and 50 meV for the less strained-MoS 2 and most strained-MoS 2 , respectively, indicating a strain-induced OBGterm·dom reduction 6 , 7 . From the magnitude of the redshift and our theoretical calculation, we estimate approximately 0.2 and 0.5% biaxial tensile strainsterm·key are optically sampled in less strained-MoS 2 and most strained-MoS 2 , respectively. These values agree well with the strains derived from Raman peak shifts above. Third, the mapping of the PLterm·mth wavelength ( Fig. 3b ) shows that spatially varying OBGterm·dom reduction is consistently observed over scanned areas. Finally and significantly, the A exciton peak intensity is more than doubled in the most strained-MoS 2 ( Fig. 3a ), and the intensity increase is highly reproducible over the scanned region ( Fig. 3c ). There are a few factors that may affect the PLterm·mth intensity including strain-modulated oscillator strength, varying local emission geometry, variation in underlying SiO 2 thickness and strain-induced exciton funnelling 29 . First, according to our exciton calculations (see Discussion below), the change of the oscillator strength on elastic strain is relatively small (∼6% increase under 1% biaxial strain), which cannot explain the observed >100% PLterm·mth intensity enhancement. Second, the geometry-dependent PLterm·mth intensity is expected to be enhanced on a flat substrate as the PLterm·mth intensity of monolayer MoS 2term peaks at normal collection angle 30 , 31 , which is opposite to our observation. Third, a recent study of PLterm·mth emission from MoS 2term shows a flat dependence on underlying SiO 2 thickness in the range of 180–270 nm, corresponding to oxide thicknesses variations in our samples from etching the nanoconesterm 32 . In fact, the PLterm·mth emission intensity of homogeneously strained monolayer MoS 2term was experimentally found to decrease when strain increases due to the increased probability of non-radiative relaxations 6 , again opposite our observations. Finally, we note that enhanced PLterm·mth intensity due to exciton drifting and concentrating has been observed in strained semiconductor nanowires 29 , 33 , 34 . Therefore, we rule out alternate factors discussed above and attribute the anomalous enhanced PLterm·mth intensity to the novel 2Dterm·dom exciton funnel effectterm·dom 8 . The Raman mappings ( Fig. 2b,c ) show that the tensile strainterm·dom increases from the perimeters to the tips of the nanoconesterm, so the band gapterm·dom of MoS 2term decreases from the perimeters to the tips of the nanoconesterm. Consequently, a built-in electric field pointing from the tip towards the perimeter of the nanoconeterm is created ( Fig. 3d ) and the photogenerated excitons drift towards the funnel center, as can be modelled analytically and numerically 29 . Since the photogenerated excitons in monolayer MoS 2term can drift up to 660 nm before recombination 8 , the majority of photogenerated excitons are able to drift from the valleys to the tips of nanoconesterm ( 245 nm from pitch radius) without significant recombination. As a result, excitons are concentrated at the tips of nanoconesterm upon illumination and they eventually recombine, giving rise to the enhanced PLterm·mth emission localized at the nanoconeterm tips ( Fig. 3c,d ) and supporting the artificial atomterm·dom and energy funnel concept.
Scanning PLterm·mth spectroscopy of the MoS 2term strain crystal. ( a ) PLterm·mth spectra of most strained-MoS 2 , less strained-MoS 2 and unstrained-MoS 2 . Symbols are measurement data; curves are fitting data. Scanning PLterm·mth maps with ( b ) wavelength and ( c ) peak intensity of the same sample and area depicted in Fig. 2 . Scale bars are 1 μm. ( d ) Schematic of the funnel effect that consists of three processes: (I) excitons are induced in MoS 2term upon illumination; (II) photogenerated excitons drift in the artificial atomterm·dom potential towards the atom center formed by the nanoconeterm tip; and (III) concentrated excitons give emission with longer wavelength.
STMterm·mth and STSterm·mth measurements of the artificial-atom crystal The local electronic structure modulation of MoS 2term caused by strain is directly verified by STMterm·mth. Figure 4a shows an STMterm·mth topograph ( V =2.4 V, I =18 pA) in the vicinity of three nanoconesterm with height variations of 80 nm. Scanning tunnelling spectroscopyterm·key (STSterm·mth) is performed in different regions of the area shown, and representative d I/ d V tunnel spectra for unstrained-MoS 2 , less strained-MoS 2 , and most strained-MoS 2 are shown in Fig. 4b . It is worth noting that these spectra show the Fermi level near mid-gap position due to the electron depletion caused by the gold substrate 35 . The QBGterm·dom sizes extracted from the d I/ d V spectra ( Supplementary Fig. 5 ) are labelled at each strain level. Unstrained-MoS 2 shows a QBGterm·dom of 2.29 eV, which is consistent with the OBGterm·dom of 1.83 eV obtained by PLterm·mth measurement considering the exciton binding energyterm·dom ∼0.5 eV 8 . The extracted local QBGterm·dom varies from 2.29 eV down to 1.83 eV from STSterm·mth measurements acquired from unstrained-MoS 2 (topographic valley), through less strained-MoS 2 (intermediate regions) and to most strained-MoS 2 (topographic peak) locations. This corresponds to a measured local strain approaching ∼3% for most strained-MoS 2 . These strains are much higher than the maximum of ∼0.6% measured by Raman spectroscopyterm·key, which can be explained by the inherently atomic scale measurement of STM/STSterm·mth compared with the optical measurementsterm·mth, which average over the finite laser beam size (∼450 nm).
STM/STSterm·mth of the MoS 2term strain crystal and experimentterm·mth–theory correlation. ( a ) STMterm·mth topography in the vicinity of three nanoconesterm. Height colour bar indicates unstrained (topographic valleys), less strained (intermediate strain) and most strained (topographic peaks) to denote the amount of local strain expected at each height z (dashed arrow indicates direction of increasing strain). Scale bar is 100 nm. ( b ) Representative local d I/ d V measurements acquired from the region shown in ( a ) from unstrained (grey), less strained (blue) and most strained (red) locations. Each strain shows three individual d I/ d V measurements (open symbols), which are acquired in tight groups <10 nm in extent over each location. The solid lines are the averages of each group of three curves. Band gapsterm·dom extracted from the curves are enumerated for each strain amount with the trend indicated by dashed arrows. ( c ) Calculated local biaxial strain distribution over several unit cells of the crystal. ( d ) Cross-section of the strain profile showing local atomic strain (red), measured by STSterm·mth and ranging from 0 to 2.85% tensile strainterm·dom, and the optically averaged strain (green) sampled by scanning Raman/PLterm·mth measurements, ranging from 0.23 to 0.56% tensile strainterm·dom. The broadened distribution is calculated from theoretical local strain using the 450-nm optical Gaussian beam diameter. ( e ) Top panel shows theoretical (open symbols) and experimental (filled circles) Raman frequencies for the indicated phonon modes as a function of strain. Dashed lines are linear fits to the theory (−1.02 cm -1 per % for A 1g phonon and −4.48 cm -1 per % for phonon) and are used for the optically averaged strain assignment (top axis). Bottom panel shows theoretical (open symbols) and experimental (closed symbols) data for the OBGterm·dom (magenta, right axis) and the local QBGterm·dom (cyan, left axis). Axes have been scaled using the results of ( d ) as discussed in main text. Dashed lines match fit of −0.11 eV per % (direct OBGterm·dom) and dotted line shows an increased −0.24 eV per % (indirect OBGterm·dom) falloff of the OBGterm·dom beyond 2% biaxial strain. Star symbols denote the three specific measurements shown in ( b ). Error bars are determined by s.d. of each spectroscopic measurement.
To quantify this argument and verify the complete strain profile of the crystal, we simulate the strain induced in a monolayer MoS 2term sheet by applying a constant pressure on the sheet, and Lennard–Jones interatomic interactions between the sheet and substrate ( Fig. 4c , Supplementary Fig. 6 ). To calibrate the mapping between the local tunnelling measurements and the optically averaged Raman/PLterm·mth measurements, we plot in Fig. 4d the cone-to-cone calculated strain profiles ( Fig. 4c ) before and after a convolution step. The raw atomic strain is convolved with a 2Dterm·dom Gaussian of 450-nm 1/ e 2 width, corresponding to the 450-nm diameter Gaussian beam used in our optical experimentsterm·mth. With no fitting parameters, this yields a predicted optically averaged strain sampled by scanning Raman/PLterm·mth; this average strain ranges from 0.233 to 0.562% and is in excellent agreement with the Raman/PLterm·mth results from less strained-MoS 2 and most strained-MoS 2 regions presented above. This result provides confirmation that the local atomic strain is approaching the unprecedentedly high value of 3%.
Discussion We use this calibration to unify all experimental (closed symbols) and theoretical (open symbols) results ( Fig. 4e ). We calculated Raman spectra under from 0 to 1% (red and blue triangles in Fig. 4e ; Supplementary Fig. 7a ). As increases from 0 to 1%, the and A 1g peaks shift towards lower frequencies. Such Raman peak shifts vary linearly with biaxial strain, and the slopes are −4.48 and −1.02 cm −1 per 1% of biaxial strain for and A 1g modes, respectively (dashed red and blue lines in Fig. 4e ). The fit to all Raman data in unstrained, less strained and most strained regions with respect to these two lines yields values quoted earlier, (0.230±0.035)% (less strained) and (0.565±0.025)% (most strained) that are shaded in Fig. 4e . The calculated A exciton energy at various ranging from 0 to 1% is shown in Fig. 4e (lower panel, open purple triangles; Supplementary Fig. 7b ). The A exciton peak exhibits a linear redshift rate of −0.11 eV per 1% of biaxial tensile strainterm·key (dashed purple line in Fig. 4e , also in good agreement with other calculations 1 , 4 ). Our recorded PLterm·mth energies when assigned to the Raman-extracted strain values above fall along this redshift line within experimental error.
The above discussion correlates OBGterm·dom measurements to . To make the final quantitative link to the intrinsic QBGterm·dom and the local atomic strain within the artificial crystal, we use the results of the convolution analysis elaborated above. Accordingly, we show in Fig. 4e a local atomic strain axis , which is linked to the optically averaged strain axis by the ratio of : =2.85:0.562 ∼ 5:1. On this axis we first plot the calculated theoretical QBGterm·dom from 0 to 5% local strain for direct (open cyan triangles) and indirect (open cyan circles) transitions 8 . The fit to the direct gap calculations ( Fig. 4e , dashed cyan line) also diminishes at −0.11 eV per % biaxial strain and the gap axis there is scaled by the same 5:1 ratio to show this match. The calculations 8 furthermore reveal a direct-to-indirect gap transitionterm·dom at ∼2% biaxial tensile strainterm·key, resulting in an increased drop of ∼−0.24 eV per % of the (now indirect) gap with strain ( Fig. 4e , dotted cyan line). We add other acquired STSterm·mth data to this plot. The closed cyan star symbols correspond to the curves shown in Fig. 4b and provide the anchor for the strain measurement: the highest QBGterm·dom of 2.29 eV corresponds to zero local strain, and the lowest QBGterm·dom of 1.83 eV corresponds to the highest strain at the artificial-atom nanoconeterm tips, and must correspond to the largest optically averaged strains deduced. The remaining STSterm·mth measurements have known gap values, and strain values that can be inferred by assigning to each value along the dotted line: gaps falling at −0.11 eV per % from the unstrained-MoS 2 value and rising at 0.24 eV per % from the most strained-MoS 2 value, meeting at the 2% direct-to-indirect transition. We note that the strain magnitude of 3% is calculated based on biaxial strain. This is the lower bound as larger strain magnitude is necessary to achieve the observed band gapterm·dom modulation if the strain is uniaxial, which could exist in local areas due to the imperfect geometry of the nanoconesterm.
We note that this summary shows that our local crystal strain is sufficiently high to access the indirect band gapterm·dom of monolayer MoS 2term . However, because the Raman/PLterm·mth measurements are optically averaged, they are dominated by the majority of the points within the laser beam that have direct transition as evidenced by the high PLterm·mth efficiency. The measurements also confirm a remarkably large exciton binding energyterm·dom of ∼0.5 eV, only recently verified to be a general feature of dichalcogenides 36 . From the STSterm·mth measurements, a modulation of over 20% in the QBGterm·dom is directly observed. From the mapping to the optically averaged strain ( Fig. 4 ) and the deduced exciton binding energyterm·dom, this represents a huge modulation of the OBGterm·dom, exceeding 25%.
This engineered OBGterm·dom enables a broadband light absorption by increasing the absorption bandwidth from 677 nm (unstrained-MoS 2 ) to 905 nm (most strained-MoS 2 ), which covers the entire visible wavelength and most intensive wavelengths of the solar spectrum. While already without precedent, since these strains are not yet even rupture limited, we anticipate even larger band gapterm·dom variations and electronic fields can be embedded in such artificial crystals in the future.
Methods Transfer and strain of MoS 2term monolayer MoS 2term monolayers grown by chemical vapour deposition were transferred onto the SiO 2 nanoconeterm substrate using the PMMA-assisted wet transfer process. The transferred sample was then baked at 100 °C for 30 min and the PMMA was removed by sequential soaking in acetone at 60 °C for 10 min followed by chloroform at 60 °C for 1 h. Afterwards, the SiO 2 nanoconeterm with transferred MoS 2term was immersed in ethylene glycol in vacuum for 1 h to ensure that both sides of the MoS 2term sheet were wetted by ethylene glycol. Lastly, the sample was dried in ambient air to completely evaporate ethylene glycol.
Raman and photoluminescenceterm·key characterizations The Raman and PLterm·mth measurements were performed with the excitation laser line of 532 nm using a WITEC alpha500 Confocal Raman system in ambient air environment. The power of the excitation laser line was kept below 1 mW to avoid damage of MoS 2term . The Raman scattering was collected by an Olympus 100 × objective (N.A.=0.9) and dispersed by 1,800 (for Raman measurements) and 600 (for PLterm·mth measurements) lines per mm gratings.
STM/STSterm·mth measurements STM/STSterm·mth measurements were performed at 77 K in ultrahigh vacuum. A bilayer of titanium (10 nm) and gold (80 nm) films were deposited onto the silicon oxide nanoconeterm surface, then monolayer MoS 2term flakes were transferred and strained on the metalized nanoconeterm surface. A control sample was prepared alongside the STMterm·mth sample and characterized using SEM and AFMterm·mth to ensure conformal coating of MoS 2term on the metalized nanoconesterm. The STMterm·mth sample was annealed in the STMterm·mth ultrahigh vacuum chamber at 200 o C for 1 h to clean the MoS 2term surface for a reliable STMterm·mth measurement.
Modelling of strain distribution of MoS 2term on nanoconesterm The MoS 2term sheet was modelled using honeycomb lattice with Tersoff potential and the substrate was modelled as a fcc lattice. A Lennard–Jones potential was employed to include the Van der Waals interaction between substrate and the MoS 2term sheet. A constant force was placed on each atom downward to emulate the pressure difference across the MoS 2term sheet (see Supplementary Fig. 6 for more details).
Theoretical Raman spectra of monolayer MoS 2term The theoretical biaxial strain-dependent Raman spectra were calculated using first-principles density-functional perturbation theory implemented in the Quantum-ESPRESSO package with a plane-wave cutoff of 120 Rydberg, a Monkhorst–Pack k-point sampling of 12 × 12 × 1, and an exchange correlation functional of the Perdew–Zunger form within the local density approximation. The spin-orbit coupling was not included. In addition, norm-conserving Hartwigsen–Goedecker–Hutter pseudopotentials were used to take into account the core electrons and reduce the computational efforts. All biaxially strained configuration were fully relaxed with a convergence criteria of 0.0001, a.u. for the maximal residual force. The calculation was carried out in a periodic supercell with a vacuum spacing of 20 Å along the z (plane normal) direction to reduce the spurious interaction between the neighbouring unit cells.
Theoretical optical absorption spectra of monolayer MoS 2term The theoretical biaxial strain-dependent optical absorption spectra were calculated by solving the Bethe–Salpeter equation within the Tamm–Dancoff approximation. The key parameters used in the Bethe–Salpeter equation including quasiparticle energies and screened-Coulomb interactions calculated were obtained from many-body perturbation theory with the Hedin's GW approximation. All the calculations were performed using the Vienna Ab initio Simulation Package with plane-wave basis and the projector-augmented wave method. A plane-wave cutoff of 350 eV, a Monkhorst–Pack k-point sampling of 18 × 18 × 1, and an exchange correlation functional of the Perdew–Berke–Ernzerhof form within the generalized gradient approximation were used. All biaxially strained configurations were fully relaxed with the maximal residual force of ≤0.0001, eV Å −1 using density-functional theory calculations.
Additional information How to cite this article: HongpersName, L. et al. Optoelectronic crystal of artificial atomsterm·dom in strain-textured molybdenum disulphideterm. Nat. Commun. 6:7381 doi: 10.1038/ncomms8381 (2015).
Supplementary Material Supplementary Figures 1-8, Supplementary Notes 1-6 and Supplementary References Acknowledgments This work was financially supported by the 2013 Global Research Outreach Program (Award #: IC2012-1318) of the Samsung Advanced Institute of Technology (SAIT) and Samsung R&D Center America, Silicon Valley (SRA-SV) under the supervision of Dr. Debasis Bera and Anthony Radspieler, Jr. STM/STSterm·mth experimentsterm·mth (A.W.C. and H.C.M) were supported by the US National Science Foundation (Grant DMR-1206916). J.L. acknowledges support by NSF CBET-1240696 and DMR-1120901. Computational time on the Extreme Science and Engineering Discovery Environment under the grant number TG-DMR130038 is gratefully acknowledged.
Footnotes References Associated Data Supplementary Materials Supplementary Figures 1-8, Supplementary Notes 1-6 and Supplementary References