Nano-Micro Letters

Recent Advances in Strain-Induced Piezoelectric and Piezoresistive Effect -Engineered 2D Semiconductors for Adaptive Electronics and Optoelectronics

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Feng Li1, Tao Shen2, Cong Wang1, Yupeng Zhang1, Junjie Qi2, *, Han Zhang1, *

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Nano-Micro Lett. (2020) 12: 106

First Online: 04 May 2020 (Review)

DOI:10.1007/s40820-020-00439-9

*Corresponding author. E-mail: junjieqi@ustb.edu.cn (Junjie Qi), hzhang@szu.edu.cn (Han Zhang)

 

Abstract

 


Toc

The development of two-dimensional (2D) semiconductors has attracted widespread attentions in the scientific community and industry due to their ultra-thin thickness, unique structure, excellent optoelectronic properties and novel physics. The excellent flexibility and outstanding mechanical strength of 2D semiconductors provide opportunities for fabricated strain sensitive devices and utilized strain tuning their electronic and optic-electric performance. The strain engineered one-dimensional materials have been well investigated, while there is a long way to go for 2D semiconductors. In this review, starting with the fundamental theories of piezoelectric and piezoresistive effect resulted by strain, following we reviewed the recent simulation works of strain engineering in novel 2D semiconductors, such as Janus 2D and 2D-Xene structures. Moreover, recent advances in experimental observation of strain tuning PL spectra and transport behavior of 2D semiconductors are summarized. Furthermore, the applications of strain engineered 2D semiconductors in sensors, photodetectors and nanogenerators are also highlighted. At last, we in-depth discussed future research directions of strain engineered 2D semiconductor and related electronics and optoelectronics device applications.


 

Keywords

2D semiconductors, Strain, Piezoelectric effect, Piezoresistive effect, Electronic and optoelectronics

 

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1 Introduction

    Strain engineering has become a strong approach to improve the performance of functional materials, especially for semiconductors  [1-3]. The introduce of strain into semiconductors is significant to the studies involving basic science as well as device applications. The strain induced piezoelectric and piezoresistive effect is two crucial mechanisms in wurtzite-structured and asymmetric structure crystal. For bulk materials, the piezoelectric effect always exists in brittle materials, such as piezoelectric ceramics [4], and the piezoresistive effect have been well studied in semiconductors [5]. Interestingly, the mechanical properties of materials become more excellent when their size decrease to the nanoscale, which facilitate their application on the fabrication of flexible devices. Meanwhile, the properties of nano-materials are sensitive to the strain due to the ultrathin size which can be used for manufacture sensors and offers method to improve their properties. More importantly, the strain tuning electric and opto-electric in low dimensional semiconductors give rise to many high-performance and multifunctional fascinating devices which will be applied widely in semiconductor technology.
    Single atomic layer graphene was peeled off by adhesive tape from graphite in 2004 [6], since then, graphene-likes 2D materials gradually brought into the limelight. In the last decade, more and more 2D crystals have been uncovered and synthesized. Recently, 1825 low exfoliation energy materials were selected from more than 100,000 kinds of three-dimensional compounds, containing intrinsic metallic, semi-conducting, insulating and magnetic materials [7]. 2D materials have demonstrated unparalleled opportunities in science and industry, and have caused great attention due to their sub-nanometer thickness, unique structure and unusual electronic properties provides advance in electronic [8], optoelectronic [9-13], ultrafast photonics [14-19] sensor [20-22], energy field [23-28] and biological medicine [29-32]. Some novel physical phenomena have been found and proved in 2D materials, such as Hofstadter butterfly, Ising superconductivity, valley Hall effect and valley-tronics [33-36]. Both theoretical predictions and experimental results demonstrated the excellent mechanical properties of 2D materials, such as high elasticity modulus (180±60 N m1 for monolayer MoS2), Young's modulus (270±100 GPa for monolayer MoS2) and can sustain over 10% strain [37]. The good mechanical properties of 2D semiconductors provide opportunities in developing flexible electronic devices as well as conditions for study the strain engineered their properties.
    The piezoelectric and piezoresistive effect are predicted in 2D transition metal dichalcogenides (TMDs) as early as 2012 and the two effects were observed in experiment subsequently [38-40]. Recently, the effect of strain on phonon structure, band structure, interface characteristic, transport behavior and optoelectronic performance of 2D semiconductors were investigated [2, 41, 42]. The strain effect in emerging new 2D semiconductors have made great progress in theoretical calculations. And some experimental methods were developed. Besides, the 2D semiconductors with relatively mature synthetic technology have been studied in force sensors, piezoelectric optoelectronic devices, piezoelectric generators, etc. So far, the review article which covered both piezoelectric and piezoresistive effects caused by strain in 2D semiconductors has not been mentioned, however, both the two effects have large impact on the photoelectric properties of 2D semiconductors and the synergistic effects are worth to study.
    Here, we shall comprehensively review the recent progress of strain-induced piezoelectric effect and piezoresistive effect in 2D semiconductors and their electronic and optoelectronic applications. As illustrated in Fig. 1, we shall outline the fundamental theories, simulation studies, experiments characterization and device applications. And provide an outlook about the future research directions and the applications in electronics and optoelectronics of strain engineered 2D materials. This work has significance for improving the performance and multifunctional of 2D semiconductors and developing novel devices for their applications in electronics and optoelectronics.

Fig. 1 Strain engineering in 2D materials: from basic theories to applications

Fig. 1 Strain engineering in 2D materials: from basic theories to applications

2 Fundamental Theories and Simulations

    Strain-induced piezoelectric and piezoresistive effect have been found for more than 140 [48] and 80 years [49], respectively, there are some relatively mature theoretical basis and demonstrating new opportunities in 2D materials. The broad basic concepts, commonly used mechanisms and their historical evolution of strain in materials was described in the theories section and some typical calculation results of 2D semiconductors by using different methods based on the density functional theory was exhibited in the simulation studies section.
2.1 Theories of Strain in Semiconductors
2.1.1 Piezoelectric Effect
    The piezoelectric effect is the generation of electricity or electric polarization in a crystal as a result of applying mechanical strain. The piezoelectric effect was first detected in quartz by the brothers Jacques and Pierre Curie in 1880 [48]. Most concerned piezoelectric materials are insulated ceramics at the early stage, such as lead zirconate titanate (PZT) which has successfully applied to commercial sensor [50]. The piezoelectric effect in nanostructured semiconductor attract more and more attentions in recent years since Zhong Lin Wang group observed piezoelectric generation in a ZnO nanowire and coined a new term in 2006, which is piezotronics [51-53]. The piezotronics take advantage of the coupling properties of piezoelectric effect and semiconductor characteristic. Then, the piezo-phototronics was also put forward by Zhong Lin Wang, which introduces the photoexcitation into piezotronics [54].
    The piezoelectricity exists in the semiconductors whose crystal structure having non central symmetry, for instance, wurtzite and zincblende crystal structures. The center of positive and negative ions is coincident without applied force and the total dipole moment is zero. While the ions center is misplaced when applied force and create non-zero dipole moment unit in the crystal [55]. Then superposition of all non-zero dipole moment units form a macroscopic potential difference along the force direction in the materials. The piezoelectric effect can be defined by the piezoelectric coefficients of dij, eij, gij, and hij, the equations as below [51]:

12 106 21

where D is induced electric, E is electric field strength, X is mechanical force and x is strain. The front set of four equations corresponds to the direct piezoelectric effect and the latter set corresponds to the converse piezoelectric effect. There are 21 non-centro-symmetric crystal classes in the total 32 crystal classes and 20 exhibit direct piezoelectricity. The strong piezoelectricity was observed in the group III–V and II–VI semiconductors, especially for wurtzite structure, such as GaN, InN, AlN, and ZnO.
    In semiconductors, the electrons and holes in the semiconductor will move to opposite directions under the influence of the piezoelectric potential, which is named piezoelectric polarization effect [57]. The electronic transport and photoelectric properties will be modulated through the modulate interfacial properties by piezoelectric effect [58]. The performance of two typical devices based on metal-semiconductor (MS) Schottky contacts and p-n junctions could be modulated by piezoelectric potential. Taking a MS Schottky contact between n-type piezoelectric semiconductor and metal electrode as an example, the strain induced electrons or holes move to the interface between metal and semiconductor. The enrichment of electrons at the interface leading to increased Schottky barrier height (SBH), as shown in Fig. 2a, while the enrichment of holes at the interface leading to decreased SBH, as shown in Fig. 2b. The principle will become complicated for p-n heterojunction, take a p-n heterojunction between a n-type piezoelectric semiconductor and a p-type semiconductor without piezoelectric as an example, the enrichment of electrons at the interface resulting in that the depletion width increased in n-type part and decreased in p-type part. Meanwhile, the depletion region moves to the n-type semiconductor part (Fig. 2c), while the opposite happened when the enrichment of holes at the interface (Fig. 2d) [59]. The piezo-phototronics is introduced the optical process on the basis of the coupling between piezoelectricity and electric transport. Strain-induced piezoelectric potential can effectively affect the optical processes, such as separation and recombination of photogenerated electron and holes in optoelectronic devices based on piezoelectric semiconductors [55].

Fig. 2 Schematic for illustrating the modulation of photoelectric device based on 2D piezoelectric semiconductors. The variation of energy-band profiles and carrier distribution of a Schottky contact induced by tensile strain (a) and compressive strain (b). The variation of energy-band profiles and carrier distribution of a p-n junction induced by tensile strain (c) and compressive strain (d)

Fig. 2 Schematic for illustrating the modulation of photoelectric device based on 2D piezoelectric semiconductors. The variation of energy-band profiles and carrier distribution of a Schottky contact induced by tensile strain (a) and compressive strain (b). The variation of energy-band profiles and carrier distribution of a p-n junction induced by tensile strain (c) and compressive strain (d)

2.1.2 Piezoresistive Effect
    The piezoresistive effect is a change in the electrical resistivity of a semiconductor or metal when mechanical strain is applied. Different from the piezoelectric effect, the piezoresistive effect causes a change only in electrical resistance, not in electric potential. The strain-induced change in conductivity of metal was first found in 1856 [61], and the term of piezoresistive effect was first coined by Cookson in 1935 [49]. The piezoresistive effect can be observed in a metal or a or a semiconductor, while the piezoresistive effect in semiconductor materials is generally much stronger than in metals. The resistance (R) of a material is defined as: R=ρl/a, where l is the length and a is the cross-sectional area of the material, ρ is electrical resistivity. The changing of R with force is normally a function of strain and R, which can be described by the gauge factor (GF) as follow:

12 106 22

where R is original resistance and ΔR is change in resistance, ε is strain, ν is Poisson's ratio. The GF of semiconductors is two orders of magnitudes larger than that of metals which is only 0.8~3.0, while the GF of ZnO is about 350 [62]. The piezoresistance coefficient always relative the change in conductivity when applied force, the computational formula is similar to Eq. (2-2), as below [50]:

12 106 23

where σ is original conductivity, Δσ is change in conductivity and Х is the force. Smith et al have learned the effect of strain on the semiconductors of silicon and germanium in 1954 [63]. The piezoresistance coefficient will increase with the decrease of scale of materials. Take silicon for example, the piezoresistance coefficient of a Si nanowires reach up to -3550×10-11/Pa, which value is -94×10-11/Pa for a bulk material [64]. The GF of carbon nanotube can be as high as 2900 [65].
    The piezoresistive effect is anisotropic for a single crystal which associated with Miller Indices of the crystal. For instance, the piezoresistance coefficient of 2D ReS2 is positive along the a-axes, but negative along b-axes, with the ratio of GF being GFa : GFb = −1 : 1.21 [66]. The state of force for a crystal can be express by nine components, σij as follows:

12 106 24

where i indicates the direction of the applied force, while j denotes the direction of the force. The strain can be inferred from applied force by Hooke’s Law for a homogeneous material, as in:

12 106 25

where E is Young’s modulus.
    The large piezoresistive effects in semiconductors demanded a fundamental theory of the physics. Strain in a crystalline solid modifies the lattice constants and reduces the crystal symmetry leading to significant shifts in the energy band edges [67]. The existing theories were based on the change of energy band structure (including band warping and splitting) [68]. The non-uniform density of states and lattice symmetry broken when applied strain on the crystal. Then the shift of bandgap and the change of electrons mass under strain lead to the change of conductivity and carrier mobility [69]. Most theoretical models exhibit crystal orientation dependence of band structure, electron energies and the effective masses of the carriers [70].
2.2 Simulation Studies
    The 2D semiconducting TMDs, such as MoS2, was first used to fabricated field effect transistors in 2011 and attracted lots of research interests due to they possess a band gap [71]. The excellent mechanical properties of 2D TMDs, which fracture strains as high as 11% [72], makes them promising candidates for study the properties of strain, electric, photon and other properties coupling. A lot of papers reported on the theoretical simulation of piezoelectric and piezoresistive effects in 2D TMDs materials stating in 2012. As more and more 2D materials are developed, the simulation studies of strain in these materials are always published before experimental studies.
2.2.1 Simulation Studies of Piezoelectric Effect in 2D Semiconductors
    The piezoelectric properties of 2D semiconductor can be calculated use different method on the basis of the density functional theory (DFT), such as the norm-conserving pseudopotential [73] or projector-augmented wave potential [74] approaches. In 2017, Cheon, et al selected 325 potential 2D piezoelectric monolayers from over 50,000 inorganic crystals, the 2D monolayers are lack of centrosymmetry and have a non-zero band gap, which are not piezoelectric in their bulk structure [75].
    Based on the modern theory of polarization, the linear piezoelectric effect (dijk) of a flat 2D material can be calculated by evaluating the change of polarization under uniaxial strains (eijk). The third-rank piezoelectric tensors eijk and dijk can be evaluated by their respective Maxwell relations [71]:

12 106 26

where εjk, σjk, and Pi represent the strain tensor, stress tensor and polarization tensor, respectively. In the contracted Voigt notation, the eijk and dijk are reduced to eil and dil, respectively. The DFT simulations to calculate the piezoelectric coefficients of eil and dil using the relation:

12 106 27

where Ckl is the elastic stiffness tensor. The eil, dil and Ckl tensor is restricted by the symmetry elements of a crystal and the number of independent tensor coefficients can be further reduced using the point groups of the 2D materials. Take 2H phase TMDs as example, which belong to the D3h point group symmetry, the in-plane and out-of-plane piezoelectric coefficients of e11, d11, e31, and d31, which values related to the elastic stiffness coefficients as:

12 106 28

For the 2D materials with C2v point group symmetry, the piezoelectric coefficients can be described as [77]:

12 106 29

    At present, people pay more attention to the in-plane piezoelectric effect of 2D semiconductors, especially to the piezoelectric effect in the armchair crystal direction of monolayer TMDs. In 2012, Duerloo, et al. [78] have predicted the piezoelectric in 2D TMDs for the first time. Figure 3a, b shows schematic diagram of piezoelectric potential generation in monolayer materials. The piezoelectric coefficients were calculated by using the generalized gradient approximation based on DFT. TMDs are a class of layered materials with the formula MX2, where M is a transition metal element from group IV, group V or group VI), and X is a chalcogen [79]. Monolayer TMDs with trigonal prismatic (D3h) and octahedral (D3d) coordinations, corresponding to 2H and 1T phase. The 2H phase TMDs usually behave as semiconductors, while the 1T phase TMDs are metallic [80]. Top view of 2H TMDs in Fig. 3b shows a honeycomb structure where adjacent sites are occupied by two alternating species. Each layer formed X-M-X structure with the chalcogen atoms in two hexagonal planes separated by a plane of metal atoms, as shown in Fig. 3h. The strain dependence of piezoelectric polarization as shown in Fig. 3c. The results show that a periodic trend of e11 and d11 coefficients in the 2D TMDs monolayers. The symmetry of monolayer hexagonal structures TMDs belong to D3h group, which symmetry is broken and giving rise to piezoelectricity.

Fig. 3 Simulation studies of in-plane piezoelectric effects in 2D semiconductors. a Schematic diagram of piezoelectric potential generation in monolayer materials. b Monolayer top view geometry of monolayer 2H-MoS2. c Variation of polarization induced by strain in monolayer materials. d Top views of the C2v orthorhombic monolayer. e Calculated piezoelectric coefficients of monolayer group IV monochalcogenides and f comparison of piezoelectric coefficient (d11) with previously known piezoelectric materials. g Calculated piezoelectric coefficients of 2D materials. Materials structures are illustrated for h 2H, i planar hexagonal, and j buckled hexagonal structures.

Fig. 3 Simulation studies of in-plane piezoelectric effects in 2D semiconductors. a Schematic diagram of piezoelectric potential generation in monolayer materials. b Monolayer top view geometry of monolayer 2H-MoS2. c Variation of polarization induced by strain in monolayer materials. d Top views of the C2v orthorhombic monolayer. e Calculated piezoelectric coefficients of monolayer group IV monochalcogenides and f comparison of piezoelectric coefficient (d11) with previously known piezoelectric materials. g Calculated piezoelectric coefficients of 2D materials. Materials structures are illustrated for h 2H, i planar hexagonal, and j buckled hexagonal structures.

    Fei et al. [81] found the large piezoelectricity in monolayer group IV monochalcogenides, such as monolayer SnS, SnSe, GeS, and GeSe, their atomic structure exhibited a C2v point group, as presented in Fig. 3d. Their monolayer structures are non-centrosymmetric allowing them to be piezoelectric. The band gaps of monolayer MX is between 1.2 and 2.7 eV, with huge excitonic effects, which are promising for solar energy applications [82]. Figure 3e, f shows that the piezoelectric coefficients (e11, e12, d11, and d12) of monolayer MX are 10-100 times larger than conventionally used piezoelectric semiconductors, such as ZnO and monolayer MoS2. They also found that the d11 and d12 coefficients follow a periodic trend, monolayer GeS possess the minimum value of piezoelectric coefficient and monolayer SnSe has the largest coefficient which d11 up to 250.58 pm V-1. More detailed theoretical calculations of piezoelectric coefficient of two stable structural phases (A-MX and H-MX phases) of monolayer group IV monochalcogenides has been reported by Ting et al. [77]. The piezoelectric coefficient of A-MX phase monolayers is 1-2 magnitude orders larger than those of H-MX phase monolayers. The similar results of A-MX and H-MX phase also reported in any other paper [83, 84]. Recently, the performance of 2D piezo-phototronic in monolayer group IV monochalcogenides have been calculated by Michael et al, the effect of piezoelectric potential on MS Schottky barrier contact was investigated [85]. The output power, open circuit voltage, fill factor and power conversion efficiency of the monolayer MX based solar cell are decreasing with the applied strain increase from -1% to 1%. It indicates that the compressive strain helps to improve the photoelectric properties of the IV monochalcogenides monolayers.
    The group III–V buckled honeycomb monolayers belong to the point group of 3m and have no inversion symmetry. The 3m symmetry of these bucked structures supports nonzero e11, e31, d11, and d31 piezoelectric coefficients. The piezoelectric effect in monolayer GaS, GaSe, and InSe were also calculated used first-principles calculations, those materials have linear ε11 piezoelectric coefficients and the same order of magnitude as monolayer MoS2 and h-BN [46]. The high piezoelectric effects have also been predicated in monolayer SbAs, SbN, and SbP, which calculated d11 piezoelectric coefficients is 243.45, 142.44, and 118.29 pm V-1, respectively [86].
    Black phosphorus (BP) is a layered material where all layers are stacked together by weak van der Waals interactions [87]. Similar to graphene, each phosphorus atom is bound to three neighbors. However, unlike graphene, BP displays out-of-plane distortion resulting in a ridge structure along the zigzag direction and a puckered structure along the armchair direction, and thus non-equal bond lengths and bond angles [88]. This leads to BP with a linked ring structure and substantial in-plane anisotropy including optical, electrical, thermal, and mechanical anisotropy [89, 90]. Due to its non-centrosymmetric crystal structure, the piezoelectric property of BP has been demonstrated. Drissi et al. [91] used DFT calculations to predict the piezoelectric responses of BP. The calculations show the values of force piezoelectric responses values, the e11 is 59 pC m-1 and e31 is 1.06 pC m-1. The calculated piezoelectric coefficient d11 is -9.48 pm V-1, which is comparable with other known 2D metal dichalcogenides. The chemical functionalization with oxygen atoms or surface oxidation can break the structural symmetry of BP and enhanced its piezoelectric properties. Piezoelectric effects of surface-oxidized BP was studied employed DFT method by Li et al. [92]. The piezoelectric coefficients d11 for surface-oxidized BP is up to 88.54 pm V-1, which is larger than those of 2D h-BN and MoS2. The piezoelectric effect of 2D materials can also be applied to tune the properties of p-n heterostructure. Huang et al. [93] investigated the electronic transport and optical properties of BP/MoS2 bilayer by first principles calculations. The results show that the band gap of BP/MoS2 heterostructures decreases with the increase of applied compressive strain and found a semiconductor to metal transition. The results also show that the carrier effective mass and carrier concentration of BP/MoS2 junctions can also be controlled by the applied strain. Moreover, the band alignment of BP/MoS2 bilayer can be tunable under applied compressive strain, which can facilitate carriers transferring between BP and MoS2 layer. The first-principles simulation results show that piezoelectricity of 2D monolayer phosphorene oxides is enhanced, with piezoelectric coefficient d11, d31, and d26 with values of 54, 10, and 21 pm V-1 [94].
    More systematic study has been reported by Blonsky and his colleagues [95]. The smallest piezoelectric effect was calculated in monolayer WS2, the piezoelectric increase when downward group 16 or moving upward in group 6, the largest coefficient was found in monolayer CrTe2 (Fig. 3g). The calculated piezoelectric coefficients of monolayer MoS2 is compare favorably with bulk α-quartz and wurtzite GaN, the piezoelectric coefficients of CrTe2 is much larger than frequently used piezoelectric semiconductor.
    Few people pay attentions to the out-of-plane piezoelectric properties of monolayer crystals early due to their vertically symmetrical. Recently, Janus 2D semiconductors have become a research hotspot thanks to their out-of-plane asymmetry structure and display piezoelectric effect [98, 99]. Different from conventional 2D materials which only have in-plan piezoelectricity, the Janus 2D materials possess both out-of-plane and in-plane piezoelectricity. Janus 2D TMD materials was first synthesized in 2017 and their piezoelectricity was calculated then. [100] Dong et al reported the out-of-plane and in-plane piezoelectric effect in Janus 2D TMDs based on ab initio calculations [96]. The Janus MXY monolayers (such as MoSSe) is similar to 2H MX2 monolayers (Such as MoS2), In comparison to regular MXxY1-x, the X atoms and Y atoms in Janus monolayers never coplanar. The crystal structure and schematic diagram of out-of-plane and in-plane piezoelectric potential generation in Janus 2D TMDs as shown in Fig. 4a. The un-equivalent of M-X and M-Y bonding lengths in MXY monolayers lead to the out-of-plane piezoelectricity. The results show that the in-plan piezoelectric coefficient (e11 and d11) of monolayer MXY is fall between the values of MX2 and MY2, the d11 values is between 2.02 and 7.00 pm V-1. The out-of-plan piezoelectric coefficient (e31 and d31) of monolayer MXY is smaller than the in-plane values, which values is only between 0.007 and 0.038 pm V-1. More significantly, the piezoelectric coefficient of some MXY multilayers is enhanced, the e31 values of WSTe increase from 0.010 to 0.140 C m-2 (Fig. 4b) and the d31 value of MoSTe increase from 0.030 to 0.447 pm V-1 (Fig. 4c). DFT calculated results show that the piezoelectric coefficient d22 of the Janus semiconducting group IVB TMDs is 4.68~14.58 pm V-1, and the max d31 value is 0.414 pm V-1. The results also indicate that the applied 9% strain along the armchair direction can dramatically enhance the d22 values, increase from 4.68 to 123.04 pm V-1 for HfSSe Janus monolayers [101]. There are two kind of Janus structures in group-III monochalcogenide monolayers due to their four atomic layer structure, which is M2XX’ and MM’X2. The results show that the in-plane piezoelectric coefficient d11 of Janus monolayers are higher than that of conventional monolayers (Fig. 4d). The out-of-plane piezoelectric coefficients d31 is 0.07~0.46 pm V-1 (Fig. 4e) [97]. Cai et al found that the in-plane interlayer sliding in bilayer Janus monolayer TMDs could enhance the out-of-plane piezoelectric effect [102]. Overall, the Janus 2D materials with both in-plane and out-of-plan piezoelectric effect offers a new sight for 2Dsemiconductros in piezoelectric related applications [99].

Fig. 4 Simulation studies of out-of-plane piezoelectric effect in 2D semiconductors. a Schematic diagram of in-plane and out-of-plane piezoelectric potential generation in Janus monolayer TMDs. The out-of-plane piezoelectric coefficient b e33 and c d33 of multilayer Janus monolayer TMDs. The piezoelectric coefficients d d11 and e d31 of Janus group-III chalcogenide monolayers, the insert is top view and side view of Janus structures M2XX’.

Fig. 4 Simulation studies of out-of-plane piezoelectric effect in 2D semiconductors. a Schematic diagram of in-plane and out-of-plane piezoelectric potential generation in Janus monolayer TMDs. The out-of-plane piezoelectric coefficient b e33 and c d33 of multilayer Janus monolayer TMDs. The piezoelectric coefficients d d11 and e d31 of Janus group-III chalcogenide monolayers, the insert is top view and side view of Janus structures M2XX’.

    Some advantages of 2D piezoelectric materials can be inferred from this part. First of all, some non-piezoelectric bulk materials will have intrinsic piezoelectric characteristics in their 2D crystals due to the broken inversion symmetry. And the relatively higher piezoelectric coefficient was calculated in 2D semiconductors, such as monolayer group IV monochalcogenides. In addition, the piezoelectric properties of 2D materials can be modulated through structural regulation and surface modification. While the piezoelectricity in 2D TMDs is limited to in-plane specific direction and odd number layers, which makes it limited in application. As more and more 2D piezoelectric semiconductors are discovered, such as wurtzite structure, Janus materials and monolayer SnSe which have been predicted to process highest piezoelectric coefficient. Their piezoelectric properties urgently need to be observed experimentally.
2.2.2 Simulation Studies of Piezoresistive Effect in 2D Semiconductors
    Different from the simulations of piezoelectric coefficients, the researchers rarely calculate changes in resistivity directly in 2D materials by using first principle calculations. It is usually predicted by calculating the energy band and effective carrier mass. The change in lattice constant under strain is the basis for calculating band structure of strained materials by using DFT. The theoretical mechanical strains can be calculated by ε=Δa/a0, where a0 is the lattice constant without strain and Δa is the change of the lattice constant under strain [104]. The change variation of the electronic band structure of monolayer TMDs with applied five different types of strain, such as tensile and compression strain [38]. The results show that monolayer TMDs are very sensitive to the strain. Especially, it is found that the tensile and shear strain can increase the valence band and decrease conduction band, cause the reduction of TMDs’ band gap. The band gap of 2D TMDs reduced faster under biaxial strain than that under uniaxial strain, and the monolayer semiconductors will turn into metals under over 10% strain, which is stems from the overlapping of dz2 orbital at Fermi level. In addition, a direct-to-indirect band gap is observed in 2D TMDs when under 1~3% tensile strain and the needed strain is gradually increases in chalcogens from sulfides to tellurides, which strain for MoS2 is about 1% and for MoSe2 up to 3% [105]. The band gap of monolayer MTe2 decreases relatively faster with increasing strain and bring about a semiconductor-to-metal transition need apply 10% strain due to the diffuse nature of heavier chalcogens [106]. Some similar results were also published during the same period [107-109].
    Deformation potential (DP) is the variation of the electronic band structure with applied strain. The effect of strain on DP and effective masses of electrons and holes also been reported. [110] The simulations results reported by Chang et al. demonstrated that the band gaps of 2D TMDs most depend on the X-X bond length and the X-M-X bond angle, and the direct band gaps can be obviously widened by applied compressive biaxial strains [111, 112]. Lu’s results also showed that the direct band gap can be enlarged at first under the compressive strain less than 2% [113, 114].
    Bilayer TMDs are usually indirect band gap semiconductors. Similar to monolayer TMDs, the in-plane strains can also reduce band gap energy of bilayer TMDs and cause semiconductor- metal transitions when applied a critical strain. The change rule of energy band structure are depend on the types of applied strain [115]. The carrier effective masses in bilayer MoS2 can also be tuned by applied strain [116].
    The 2D wide bandgap semiconductors arsenene and antimonene of β phase (which is most stable) were developed based on first-principles calculations in 2015 [120]. Figure 5a shows the crystal structures (top and side views) of arsenene. The single-layer arsenene and antimonene are indirect bandgap semiconductor which is not conducive to its application in optoelectronic. Interestingly, the results show that the band gap is decreased with the increase of biaxial strain and a significant indirect-to-direct band-gap transition in arsenene and antimonene occur when applied a relatively small strain. The CBM move to G high symmetry point, which imply the arsenene turn into a direct band gap semiconductor. As shown in Fig. 5b, with applied strain increasing, the band gap of arsenene and antimonene increase initially and decrease afterwards. Indirect-to-direct band-gap transition occurs when applied 8% and 9% for arsenene and antimonene. Figure 5c shows the variations of band structure of arsenene under different strain [118]. The direct band of the strained monolayers arsenene and antimonene have obvious advantages for their applications in optoelectronic devices. Subsequently, the effect of strain on the electrical transport and photoelectric properties of single-layer arsenene and antimonene was also predicted by DFT. Simulation results of Kripalani and his colleagues show that the band gap of antimonene and arsenene is not sensitive to the applied strain along the zigzag direction of the crystals, while an indirect-direct band gap transformation is observed when applied 4% strain along the armchair directions [117]. And the work function of suspended antimonene increase from 4.59 to 5.07 eV under applied 4% biaxial strain [117]. Shu et al. [118] employed DFT combined with G0W0 and BSE calculations also found that the optical absorption spectra of monolayer arsenene and antimonene red-shift significantly with increasing strain and the optical absorption is improved in the range of 1.2-2.2 eV energy region. In addition, they also found that the optical absorptions can be enhanced by strong electric field.

Fig. 5 Simulation studies of piezoresistive effect in 2D semiconductors and their heterostructures. a Crystal structures of monolayer β-As and β-Sb. b Bandgap variation under biaxial tensile strain. The dot dash line shows the position of the critical strain of indirect-direct gap transition. c Positions of conduction and valence band edges under different strains. d Geometric structures of the heterostructures containing a total of twenty MoX2 and WX2 units per supercell and applied uniaxial strain ε along the armchair direction. e-g Strain dependence of PCE in lateral heterostructures.

Fig. 5 Simulation studies of piezoresistive effect in 2D semiconductors and their heterostructures. a Crystal structures of monolayer β-As and β-Sb. b Bandgap variation under biaxial tensile strain. The dot dash line shows the position of the critical strain of indirect-direct gap transition. c Positions of conduction and valence band edges under different strains. d Geometric structures of the heterostructures containing a total of twenty MoX2 and WX2 units per supercell and applied uniaxial strain ε along the armchair direction. e-g Strain dependence of PCE in lateral heterostructures.

    Monolayer SnSe is a nearly direct band gap semiconductor. The direct-indirect band gap transition caused by applied strains was also found in monolayer SnSe. And the band gap reduces from 1.05 to 0 eV when applied 12% compression strain, while the band gap only decreases to about 0.7 eV applied 12% tensile strain. The band gap of the sample under 12% tension biaxial strain always higher than that of under 12% compression strain and 2-4% compression can enlarge the band gap of SnSe [84]. A DFT calculations show that the light absorption of monolayer SnSe is increased in the ultra-violet region by applied strain [121]. The electron and hole mobility are decrease with the increase of biaxial tensile strain, which is due to the increasing effective mass of carriers caused by strain, which electrons increased by 147% and holes increased by 968% under a small biaxial tensile strain [122].
    Lee et al. [119] used first-principles DFT calculations show that the uniaxial tensile strain can be used to improve optical properties of 2D TMDs lateral heterostructures MoX2-WX2 (X = S, Se, Te). A uniaxial strain is applied along the armchair direction of the lateral heterostructures, as shown in Fig. 5d. The applied strain can significantly improve the power conversion efficiency (PCE) of MoX2-WX2 lateral heterostructures due to the strain-induced bandgap offset. Under 4% uniaxial tensile strain, the PCE of the MoS2/WS2 (Fig. 5e) and MoSe2/WSe2 (Fig. 5f) heterostructures can be increased by about 35% and 15% compared with that of the unstrained system. While the PCE of lateral MoTe2/WTe2 (Fig. 5g) heterostructures is continuously decreases under the uniaxial strains. The effect of intrinsic strain (induced by the lattice mismatch) on the properties of in-plane junctions based on 2D TMDs were also be calculated. The intrinsic strain in MoSe2/WSe2 and MoS2/WS2 interface can be ignored due to the small lattice mismatch. However, the intrinsic strain in MoS2/WSe2 and MoS2/MoSe2 junctions can lower the coupling strength between nonmetal p and metal d orbitals, and therefore modifies the splitting between bonding and antibonding states at the high-symmetry k-points [123]. The effect of applied strain on the electric and opto-electric performance of van der Waals heterostructures of MoS2/WSe2 [124], InSe/arsenene [125], arsenene/MoTe2 [126], arsenene/C3N [127], and MXene/blue phosphorene [128] also have been calculated.
    The piezoresistive effect exists in all 2D semiconductors, and is not exemplified herein. Its influence on the electrical and optoelectronic properties of 2D semiconductors cannot be ignored. The main commercial application of piezoresistive effect in materials is strain sensor. Generally, the piezoresistance coefficient, which determines the sensitivity and GF of a strain sensor, is increase with decreasing the size of materials. The wide strain controllable of band gap in 2D semiconductors suggests wide strain sensor applications, such as tactile sensor at the joint. In addition, some simulation results can support that photoelectric performance of can be tuned by piezoresistive effect. Firstly, strain modulate band gap imply the change in absorption wavelength. And the strain-induced interchange between direct and indirect band gap associated with the efficiency of photogenerated carrier transition. In addition, the stain-induced the shift of optical absorption spectra which directly determines the optical detection performance. Furthermore, under strain, the type-I band alignment can be transformed to type-II band alignment for some 2D van der Waal heterostructures, which affect light detection mechanism of the heterojunction. At last, the strain can enhance the fill factor and PCE of photovoltaic devices based on 2D heterostructure due to the piezo potential which can further enhance the maximum output power and open circuit voltage. Therefore, the piezoresistive effect in 2D semiconductors has great application prospects in the field of high-sensitivity sensor devices and improving their photoelectric performance.
    In this section, the theories of strain engineered 2D materials are described. And we reviewed the recently simulation studies of piezoresistive effect and strain engineered band structure in 2D semiconductors. For the calculations of piezoelectric effect, most of DFT studies were performed by the Vienna ab initio Simulation Package (VASP), and a few studies were implemented in Quantum-ESPRESSO software package. The structural relaxation and the calculations of the elastic and piezoelectric tensors usually employ the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximations (GGA) exchange-correlation functional. While the piezoresistive effect of 2D semiconductor are not directly calculated, it is usually predicted by calculating the energy band and effective carrier mass. DFT calculated the change of band gap depends on the change of the crystal lattice under strain. VASP still the most commonly used software, as well as Quantum-ESPRESSO, Cambridge Sequential Total Energy Package (CASTEP), Grid-based projector-augmented wave (GPAW) and Abinit etc. Electronic band structures can be calculated by a hybrid functional based on Heyd–Scuseria–Ernzerhof (HSE06). The GW approximation was treated to obtain quasiparticle (QP) energies, the coupled electron-hole excitation energies and exciton wave functions were obtained by solving the Bethe-Salpeter equation (BSE). The calculated band gap of 2D materials based on GW always larger than that based on DFT due to the reduced electronic screening in the 2D system [129, 130]. In order to calculate accurate band structure, the Spin-orbit coupling and van der Waals force can also be considered in calculation methods, especially for heavy elements [117]. Some simulation results have been well verified in experiment and some significative results still need to be verified experimentally. Above all, these simulation studies point out some directions for experimental research. The vertical piezoelectric effect in 2D wurtzite crystals and Janus 2D materials seems more easier to apply to energy conversion devices and strain sensors. The piezoresistive effect in 2D b-As, b-Sb, and van der Waal heterostructures need to be confirmed which have great application prospects in optoelectronic devices.

3 Experimental Studies of Strain Engineered 2D Semiconductors

    The key problem of experimentally observe piezoelectric effect and piezoresistive effect in 2D semiconductor materials is how to applied strain or force to 2D materials. So far, the strain and force can be applied by a variety of approaches. Experimental techniques to applied strain on 2D materials such as bending and stretching of flexible devices and using atomic force microscopy (AFM) tip have been summarized. When applied strain, the detection of electrical or optical signals is used to analyze the piezoelectric effect and piezoresistive effect is also very important.
3.1 Apply Strain by Flexible Devices
    Transfer samples onto a flexible substrate and applied strain through bent or elongate the substrate is one of most common methods to study the effect of strain on the performance of low dimensional materials. In 2014, the piezoelectric effect in the 2D MoS2 was observed experimentally for the first time by Wu et al. [39] According to the predication, the piezoelectric effect in MoS2 only in Armchair direction, so the crystal structure is confirmed by using by second-harmonic generation instrument. Figure 6a shows that a 2D MoS2 device fabricated on a flexible polyethylene terephthalate (PET) substrate and the strain was applied by bending the device. The piezoelectric current and voltage are increase with the increase of strain (Fig. 6b) and the variation of the piezoelectric effect with increasing the number of layers was investigated. The asymmetric changing of I-V curve in a monolayer MoS2 device under strain in Fig. 6c shows characteristics of the piezoelectric effect. This work established the experimental basis for the 2D hexagonal piezoelectric effect and the above conclusions are universal in the 2D hexagonal piezoelectric system. The authors also put forward some forward-looking views. They think using mechanical strain can be used as a gating signal to modulate the transport behavior based on 2D material electronic devices. The piezoelectric polarization charge generated by the piezoelectricity can adjust a MS Schottky barrier or a p-n junction characteristic based on 2D semiconductors, thereby adjusting the photoelectric performance of the device.

Fig. 6 Apply strain on 2D semiconductors by flexible devices. a A flexible device with monolayer MoS2 flake along armchair direction. b Evolution of the piezoelectric outputs with increasing number of atomic layers in MoS2 flakes. c Asymmetric modulation of I-V curve by strains shows the piezoelectric effect. f Schematic diagram of flexible device and fabrication process g Transfer curves and h I-V curves of a flexible monolayer MoS2 transistor measured before applied strain and applied 0.07% strain.

Fig. 6 Apply strain on 2D semiconductors by flexible devices. a A flexible device with monolayer MoS2 flake along armchair direction. b Evolution of the piezoelectric outputs with increasing number of atomic layers in MoS2 flakes. c Asymmetric modulation of I-V curve by strains shows the piezoelectric effect. f Schematic diagram of flexible device and fabrication process g Transfer curves and h I-V curves of a flexible monolayer MoS2 transistor measured before applied strain and applied 0.07% strain.

    The piezoresistive effect is a change in the electrical resistivity of a semiconductor or metal when mechanical strain is applied. The piezoresistive effect was first investigated in a flexible MoS2 field-effect transistors (Fig. 6d) through transport behavior in 2015 by Tsai et al. [131], which carried out on a 2 nm thickness (trilayer) MoS2. The MoS2 transistor is very sensitive to strain, a shift to lower back-gate voltages of transfer curve (Fig. 6e) and an increase of device current (Fig. 6f) are observed under strain. The reflection spectroscopy was used to proven that the observed phenomenon originating from the change of band gap. The band gap of the trilayer MoS2 liner decrease from 1.58 to 1.52 eV under 0.2% strain, with a slope of -300 meV/% strain applied. There are also some studies show that the small strain has little influence on the transport behavior of 2D MoS2 [132, 133].
    Applied bending strain on a 2D graphene material was reported as early as 2009 [134], the same method was performed on 2D MoS2 was reported in 2013 [40]. The changes about the structure and properties of materials can easily observed through the spectrum [135]. A four-point bending apparatus was used to applied uniaxial tensile strain on 2D MoS2, the schematic and the strain calculation method as shown in Fig.7a, b. The applied strain is in the range of 0~2.2%. Figure 7c, d shows that the photoluminescence (PL) energy and intensity are decrease with increasing applied bending strain, revealing that a band gap decrease in monolayer and bilayer MoS2 is approximately ∼45 and ∼120 meV/% strain, respectively. The suppression and enhancement of PL efficiency of monolayer MoS2 under strain can be used for quantified the changes in carrier populations and band structure. Besides, the direct and indirect transitions can also be identified by PL spectra.

Fig. 7 Applied uniaxial strain to 2D semiconductors. a Schematic of applied bending strain on MoS2 device and b the strain calculation method. c PL spectra of a representative monolayer device as it is strained from 0 to 1.8%. d Position of the PL peak as a function of strain. e A schematic of a two-point bending apparatus used for applying uniaxial compressive strain. f PL spectra of a multilayer InSe flake of thickness ~14 nm under different uniaxial compressive strains.

Fig. 7 Applied uniaxial strain to 2D semiconductors. a Schematic of applied bending strain on MoS2 device and b the strain calculation method. c PL spectra of a representative monolayer device as it is strained from 0 to 1.8%. d Position of the PL peak as a function of strain. e A schematic of a two-point bending apparatus used for applying uniaxial compressive strain. f PL spectra of a multilayer InSe flake of thickness ~14 nm under different uniaxial compressive strains.

    The bending strain-induced large response in resistance of a 20 nm BP based flexible FET was observed, while the strain has no effect on the mobility of the device. And the infrared extinction spectra results show 99 ± 4 meV/% strain in the armchair direction and 109 ± 2 meV/% strain in the zigzag direction [136]. Recent results about strain-induced band gap tuning of 2D SnSSe indicated an improved sensitivity with a decrease in the thickness of sample [137]. The similar work also reported in Ref. [138-140]. Applied uniaxial tensile strain by transfer 2D materials onto a flexible and observed the piezoresistive effect through PL spectra also have been performed in 2D WS2 [141], MoSe2 [142], WSe2 [143, 144], BP [145], InSe [146].
    The above works are applied uniaxial tensile on 2D semiconductors, the effect of uniaxial compressive strain on the PL spectra of 2D materials have also been studied. The 2D material adhere to outside surface of bent substrate is applied uniaxial tensile strain on it, Fig. 7a for example. While the 2D materials adhere to inside surface of bent substrate is applied uniaxial compressive strain on it, Fig. 7e for example. Figure 7f shows that the bandgap of InSe is increases with increasing uniaxial compressive strain, compared with a decrease of the bandgap achieved under uniaxial tensile strain [146].
    In most 2D materials, the tensile strain causes red shift (band gap narrowing) of its excitation spectrum and the compressive strain causes blue shift (band gap widening) of its excitation spectrum, but 2D BP is an exception. Jia et al. [147] found that the optical absorption behaviors are strain-dependent, and the first absorption peak of BP monotonically blue shift with the increasing tensile strain applies along the armchair direction, while this uncovered for that along the zigzag direction of BP. And Zhang et al also observed similar results on a 6L BP through infrared extinction spectra [145]. The varying tensile strains (up to 0.92%) was applied along the armchair and zigzag directions of BP crystal. The results show that the two characteristic peaks of E11 and E22 both blueshift monotonically with the increase of strain. Corresponding optical bandgap (E11) increase from 0.54 to 0.65 eV. The blueshift rate of E11 in armchair direction and zigzag direction is 117 and 124 meV/%, respectively. Furthermore, there is no difference of the shift of E22 in two crystal directions, which is blue shift of 99 meV/%. The tensile strain will induce decreasing distance between layers in BP due to large out-of-plane Poisson’s ratio, which will increase the interlayer interaction and band gap. So, the tensile strain induced blue shift in optical absorption spectra or infrared extinction spectra of BP [148].
    Uniaxial strain is usually and easily applied to the 2D material, there are also some ingenious experimental designs can apply biaxial strain to the 2D material. In 2015, Plechinger et al. [149] transferred the monolayer MoS2 on the large thermal expansion PDMS substrate and applied biaxial tensile strain on the sample through heating the substrate, Fig. 8a, b shows the experiment schematic. The PL (Fig. 8c) was used to estimate the strain, larger redshift of MoS2 on PDMS as compared to SiO2 substrates (Fig. 8d). They also found that 0.2% biaxial tensile strain could be introduced by SiO2 substrate, which will result in a band gap changing of 105 meV/% biaxial tensile strain. Yang et al. [150] transferred 2D MoS2 on PDMS substrate and applied the biaxial tensile strain to the sample supported by a novel blown-bubble bulge technique, the measurement setup as shown in Fig. 8e. The strain is isotropic biaxial at <1.2% strain and becomes anisotropic because of the sliding at larger strains. PL spectroscopy of monolayer MoS2 show that the bandgap decreases with increasing strain, and the fracturing strain is about ~9.4%, as shown in Fig. 8f. The similar work also reported by Lloyd et al. [152]. And Hui et al. [151] applied biaxial compressive strain to a 3L MoS2 by transfer it on a piezoelectric substrate, as shown in Fig. 8g. The largest applied compressive strain is about 0.2%. The PL results in Fig. 8h, i show that the blue shift of the direct band gap for∼300 meV/% strain and the PL intensity is also enhanced.

Fig. 8 Applied biaxial strain to 2D semiconductors. a Schematic of applied biaxial strain on MoS2 through heating PDMS substrate. b Top view of a monolayer MoS2 on PDMS substrate. c Temperature-dependent PL spectra of MoS2 on PDMS substrate. d Temperature-dependent shift of the A exciton peak position on PDMS and SiO2 substrates. e Measurement setup of blown-bubble bulge technique. f Extracted PL peak position shift with applied strain in PDMS. g Schematic of applied biaxial compressive strain to 2D MoS2. Effect of biaxial compressive strain on the PL spectra h and PL peak energy i of the MoS2.

Fig. 8 Applied biaxial strain to 2D semiconductors. a Schematic of applied biaxial strain on MoS2 through heating PDMS substrate. b Top view of a monolayer MoS2 on PDMS substrate. c Temperature-dependent PL spectra of MoS2 on PDMS substrate. d Temperature-dependent shift of the A exciton peak position on PDMS and SiO2 substrates. e Measurement setup of blown-bubble bulge technique. f Extracted PL peak position shift with applied strain in PDMS. g Schematic of applied biaxial compressive strain to 2D MoS2. Effect of biaxial compressive strain on the PL spectra h and PL peak energy i of the MoS2.

3.2 Apply Strain by Creating Wrinkles in 2D Semiconductors
    Large localized uniaxial strain exists in the wrinkles 2D semiconductors. Transfer the sample to an elastomeric substrate and stretched, the wrinkles would be formed during the tension releasing process thanks to the mismatch of elastic modulus between 2D materials and elastomeric substrate. This method has been used for applied strain on graphene and nanoribbons early [156-158]. Figure 9a show the SEM image of a wrinkles of 3-5 layers MoS2, the largest uniaxial strain in the wrinkles part was estimated at 2.5%. A red shift of PL spectra was observed in wrinkles part of MoS2, as shown in Fig. 9b, suggests that the strain reduced the bandgap (~90 mV/%). The band structure as shown in Fig. 9c reveals that photogenerated excitons move to the area where applied higher strain. The simulation results based on a tight-binding theory was consistent with the experimental observations [153]. The method was also carried out on a 2D ReSe2, a sample with wrinkles as shown in Fig. 9d. Except for the red shift of PL spectra (Fig. 9e), the electrical properties was also be changed and induced magnetism [154]. Quereda et al. [155] used the same method to modulate the optoelectronic properties multilayer BP, the optical image and corresponding optical absorption mapping of a wrinkled 10 nm BP is displayed in Fig. 9f, g, respectively. The band gap in Fig. 9h extracted from the optical absorption spectra showing a ∼0.7 eV shift between the +10% tensile strain region and -30% compressive region, which greatly larger than strain adjustable range reported for 2D TMDs. Besides, these experimental results are good agreement to theoretical models.

Fig. 9 Observed piezoresistive effect in wrinkles 2D materials. The SEM image of a MoS2 and d ReSe2 wrinkles. PL spectra measured on the flat and on the wrinkle regions of b MoS2 and e ReSe2. c Band diagram in the wrinkled MoS2. f Optical image of a wrinkled 10 nm thick black phosphorus flake and g corresponding optical absorption mapping. h Optical absorption spectra acquired on ripple summits, valleys and flat regions.

Fig. 9 Observed piezoresistive effect in wrinkles 2D materials. The SEM image of a MoS2 and d ReSe2 wrinkles. PL spectra measured on the flat and on the wrinkle regions of b MoS2 and e ReSe2. c Band diagram in the wrinkled MoS2. f Optical image of a wrinkled 10 nm thick black phosphorus flake and g corresponding optical absorption mapping. h Optical absorption spectra acquired on ripple summits, valleys and flat regions.

    Recently, Du et al. [159] use the same method found that the 2D PbI2 mutilayer maintains a direct bandgap nature under a large experimental strain up to 7.69%. The strained 2D PbI2 offers reference for potential optoelectronic device applications. The wrinkles also introduced in massive reduced graphene oxide [160], WS2 [161], and Bi2Se3/Bi2Te3 heterostructure [162] by the similar method, as well as the theoretical foundation is getting better and better [163, 164].
    The fixed and repeatable local strain can be applied to 2D materials by transferring them onto patterned substrates [167]. For example, Li et al. [165] transferred the monolayer MoS2 on a patterned nano-cone array substrate to applied biaxial tensile strain, the SEM image of sample as shown in Fig. 10a. The monolayer MoS2 on top of the nano-cones is applied high strain and the strain gradually decreases from the highest part to the flat part. Figure 10b shows that the strong arise and red shift (~50 meV) of PL peak at top region of monolayer MoS2 (~1% biaxial tensile strain). The increased peak intensity of PL spectra is due to the exciton funnel effect. A built-in electric field pointing from the top to the bottom of the nano-cone is produced due to the different of band gap at top and bottom, as illustrated in Fig. 10c. In consequence, photo generated excitons are driven to the top region of the nano-cones leads to the enhancement of PL peak. The efficient funnelling of excitons in mono- and bi-layer WSe2 was also observed by using the similar method [166]. The mechanical exfoliated WSe2 was transferred from a PDMS substrate (Fig. 10d) to a substrate with nanopillars (Fig. 10e). The PL mapping (Fig. 10f) shows the higher peak intensity at the top of nanopillars due to the exciton funnel effect. Recently, Sortino et al. [168] also introduced strain in 2D WSe2 by transfer them on a substrate with dielectric nano-antennas. The red-shift of PL spectra was observed for decreasing the size of nano-antennas, indicates that the increase of strain in WSe2. The largest achieved strain is up to 1.4% for monolayer WSe2 and 3% strain for bilayer WSe2. This method has the prospect of manufacturing integrated circuits based on strained 2D materials. And the strain is increases as the radius decreases based on this method, micro-nano processing technology may limit the use of this method. And grown the 2D crystals on the surface of nanospheres or quantum dots may achieve large strained sample.

Fig. 10 Applied biaxial strain by transfer 2D materials to patterned substrates. a SEM image of the 2D MoS2 transferred onto a nano-cone array substrate, scale bar is 100 nm. b PL spectra of most strained, less strained and unstrained 2D MoS2. c Schematic of the funnel effect in strained MoS2. Optical micrograph of 2L WSe2 d before and e after the transfer onto the nanopillars substrate. f PL mapping of the WSe2 on nanopillars substrate.

Fig. 10 Applied biaxial strain by transfer 2D materials to patterned substrates. a SEM image of the 2D MoS2 transferred onto a nano-cone array substrate, scale bar is 100 nm. b PL spectra of most strained, less strained and unstrained 2D MoS2. c Schematic of the funnel effect in strained MoS2. Optical micrograph of 2L WSe2 d before and e after the transfer onto the nanopillars substrate. f PL mapping of the WSe2 on nanopillars substrate.

    When the relationship between PL and strain is clarified, the PL can be used as a tool to probe the magnitudes of strain in 2D semiconductor. Based on the study of the effect of strain on the PL spectrums of 2D materials, it was found that the growth substrates can also introduce strain to 2D materials. Chae et al. [173] reported that the substrate introduced built in strain in the CVD-grown MoS2 can be quantitatively probed by PL spectroscopy. The 0.4% biaxial tensile strain was observed in the monolayer MoS2 on SiO2 substrate, while only ~0.2% strain was observed in the sample on the sapphire, mica and h-BN substrate. The origin of tensile strain in CVD-grown 2D layers not only due to the thermal expansion coefficient mismatch between the layer and the substrate but also due to deviation from the weak vdW interaction at the interface that prevents slippage. Ahn et al. [174] use the similar method investigated the induced build-in strain in monolayer WSe2 grown on different substrate. The shift of PL peaks showed 1% biaxial tensile and 0.2% biaxial compressive strains in monolayer WSe2 grown on SiO2 and strontium titanate substrate, respectively.
    Based on similar principles, depositing additional layers is another way to introduce built-in strain in 2D materials. A vertically stacked carbon-MoS2 nanosheets was synthesized by Oakes et al and an average 0.1% compressive strain propagates into the MoS2 nanosheet lattice due to lattice mismatch in the carbon and MoS2 interface [175]. Hazarika et al. [176] used colloidal atomic layer deposition grown core-shell CdS/CdSe nanoplatelet heterostructures with atomic precision. The strain in core and shell can be modulated by change the number layers of core or shell. The optical gap red-shifted by 446 meV was observed in core CdSe when number layers of shell increase from 0 to 4, indicates that large strain is obtained and the strain can be controlled by change the thickness of the shell material. While the strain in shell layer was not discussed which is also worth study.
    A summary of strain tuning the optical band gap of 2D semiconductors as shown in Table 1. So far, the experimentally applied strain can reach to 5% and the changing coefficient of direct band gap is less than indirect band gap which coefficient value is mark with (I) in the table. Most of the experiments were carried out on 2D TMDs, while the larger changing coefficient of PL spectrum in 2D BP and InSe were observed recently, indicating their application potential in strained electronics. Ingenious method of applying compressive stress can increase the intensity of PL, suggesting their application potential in strain optic-electronics. Interestingly, the MoS2 and WS2 in a MoS2/WS2 van der Waals heterostructure shows approximate PL changing coefficient under strain, which is more than 3 times in difference when tested separately. This provide an idea to employ strain modulate the opto-electronic performance of 2D van der Waals heterostructures by piezoresistive effect.

Table 1 Comparison between the different strain experimental results available in the literature for 2D semiconductors

12 106 table1

3.3 Study Strain Engineered 2D Semiconductors by AFM Apparatus
3.3.1 Apply Strain by AFM Tip
    AFM apparatus can be used for quantitative applying force to the nanomaterials by the probe. Almost at the same time as the work of Zhong Lin Wang group published, Xiang Zhang group [177] also observed the piezoelectric effect in free-standing monolayer MoS2 by using an AFM. Figure 11a shows the measurement setup. The anisotropy of piezoelectricity in monolayer MoS2 was also observed. Since the crystal symmetry belongs to the D3h group, the piezoelectric coefficients of the monolayer MoS2 is as function of crystal’s angle with a period of 120°, as shown in Fig. 11b. Figure 11c shows the thickness dependence of piezoelectric coefficient, confirmed the piezoelectricity only exists in odd number layers MoS2. The measured piezoelectric coefficient of e11 is up to 2.9 × 10-10 C m−1.

Fig. 11 Applied strain to 2D semiconductors by AFM tip. a Schematic drawing of measuring piezoelectric property of monolayer MoS2 by using an AFM probe. b Measured piezoelectric coupling strength as a function of the crystal’s azimuthal angle θ. c Measured piezoelectric coefficient in one-, two- and three-layer MoS2. d Schematic illustration of the measurement setup. e I–V characteristics of the MoS2 device at different applied forces. f Current response of CVD monolayer MoS2 device at repeated force at a fixed bias voltage of 1V. g Schematic drawing of the experiment setup for electrical performance characterization of a suspended MoS2 devices under the strain applied by AFM tip. h Cantilever deflection and the drain current of the device as a function of the piezo scanner extension. i I-V curve of the device under the strain by AFM tip and without deformation.

Fig. 11 Applied strain to 2D semiconductors by AFM tip. a Schematic drawing of measuring piezoelectric property of monolayer MoS2 by using an AFM probe. b Measured piezoelectric coupling strength as a function of the crystal’s azimuthal angle θ. c Measured piezoelectric coefficient in one-, two- and three-layer MoS2. d Schematic illustration of the measurement setup. e I–V characteristics of the MoS2 device at different applied forces. f Current response of CVD monolayer MoS2 device at repeated force at a fixed bias voltage of 1V. g Schematic drawing of the experiment setup for electrical performance characterization of a suspended MoS2 devices under the strain applied by AFM tip. h Cantilever deflection and the drain current of the device as a function of the piezo scanner extension. i I-V curve of the device under the strain by AFM tip and without deformation.

    The monolayer MoS2 synthesized by the CVD method is a regular triangle with three zigzag edge, which makes it easier to confirm the crystal orientation with piezoelectric effect. We observed the piezoelectric phenomenon in a CVD grown triangular monolayer MoS2 by using AFM for the first time, Fig. 11d shows the measurement setup [178]. The results show that the source-drain current of the MoS2 devices can be regulated by strain variation (Fig. 11e). The I-t curves in Fig. 11f show that the good current response of the device to the repeated force. A built-in electric field pointing from the edge to center is created in the strain sample due to the piezoelectric effect and produce polarization carriers which lead to the varies of SBH of MS contacts, resulting in the decrease of SBH with the increase of tensile strain and the increase of SBH with the increase of compressive strain.
    The piezoresistive effect of 2D MoS2 was also observed by using an AFM by Manzeli et al. [169], the experiment setup as shown in Fig. 11g. The deflection of AFM tip is controlled by a piezoelectric device, the drain current is unchanged when the tip gradually approaching to the sample and begin to increase when the tip has toughed the sample (Fig. 11h). The drain current is increased and the resistance is decreased under the deformation (Fig. 11i). The results show that the piezoresistive GF of monolayer, bilayer, and trilayer MoS2 is about -148, -224, and -43.5, respectively.
3.3.2 Study Piezoelectric Effect by PFM Mode
    According what we have learned above, the in-plane strain was applied on a two-terminal device by an AFM tip, which can only be used to study in-plane piezoelectric coefficients, such as d11 and d22. While vertical piezoelectric coefficients, such as d33 and d31, are also important to some 2D piezoelectric materials. Piezoelectric force microscopy (PFM) is one of AFM modes, which can be used to investigated the vertical piezoelectric properties of nanomaterials [179]. In 2016, the vertical piezoelectricity of 2D CdS was evaluated by using a PFM [180]. Figure 12a shows the measurement setup. The topography images of a 3 nm thickness CdS and corresponding piezoelectric potential mapping with various applied voltages as shown in Fig. 12b, d. The extracted data in Fig. 12c suggests that the piezoelectric coefficient d33 of 2D CdS is up to 32.8 pm V-1, which is four times performance of the bulk CdS. In 2017, Lu et al. [100] synthesized the monolayer Janus MoSSe by CVD method and they use PFM observed the piezoelectric effect in vertical of the monolayer sample and the piezoelectric coefficient d31 is ∼0.1 pm V-1. Figure 12e, f displays the topography and piezoelectric amplitude mapping image of a MoSSe sample with monolayer and bilayer region. The step height and piezoelectric amplitude profile in Fig. 12g shows that the piezoelectric effect for monolayer MoSSe is larger than that of bilayer region. The out-of-plane piezoelectricity of 2D α‑In2Se3 [181] and CuInP2S6 [182] was also be investigated by PFM. The piezoelectric response was also observed in a two-terminal monolayer MoS2 [183] and odd layer WSe2 [184] device by PFM, the amplitude produced in out-of-plane is originate from the Poisson's effect in 2D materials.

Fig. 12 Observing out-of-plan piezoelectric effect by PFM mode. a Schematic illustration of PFM measurement. b AFM topography images of the 2D CdS. c Average amplitude variations versus applied voltages. d Piezoelectric amplitude images observed by PFM technology with tip voltages from 1 to 6 V. e Topography and f piezoelectric amplitude image a monolayer Janus MoSSe. g The step height and piezoelectric amplitude profile along the dashed lines in e, f.

Fig. 12 Observing out-of-plan piezoelectric effect by PFM mode. a Schematic illustration of PFM measurement. b AFM topography images of the 2D CdS. c Average amplitude variations versus applied voltages. d Piezoelectric amplitude images observed by PFM technology with tip voltages from 1 to 6 V. e Topography and f piezoelectric amplitude image a monolayer Janus MoSSe. g The step height and piezoelectric amplitude profile along the dashed lines in e, f.

3.3.3 Study Strain Engineered Vertical Transport Behavior by C-AFM Mode
    The conductive AFM (C-AFM) is also one of AFM modes and it can be used to measure the current when applied force on the conductive probe. Yang et al. [185] observed tunneling phenomena in 2D materials by using a C-AFM. Fu et al. [186] used a C-AFM apparatus, taking conductive probe and the conductive substrate as source and drain electrodes, found that the vertical resistance can be modulated attain 4 orders of magnitude by applied varies tip force thanks to the increase of the tunneling current when the tunneling layer (MoS2) is compressed under the tip force. More systematic work was published by our group [187] using the similar method, Fig. 13a shows the schematic of the measurement setup. The Simmons approximation was used to fitted the measured I-V curves (Fig. 13b) and reveal that the transport behavior is direct tunneling at low bias and Fowler-Nordheim tunneling at high bias, and the transition voltage is extracted (Fig. 13c, d). The effect of light on the tunneling current of vertical MoS2 also be investigated. We believed that the light can modulate the tunneling current by photothermal effect and photoelectric effect. Jorge et al. also reported a similar work, while they believe that the transport behavior of tip/MoS2/ITO junction is a double Schottky barrier model and rectifying behavior can be tuned by tip force [188]. In order to clarified the mechanism and characteristics of the force, electric and photon coupling, the vertical transport mechanism still needs further study and the C-AFM is a good experiment method.

Fig. 13 Strain tuning vertical transport behavior by C-AFM mode. a Schematic of the measurement setup used to obtain the vertical electrical transport property curves of MoS2. b I-V curves measured under different force. c ln(I/V2) versus 1/V curves and d local I-V curves in the forward bias for distinguishing between direct tunneling and F-N tunneling models.

Fig. 13 Strain tuning vertical transport behavior by C-AFM mode. a Schematic of the measurement setup used to obtain the vertical electrical transport property curves of MoS2. b I-V curves measured under different force. c ln(I/V2) versus 1/V curves and d local I-V curves in the forward bias for distinguishing between direct tunneling and F-N tunneling models.

3.4 Apply Strain by Surface Acoustic Wave
    The separation of electron and holes caused by the piezoelectric effect will change the in-plane carrier distribution of the 2D materials. The electrons will move to one side and the holes will move to another side drive by piezoelectric potential, leading to more exciton emission in one side and more trion emission in another side. Therefore, the PL spectrum is likely to observe piezoelectric phenomena, but rarely reported.
    A novel experiment reported by Rezk et al. [189], they use a surface acoustic wave (SAW) device (Fig. 14a) to introduce induce a propagating space periodic strain in 2D MoS2 and measured PL spectrum simultaneous. Figure 14b shows a strong quenching in the PL was clearly be observed in odd number layer MoS2 on 75 mW SAW excitation. And the relative ratio of the trion to excition peak intensities reduce with increasing SAW power. While no quenching in the PL was observed in even number layers of MoS2, PL results for bilayer MoS2 as shown in Fig. 14c. A acoustically electric field will be generated due to the inherent piezoelectric properties of odd layer MoS2 and the PL quenching is significantly weaker for three-layered MoS2 because a weaker piezoelectric electromechanical coupling coefficient compared to its single layer counterpart. This article shows that the PL spectra can also use to investigate the piezoelectric phenomena in 2D semiconductors.

Fig. 14 Applied strain to 2D semiconductors by surface acoustic wave. a Schematic illustration of the experimental setup comprising the SAW device, which consists of IDT electrodes photo-lithographically patterned on a lithium niobate substrate. PL spectra of b a monolayer and c bilayer MoS2 flake with respect to a range of SAW input powers.

Fig. 14 Applied strain to 2D semiconductors by surface acoustic wave. a Schematic illustration of the experimental setup comprising the SAW device, which consists of IDT electrodes photo-lithographically patterned on a lithium niobate substrate. PL spectra of b a monolayer and c bilayer MoS2 flake with respect to a range of SAW input powers.

    Compared with bulk and one-dimensional materials, 2D materials have a simpler crystal structure, making it easier to theoretically estimate their properties. The piezoelectric coefficients of monolayer MoS2 is predicted to be 3.73 pm V-1 (d11) and 3.64×10-10 C m-1 (e11) by first principle calculations [78]. And the experimental results show that the d11 and e11 of monolayr MoS2 is 3.78 pm V-1 [183] and 2.9×10-10 C m-1 [177], which are very close to the therotical results. While the d31 of MoSSe is about 0.1 pm V-1 observed by PFM [100], which is larger than the theoretical prediction of 0.02 pm V-1 [96]. The therotical prediction of band gap shift and indirect-direct band gap transistion were also proved experimentally. However, the change rate of the band gap with strain was observed in a large range in different articles, wihch value is between 48 and 105 meV/% strain for monolayer MoS2, as shown in Table 1. This may due to the difference in crystal quality. Overall, the experimental observations are consistent with the theoretical predictions and the simulation studies help to deepen understanding of theories in strained 2D semiconductors.
    In this section, we have summarized the experimental research progress of strain engineered 2D materials from the perspective of the methods of apply strain. The main applied strain methods contain assisted by flexible substrate, creating wrinkles and by using AFM apparatus. The various of spectrum, electrical, piezoelectric amplitude images can be used to analyze the piezoelectric effect and piezoresistive effect. Although a variety of methods for applying strain on 2D materials have been developed, most of them are limited to experimental observation and verification, while not suitable for the applications in electronic components. The new techniques, which can permanently and easily integrate applied strain on the devices based on 2D semiconductors, need to be developed. With the expansion of the 2D materials, such as wurtzite structure, Janus 2D materials and monolayer SnSe and SbAs which have been predicted to process highest piezoelectric coefficient, their piezoelectric properties urgently need to be observed experimentally.

4 Applications of Strain Engineered 2D Semiconductors

    The 2D materials are famous for their special electricity, photonics, mechanics, and thermal properties. These 2D semiconductors have been widely used for ultrafast pulse laser generation [190-193], optical switching [26, 194, 195], optoelectronics [196, 197], biophotonics [32, 198, 199], and energy [200-202]. Therefore, it is necessary to master the physical and chemical properties about 2D materials. In this section, we will highlight their application of stain-induced piezoelectric effect and piezoresistive effect in strain sensors, photodetectors and nanogenerators.
4.1 Strain Sensors
    Flexible and wearable strain sensor is becoming more and more important with the development of Internet of Things, which shows widespread applications in health monitoring, e-skin and intelligent electronics etc. One of the most important applications of piezoelectric and piezoresistive effects in 2D materials is the strain sensor, which can meet the requirements of future applications.
    In 2015, Manzeli et al. [169] presented the high GF data of 2D MoS2. Subsequently, strain sensors take advantage of the piezoresistive effect of 2D semiconductors were successively developed. In 2016, Park et al. [203] reported a large-area (2.2 × 2.2 cm2), conformal tactile sensor based on CVD grown bilayer MoS2 continuous film. The piezoresistive MoS2 strain sensor exhibited good optical transparency (over 80%), mechanical flexibility (1.98%) and high GF (72.5). Recent results show that the GF of mechanical exfoliation few layer MoS2 [204] and large area monolayer MoS2 continuous film [205] is up to 240 and 104, respectively.
    MoS2 strain sensor is well developed due to the advances in CVD preparation technology. However, the GF of CVD MoS2 sensor is low and can only withstand a limited mechanical strain (2%). Zheng et al. [206] developed a kind of strain sensor based onMoS2 Kirigami structures which was made by using a plasma etching approach. The strain sensor can be used for the elbow and knee joint of a robot, as shown in Fig. 15a. The MoS2 based Kirigami strain sensor can withstand 15% strain (Fig .15b), which is only 0.75% for the sensor based on as grown sample. Figure 15c shows the shows the good stability of the sensor. The downside is that the GF of the sensor based on Kirigami 2D MoS2 is reduced. In order to improve the GF of strain sensor. Zhu et al. [205] used V-doped MoS2 to fabricate the piezoresistive sensor. The photolithography and followed a reactive ion etching process were used to make patterned MoS2. Figure 15d shows the optical image of the strain sensor. The properties of the strain sensor were carried out using a four-point bending method (insert in Fig. 15e). The highest GF was measured in 20% V-doped MoS2 device, which is up to 140 (Fig. 15f).

Fig. 15 Piezoresistive strain sensor based on 2D semiconductors. a Kirigami structure devices on the surface of elbow of a robot. b I−V curves of the devices under different deformation rates. c Strain sensor based on the Kirigami structure devices and the time-dependent response of devices. d Optical image of the V-doped MoS2 strain sensor. e Change in resistance as function of strain. f Relationship between V-doping concentration and GFs of the sensor. g Optical image of a 2D In2Se3 strain sensor. h Device currents under both uniaxial tensile and compressive strain. i Multicycle normalized current change in the sensor under uniaxial tensile strain. j Bending beam setup with applied 2D PtSe2. k Electrical readout signal during the measurement with an absolute resistance change against time showing two PtSe2 devices. l Comparison of the sensitivity with other pressure sensors.

Fig. 15 Piezoresistive strain sensor based on 2D semiconductors. a Kirigami structure devices on the surface of elbow of a robot. b I−V curves of the devices under different deformation rates. c Strain sensor based on the Kirigami structure devices and the time-dependent response of devices. d Optical image of the V-doped MoS2 strain sensor. e Change in resistance as function of strain. f Relationship between V-doping concentration and GFs of the sensor. g Optical image of a 2D In2Se3 strain sensor. h Device currents under both uniaxial tensile and compressive strain. i Multicycle normalized current change in the sensor under uniaxial tensile strain. j Bending beam setup with applied 2D PtSe2. k Electrical readout signal during the measurement with an absolute resistance change against time showing two PtSe2 devices. l Comparison of the sensitivity with other pressure sensors.

    2D continuous films are very suitable for fabricate piezoresistive sensors. Feng et al. [47] reported a kind of electronic-skin strain sensor based on CVD grown 2D In2Se3 continuous films. Figure 15g shows the macrophotograph and microscope image of the sensor which was fabricated on a PET substrate. The I-V curves (Fig. 15h) shows symmetrically change under the tensile and compressive strain. The calculated GF is 237 and 92 for applied -0.5%~0.5% strain and 0.5%~1.5% strain. A stable response to the strain in Fig. 15i showing the good stability and mechanical robustness of the 2D In2Se3 based strain sensor. Wagner et al. [207] developed a piezoresistive pressure sensor based on CVD grown 2D PtSe2 continuous film. The negative GF of the piezoresistive sensor is up to -85 obtained experimentally in a bending cantilever beam setup (Fig. 15j). Figure 15k shows the high piezoresistive response to the 2 Kg load of 2D PtSe2 based strain sensor. The sensitivity of the sensor is higher than the similar sensors based on SWNTs, graphene and GaAs, etc., as shown in Fig. 15l.
    There are also reported a few strain sensors based on the piezoelectric effect of 2D semiconductors. Qi et al. [178] demonstrated that the highest GF of monolayer MoS2 piezoelectric strain sensors was 1160, which is much greater than that of similar 2D semiconductors based sensor. While Song et al. [208] showed that the GF of 2-3 nm PbI2 piezoelectric strain sensors was only 10-25. So far, the publications about the properties of 2D materials piezoelectric strain sensors is still very limited and still need further study.
    A list of strain sensor based on 2D semiconductors and their properties as shown in Table 2. The GF values of some piezoresistive force sensors based on 2D semiconductors are higher than state-of-the-art silicon-based strain sensors and much higher than the graphene-based strain sensors. More importantly, the strain sensors based on 2D semiconductors are flexible, transparent and can withstand larger strain compare with conventional silicon sensors. 2D crystal quality directly affects device performance, so the development of preparation technology of 2D materials is crucial for its application in the field of strain sensors. High performance, functionalization and integration are the development direction of strain sensors.

Table 2 A list of strain sensor based on 2D materials and their properties

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4.2 Tuning the Performance of Photodetector
4.2.1 Tuning the Performance of Photodetector by Piezoelectric Effect
     Strain-induced piezoelectric effect had been proved an effective method to regulate the performance of photodetector based on nano wires, nano ribbons and nano films. After observed the piezoelectric properties of 2D materials, their applications in 2D optoelectronic devices has also been studied successively. Wu et al. [209] showed the piezophototronic effect which is the first experimental demonstration in monolayer 2D MoS2 based flexible optoelectronics. The separation and transport of photo-generated carriers at the interface of MoS2–metal can be modulated effectively, which is attributed to the piezoelectric polarization charges created at the two-terminal interface by applying strain. Notably, the maximum photoresponsivity of the device reached up to 2.3 × 104 A W-1 by a compressive strain of -0.38%, with a 26-fold improvement over the reported highest photoresponsivity for single-layer MoS2 phototransistors. Recently, the analogous experiment was also performed on 2D multilayer γ-phase InSe photodetector. The responsivity and response speed of this photodetector were enhanced further by as much as 696% and 1010% when the device was subjected to a 0.62% uniaxial tensile strain due to the piezo-phototronic effect [210].
    Zhang et al. [211] designed and fabricated a flexible photodiode based on single-layer MoS2 lateral p-n homojunction by chemical doping (Fig. 16a), and piezo-phototronic effect was used to enhance the photocurrent. The device presented significant improvement in the photoresponsivity and detectivity for an external tensile strain at 0.51%. The photoresponsivity was enhanced by 619%, from 189 to 1162 A W-1 (Fig. 16b), and detection sensitivity was also improved by 319%, up to 1.72´1012 Jones (Fig. 16c). Meanwhile, a flexible photodetector fabricated by a n-MoS2/p-CuO heterojunction is also demonstrated by their group, the method as shown in Fig. 16d [212]. Because the depletion region can be broadened by piezo-potential under strain, the responsivity of the device under illumination has up to 27 times by a 0.65% tensile strain (Fig. 16e) compared to the device without strain. Besides, the maximum detectivity can reach up to 3.27´108 Jones in low light illumination (Fig. 16f). Du et al. [213] proposed a distinctive strain-gating method, which utilized piezo-polarization charges induced by the surface of ZnO nanobelt as "gate" to modulate the photogenerated carriers separation and transport at the vdWs interface of ZnO-WSe2. With the increase of tensile strain, the photocurrent of the device displayed an increase from 61to 320 pA (Fig. 16h), and the corresponding photoresponsivity of the device also showed an improvement, from 117 to 394 mA W-1 under white light illumination (Fig. 16i). Lin et al. [214] fabricated a flexible vdWs p-n photodiode by vertically stacking a few-layer p-WSe2 and single-layer n-MoS2 (Fig. 16j). The results demonstrated that the photocurrent of the heterojunction increased by 86%, and a maximum photoresponsivity reached up to ≈3.4 mA W-1 (Fig. 16k) under a low illumination power density of 1.52 mW cm-2 and a compressive strain of -0.62% along the armchair direction of MoS2. While the photocurrent of the device increased only by 6.1% under a higher illumination density of 6.47 mW cm-2 (Fig. 16l), which originates from the change of light absorption and the strain-induced piezoresistive effect in 2D materials. In short, the piezo-potential can be induced by applying external strain based piezoelectric effect, which can adjust the band structure at the interface of p-n homojunction or heterojunction, as well as the depletion region can be also broadened, resulting in a significantly increase in photogenerated carrier separation and transport. Thus, the optical sensing performance is enhanced effectively. In addition, the carrier concentration ND and NA in 2D materials increases with a high illumination intensity, which leads to a strong screening effect of piezoelectric polarization (Qpiezo) charges and a lower density of effective Qpiezo. Therefore, the modulation of strain on optical sensing performance are significant differences between a high illumination intensity and low optical intensity.

Fig. 16 Tuning the performance of photodetector by strain induced piezoelectric effect. a Home-made high-precision table for loading strain. The optical image presents a MoS2 device structure. Variations in value of b photoresponsivity and c detectivity at a bias of -10 V under different strains and various optical power intensities. d Schematic diagram of the flexible photodetector based on the p-CuO/n-MoS2 heterojunction. The strain dependence of e R/R0  and f detectivity  at different power densities at a bias of 10 V. g Schematic diagram of WSe2-ZnO Photodetector on flexible PET substrate. h Strain-dependent photocurrent and i responsivity of the device for different illumination intensity under 1 V applied external bias. j Optical image of the fabricated MoS2/WSe2 p–n photodiode device. Strain dependence of photocurrent in the device under the illumination of k 1.52 mW cm-2 and l 6.47 mW cm-2 light at zero applied bias.

Fig. 16 Tuning the performance of photodetector by strain induced piezoelectric effect. a Home-made high-precision table for loading strain. The optical image presents a MoS2 device structure. Variations in value of b photoresponsivity and c detectivity at a bias of -10 V under different strains and various optical power intensities. d Schematic diagram of the flexible photodetector based on the p-CuO/n-MoS2 heterojunction. The strain dependence of e R/R0 and f detectivity at different power densities at a bias of 10 V. g Schematic diagram of WSe2-ZnO Photodetector on flexible PET substrate. h Strain-dependent photocurrent and i responsivity of the device for different illumination intensity under 1 V applied external bias. j Optical image of the fabricated MoS2/WSe2 p–n photodiode device. Strain dependence of photocurrent in the device under the illumination of k 1.52 mW cm-2 and l 6.47 mW cm-2 light at zero applied bias.

    The piezo-phototronic effect in piezoelectric nanomaterials (thin film and nanowire) was also used to regulate the interface characteristics between 2D material and them, as a results, improving the photoelectric properties of the heterostructures, such as ZnO-MoS2 [215], GaN-MoS2 [216], and CdS-WSe2 [217] heterostructures.
    Table 3 displays a list of piezoelectricity enhanced the performance of the photodetectors constructed by 2D semiconductors and their heterostructures. The positive and negative value of strain is uniaxial tensile and compressive strain, respectively. The increased column lists the percent increased of piezoelectricity enhanced photoresponsivity compared with unstrained condition. The photodetector can be divided into two categories, which is Schottky diode and heterojunction device. Piezoelectricity can modulate the Schottky barrier of MS contacts or the depletion zone width of heterojunctions. The improved photo-response performance is due to the separation and transport of photo-generated carriers at the interface of MS or heterojunction were enhanced by strain-induced piezopolarization. Different interfaces require different piezopolarization directions to enhance their performance and the direction of polarization depends on the applied strain type (tensile or compressive). While the best photo-response performance of 2D materials by piezo-phototronic effect are achieved under about ±0.6% strain. This is easy to implement, but it also limits the possibility of further improving the photoelectric performance by applied large strain. In principle, the piezoresistive effect can also modulate the Schottky barrier of MS contacts and heterosturctures. However, there are less experimental work reported that tuning the performance of photodetectors by piezoresistive effects in 2D semiconductors.

Table 3 A list of piezoelectricity enhanced the performance of the photodetectors constructed by 2D semiconductors and their heterostructures

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4.2.2 Tuning the Performance of Photodetector by Piezoresistive Effect
    Recently, for the first time, we have proved that not only the piezoelectric effect strain but also the piezoresistive effect caused by strain can improve the performance of the monolayer MoS2 photodetector, the measurement setup as shown in Fig. 17a [218]. The results show that the photo-response speed, light-dark current ratio, and self-powered current are improved by small strain (0.8%) due to the piezoelectric effect. The I-V curves in Fig. 17b shows that the photocurrent of the photodetector was obviously enhanced under 1.4% strain. And the photoresponsivity of the device are significantly improved by relatively large strain (1.4%) thanks to the piezoresistive effect. The photocurrent increases from 0.37 to 2.35 μA and photoresponsivity increases from and 114.3 to 590.0 A W-1. Analogously, the strain induced non-linearity increased of photocurrent and photoresponsivity of monolayer MoS2 devices were also reported by Gant et al. [170]. Lately, Li et al. [219] reported that the photoresponsivity and photo-response speed of a 3.2 nm In2Se3 can be synchronously improved by piezoresistive effect, the method seen Fig. 17d. Figure 17e, f shows that the device under 0.65% tensile strain, the photoresponsivity increase from 0.22 to 0.37 A W-1 and the photo-response time decrease from 244 to 214 μs. Dai et al. [210] demonstrated the photocurrent of β-InSe multilayers based photodetector achieved a 211% enhancement ratio under a uniaxial tensile strain of 0.62% due to piezoresistive effect.

Fig. 17 Tuning the performance of photodetector by strain induced piezoresistive effect. a Schematic illustration for photoelectric performance measurement of monolayer MoS2 photodetector under strain. b I-V characteristics under light illumination and different strain. c Band diagram of the monolayer MoS2 photodetector under 0.8% strain. d Schematic diagram of the In2Se3 photodetector with applied strain. e Photoresponsivity of In2Se3 under different strain. f Response time under different strain.

Fig. 17 Tuning the performance of photodetector by strain induced piezoresistive effect. a Schematic illustration for photoelectric performance measurement of monolayer MoS2 photodetector under strain. b I-V characteristics under light illumination and different strain. c Band diagram of the monolayer MoS2 photodetector under 0.8% strain. d Schematic diagram of the In2Se3 photodetector with applied strain. e Photoresponsivity of In2Se3 under different strain. f Response time under different strain.

    The piezoresistive effect in 2D semiconductors can reduce the barrier heights of two Schottky junctions simultaneously (Fig. 17c) due to the narrowed bandgap and induced carrier density improvement. The narrowed bandgap broad the absorbed light's wavelengths and the reduced barrier heights improved the photocurrent, then the photoresponsivity is increased. Gant et al. [170] believe that the increased long-lived charge traps in sample can also explain the large increase in responsivity. In addition, the direct to in-direct band gap transition in any 2D semiconductors will also affect their photo-response performance.
    Table 4 displays a list of piezoresistivity enhanced the photo-response performance of 2D semiconductors. It is clear that the strain-induced piezoresistive effect can effectively improve the photocurrent and photoresponsivity of the device. One of these studies shows that the photo-response speed can also be improved. Because the piezoresistive effect is universal in semiconductors, the above significant studies are beneficial to the application of 2D semiconductors in optoelectronics.

Table 4 A list of piezoresistivity enhanced the performance of the photodetectors constructed by 2D semiconductors

12 106 table4

4.3 Nanogenerators
    Recently, study on energy harvesting used nanomaterials has attracted more and more attention on solving the energy and environmental problems. Nanogenerator (NG) fabricated by piezoelectric nanomaterials is an effective energy harvesting technology through convert mechanical energy into electrical energy which are which are normally no restrictions, user-friendly and ubiquitous [222]. In 2014, the work of Wu et al. [39] shows that 2D materials have potential applications for building nanogenerators. The mechanically exfoliated monolayer MoS2 can generate 15 mV and 20 pA output when applied 0.53% strain. The output of CVD grown monolayer is lower, while the voltage and current outputs can be enhanced by serial connection and parallel connection, respectively. Soon afterwards, theoretical study of odd-layer MoS2 NGs shows that outputs and energy conversion efficiency is decrease with the increasing thickness of MoS2. Compare with the NGs based nanowires and nanofilms, the outputs of 2D MoS2 based NGs is relative small [223].
    In 2016, the flexible piezoelectric nanogenerators based on CVD grown monolayer MoS2 was fabricated by Kim et al. [183], the photographic image and optical images as shown in Fig. 18a, b. The results show that the piezoelectric output power can be generated from the NGs with both armchair and zigzag direction of monolayer MoS2, while the output power of armchair direction NG is much higher than that of the zigzag direction NG under the same test conditions. Under 0.54% strain in armchair direction, the measured output piezoelectric voltage and current is over 20 mV (Fig. 18c) and over 30 pA.

Fig. 18 Piezoelectric generators based on 2D semiconductors a Photographic image of the CVD grown monolayer MoS2 based flexible piezoelectric NG. b Optical images showing energy harvesting active regions with the armchair atomic orientations of the piezoelectric NG. c Output voltage obtained from the monolayer MoS2 NG under different applied strain. d Stacking structure for bilayer-WSe2. e Piezoelectric peak output voltages of monolayer WSe2 and bilayer WSe2 as a function of strain. f Piezoelectric output voltage of m-WSe2 (black line) and tb-WSe2 with a low strain. g Crystal structure of monolayer and multilayer PbI2. h Piezoelectric output current of 2D PbI2 device. i Piezoelectric peak output voltages of devices fabricated with 2, 3, and 5 layers PbI2 nanosheets. j Atom structure of hexagonal α-In2Se3. k An α-In2Se3 piezoelectric nanogenerator is integrated on an index finger to scavenge the mechanical energy induced by finger motions. l Strain dependence of the piezoelectric voltage output.

Fig. 18 Piezoelectric generators based on 2D semiconductors a Photographic image of the CVD grown monolayer MoS2 based flexible piezoelectric NG. b Optical images showing energy harvesting active regions with the armchair atomic orientations of the piezoelectric NG. c Output voltage obtained from the monolayer MoS2 NG under different applied strain. d Stacking structure for bilayer-WSe2. e Piezoelectric peak output voltages of monolayer WSe2 and bilayer WSe2 as a function of strain. f Piezoelectric output voltage of m-WSe2 (black line) and tb-WSe2 with a low strain. g Crystal structure of monolayer and multilayer PbI2. h Piezoelectric output current of 2D PbI2 device. i Piezoelectric peak output voltages of devices fabricated with 2, 3, and 5 layers PbI2 nanosheets. j Atom structure of hexagonal α-In2Se3. k An α-In2Se3 piezoelectric nanogenerator is integrated on an index finger to scavenge the mechanical energy induced by finger motions. l Strain dependence of the piezoelectric voltage output.

    Lee et al. [220] found the manually stacked twisted bilayer WSe2 (stacked by two layered CVD grown monolayer WSe2) have reliable piezoelectric properties. DFT simulation results show that the AA and AB stacked bilayer WSe2 have relatively high piezoelectric coefficients due to their noncentrosymmetry crystal structure (Fig. 18d). The experiment results show that the output voltage of bilayer WSe2 NGs is continuous increase to 85 mV with strain increase to 0.95%, while the output voltage of monolayer WSe2 NGs is up to a maximum value of 90 mV when applied 0.64% (Fig. 18e, f).
    Song et al. [208] reported a piezoelectric nanogenerator based on CVD grown 2D PbI2 nanosheets. Figure 18g shows the crystal structure of PbI2. Figure 18h, i shows the piezoelectric current output of a 2 nm thickness PbI2 NG is about 20 pA. The output voltage of different thickness PbI2 NG suggest that the piezoelectricity is not affected by the number of layers. The max output voltage is 29.4 mV.
    The piezoelectric coefficient of d33 (out-of-plane) and d11 (in-plane) coexist in 2D α-In2Se3 without thickness effect due to its noncentrosymmetric crystal structure (Fig. 18j). Xue et al. [221] developed flexible piezoelectric NG based on multilayer α-In2Se3, with a max output current of 47.3 pA and voltage of 35.7 mV, respectively under applied 0.76% strain (Fig. 18l). They integrated the NG onto human skin and the results (Fig. 18k) indicate its application in energy harvesting and electronic skin.
    Lately, a flexible NG based on multilayer BP was reported for the first time by Du et al. [224]. The in-plane piezoelectricity is experimentally observed in multilayer BP along the armchair direction. The I-V curves of the device under different strain suggest a piezotronic effect. The intrinsic current output is about 4 pA under -0.72% compressive strain. Obviously, the output of BP NG is not very well in the similar device, while the piezoelectric effect in BP can helps improve its infrared detection performance.
    It is well known that there are intrinsic S vacancies unavoidably exist in 2D MoS2, especially for the samples prepared by CVD methods, resulting in the lower output of NG based on CVD grown MoS2. As discussed above, Han et al. [225] reported that improving the performance of NGs based on CVD grown monolayer MoS2 by passivating S vacancy. They found that the electron concentration is a key role in effecting the output of NGs. The S vacancies can be passivated effectively by employing the process of sulfur vapour treatment. S-treatment reduces the electron concentration of the monolayer MoS2 and enhanced the piezoelectric effect. The results show that the output of the S-treated monolayer MoS2 NGs are increased, the max output current reach up to 100 pA (increased by over three times) and the max output voltage is 22 mV (increased by two times). An increasing output piezoelectric current was investigated with the increase of strain rate. Interestingly, Dai et al. [226] found that grain boundaries in monolayer MoS2 can significantly enhance its piezoelectric property. The output power of piezoelectric nanogenerator made of the CVD grown butterfly shaped monolayer MoS2 was 50% higher than the device made of triangular sample. The improved piezoelectricity is attributed to the additional piezoelectric effect induced by the deformable grain boundaries which can promote polarization and generates spontaneous polarization with different piezoelectric coefficients along various directions. These results indicate that the piezoelectric performance of 2D semiconductor can be improved by controlling the defects, not only repair defects but also utilize defects, which is significance for further applications.
    In this section, we reviewed the applications of strain engineered 2D semiconductors in strain sensors, photodetectors and nanogenerators. Most of strain sensors are based on piezoresistive effects and few based on piezoelectric effect. The GF values of some piezoresistive strain sensors based on 2D semiconductors are higher than state-of-the-art silicon-based strain sensors and can withstand larger strain than traditional commercial strain sensors. 2D crystal quality directly affects device performance, so the development of preparation technology of 2D materials is crucial for its application in the field of strain sensors. So far, the performance of photodetectors based on 2D semiconductor can be improved by piezoelectricity reduce the Schottky barrier of MS contacts or widening the depletion zone of PN junctions. Some latest results also show that the photocurrent and photoresponsivity of a monolayer MoS2 photodetector are improved significantly by strain-induced piezoresistive effect. The two effects synergistically modulate the photo-response properties of the 2D materials is worthy of attention. The output of piezoelectric nanogenerator based on 2D materials are relatively small and its application prospects are worth pondering.

5 Summary and Perspective

    The mechanical strain in material can be used to develop advanced strain sensors and energy harvesting devices, the strain can also alter other physical and chemical characteristic of the material itself, such as electricity, optics, surface state, adsorption, catalysis and magnetism, which have great potential in materials science, condensed matter physics, electronic science and technology, chemistry, biology, and even quantum mechanics, etc. The strain engineering has been successfully used for improving the performance of the transistors based on traditional semiconductors. However, it is still in infancy stage for 2D materials. Compared with bulk and 1D materials, 2D materials have a simpler structure, smaller size, better flexibility, higher transparency, stronger performance adjustability and easier to pattern and manufacture integrated devices for large-area continuous 2D materials which are promising for high performance electronics and optoelectronics. On basis of large simulation studies of strain in 2D semiconductors, the piezoresistive and piezoelectric effect was experimentally investigated began 2013 and 2014, respectively. After the worldwide constant efforts in recent years, the research of strain in 2D semiconductors has made a rapid progress.
   Herein, we comprehensively review the recent progress of strain-induced piezoelectric and piezoresistive effect engineered 2D semiconductors in three aspects: The basic theories and simulation studies of piezoelectric and piezoresistive effect in different 2D semiconductors; Engineering methods, such as fabricate flexible device, employ stretchable and patterned substrate, creating wrinkles and use AFM apparatus, for introduced strain in 2D semiconductors; The applications of strain engineered 2D semiconductors in strain sensors, nanogenerators and tuning the performance of photodetectors. The fundamentals and applications of strain engineered 2D semiconductors offering exciting opportunities as well as facing great challenges, the efforts may be made in the following aspects:
    1) The piezoelectricity in 2D TMDs is limited to in-plane specific direction and odd number layers, which makes it limited in applications. With the expansion of the 2D materials, such as wurtzite structure, Janus 2D materials and monolayer SnSe which have been predicted to process highest piezoelectric coefficient, their piezoelectric properties urgently need to be observed experimentally.
    2) According to the results of calculations, the piezoresistive effect is conducive to the photo-response performance of the 2D semiconductors due to the variation of band gap, absorption spectrum and PCE performance. Four experimental studies reported in 2019 showed some inspiring results, as shown in Table 4. While the studies in this aspect is still locking, especially for 2D van der Waals heterostructures which have not been reported. Since the piezoresistive effect is universal in semiconductors, such studies are beneficial to the application of 2D semiconductors in optoelectronics. Lots of works suggested that the photo-response performance of 2D semiconductors or 2D heterostructures can be improved by piezoelectric effect, but rarely consider the piezoresistive effect. The two effects synergistically modulate the photo-response properties of the 2D materials is worthy of attention and further study mechanism and argumentation is necessary.
    3) Although a variety of methods for applying strain on 2D materials have been developed, most of them are limited to experimental observation and verification, while not suitable for the applications of electronic components. The new techniques, which can permanently and easily integrate applied strain on the devices based on 2D semiconductors, need to be developed to permanently modulate their properties for developing high performance transistors. In addition, the service performance of the devices based on strained 2D materials is also very important.
    4) High-quality and large-scale 2D crystal preparation technology with low costs is still the essential to promoting its industrial application. The core technology of controlled synthesize 2D semiconductors with stable structure and properties is inadequate. So far, the large-size some 2D materials can be synthesized by CVD method, but inevitably with a large number of defects, such as vacancies and grain boundaries. The recent studies show that the output of nanogenerator can be enhanced by repaired vacancies or utilized grain boundaries. However, studies on strain engineered defective 2D semiconductors in strain sensors and photodetectors are inadequate. Predictable, the performance of the strain sensor will be modulated by controlling the defects. In addition, the elegant integration of force sensors or nanogenerators can drive their applications. Multifunction of the strain sensors based on 2D materials is also a promising research direction.
    5) Strain engineered 2D materials also showing application prospects in the area of gas sensors, catalysis and spintronics. Especially, the cutting-edge topics of quantum orderings, such as superconductivity and ferroelectricity in 2D materials, can also be engineered by strain. Strain engineering has fascinating potential in the condensed matter physics, such as control quantum Hall effect, topological states and chiral fermions, which may bring about new physics and novel devices.

Acknowledgements

     This work is supported by the National Natural Science Foundation of China (51572025, 51627801, 61435010 and 51702219), the State Key Research Development Program of China (2019YFB2203503). the Science and Technology Innovation Commission of Shenzhen (JCYJ20170818093453105, JCYJ20180305125345378), National Foundation of China (41422050303), Beijing Municipal Science & Technology Commission, the Fundamental Research Funds for Central Universities.

 

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Citation Information

Li, F., Shen, T., Wang, C. et al. Recent Advances in Strain-Induced Piezoelectric and Piezoresistive Effect-Engineered 2D Semiconductors for Adaptive Electronics and Optoelectronics. Nano-Micro Lett. 12, 106 (2020). https://doi.org/10.1007/s40820-020-00439-9

History

Received: 07 February 2020 / Accepted: 20 March 2020 / Published online: 04 May 2020


Additional Info

  • Type of Publishing: JOUR - Journal
  • Title: Recent Advances in Strain-Induced Piezoelectric and Piezoresistive Effect -Engineered 2D Semiconductors for Adaptive Electronics and Optoelectronics
  • Author: Feng Li, Tao Shen, Cong Wang, Yupeng Zhang, Junjie Qi, Han Zhang
  • Year: 2020
  • Volume: 12
  • Journal Name: Nano-Micro Letters
  • ISSN: 2150-5551
  • URL: http://dx.doi.org/10.1007/s40820-020-00439-9
  • Abstract: The development of two-dimensional (2D) semiconductors has attracted widespread attentions in the scientific community and industry due to their ultra-thin thickness, unique structure, excellent optoelectronic properties and novel physics. The excellent flexibility and outstanding mechanical strength of 2D semiconductors provide opportunities for fabricated strain sensitive devices and utilized strain tuning their electronic and optic-electric performance. The strain engineered one-dimensional materials have been well investigated, while there is a long way to go for 2D semiconductors. In this review, starting with the fundamental theories of piezoelectric and piezoresistive effect resulted by strain, following we reviewed the recent simulation works of strain engineering in novel 2D semiconductors, such as Janus 2D and 2D-Xene structures. Moreover, recent advances in experimental observation of strain tuning PL spectra and transport behavior of 2D semiconductors are summarized. Furthermore, the applications of strain engineered 2D semiconductors in sensors, photodetectors and nanogenerators are also highlighted. At last, we in-depth discussed future research directions of strain engineered 2D semiconductor and related electronics and optoelectronics device applications.
  • Publish Date: Monday, 04 May 2020
  • Start Page: 106
  • DOI: 10.1007/s40820-020-00439-9