A Review of Ultrathin Piezoelectric Films

Abstract

Due to their high electromechanical coupling and energy density properties, ultrathin piezoelectric films have recently been intensively studied as key materials for the construction of miniaturized energy transducers, and in this paper we summarize the research progress. At the nanoscale, even a few atomic layers, ultrathin piezoelectric films have prominent shape anisotropic polarization, that is, in-plane polarization and out-of-plane polarization. In this review, we first introduce the in-plane and out-of-plane polarization mechanism, and then summarize the main ultrathin piezoelectric films studied at present. Secondly, we take perovskite, transition metal dichalcogenides, and Janus layers as examples to elaborate the existing scientific and engineering problems in the research of polarization, and their possible solutions. Finally, the application prospect of ultrathin piezoelectric films in miniaturized energy converters is summarized.

1. Introduction

Since the discovery and synthesis of piezoelectric materials, researchers have gradually realized that piezoelectric technology can be widely used in biomedicine [1,2,3], flexible electronic devices [4,5], flexible generators [6,7,8,9], ultrathin film vibrators [10], piezoelectric photoelectronic solar cells [11,12] and many other fields. Many kinds of piezoelectric materials have been reported to have high piezoelectric properties and high electromechanical coupling, such as epitaxial wurtzite Sc_xAl_1-xN ultrathin films [13] and nanocomposite [14,15]. In addition, the premise of high performance, coupled with the principle of being green, environmentally friendly, safe and sustainable, calls for the emergence of a number of new materials; for instance, lead-free 0.5Ba(Zr_0.2Ti_0.8)O₃–0.5(Ba_0.7Ca_0.3)TiO₃ nanowire [16], lead-free perovskite [17] and lead-free nanocomposites [18].

Generally speaking, microscopically, potential piezoelectric materials only originate from materials with a non-centrosymmetric microstructure. The work of Gowoon Cheon et al. [19] describes 325 potential two-dimensional (2D) piezoelectric materials. They are not piezoelectric in the bulk phase but lack central symmetry in the monolayer. There are 32 crystal symmetry groups, among which 21 have broken central symmetry. Surprisingly, 20 of them have directly observed piezoelectric responses. Piezoelectric materials were first discovered in naturally occurring natural products (quartz crystals and Rochelle salt). Monocrystalline, polycrystalline and polymer materials with better piezoelectric properties were discovered or synthesized later [20]. The classification of piezoelectric materials is given in Figure 1. Grounding three different criteria, completely different classification results will be showed. Furthermore, each type of material uses several materials to illustrate [21,22]. Most importantly, our focus is on all the parts of the diagram marked blue, that is to say, the type of polarization is a key factor. In Section 3, in-plane and out-of-plane polarization will be introduced in more detail.

Nevertheless, previous attention and research has focused mainly on materials with broken central symmetry [23,24,25]. Recently, in the reporting of D.-S. Park et al. [26], the piezoelectric phenomenon was realized in a centrosymmetric oxide. Unlike other methods, this exciting breakthrough was achieved by regulating the inserted oxygen vacancy with an applied electric field. In this regard, it also provides a new way to induce piezoelectricity. Under the action of a direct current (DC) electric field, the degree of defect migration has been significantly improved, which is represented by the numerical leap of dielectric constant. As a result, the achievement leads to the ultra-high voltage electrical property of the film [27]. Xiaoqing Yang et al. also used the first-principles method to predict the longitudinal piezoelectric effect of the oxide family AO (A = Cd, Ba, Sr, Ca, Mg, etc.) under the action of biaxial strain [28]. After this, it was also proved experimentally that the piezoelectric constant is enhanced in the 2D limit [29]. At the macro scale, a strain with a particular large gradient is required to cause significant polarization in the material, whereas, at the nano scale, even a small strain can do so [30,31]. For example, for the star material MoS₂ in the 2D monolayer, an independent monolayer material is obtained experimentally through various preparation methods, and its piezoelectric properties are characterized [32,33]. These works provide an experimental basis and proof for 2D ultrathin piezoelectricity. Additionally, the layer odd–even dependence of the piezoelectric response was also found [33].

Aiming to achieve more adjustable piezoelectricity, a new fabrication method of traditional 2D materials [34] has been developed. At the same time, large piezoelectric responses have been achieved in the Janus monolayer through first-principles calculations [35]. Typically, the effect of inducing vertical dipoles by breaking the symmetry of the out-of-plane structure caused this huge response [36]. Of course, this mechanism can also be applied to group-III chalcogenide monolayers, such as Ga₂SSe, with both inversion breaking and specular symmetry [37], though they still remain thermodynamically stable. Very recently, with the continuous progress of scientific and technological means, Bohayra Mortazavi et al. realized the first-principles study of piezoelectricity on MA₂Z₄ (M = Cr, Mo, W; A = Si, Ge; Z = N, P) monolayer through machine learning [38]. It is enough to raise concerns about new types of ultrathin films. The unique excellent performance of this group can even have a certain competitiveness in various application fields (nanoelectronics, optoelectronics and energy conversion nanosystems) [39].

In this review, we first elaborate the basic working principle of the piezoelectric effect in Section 2, and discuss the piezoelectric properties of thin film materials. Additionally, we also observe that the intrinsic difference of polarization mechanism between thin film and bulk material lies in the difference of anisotropy. Afterwards, we find that there are layer thickness effects and odd–even effects in these materials that already have theoretical and experimental foundations. Hence, we also summarize the physical mechanism grounding the instance of MoS₂ and hexagonal boron nitride (h-BN). Notably, the modes applied by the strain have the potential to induce novel quantum effects, which will be the focus of future research. In Section 3, we classify ultrathin piezoelectric films from an entirely different perspective from most of the previous reviews: ultrathin in-plane piezoelectric films and ultrathin out-of-plane piezoelectric films. Moreover, based on transition metal dichalcogenides (TMDs), Janus structure and novel ultrathin films, the piezoelectric polarization mechanism and modification methods are analyzed. For the purpose of helping the workers who are interested in ultrathin piezoelectric films to clarify the components and their respective characteristics, we compiled the details included in this review. Finally, in Section 4, we summarize the current research progress of ultrathin piezoelectric films and their applications in energy harvesting and conversion and point out that there are still unavoidable defects and limitations in the fabrication of 2D materials within the scope of current technology.

2. Piezoelectric Effect and Polarization Mechanisms

The piezoelectric effect results from the uneven distribution of ions in the crystal structure in some materials [40]. “Electric charge that accumulates in response to applied mechanical stress in materials that have non-centrosymmetric crystal structures” is defined as piezoelectricity [41]. A piezoelectric material is one that can achieve energy collection and conversion through the piezoelectric effect. Typically, the dipoles are randomly distributed in the crystal structure and call for an equilibrium state of electroneutrality on a macroscopic level. In these materials, though, electrons and holes move in opposite directions towards the metal-semiconductor interface due to a piezoelectric potential, which is generated by an external stimulus (polarization). The behavior by which the dipole tends to the same random direction is known as the piezoelectric polarization effect [42]. The connection between elasticity and electrical behavior is made successfully from then.

The piezoelectric effect can be modulated by regulating the interface properties of the electron transport as well as photoelectric properties [43]. The piezoelectric polarization effect can be divided into direct effect and inverse effect. The schematic diagram of the two working mechanisms is shown in Figure 2. Direct piezoelectric effects occur when the existing dipole balance in the crystal structure is disturbed due to the application of mechanical stress (stretching or compression) or vibrations. This disturbance results in an unbalanced distribution of charge, contributing to a surface charge density that is able to be captured by the electrode [44]. In this process, mechanical energy is converted to electric energy [45]. Conversely, the conversion of electrical energy into mechanical energy is an inverse piezoelectric effect. The whole process can be described as applying an electric field of a certain magnitude to the piezoelectric material. This effect causes a mechanical displacement within the material. The intrinsic equation of the two effects can be expressed as bellow [41]:

$$\mathrm{Direct} \mathrm{Effect}: D=dT+\epsilon E$$

(1)

$$\mathrm{Inverse} \mathrm{Effect}: S=sT+dE$$

(2)

where $T$ stands for the stress, $d$ stands for the piezoelectric constant, $S$ stands for the strain, $D$ stands for the electric displacement, $E$ stands for the electric field intensity, $s$ stands for the mechanical flexibility, and $\epsilon$ stands for the dielectric constant of the material. The four piezoelectric coefficients $d_{ij}$, $e_{ij}$, $g_{ij}$, $h_{ij}$ are expressed as [46]:

$$\left\{\begin{array}{c}{d}_{ij}={\left(\frac{\partial D_i}{\partial T_j}\right)}^E={\left(\frac{\partial S_j}{\partial E_i}\right)}^T\\ e_{ij}={\left(\frac{\partial D_i}{\partial S_j}\right)}^E={-\left(\frac{\partial T_j}{\partial E_i}\right)}^S\\ g_{ij}={-\left(\frac{\partial E_i}{\partial T_j}\right)}^D={\left(\frac{\partial S_j}{\partial D_i}\right)}^T\\ h_{ij}=-{\left(\frac{\partial E_i}{\partial S_j}\right)}^D=-{\left(\frac{\partial T_j}{\partial D_i}\right)}^S\end{array}\right.$$

(3)

these two terms after the equal sign correspond to direct and inverse piezoelectric effects, respectively.

Taking 2D TMDs as an example, the 2H phase structure has the symmetry of $D_{3h}$ space group. The in-plane and out-of-plane piezoelectric coefficients $d_{11}$, $d_{31}$ and the elastic stiffness coefficients $c_{11}$, $c_{31}$ satisfy the following relation [47]:

$$d_{11}=\frac{e_{11}}{C_{11}-C_{12}}, d_{31}=\frac{e_{31}}{C_{11}+C_{12}}.$$

(4)

With regard to 2D materials with $C_{2v}$ space group symmetry, this relationship becomes [48]:

$$d_{11}=\frac{e_{11}{C}_{22}-e_{12}{C}_{12}}{C_{11}{C}_{22}-{C_{12}}^2}, d_{12}=\frac{e_{12}{C}_{11}-e_{11}{C}_{12}}{C_{11}{C}_{22}-{C_{12}}^2}.$$

(5)

Piezoelectric energy conversion and collection devices usually work with a direct piezoelectric effect, and the types are mainly the 33, 11 and 31 modes; these are shown in Figure 2a–c. In the 33 and 11 modes, the applied stress is in the same direction as the generated voltage, while in the 31 mode the applied stress is axial, and the voltage is vertical. The piezoelectric output is under the control of the operation mode. The 33 mode has excellent voltage output, while a superior manifestation aspect to high current output is found in the 31 mode [49,50]. On the other hand, the inverse piezoelectric effect is put into use in piezoelectric actuators, as shown in Figure 2d.

In various polarization mechanisms [51,52], it is common that the layer thickness effect and odd–even effect are reported [53]. As a matter of fact, they are attributed to changes in interlayer coupling and symmetry. Even layers samples have inversion symmetry, while odd layers samples destroy that. For example, direct and inverse piezoelectric effects have been experimentally confirmed in a single and few layers of MoS₂. Nevertheless, in-plane piezoelectricity only exists in odd layers, and decreases rapidly with increasing number of layers. The reason for the phenomenon is that the response of the opposite direction layers is cancelled out. Meanwhile, any strain or electric field perpendicular to its surface will theoretically produce a zero piezoelectric response [30].

3. Piezoelectric Thin Films

The single layer of piezoelectric film is prepared experimentally, and the piezoelectricity constant is enhanced in the 2D limit [29,32,33]. These results and data mean the nano-scale ultrathin piezoelectric films are not only limited to theoretical calculation, but also signal a new era in the field of piezoelectric research.

Table 1. Piezoelectric coefficient of common piezoelectric materials (pm V⁻¹).

Materials	${\mathit{d}}_{11}$ (pm V−1)	${\mathit{d}}_{12}$ (pm V−1)	${\mathit{d}}_{33}$ (pm V−1)	${\mathit{d}}_{31}$ (pm V−1)	Ref
Graphene/SiO2			14		[54,55]
Graphene oxide				0.24	[56]
Graphene (K doped)				0.23	[57]
Graphene (Li doped)				0.15	[57]
Graphene (H doped)				0.11	[57]
Graphene (F doped)				0.0018	[57]
Graphene (F, Li doped)				0.30	[57]
Graphene (H, F doped)				0.03	[57]
BaTiO3			8		[58]
PZT			7–15		[59]
PVDF			−36		[60]
C3N4			1		[61]
LiNbO3			7.50		[30]
GaPO4			~8.50		[62]
CuInP2S6 (3.5 nm)			17.40		[63]
CuInP2S6 (82 nm)			83		[63]
2H-CrS2	6.15				[64]
2H-CrSe2	8.25				[64]
2H-CrTe2	13.45				[64]
2H-MoS2	3.65				[64,65]
	2.5–4				[54,66]
	3.73				[66,67,68,69]
	3.34				[65]
	3.73				[65]
			1.35		[30]
			1.03		[70]
	3				[66,71]
2H-MoSe2	4.55				[64,65]
	4.17				[65]
	4.72				[65,66]
2H-MoTe2	7.39				[64,65]
	7.00				[65]
	9.13				[65,66]
2H-WS2	2.12				[64,65]
	2.02				[65]
	2.19				[65,66]
2H-WSe2	2.64				[64,65]
	2.53				[65]
	2.79				[65,66]
	~3.26				[72]
2H-WTe2	4.39				[64,65]
	4.29				[65]
	4.60				[65,66]
2H-NbS2	3.12				[64]
2H-NbSe2	3.87				[64]
2H-NbTe2	4.45				[64]
2H-TaS2	3.44				[64]
2H-TaSe2	3.94				[64]
2H-TaTe2	4.72				[64]
BeO	1.39				[64]
MgO	6.63				[64]
CaO	8.47				[64]
ZnO	8.65		14.30–26.70		[64,73]
			23.70		[74]
			21.50		[75]
CdO	21.70				[64]
PbO	73.10		29.60	3.90	[64,76]
$\alpha$-SbAs	243.45	−63.65			[69]
$\alpha$-SbP	142.44	−27.64			[69]
$\alpha$-SbN	118.29	−13.20			[69]
$\alpha$-AsP	18.90	−4.74			[69]
$\alpha$-AsN	29.14	−5.75			[69]
$\alpha$-PN	6.94	−2.44			[69]
$\beta$-SbAs	1.65			−0.03	[69]
$\beta$-SbP	2.26			−0.03	[69]
$\beta$-SbN	5.30			−0.26	[69]
$\beta$-AsP	0.67			0.01	[69]
$\beta$-AsN	4.83			−0.09	[69]
$\beta$-PN	2.77			−0.09	[69]
BP	2.18				[64]
surface-oxidized BP	88.54				[77]
BAs	2.19				[64]
BSb	3.06				[64]
AlN	2.75				[64]
AlP	0.09				[64]
AlAs	0.38			0.57	[42,64]
AlSb	0.79			0.35	[42,64]
GaN	2.00				[64]
GaP	1.29			0.31	[42,64]
GaAs	1.50			0.13	[42,64]
GaSb	1.42			0.02	[42,64]
InN	5.50				[64]
InP	0.02			0.39	[42,64]
InAs	0.08			0.25	[42,64]
InSb	1.15			0.06	[42,64]
BN	0.61				[64]
h-BN	0.60				[47,66,67]
CdS			32.80		[78]
GaS	1.72				[37]
	2.06				[47,76]
GaSe	1.77				[37]
	2.30				[47,68,76]
GaTe	1.93				[37]
InS	1.12				[37]
InSe	1.98				[37]
	1.46				[47,76]
InTe	1.18				[37]
GeS	75.43	−50.42			[42,68]
A-GeS	20.71	11.16			[48]
H-GeS	−5.65	5.65			[48]
GeSe	212.13	−97.17			[42,68,69]
A-GeSe	40.61	14.96			[48]
H-GeSe	−4.88	4.88			[48]
SnS	144.76	−22.89	~1.85		[42,68,79]
A-SnS	91.56	−4.02			[48]
H-SnS	−5.28	5.28			[48]
SnSe	250.58	−80.31			[42,68,69]
A-SnSe	74.73	0.85			[48]
H-SnSe	−4.63	4.63			[48]
SnS2			2.20		[80]
			~5		[81]
$\alpha$-In2Se3			0.34		[82]
			0.53		[63]
In2Te3	10.64			0.40	[83]
Ga2SSe	5.23			0.07	[37,76]
Ga2STe	2.46			0.25	[37,76]
Ga2SeTe	2.32			0.21	[37,76]
In2SSe	8.47			0.18	[37,76]
In2STe	1.91			0.25	[37,76]
In2SeTe	4.73			0.13	[37,76]
GaInS2	8.33			0.38	[37,76]
GaInSe2	3.19			0.46	[37,76]
GaInTe2	2.99			0.32	[37,76]
InCrTe3	6.94			0.52	[83]
1H-WSO	1.8				[35]
1H-WSeO	1.9				[35]
1H-WTeO	2.8				[35]
MoSSe	3.76		0.10	0.02	[36,54,65,76]
MoSeTe	5.30			0.03	[65,76]
MoSTe	5.04			0.03	[65,76]
WSSe	2.26			0.01	[65,76]
WSeTe	3.52			0.01	[65,76]
WSTe	3.33			0.01	[65,76]
ZrSSe				0.01	[84]
ZrSeTe				−0.19	[84]
ZrSTe				0.004	[84]
HfSSe				0.05	[84]
HfSeTe				0.41	[84]
HfSTe				0.18	[84]
BiTeI	8.49			0.56	[85]
Sc2CO2				0.78	[86]
Y2CO2				0.40	[86]
La2CO2				0.65	[86]
LiAlS2	2.64			0.53	[87,88]
$\gamma$-LiAlS2	8.04			1.17	[88]
LiAlSe2	3.57			0.61	[87,88]
$\gamma$-LiAlSe2	10.50			1.62	[88]
LiAlTe2	4.58			0.83	[87,88]
$\gamma$-LiAlTe2	11.30			0.39	[88]
LiGaS2	5.03			0.47	[87,88]
$\gamma$-LiGaS2	12.02			0.05	[88]
LiGaSe2	6.60			0.49	[87,88]
$\gamma$-LiGaSe2	14.48			0.31	[88]
LiGaTe2	8.66			0.70	[87,88]
$\gamma$-LiGaTe2	17.44			0.84	[88]
LiInS2	1.48			0.38	[87,88]
$\gamma$-LiInS2	5.90			0.12	[88]
LiInSe2	2.18			0.29	[87,88]
$\gamma$-LiInSe2	7.81			0.28	[88]
LiInTe2	3.13			0.24	[87,88]
$\gamma$-LiInTe2	8.93			0.83	[88]
Zr2P2IBr			29.95	0.93	[89]
Zr2P2ICl			91.12	2.65	[89]
Zr2P2IF			33.87	0.43	[89]
Zr2P2BrCl			129.71	3.21	[89]
Zr2P2BrF			22.77	0.09	[89]
Zr2P2ClF			51.05	0.91	[89]

and

Table 2. Piezoelectric coefficient of common piezoelectric materials (pC N⁻¹).

Materials	${\mathit{d}}_{11}$ (pC N−1)	${\mathit{d}}_{12}$ (pC N−1)	${\mathit{d}}_{33}$ (pC N−1)	${\mathit{d}}_{31}$ (pC N−1)	Ref
BaTiO3			191	78	[90]
			~190		[90,91]
ZnO			5.90		[90]
			12		[92]
			12.40		[93]
			~5–10		[90,94]
Quartz	2.30				[90]
ST-cut Quartz	2.30				[92]
PMN-PT			~2000–3000		[90]
PMN-PZT/PT			~1500–2000		[95,96]
PZT			~60–130		[90]
			225–590	110	[41,44,93]
			289–380		[92]
			117		[92]
			~250–700		[97]
AlN			4.50		[92]
			6.40		[92]
			5		[98,99]
Sapphire			6.40		[92]
GaN			4.50		[92]
128° cut LiNbO3			12		[92]
36° YX cut LiTaO3			12		[92]
PVDF Film			−33	23	[44]
			−35		[92]
			~20–30		[90,100]

show the piezoelectric coefficients of 2D piezoelectric film measured under the inverse piezoelectric effect and the direct piezoelectric effect, respectively. We find that several of these materials, such as ZnO, MoS₂ and Zr₂P₂BrCl, show strong anisotropic piezoelectric polarization effects. This property is useful in that can be used to achieve different energy conversion effects by applying stretching or compression effects in different directions. In order to screen, distinguish and store different energy signals, it is often necessary to use anisotropic materials to design devices.

3.1. Ultrathin In-Plane Piezoelectric Films

With the development of energy equipment towards miniaturization, the critical scale of transducers needs to be reduced. The scale of ultrathin films in this review is defined to the nanometer scale. Most 2D materials have intrinsic piezoelectric polarization. We introduce the piezoelectric properties of TMDs, h-BN and black phosphorus (BP). A schematic of each of these structures is shown in Figure 3.

Ultrathin piezoelectric films are expected to be widely used as a result of their stress-electric conversion characteristics. Graphene has the longest history of study among 2D materials [103,104,105], and therefore was the material in which researchers initially tried to achieve the piezoelectric effect. Grounding the piezoelectric mechanism, the effect calls for the breaking of central symmetry. Swapnil Chandratre and Pradeep Sharma achieved the piezoelectric effect in 2D materials for the first time by digging triangular holes in graphene [106]. Shortly after, Mitchell T. Ong et al. chemically modified graphene with hydrogen and fluorine adsorbed on different position, and induced both in-plane and out-of-plane piezoelectric effects [107], as shown in Figure 4.

Ultrathin nanosheets of layered TMDs have tunable electronic structures, so as to be attractive for piezoelectric energy harvesting. TMDs can be represented as MX₂ (M = Cr, Mo, W, Nb, Ta and X = S, Se, Te) [64]. Monolayer TMDs are constructed by a metal plane surrounded by two dichalcogenide planes [108]. Hexagonal structured monolayer TMDs are usually semiconductors and belong to $D_{3h}$ space group, the breaking of whose symmetry leads to piezoelectricity [109]. Duerloo et al. first predicted that 2D TMD materials are piezoelectric by the first-principles method [66]. MoS₂ is the most widely studied TMD and it is worth going into more detail on. Monolayer MoS₂ generates intrinsic electric dipoles due to the displacement of cationic Mo atoms and anionic S atoms when subjected to external strains. Additionally, the inherent electric dipoles lead to a voltage between the two sides of MoS₂. The piezoelectric property of monolayer MoS₂ is only restricted to the in-plane ($d_{11}$) direction rather than the out-of-plane ($d_{33}$) direction, since the symmetry feature along the vertical z-axis of monolayer MoS₂ stays the same as in the initial state. Furthermore, Wu [71] and Zhu [33] et al. experimentally realized piezoelectricity in monolayer MoS₂. Zhu et al. measured a piezoelectric coefficient of $e_{11}$ = 2.9 × 10^–10 C m⁻¹ in a free-standing single layer of MoS₂. Additionally, they observed a finite and zero piezoelectric response in odd and even numbers of layers, respectively, which is in sharp contrast to bulk piezoelectric materials [33]. This is because the intrinsic difference of the polarization mechanism between thin film and bulk material relies on the difference of anisotropy. The measurement results are shown in Figure 5b. This is because symmetry is broken only in odd layers, while it is restored in even layers. The measurement method is shown in Figure 5a. The MoS₂ film was indented with a scanning atomic force microscopy (AFM) probe, aiming to convert the in-plane stress to an out-of-plane force. The induced stress then changed the load on the tip and the curvature of the cantilever, which could be measured by the deflection of a laser beam [33]. Additionally, in the study of Wu et al., as shown in Figure 6, MoS₂ was placed on a polyethylene terephthalate (PET) flexible substrate [71]. Uniaxial strain was applied to the MoS₂ in the manner of mechanically bending the substrate. Therefore, periodic stretching and releasing of the substrate can generate piezoelectric outputs in external circuits with alternating polarity [71]. However, in principle, the exfoliated monolayer MoS₂ lacks mechanical durability. Ju-Hyuck Lee et al. fabricated bilayer WSe₂ with a mechanical durability of up to 0.95% of strain via turbostratic stacking [Figure 7a]. This form can increase the degrees of freedom in the bilayer symmetry and finally lead to non-centrosymmetry in the bilayers [Figure 7b] [72,110]. The density function theory (DFT) simulation results are shown in Figure 7c.

There has been a boom in research about in-plane piezoelectric 2D materials. Yang et al. calculated the piezoelectric coefficient of monolayer MX (M = Sn or Ge, X = Se or S) and found that the in-plane piezoelectric coefficient d₁₁ of MX was the biggest among 2D materials [68]. This result is two orders of magnitude larger than that of routinely used piezoelectric semiconductors, such as ZnO and monolayer MoS₂. This is because monolayer group IV monochalcogenides have a unique “puckered” $C_{2v}$ symmetry, as well as electronic structure.

Monolayer h-BN is a wide-band insulator with the same crystal structure as graphene. Unlike graphene, monolayer h-BN is piezoelectric due to the asymmetry introduced into the structure by the two sublattices (B and N). The elastic and piezoelectric effects were theoretically calculated using Born’s long-wavelength theory [111]. In 2020, Yang Nan et al. studied hexagonal boron nitride nanosheets through molecular dynamics simulations. Their simulation results indicated that the piezoelectric constants of boron nitride nanosheets depend very strongly on the macroscopic shape (Figure 8), while being nearly independent of the macroscopic size (Figure 9) [101]. In addition, when strain is applied to h-BN, some novel quantum effects, such as the quantum spin Hall phase [112], are born. These novel quantum effects, when combined with piezoelectric polarization effects, are bound to prompt researchers to ponder more interesting scientific questions.

Black phosphorus (BP) is a layered material that can be obtained by mechanical stripping. The piezoelectric properties of BP are demonstrated due to its non-centrosymmetric crystal structure [113]. In addition, surface-oxidization is an effective way to enhance the piezoelectricity of black phosphorene, since this method can break the structural symmetry. By first-principles methods, the calculated piezoelectric coefficients $d_{11}$ for surface-oxidized BP are manifested as 88.54 pm V⁻¹, which is comparable to those of group-IV monochalcogenides and larger than that of 2D h-BN and MoS₂ [77]. However, this method of stripping or traditional chemical and physical vapor deposition can likely introduce defects or other impurities, which can interfere with the results of the study. It is worth further consideration by researchers.

There are many kinds of means to control the properties of 2D materials, such as substitutional doping, staking, surface adatoms, or defects to break the centrosymmetry of pristine materials [114]. However, these strategies of regulating mainly affect the out-of-plane piezoelectric properties, which will be discussed later. The in-plane piezoelectric properties are little affected by these methods in principle, since the intrinsic asymmetry of materials is the factor most important to in-plane piezoelectric properties. Unconventionally, in 2022, Park et al. induced high levels of piezoelectricity in centrosymmetric oxides [26]. They used a DC electric field to rearrange the oxygen vacancies in the CeO_2–x (CGO) thin film. The crystallographic symmetry was broken and piezoelectric effects were induced in centrosymmetric materials. The piezoelectricity is measured by applying an additional alternating current (AC) electric field (E_AC). When the AC electric field is in the same direction as DC, oxygen vacancies are pushed up, which causes the material to expand. Conversely, when the AC electric field is in the opposite direction to DC, oxygen vacancies are pushed oppositely [27]. Their results show that the piezoelectric coefficients ($d_{33}$) can reach up to nearly 200,000 pm V⁻¹ at a frequency of 10 mHz under a DC electric field of 1 MV cm⁻¹. This data is particularly significant, being two orders of magnitude larger than the ferroelectric oxide. They also discovered that the field-induced redistribution of oxygen vacancies could induce a cubic-to-tetragonal structural transition [26], as shown in Figure 10b. This inspired people to apply this method to more materials or look for new mechanisms to generate piezoelectricity.

3.2. Ultrathin Out-of-Plane Piezoelectric Films

With the systematic study of piezoelectricity in 2D materials, a variety of correlated novel piezoelectric devices have been successively fabricated in the field of energy harvesting, actuators, strain-tuned electronics, and optoelectronics. Most 2D materials, as shown in Figure 11a,b, have only in-plane piezoelectricity, which limits their applications in vertically integrated nanoelectromechanical systems [64]. Due to the limitation of external conditions and structural stability, it is difficult to make advanced functional devices with piezoelectric materials. Herein,

Table 3. Relevant information of the experimentally confirmed piezoelectric 2D materials [54]. Reproduced with permission from [54]. Copyright 2018, Springer Nature.

2D Materials	Crystal Structure	Piezoelectric Direction	Estimated Piezocoefficient	Notes
Monolayer MoS2	Hexagonal	In-plane Angle dependence	$d_{11}=2.5-4 \mathrm{p}\mathrm{m}/\mathrm{V}$ [66] $e_{11}=250-400 \mathrm{p}\mathrm{C}/\mathrm{m}$ [33,66]	Odd–even effect with the thickness increased
Monolayer h-BN	Hexagonal	In-plane Angle dependence	$e_{11}=100-400 \mathrm{p}\mathrm{C}/\mathrm{m}$ [66]	Odd–even effect with the thickness increased [53]
Graphitic carbon nitride		In-plane	$e_{11}=218 \mathrm{p}\mathrm{C}/\mathrm{m}$ [61]	Existence of piezoelectricity regardless of thickness
Doped graphene	Hexagonal	Out-of-plane	$d_{33}=1.4 \mathrm{n}\mathrm{m}/\mathrm{V}$ [55]	Extrinsic piezoelectricity
$\alpha$-In2Se3	Rhombohedral	Out-of-plane and in-plane		Indirectly confirmed by the ferroelectricity [116]
Janus MoSSe	Hexagonal	Out-of-plane and in-plane	$d_{33}=0.1 \mathrm{p}\mathrm{m}/\mathrm{V}$ [36]

shows that the piezoelectric properties of common materials in different polarization directions are experimentally confirmed [54,115]. If 2D materials can obtain large out-of-plane piezoelectricity, they will be more widely used in a variety of piezoelectric applications. It has stimulated more and more research on innovative regulatory means, such as doping, construction of Janus structures and so on, because of the puzzle of how to obtain out-of-plane polarization.

3.2.1. Out-of-Plane Piezoelectricity Obtained by Controlling Structures

Out-of-plane piezoelectricity is usually obtained by controlling the crystal structure of the 2D materials, such as through defect engineering, deformation or doping. TMDs are ideal candidates as low-dimensional piezoelectric materials, owing to their structural non-centrosymmetry [33]. Due to in-plane inversion symmetry breaking, it was proved through experimental characterization and theoretical calculation that only intrinsic in-plane piezoelectricity exists in TMDs [64,66,117]. From this, breaking inversion symmetry in an out-of-plane direction is an efficient method to realize the out-of-plane piezoelectric polarization [115]. It is noted that the layered TMDs have the natural advantage of being established into out-of-plane piezoelectric samples through crystal structure transformation.

Deformation

While only in-plane piezoelectricity exists on the crystal symmetry, it is also possible to generate out-of-plane piezoelectricity by way of bringing strain to the gradient. The schematic diagram of different degrees of corrugation is shown in Figure 12a. As long as the 2D TMDs deform along the out-of-plane direction, the internal flexoelectricity polarization occurs along this axial direction. In this sense, the out-of-plane piezoelectricity of 2H phase MoTe₂ can be modulated by either controlling the roughness of the substrate or the thickness of MoTe₂ sample [118], as shown in Figure 12b.

Defect Engineering

Studies to date have demonstrated the possibility of generating an out-of-plane piezoelectric property in TMDs through defect engineering [114]. Still, it is a challenge to effectively modulate surface corrugation due to the limited modulation of substrate roughness or thickness. Thus comes the question of whether flexoelectricity can be generated at atomic scales or not. If so, out-of-plane piezoelectricity will be generated regardless of the roughness or thickness. The surface vacancy of a Te atom is generated by the thermal annealing process, which contributes to greater surface curvature and thus produces greater out-of-plane piezoelectricity [119].

Furthermore, out-of-plane piezoelectricity in TMDs with layered structure can be formed by using ion beams to engineer the defects. For instance, the formation of Te defects caused by helium ion beam irradiation on the multilayer MoTe₂ actually leads to the out-of-plane piezoelectricity [120].

Doping

Chemical doping is also a new choice for obtaining out-of-plane piezoelectricity. Growing the material on the substrate can achieve this aim experimentally. The growth of graphene on SiO₂ substrate causes the chemical interaction between graphene and SiO₂ surface, thus realizing periodic doping. This interaction can induce band gap opening and dipole moment polarization of the graphene layer. Hence, it grants the material out-of-plane piezoelectricity [55]. In electronics manufacturing and energy harvesting applications, it is possible to use piezoelectric effects along the vertical direction in 2D TMDs.

3.2.2. Out-of-Plane Piezoelectricity in Janus Structures

Conventional TMDs Janus Structures

Another atomic-scale approach has been proposed to induce out-of-plane piezoelectricity through constructing asymmetric TMD monolayers, known as conventional Janus structures. In addition to the most common MoSSe [65], NiXY (X/Y = Cl, Br, I; X $\ne$ Y) is also an example. The structure diagram is shown in Figure 13a–c. In this regard, NiXY is a novel piezoelectric ferromagnetic material with these two unique properties. These Janus monolayer materials, such as NiClBr and NiBrI, have strong in-plane as well as out-of-plane piezoelectricity. It is found that NiClI is a ferrovalley material with magnetic anisotropy, which is an ideal material for ultrathin piezoelectric devices [121].

Janus Derivatives

As a matter of fact, Janus can not only be based on TMDs, but also be built in typical single-layer structures with hexagonal primitive cells or a buckled honeycomb monolayer. A series of Janus derivatives are obtained by substituting atoms (GeP–GaS, SiP–AlS, and SnP–InS). The structure diagram is shown in Figure 13d,e. This type of structure lacks mirror symmetry, leading to a large out-of-plane piezoelectricity [123]. Single-layer SiN–GaS also exhibits considerable out-of-plane piezoelectricity [124]. Janus M₂SeX (M = Ge, Sn; X = S, Te) have both large in-plane piezoelectric coefficients $d_{11}$ (up to 345.08 pm/V) and out-of-plane piezoelectric coefficients $d_{31}$ (up to 3.83 pm/V) [125]. As well as the larger surface piezoelectricity, Janus derivatives can also combine a variety of properties to offer opportunities for the manufacture of multifunctional devices. The research of the Janus structure of X₂PAs monolayers shows that the out-of-plane piezoelectricity and flexible properties play an important part in improving the performance of multifunctional sensing and controlling of nanodevices [126]. The piezoelectric ferromagnetism material Fe₂IX (X = Cl and Br) combines piezoelectricity, topological properties and ferromagnetism orders. In this sense, it provides a potential platform for multi-functional spintronic devices with a large gap and high T_C (429 K) [127].

Janus materials also have tribo-piezoelectricity. The sliding of the in-plane interlayer leads to a remarkable enhancement in the vertical piezoelectricity aspect. In the process of Janus bilayer sliding, the tribological energy will convert into electrical energy. Hence, it brings a new perspective to creating new piezoelectric nanogenerators [122]. The construction of a Janus structure can fully demonstrate the modification of traditional 2D ultrathin films.

3.2.3. Out-of-Plane Piezoelectricity in Multi-Element Transition Metal Materials

If simple Janus can achieve structure asymmetry, can more complex structures do the same? The answer is, of course, yes. In 2D materials, a quantity of three- and four-membered compound monolayers are non-centrosymmetric, such as MXenes, lithium-based ternary chalcogenides and so on. A schematic of each of these structures is shown in Figure 14. Due to the uneven charge distribution caused by non-mirror symmetry, these multi-element transition metal materials have strong out of plane piezoelectricity.

Strikingly, M₂CO₂ (M = Sc, Y, La) has an in-plane piezoelectricity comparable to 2H-MoS₂ as well as extraordinary out-of-plane piezoelectricity. The piezoelectric coefficient $d_{31}$ of Sc₂CO₂ MXene reaches 0.78 pm V⁻¹. At 2.5% strain, 0.1 V vertical piezoelectric voltage can only be produced in such ultrathin Sc₂CO₂ monolayer [86]. Similarly, BiCrX₃(X = S, Se, and Te) is a kind of piezoelectric ferromagnetism material with both in-plane and out-of-plane polarization at room temperature. Additionally, this is another breakthrough in high-performance piezoelectric materials [128].

The out-of-plane piezoelectric coefficients $d_{31}$ of 2D monolayer Li-based ternary chalcogenides LiMX₂ (M = Al, Ga, In; X = S, Se, Te), such as LiAlSe₂, LiGaTe₂ and LiAlTe₂, reach up to 0.61, 0.70 and 0.83 pm/V, respectively. This is owing to the unique double-buckled stacking structure of these LiMX₂ monolayers [87]. Later, it was found that $\gamma$ phase structure ($\gamma$-LialS₂ and $\gamma$-LialSe₂) also has an excellent out-of-plane piezoelectric coefficient; even the number is twice as high as that of $\beta$ phase structure [88]. When compared with the piezoelectric coefficients of other materials as shown in Figure 15, it is evident that the $\gamma$-LiMX₂ structures are very promising materials for high-performance piezoelectric nanodevices.

Zr₂P₂BrCl monolayer is of particular interest for its ferroelasticity, controllable anisotropic properties along the in-plane direction and outstanding out-of-plane piezoelectricity. These monolayers have a strong out-of-plane piezoelectricity since the heterogeneous charge distribution results from its broken mirror symmetry. The piezoelectric coefficient $d_{33}$ = 129.705 pm V⁻¹ of Zr₂P₂BrCl monolayer is actually significant, which is two orders of magnitude higher than MoSTe multilayers. It can even be a new alternate material for the design of memory devices, robot bionic skin or multipurpose nanodevices [89].

In addition to the materials mentioned above, the low-layer CuInP₂S₆ (CIPS) nanosheet also exhibits great performance. CIPS is a ferroelectric material with a high $d_{33}$ piezoelectric coefficient of 17.4 pm V⁻¹. The data is superior to that of other reported 2D piezoelectric films to date. The intense out-of-plane piezoelectricity in the ultrathin CIPS contributes to the integration of nanoscale energy transducers, and thus eventually the production of nanogenerators [63]. A CIPS-based piezotronics device under compressive stress is shown in Figure 16.

4. Concluding Remarks

The intrinsic differences of ultrathin films, thick films and bulk materials regarding polarization due to gradually reduced anisotropy are explored in the first part of this review. When the thickness of material gradually decreases to several atoms thick, the effective piezoelectric polarization will enhance significantly. Secondly, several promising materials with strong anisotropy, such as ZnO, MoS₂ and Zr₂P₂BrCl monolayer, are screened by summarizing the piezoelectric coefficient, polarization direction and preparation quality of the ultrathin films. It is noted that there are great difficulties in the acquisition and preparation of ultrathin piezoelectric films. The available methods have inevitable shortcomings and limitations, such as introducing a large number of defects, which is also a great challenge faced by the large family of 2D materials. Thirdly, based on the traditional piezoelectric hexagonal boron nitride structure, the effect of layer thickness, strain modes and sizes on polarization, and the novel quantum effects induced by it, such as topological state, quantum Hall effect, etc., are analyzed in detail. Particularly, the polarization mechanism of a few-atom-thick material is demonstrated by taking the symmetrically polarized monolayer TMDs as an example. In addition, to illustrate the construction and modification of a 2D piezoelectric material module, the Janus structure is taken as an example. Through this review, we have found that ultrathin piezoelectric films have made rapid progress and become a promising structure in the development of miniaturized energy conversion equipment.