ScAlN laminate and its manufacturing method

Abstract

To provide an ScAlN laminate with improved piezoelectric performance.SOLUTION: According to an embodiment of the present invention, there is provided an ScAlN laminate including a substrate, an underlayer formed on the substrate, and an ScAlN thin film formed on the underlayer, and the underlayer is composed of any one of yttrium, lutetium, gadolinium, and cerium. According to an embodiment of the present invention, it is possible to provide an ScAlN laminate with improved piezoelectric performance.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an ScAlN laminate and a method for producing the same. [Background technology]

[0002] AlN thin films exhibit excellent piezoelectric performance and are therefore used in a variety of devices (e.g., FBAR high-frequency filters for mobile communications, piezoelectric sensors, energy harvesters, MEMS microphones, and fingerprint authentication sensors).

[0003] In recent years, there has been a demand for diverse and highly functional sensors, and as communication frequencies continue to increase, there is a demand for further improvements in the piezoelectric performance of AlN thin films.

[0004] Incidentally, as disclosed in Patent Document 1, for example, an AlN thin film to which Sc is added, that is, an ScAlN thin film, is known to exhibit higher piezoelectric performance than an AlN thin film. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Publication No. 2019-145677 Summary of the Invention [Problem to be solved by the invention]

[0006] Theoretical calculations (first-principles calculations) have shown that the ScAlN thin film exhibits higher piezoelectric performance (higher piezoelectric constant) as the amount of Sc added increases. For this reason, in Patent Document 1, Sc is added to the ScAlN thin film at a concentration of more than 43 mol%.

[0007] However, when the present inventors investigated the piezoelectric performance of the ScAlN thin film disclosed in Patent Document 1, the piezoelectric performance expected from theoretical calculations was not observed.

[0008] Therefore, the present invention has been made in view of the above problems, and an object of the present invention is to provide an ScAlN laminate with improved piezoelectric performance. [Means for solving the problem]

[0009] In order to solve the above problem, according to one aspect of the present invention, there is provided an ScAlN laminate comprising a substrate, an underlayer formed on the substrate, and an ScAlN thin film formed on the underlayer, characterized in that the nearest neighbor interatomic distance, which is the distance between the nearest atoms in a lattice plane parallel to the surface of the underlayer, is shorter than the a-axis length of the ScAlN thin film.

[0010] Here, the ScAlN thin film may contain Sc in an amount of more than 43 mol % relative to the total number of Al and Sc atoms.

[0011] The ScAlN thin film may contain 59 mol % or more of Sc relative to the total number of Al and Sc atoms.

[0012] The ScAlN thin film may contain 81.5 mol % or less of Sc relative to the total number of Al and Sc atoms.

[0013] The ScAlN thin film may contain 67 mol % or less of Sc relative to the total number of Al and Sc atoms.

[0014] The interatomic distance of the underlayer may be 3.34 Å or more and 3.71 Å or less.

[0015] The underlayer is YN <111> An alignment film may be included.

[0016] The thickness of the ScAlN thin film may be 100 nm or less.

[0017] The semiconductor device may also be used in one or more selected from the group consisting of a transistor, an inverter, a ferroelectric memory, and an MEMS device.

[0018] According to another aspect of the present invention, there is provided a method for producing an ScAlN laminate, comprising the steps of forming an underlayer on a substrate and forming an ScAlN thin film on the underlayer, wherein the nearest neighbor interatomic distance, which is the distance between the nearest atoms in a lattice plane parallel to the surface of the underlayer, is shorter than the a-axis length of the ScAlN thin film. [Effects of the Invention]

[0019] According to the above-described aspects of the present invention, it is possible to provide an ScAlN laminate with improved piezoelectric performance and a method for producing the same. [Brief explanation of the drawings]

[0020] [Figure 1] 1 is a side view showing a schematic configuration of an ScAlN laminate according to one embodiment of the present invention. [Figure 2] 1 is a graph showing the enthalpy of formation (kJ / mol) of the wurtzite phase and the rock salt phase. [Figure 3] 1 is a graph showing the enthalpy of formation (kJ / mol) of the wurtzite phase and the rock salt phase. [Figure 4] 1 is a graph showing the enthalpy of formation (kJ / mol) of the wurtzite phase and the rock salt phase. [Figure 5] 1 is a graph showing the enthalpy of formation (kJ / mol) of a wurtzite phase ScAlN thin film compared with the enthalpy of formation (kJ / mol) of a bulk ScAlN. [Figure 6] 1 is a graph showing the formation enthalpy (kJ / mol) of a rock-salt phase ScAlN thin film compared with the formation enthalpy (kJ / mol) of a bulk ScAlN film. [Figure 7] 5 and 6 are overlapping graphs. [Figure 8] 1 is a graph showing the correlation between the molar concentration (mol %) of Sc and the a-axis length (Å) of an ScAlN thin film. [Figure 9] 1 is a graph showing a comparison of the enthalpy of formation (kJ / mol) of the wurtzite phase and the rock salt phase when the interatomic distance of the underlayer is 3.71 Å. [Figure 10]1 is a graph showing a comparison of the enthalpy of formation (kJ / mol) of the wurtzite phase and the rock salt phase when the interatomic distance of the underlayer is 3.34 Å. [Figure 11] YN as the base layer <111> 1 is a graph showing a comparison of the enthalpy of formation (kJ / mol) of the wurtzite phase and the rock salt phase when an alignment film is used. [Figure 12] 1 is a graph showing a comparison of the enthalpy of formation (kJ / mol) of the wurtzite phase and the rock salt phase when the thickness (h) of the ScAlN thin film is changed and the nearest-neighbor interatomic distance of the underlayer is 3.50 Å. [Figure 13] 10 is a graph showing a comparison of the enthalpy of formation (kJ / mol) of the wurtzite phase and the rock salt phase when the thickness (h) of the ScAlN thin film is changed and the nearest-neighbor interatomic distance of the underlayer is 3.60 Å. DETAILED DESCRIPTION OF THE INVENTION

[0021] Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings. A numerical range indicated by "to" means a range that includes the numerical values ​​before and after "to" as the lower and upper limits. Numerical values ​​indicated as "greater than" or "less than" are not included in the numerical range.

[0022] <1. Investigation by the Inventor> First, the inventors' investigations will be described. Two phases are known for ScAlN thin films: the wurtzite phase and the rock salt phase. Of these, it is believed that the more stable phase is more prevalent in ScAlN thin films. Since the wurtzite phase exhibits piezoelectricity, it can be said that when the wurtzite phase is stably present in an ScAlN thin film, the ScAlN thin film exhibits high piezoelectric performance. Therefore, the inventors first investigated which phase becomes stable when Sc is added.

[0023] It can be said that the lower the formation enthalpy of each phase, the more stable it is. The formation enthalpy ΔH is expressed by the following formula (1). Note that in this case, it was assumed that the ScAlN thin film was formed directly on some kind of substrate.

[0024]

number

[0025] The total energy in Equation (1) is automatically calculated by first-principles calculation (code: VASP). In other words, in this embodiment, theoretical calculations such as first-principles calculations are automatically performed by an electronic computer capable of executing such theoretical calculations. The results are shown in FIG. 2. FIG. 2 shows the correlation between the molar concentration of Sc dissolved in the AlN thin film (the molar concentration relative to the total number of Sc and Al atoms) and the formation enthalpy of the wurtzite phase or rock salt phase. Specifically, the horizontal axis of FIG. 2 represents the molar concentration of Sc in the ScAlN thin film, and the vertical axis represents the formation enthalpy (kJ / mol). Point P10 represents the formation enthalpy of the wurtzite phase for each composition (each molar concentration of Sc) of the ScAlN thin film, and graph L10 represents a linear connection of points P10. Point P20 represents the formation enthalpy of the rock salt phase for each composition (each molar concentration of Sc) of the ScAlN thin film, and graph L20 represents a linear connection of points P20.

[0026] As is clear from Figure 2, the wurtzite phase is thermodynamically stable in the region where the Sc molar concentration is lower than dashed line A, and the rocksalt phase is thermodynamically stable in the region where the Sc molar concentration is higher than dashed line A. Dashed line A indicates the intersection of graphs L10 and L20. Hereinafter, the Sc molar concentration value indicated by dashed line A will also be referred to as the Sc solid solubility limit of the wurtzite phase. In other words, in the region where the Sc molar concentration is lower than dashed line A, a large amount of wurtzite phase exists in the ScAlN thin film, and in the region where the Sc molar concentration is higher than dashed line A, a large amount of rocksalt phase exists in the ScAlN thin film.

[0027] Therefore, the inventors considered that if the position of dashed line A could be shifted toward a higher Sc concentration, as shown in Figure 3, it would be possible to dissolve Sc at a higher concentration in the AlN thin film while maintaining the stable existence of the wurtzite phase. This would improve the piezoelectric performance of the ScAlN thin film. The horizontal and vertical axes in Figure 3 are defined in the same way as in Figure 2. Point P11 indicates the enthalpy of formation of the wurtzite phase for each composition (each molar concentration of Sc) of the ScAlN thin film, and graph L11 is a linear connection of points P11. Point P21 indicates the enthalpy of formation of the rocksalt phase for each composition (each molar concentration of Sc) of the ScAlN thin film, and graph L21 is a linear connection of points P21.

[0028] The inventors focused on the underlayer in order to shift the position of dashed line A to the higher Sc concentration side. In other words, an underlayer is interposed between the substrate and the ScAlN thin film. This underlayer then introduces strain energy into the ScAlN thin film. If this makes it possible to relatively destabilize the rocksalt phase compared to the wurtzite phase (to increase the formation enthalpy), it is possible to shift the position of dashed line A to the higher Sc concentration side. The formation enthalpy ΔH taking into account the strain energy is thin film is expressed by the following formula (2): The method for calculating the enthalpy of formation ΔH in formula (2) is the same as formula (1).

[0029]

number

[0030] The strain energy E in Eq. (2) strain are expressed by the following formulas (3) and (4). In formulas (3) and (4), V is the molar volume (volume occupied by one mole of atoms), which is automatically calculated by first-principles calculation. h is the film thickness of the ScAlN thin film, G is the modulus of rigidity of the ScAlN thin film, ν is Poisson's ratio, ε is strain, and h c is the critical film thickness (film thickness at which misfit dislocations are introduced). Here, misfit dislocations are dislocations that are introduced into the ScAlN thin film due to the lattice misfit between the underlayer and the ScAlN thin film.

[0031]

number

[0032] The rigidity is expressed by the following formulas (5) to (10). In formula (6), B V is the bulk modulus of the ScAlN thin film (Voigt notation). ij (i, j: natural numbers in formulas (6) to (10)) is the elastic modulus tensor, which is automatically calculated by first-principles calculation.

[0033]

number

[0034] Poisson's ratio is expressed by the following formulas (11) to (13). B in formula (11) is the bulk modulus, and B in formula (12) is R is the bulk modulus of the ScAlN thin film (Reuss notation). V , C 2 and M are expressed by the formulas (5) to (10).

[0035]

number

[0036] The strain ε is the lattice misfit between the underlayer and the ScAlN thin film, and is expressed by the following formula (14). In formula (14), a is the lattice constant (a-axis length) of the ScAlN thin film in the a-axis direction, and is calculated automatically by first-principles calculation. a0 is the nearest atomic distance of the underlayer (described later), and takes a different value depending on the material that makes up the underlayer. For example, if the underlayer is made of YN, <111> When used as an alignment film, a0 is 3.46 Å.

[0037]

number

[0038] The critical film thickness is given by the following formula (15). In formula (15), ε is the strain and ν is the Poisson's ratio, which can be calculated using the formula above. b is the Burgers vector. The Burgers vector of the wurtzite phase is given by the following formula (16), and the Burgers vector of the rocksalt phase is given by the following formula (17). In formulas (16) and (17), a is the lattice constant in the a-axis direction (a-axis length), which is calculated automatically using first-principles calculations. In formula (16), c is the lattice constant in the c-axis direction, which is calculated automatically using first-principles calculations.

[0039]

number

[0040] According to the above-mentioned formulas (2) to (17), the enthalpy of formation △H thin film is dependent on the interatomic distance of the underlayer. Therefore, by appropriately determining the interatomic distance of the underlayer, it is possible to make the rocksalt phase relatively less stable than the wurtzite phase, and it is believed that the position of the dashed line A in Figure 2 can be shifted to a higher Sc concentration side. Therefore, the inventors have conducted extensive research into the interatomic distance of the underlayer. As a result, it has been found that when the nearest-neighbor interatomic distance, which is the distance between the closest atoms in a lattice plane parallel to the surface of the underlayer, is shorter than the a-axis length of the ScAlN thin film, the position of the dashed line A can be shifted to a higher Sc concentration side than when there is no underlayer (as in Figure 2). Note that the nearest-neighbor interatomic distance is a value after the ScAlN thin film is laminated on the surface of the underlayer, and is a value obtained by first-principles calculations. In other words, by making the nearest-neighbor interatomic distance of the underlayer shorter than the a-axis length of the ScAlN thin film, it is possible to fabricate a wurtzite-phase ScAlN thin film containing a high Sc concentration. An example of a material that satisfies the requirements for the nearest-neighbor interatomic distance is YN. <111> An example is an alignment film.

[0041] <2. Distance between nearest neighbor atoms> The inventors further investigated the nearest-neighbor atomic distance. In Figure 5, the horizontal axis represents the molar concentration of Sc (the molar concentration relative to the total number of Al and Sc atoms), and the vertical axis represents the formation enthalpy. Graph L30 schematically shows the correlation between the molar concentration of Sc and the formation enthalpy of an ScAlN bulk body. Here, the ScAlN bulk body is essentially synonymous with an ScAlN thin film without an underlayer. Graph L31 schematically shows the correlation between the molar concentration of Sc and the formation enthalpy of an ScAlN thin film. Note that both the ScAlN thin film and the ScAlN bulk body are wurtzite phases, and the underlayer of the ScAlN thin film is a material with a nearest-neighbor atomic distance of 3.34 Å. The thickness of the ScAlN thin film was 5 nm. As shown in Figure 5, graphs L30 and L31 intersect at point P30. The Sc molar concentration corresponding to point P30 is 43 mol%. In other words, when the molar concentration of Sc is 43 mol%, the formation enthalpy of the ScAlN bulk body and the formation enthalpy of the ScAlN thin film are the same. In other words, the formation enthalpy is fixed. In this case, no strain energy is generated in the ScAlN thin film. This means that the a-axis length of the ScAlN thin film and the nearest interatomic distance of the underlayer are the same. When the molar concentration of Sc is different from 43 mol%, the a-axis length of the ScAlN thin film and the nearest interatomic distance of the underlayer do not match, so strain energy is generated in the ScAlN thin film and the formation enthalpy increases. Therefore, the formation enthalpy of the ScAlN bulk body and the formation enthalpy of the ScAlN thin film do not match. Hereinafter, the point where the formation enthalpy of the ScAlN bulk body and the formation enthalpy of the ScAlN thin film match is also referred to as the "fixed point." Point P30 is an example of a fixed point.

[0042] The horizontal axis of Figure 6 represents the molar concentration of Sc (the molar concentration relative to the total number of Al and Sc atoms), and the vertical axis represents the formation enthalpy. Graph L40 shows a schematic representation of the correlation between the molar concentration of Sc and the formation enthalpy of the ScAlN bulk. Graph L41 shows a schematic representation of the correlation between the molar concentration of Sc and the formation enthalpy of the ScAlN thin film. The ScAlN thin film and the ScAlN bulk were both rock salt phases, and the underlayer of the ScAlN thin film was a material with a nearest-neighbor interatomic distance of 3.34 Å. The thickness of the ScAlN thin film was 5 nm. As shown in Figure 6, graphs L40 and L41 do not intersect. That is, at any Sc concentration, the a-axis length of the ScAlN thin film does not match the nearest-neighbor interatomic distance of the underlayer. Therefore, strain energy is generated in the ScAlN thin film regardless of the Sc concentration.

[0043] Figure 7 is a superposition of Figures 5 and 6. When comparing ScAlN bulk materials, the wurtzite phase stabilizes when the Sc concentration is lower than point P51 (the Sc solid solubility limit). The molar concentration of Sc indicated by point P51 is 59 mol%. On the other hand, when comparing ScAlN thin films, the wurtzite phase stabilizes when the Sc concentration is lower than point P52 (the Sc solid solubility limit). The molar concentration of Sc indicated by point P52 is 67 mol%, which is higher than point P51. Therefore, it is possible to fabricate wurtzite-phase ScAlN thin films containing higher Sc concentrations.

[0044] The above phenomenon is thought to occur when the distance between nearest neighbor atoms in the underlayer is shorter than the a-axis length of the ScAlN thin film. In other words, when the distance between nearest neighbor atoms in the underlayer is shorter than the a-axis length of the ScAlN thin film, a fixed point exists, and the Sc solid solubility limit of the ScAlN thin film can be shifted to a higher concentration than the Sc solid solubility limit of the bulk. The shift in the Sc solid solubility limit is thought to be particularly large when the Sc molar concentration exceeds 43 mol%.

[0045] The horizontal axis of Figure 8 represents the Sc molar concentration (mol%), and the vertical axis represents the a-axis length (Å) of the ScAlN thin film. Point P60 shows the correlation between the Sc molar concentration and the a-axis length of the ScAlN thin film calculated by first-principles calculations, and graph L60 is a linear connection of points P60. Point P61 shows the correlation between the Sc molar concentration and the a-axis length (experimental value) of the ScAlN thin film calculated by experiment. Here, the experimental value was calculated from the electron diffraction pattern of the thin film fabricated by magnetron sputtering. As shown in Figure 8, there is a good correlation between the first-principles calculated value and the experimental value.

[0046] Referring to this graph, when the molar concentration of Sc is 43 mol%, the a-axis length of the ScAlN thin film is 3.34 Å, and when the molar concentration of Sc is 100 mol%, the a-axis length of the ScAlN thin film (ScN thin film) is 3.71 Å. Therefore, when the molar concentration of Sc in the ScAlN thin film exceeds 43 mol%, the material of the underlayer should be determined so that the nearest-neighbor interatomic distance in the underlayer is 3.34 Å or more and 3.71 Å or less, and is shorter than the a-axis length of the ScAlN thin film.

[0047] The horizontal axis of Figure 9 shows the molar concentration of Sc (mol%), and the vertical axis shows the formation enthalpy (kJ / mol) of the wurtzite or rock salt phase. Graph L70 shows the correlation between the molar concentration of Sc and the formation enthalpy of the ScAlN bulk. Graph L71 shows the correlation between the molar concentration of Sc and the formation enthalpy of the ScAlN thin film. The ScAlN thin film and ScAlN bulk in graphs L70 and L71 are both in the wurtzite phase, and the nearest-neighbor interatomic distance of the underlayer of the ScAlN thin film is 3.71 Å. The thickness of the ScAlN thin film is 5 nm.

[0048] Graph L80 shows the correlation between the molar concentration of Sc and the formation enthalpy of the ScAlN bulk. Graph L81 shows the correlation between the molar concentration of Sc and the formation enthalpy of the ScAlN thin film. The ScAlN thin film and ScAlN bulk in graphs L80 and L81 are both rock salt phases, and the nearest-neighbor interatomic distance of the underlayer of the ScAlN thin film is 3.71 Å. The film thickness of the ScAlN thin film is 5 nm.

[0049] As is clear from Figure 9, the formation enthalpy of wurtzite-phase ScAlN thin films is lower than that of rocksalt-phase ScAlN thin films, regardless of the Sc molar concentration. In contrast, when focusing on bulk ScAlN, the solubility limit of Sc in wurtzite-phase ScAlN bulk is 59 mol%. In other words, wurtzite-phase ScAlN bulk cannot exist stably unless the Sc molar concentration is 59 mol% or less. Therefore, by forming an underlayer with a nearest-neighbor interatomic distance of 3.71 Å, Sc can be dissolved in the ScAlN thin film at a high concentration, while maintaining the stable existence of the wurtzite phase.

[0050] The horizontal axis of Figure 10 shows the molar concentration of Sc (mol%), and the vertical axis shows the formation enthalpy (kJ / mol) of the wurtzite or rocksalt phase. Graph L70 shows the correlation between the molar concentration of Sc and the formation enthalpy of the ScAlN bulk. Graph L91 shows the correlation between the molar concentration of Sc and the formation enthalpy of the ScAlN thin film. The ScAlN thin film and ScAlN bulk in graphs L70 and L91 are both in the wurtzite phase, and the nearest-neighbor interatomic distance of the underlayer of the ScAlN thin film is 3.34 Å. The thickness of the ScAlN thin film is 5 nm.

[0051] Graph L80 shows the correlation between the molar concentration of Sc and the enthalpy of formation of the ScAlN bulk. Graph L101 shows the correlation between the molar concentration of Sc and the enthalpy of formation of the ScAlN thin film. The ScAlN thin film and ScAlN bulk in graphs L80 and L101 are both rock salt phases, and the nearest-neighbor interatomic distance of the underlayer of the ScAlN thin film is 3.34 Å. The film thickness of the ScAlN thin film is 5 nm.

[0052] As is clear from Figure 10, when the nearest-neighbor interatomic distance of the underlayer is 3.34 Å, the solubility limit of Sc in the wurtzite-phase ScAlN thin film is 67 mol% (point P91). In contrast, when focusing on the bulk, the solubility limit of Sc in the wurtzite-phase ScAlN bulk is 59 mol%. In other words, the ScAlN bulk cannot exist stably unless the molar concentration of Sc is 59 mol% or less (point P92). Therefore, by forming an underlayer with a nearest-neighbor interatomic distance of 3.34 Å, it is possible to dissolve Sc at a high concentration in the ScAlN thin film while maintaining the stable existence of the wurtzite phase.

[0053] From the above, it can be seen that when the thickness of the ScAlN thin film is 5 nm and the molar concentration of Sc exceeds 43 mol %, the distance between nearest neighbor atoms in the underlayer is preferably 3.34 Å to 3.71 Å.

[0054] In addition, YN's <111> The distance between the nearest neighboring atoms in the alignment film is 3.46 Å, which satisfies the condition of 3.34 Å to 3.71 Å. <111> The correlation between the molarity of Sc and the formation enthalpy of wurtzite or rocksalt phase ScAlN thin films when an oriented film is used is shown.

[0055] More specifically, the horizontal axis of FIG. 11 indicates the molar concentration of Sc (mol%), and the vertical axis indicates the formation enthalpy (kJ / mol) of a wurtzite or rocksalt phase ScAlN thin film. Point P110 shows the correlation between the molar concentration of Sc and the formation enthalpy of a wurtzite phase ScAlN thin film. Graph L110 is a linear connection of points P110. Point P111 shows the correlation between the molar concentration of Sc and the formation enthalpy of a rocksalt phase ScAlN thin film. Graph L111 is a linear connection of points P111. As is clear from FIG. 11, when the underlayer contains YN, <111> By using an oriented film, the solubility limit of Sc in the ScAlN thin film can be increased to 81.5 mol %. Based on this knowledge, the inventors arrived at the ScAlN laminate according to this embodiment. The ScAlN laminate according to this embodiment will be described below.

[0056] <3. Structure of ScAlN laminate> Next, the configuration of the ScAlN laminate 1 according to this embodiment will be described with reference to Fig. 1. The ScAlN laminate 1 includes a substrate 10, an underlayer 20, and an ScAlN thin film (piezoelectric film) 30.

[0057] There is no particular limitation on the type of substrate 10, and any substrate may be used as long as it is possible to laminate the underlayer 20 and ScAlN thin film 30 described below. The substrate 10 may be made of, for example, silicon, conductive metal, sapphire, SiC, glass, or an organic material.

[0058] As described above, the underlayer 20 introduces strain energy into the ScAlN thin film 30, thereby making the rocksalt phase of the ScAlN thin film relatively more unstable than the wurtzite phase. The nearest interatomic distance of the underlayer 20 is shorter than the a-axis length of the ScAlN thin film. For example, when the molar concentration of Sc in the ScAlN thin film exceeds 43 mol%, the nearest interatomic distance of the underlayer 20 is 3.34 Å to 3.71 Å, and is shorter than the a-axis length of the ScAlN thin film. The a-axis length of the ScAlN thin film varies depending on the molar concentration of Sc in the ScAlN thin film. Therefore, the a-axis length corresponding to the molar concentration of the ScAlN thin film can be calculated by first-principles calculation, and an underlayer (material) whose nearest interatomic distance is shorter than the a-axis length can be selected. The underlayer 20 is formed on the substrate 10 by, for example, sputtering. The underlayer 20 is made of, for example, YN. <111> Alternatively, the underlayer 20 may be an orientation film. The underlayer 20 may have a multilayer structure. In this case, the distance between the nearest neighbor atoms of at least the layer in contact with the ScAlN thin film 30 is shorter than the a-axis length of the ScAlN thin film. For example, the underlayer 20 may have a multilayer structure, and the layer in contact with the ScAlN thin film 30 may be a YN layer. <111> It may be made of an alignment film.

[0059] The ScAlN thin film 30 is an AlN thin film containing Sc in solid solution. The ScAlN thin film 30 may be a single layer, or may be a multi-layer ScAlN thin film with different polarization directions. The ScAlN thin film contains Sc in solid solution at a level equal to or lower than the solubility limit of Sc in the wurtzite phase. The underlayer 20 increases the solubility limit of Sc in the wurtzite phase compared to when the underlayer 20 is not present. Therefore, the ScAlN thin film 30 exhibits high piezoelectric performance. The molar concentration of Sc in the ScAlN thin film is not particularly limited, but the lower limit may be greater than 43 mol% or may be 59 mol% or higher. 59 mol% is the solubility limit of Sc in a ScAlN bulk body, but in this embodiment, more Sc can be dissolved in the AlN thin film. The upper limit may be 81.5 mol% or lower, or may be 67 mol% or lower. The underlayer may contain YN. <111> When an oriented film is selected, the solubility limit of Sc is 81.5 mol %, so a maximum of 81.5 mol % of Sc can be dissolved in the AlN thin film. 67 mol % is the solubility limit when the interatomic distance of the nearest neighbors in the underlayer 20 is 3.34 Å.

[0060] As shown in equations (3) and (4), the strain energy introduced into the ScAlN thin film 30 is also affected by the film thickness (h) of the ScAlN thin film 30. The inventors of the present invention have investigated the film thickness and found that the solubility limit of Sc in the wurtzite phase is particularly high when the thickness of the ScAlN thin film is 100 nm or less. The film thickness is preferably 10 nm or less, and more preferably 5 nm or less. There is no particular lower limit to the film thickness, and it is sufficient as long as it is greater than 0 nm. The variation in strain energy due to film thickness will be explained with reference to FIG. 4.

[0061] 4(a) to (c) show the correlation between the molar concentration of Sc dissolved in the ScAlN thin film (molar concentration relative to the total number of Sc and Al atoms) and the formation enthalpy of the wurtzite phase or rock salt phase when the film thickness is 100 nm, 50 nm, and 10 nm, respectively. An example in which the film thickness of the underlayer 20 is 5 nm is shown in FIG. 11. The underlayer 20 is made of YN. <111> The film was an oriented film (nearest-neighbor interatomic distance a0 = 3.46 Å). The definitions of the vertical and horizontal axes are the same as in Figure 2. Point P12 shows the formation enthalpy of the wurtzite phase for each composition (each molarity of Sc) in a 100-nm-thick ScAlN thin film, and graph L12 is a linear connection of points P12. Point P22 shows the formation enthalpy of the rocksalt phase for each composition (each molarity of Sc) in a 100-nm-thick ScAlN thin film, and graph L22 is a linear connection of points P22. As shown in Figure 4(a), the solubility limit of Sc in the wurtzite phase at a film thickness of 100 nm is 61 mol%.

[0062] Point P13 shows the enthalpy of formation of the wurtzite phase for each composition (each molarity of Sc) in a 50-nm-thick ScAlN thin film, and graph L13 is a linear connection of points P13. Point P23 shows the enthalpy of formation of the rocksalt phase for each composition (each molarity of Sc) in a 50-nm-thick ScAlN thin film, and graph L23 is a linear connection of points P23. As shown in Figure 4(b), the solubility limit of Sc in the wurtzite phase at a film thickness of 50 nm is 62.5 mol%.

[0063] Point P14 shows the enthalpy of formation of the wurtzite phase for each composition (each molarity of Sc) in a 10-nm-thick ScAlN thin film, and graph L14 is a linear connection of points P14. Point P24 shows the enthalpy of formation of the rocksalt phase for each composition (each molarity of Sc) in a 10-nm-thick ScAlN thin film, and graph L24 is a linear connection of points P24. As shown in Figure 4(c), the solubility limit of Sc in the wurtzite phase at a film thickness of 10 nm is 75.5 mol%.

[0064] According to first-principles calculations, if the wurtzite phase is stable when the molar concentration of Sc is about 70%, the piezoelectric constant of the ScAlN thin film will be at its maximum (approximately 100 pC / N). Therefore, it is preferable that the wurtzite phase is stable when the molar concentration of Sc is, for example, 59 to 81.5 mol%, and therefore the film thickness is preferably 10 nm or less. This is because the solubility limit of Sc in the wurtzite phase exceeds 70 mol% when the film thickness is 10 nm or less.

[0065] Therefore, one example of a preferred embodiment of the ScAlN laminate 1 is as follows. First, the underlayer 20 is made of YN. <111> It is composed of an oriented film. The thickness of the ScAlN thin film 30 is 10 nm or less, and Sc is dissolved at more than 43 mol %, preferably 59 to 81.5 mol %, and more preferably 70 mol %. In this case, the ScAlN thin film 30 exhibits very high piezoelectric performance. Of course, this is just one example, and the ScAlN thin film 30 will exhibit high piezoelectric performance as long as it meets the requirements of this embodiment. Other examples of the underlayer include films using Y, La, Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, Tm, Lu, and Tl.

[0066] Furthermore, the variation in strain energy due to the film thickness when the nearest interatomic distance of the underlayer 20 is changed will be described with reference to FIGS.

[0067] Figures 12(a)-(c) show the correlation between the molar concentration of Sc dissolved in the ScAlN thin film (the molar concentration relative to the total number of Sc and Al atoms) and the formation enthalpy of the wurtzite or rock salt phase when the underlayer 20 has a nearest neighbor interatomic distance a0 of 3.50 Å and a film thickness of 100 nm, 50 nm, and 10 nm, respectively. The definitions of the vertical and horizontal axes are the same as in Figure 2. Point P120 represents the formation enthalpy of the wurtzite phase for each composition (each Sc molar concentration) of the 100 nm-thick ScAlN thin film. Graph L120 is a linear connection of points P120. Point P220 represents the formation enthalpy of the rock salt phase for each composition (each Sc molar concentration) of the 100 nm-thick ScAlN thin film. Graph L220 is a linear connection of points P220. As shown in Figure 12(a), the solubility limit of Sc in the wurtzite phase at a film thickness of 100 nm is 63.5 mol%.

[0068] Point P121 shows the enthalpy of formation of the wurtzite phase for each composition (each molarity of Sc) in a 50-nm-thick ScAlN thin film, and graph L121 is a linear connection of points P121. Point P221 shows the enthalpy of formation of the rocksalt phase for each composition (each molarity of Sc) in a 50-nm-thick ScAlN thin film, and graph L221 is a linear connection of points P221. As shown in Figure 12(b), the solubility limit of Sc in the wurtzite phase at a film thickness of 50 nm is 68.5 mol%.

[0069] Point P122 shows the enthalpy of formation of the wurtzite phase at each composition (each molarity of Sc) in a 10-nm-thick ScAlN thin film, and graph L122 is a linear connection of points P122. Point P222 shows the enthalpy of formation of the rocksalt phase at each composition (each molarity of Sc) in a 10-nm-thick ScAlN thin film, and graph L222 is a linear connection of points P222. As shown in Figure 12(c), the solubility limit of Sc in the wurtzite phase at a film thickness of 10 nm is 86.5 mol%.

[0070] Figures 13(a)-(c) show the correlation between the molar concentration of Sc dissolved in the ScAlN thin film (molar concentration relative to the total number of Sc and Al atoms) and the formation enthalpy of the wurtzite or rock salt phase when the underlayer 20 has a nearest neighbor interatomic distance a0 of 3.60 Å and a film thickness of 100 nm, 50 nm, and 10 nm, respectively. The definitions of the vertical and horizontal axes are the same as in Figure 2. Point P123 represents the formation enthalpy of the wurtzite phase for each composition (each Sc molar concentration) of the 100 nm-thick ScAlN thin film. Graph L123 is a linear connection of points P123. Point P223 represents the formation enthalpy of the rock salt phase for each composition (each Sc molar concentration) of the 100 nm-thick ScAlN thin film. Graph L223 is a linear connection of points P223. As shown in Figure 13(a), the solubility limit of Sc in the wurtzite phase at a film thickness of 100 nm is 63.5 mol%.

[0071] Point P124 shows the enthalpy of formation of the wurtzite phase at each composition (each molarity of Sc) in a 50-nm-thick ScAlN thin film, and graph L124 is a linear connection of points P124. Point P224 shows the enthalpy of formation of the rocksalt phase at each composition (each molarity of Sc) in a 50-nm-thick ScAlN thin film, and graph L224 is a linear connection of points P224. As shown in Figure 13(b), the solubility limit of Sc in the wurtzite phase at a film thickness of 50 nm is 67.5 mol%.

[0072] Point P125 shows the enthalpy of formation of the wurtzite phase for each composition (each molarity of Sc) in a 10-nm-thick ScAlN thin film, and graph L125 is a linear connection of points P125. Point P225 shows the enthalpy of formation of the rocksalt phase for each composition (each molarity of Sc) in a 10-nm-thick ScAlN thin film, and graph L225 is a linear connection of points P225. As shown in Figure 13(c), the solubility limit of Sc in the wurtzite phase at a film thickness of 10 nm is 86 mol%.

[0073] As described above, even when the nearest neighbor interatomic distance a0 of the underlayer 20 is 3.50 Å or 3.60 Å, the thinner the film thickness (h) of the ScAlN thin film 30, the higher the solubility limit of Sc in the wurtzite phase. When the film thickness of the ScAlN thin film is 10 nm or less, the solubility limit of Sc in the wurtzite phase exceeds 70 mol %. Therefore, it is preferable that the film thickness of the ScAlN thin film is 10 nm or less.

[0074] 4. Method for manufacturing ScAlN laminate The manufacturing method is not particularly limited, and any manufacturing method may be used as long as it can obtain the ScAlN laminate 1 with the above-mentioned characteristics. One example of the manufacturing method is a manufacturing method including the steps of forming an underlayer 20 on a substrate 10 and forming an ScAlN thin film 30 on the underlayer 20. The underlayer 20 and the ScAlN thin film 30 are formed by, for example, a sputtering method. Here, the molar concentration of Sc and the material of the underlayer 20 are selected so that the distance between nearest neighbor atoms in the underlayer 20 is shorter than the a-axis length of the ScAlN thin film 30.

[0075] <5. Application examples of ScAlN laminates> The ScAlN laminate 1 is applicable to various fields. For example, the ScAlN laminate 1 may be used in one or more selected from the group consisting of transistors, inverters, ferroelectric memories, and MEMS devices (including piezoelectric devices). The ScAlN laminate 1 may also be used in FBAR high-frequency filters for mobile communications, piezoelectric sensors, energy harvesters, MEMS microphones, and fingerprint authentication sensors.

[0076] Although the preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings, the present invention is not limited to these examples. It is clear that a person skilled in the art to which the present invention pertains can conceive of various modifications and alterations within the scope of the technical ideas set forth in the claims, and it is understood that these also naturally fall within the technical scope of the present invention. [Explanation of symbols]

[0077] 1 ScAlN laminate 10 Substrate 20 Base layer 30 ScAlN thin film

Claims

1. A substrate; an underlayer formed on the substrate; a ScAlN thin film formed on the underlayer, the underlayer is made of any one of yttrium, lutetium, gadolinium, and cerium; The ScAlN thin film contains Sc in an amount of more than 43 mol % relative to the total number of Al and Sc atoms, and has a higher proportion of wurtzite phase than rock salt phase.

2. 2. The ScAlN laminate according to claim 1, wherein the ScAlN thin film contains 59 mol % or more of Sc relative to the total number of Al and Sc atoms.

3. 3. The ScAlN laminate according to claim 1, wherein the ScAlN thin film contains 81.5 mol % or less of Sc relative to the total number of Al and Sc atoms.

4. 3. The ScAlN laminate according to claim 1, wherein the ScAlN thin film contains 67 mol % or less of Sc relative to the total number of Al and Sc atoms.

5. 3. The ScAlN laminate according to claim 1, wherein the interatomic distance between the nearest neighbors of the underlayer is 3.34 Å or more and 3.71 Å or less.

6. 6. The ScAlN laminate according to claim 5, wherein the underlayer includes a <111> oriented film of YN.

7. 3. The ScAlN laminate according to claim 1, which is used in at least one selected from the group consisting of a transistor, an inverter, a ferroelectric memory, and a MEMS device.

8. forming an underlayer on the substrate; forming a ScAlN thin film on the underlayer; the underlayer is made of any one of yttrium, lutetium, gadolinium, and cerium; The ScAlN thin film contains Sc in an amount of more than 43 mol % relative to the total number of Al and Sc atoms, and has a wurtzite phase in a greater proportion than a rock salt phase.

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