Stylo-epitaxial piezoelectric and ferroelectric devices and method of manufacturing
09761785 · 2017-09-12
Assignee
Inventors
- Glen R Fox (Colorado Springs, CO, US)
- Ronald G. Polcawich (Derwood, MD, US)
- Daniel M Potrepka (Silver Spring, MD, US)
- Luz M Sanchez (Laurel, MD, US)
Cpc classification
C30B29/32
CHEMISTRY; METALLURGY
C23C18/1295
CHEMISTRY; METALLURGY
C30B25/183
CHEMISTRY; METALLURGY
International classification
C30B29/32
CHEMISTRY; METALLURGY
Abstract
A ferroelectric device comprising a substrate; a textured layer; a first electrode comprising a thin layer of metallic material having a crystal lattice structure divided into granular regions; a seed layer; the seed layer being epitaxially deposited so as to form a column-like structure on top of the granular regions of the first electrode; at least one ferroelectric material layer exhibiting spontaneous polarization epitaxially deposited on the seed layer; the ferroelectric material layer, the seed layer, and first electrode each having granular regions in which column-like structures produce a high degree of polarization normal to the growth plane and a method of making.
Claims
1. A ferroelectric device comprising: a substrate; a textured layer; a first electrode comprising a thin layer of metallic material having a crystal lattice structure divided into granular regions; a seed layer; the seed layer being epitaxially deposited so as to form a column-like structure on top of the granular regions of the first electrode; at least one ferroelectric material layer exhibiting spontaneous polarization epitaxially deposited on the seed layer; the ferroelectric material layer, the seed layer, and first electrode each having granular regions in which column-like structures produce a high degree of polarization normal to the growth plane.
2. The device of claim 1 wherein the ferroelectric device is a piezoelectric device further comprising a second electrode positioned on the ferroelectric material layer, the second electrode having a thickness in the range of approximately 10 nm to 500 nm and wherein the second electrode comprises one or more of Pt, Ir, Ru, Pd, Ni, Au, Cu, Ag, IrO.sub.2, RuO.sub.2, LaSrCoO.sub.3, SrRuO.sub.3, LaNiO.sub.3, InSnO.sub.2.
3. The device of claim 1 wherein the maintaining of the crystal planes within column-like structure of the ferroelectric material provide optimum spontaneous polarization perpendicular to the growth plane and wherein the granular regions of the seed layer, ferroelectric layer and first electrode are in registration such that the columns in the ferroelectric layer extend from the granular regions of the seed layer, and the granular regions of the seed layer extend from the granular regions of first electrode, and wherein the crystallographic planes within the granular regions and the column-like structures are substantially planar to the growth plane with a tilt of less than or equal to approximately 10 degrees from the growth plane, and wherein the crystal orientation within the ferroelectric material layer is predominately {001}.
4. The device of claim 1 wherein each of the ferroelectric material and seed layers have a textured perovskite crystal structure, and wherein the column-like structures have diameters that vary from 1 nm to 10 um with a preference in the range of 10 nm to 500 nm and wherein the length of the columns vary from 1 nm to 500 um with a preference in the range of 10 nm to 10 um.
5. The device of claim 1 wherein the substrate comprises one or more of silicon, Ge, GaAs, Al.sub.2O.sub.3, ZrO.sub.2, MgO, spinel (MgAl.sub.2O.sub.4), Yttria Stabilized Zirconia (YSZ), ZrO.sub.2, Cu, Ni, Ti, SOI, stainless steel, quartz, silicate glasses, low expansion glasses, AlN, SiC, SiN.sub.x, Al.sub.2O.sub.3, ZrO.sub.2, metal, such as Cu, Ni, stainless steel, or SiO.sub.2, and wherein the substrate further comprises an amorphous coating that does not have a crystal form and provides the base for the growth of crystals; the amorphous coating comprising an amorphous oxide or an amorphous nitride selected from the group of SiO.sub.2, AlO.sub.x, or SiO.sub.2/SiN.sub.x/SiO.sub.2 stacks, silicate glass, AlO.sub.x (1<x<2), SiN.sub.x (1<x<2), SiC, AlN, SiON, RuO.sub.x (1<x<2), ZrO.sub.x (1<x<2), MgAl.sub.2O.sub.4.
6. The device of claim 4 wherein the textured layer is deposited onto an amorphous coating, the textured layer having a thickness in the range of 1 to 200 nm, preferably 30 to 50 nm, wherein the textured material is formed from one or more of Ti, Al, Ir, Ru, Mg, Ca, Cr, Fe, Ni, Sr, Ba, Zn, V, Mn, Ce, Co, or Sn, wherein the metals oxidize, fluorinate or form a nitride to form a {100} textured rutile or {0001} textured wurtzite film for a lattice match to the first electrode.
7. The device of claim 4 wherein the textured layer is formed from one of the group of TiO.sub.2, SnO.sub.2, MgO, CaO, SrO, FeO, ZnO, NiO, CeO, CoO, TiN, AlN, CrN, BN, GaN, CaF.sub.2, and wherein in the case of {100} rutile and the case of {0001} wurtzite, the planes lie in the growth plane.
8. The device of claim 4 wherein the textured layer is approximately 1 nm to 300 nm thick and wherein the texture layer is the result of an oxidation anneal and forms a rutile structure which facilitates the formation of a granular structure.
9. The device of claim 4 wherein the first electrode layer has a thickness in the range of 10 to 500 nm, preferably within the range of 30 to 100 nm, and wherein the crystal structure is formed by sputter deposited epitaxy, and wherein the electrode layer material comprises one or more of Pt, Ir, Ru, Pd, Au, Ag, Cu, and preferably has a face-centered-cubic crystal structure and is {111} textured.
10. The device of claim 1 wherein the seed layer is one of a textured oxide having perovskite structure and a thickness in the range of 1 to 200 nm, preferably 20 to 50 nm.
11. The device of claim 1 wherein the seed layer is PbTiO.sub.3 and one of rapid ramp and double ramp anneals are performed on each of the PbTiO.sub.3 seed layer and the electrode layer, and wherein the PbTiO.sub.3 seed layer is formed with excess Pb in the range of between approximately 0% to 20%.
12. The device of claim 1 wherein the seed layer comprises PbTiO.sub.3 with excess Pb in the range of between approximately 0% to 20%, and wherein the seed layer is formed by chemical solution deposition, spinning for a predetermined period of time, pyrolizing at a temperature ranging from approximately 300° C. to 450° C., and rapid thermally annealing at a temperature in the range of approximately 600° C. to 700° C.
13. The device of claim 1 wherein the seed layer comprises one of PbTiO.sub.3, (PbLa)TiO.sub.3, SrTiO.sub.3, BaTiO.sub.3, PbNiNbO.sub.3, Pb(Zr.sub.xTi.sub.1-x)O.sub.3 (0≦x≦1.0), PbYbNbO.sub.3, PbScTaO.sub.3, and wherein the seed layer is a polycrystalline {001}-textured perovskite seed with RC-FWHM≦10° and wherein the volume of {100}-textured grains is greater than 90% and the volume of {001}/({001}+{100})>80%.
14. The device of claim 1 wherein the at least one ferroelectric layer comprises Pb(Zr.sub.x Ti.sub.1-x)O.sub.3, wherein x is less than or equal to one and wherein the ferroelectric layer comprises a perovskite crystal orientation having a {001} orientation and wherein the {001} planes lie parallel to the growth plane.
15. The device of claim 1 wherein the textured layer comprises titanium deposited at room temperature that is oxygen annealed at a temperature ranging from approximately 600° C. to 800° C., preferably 750° C., to convert the Ti to TiO.sub.2, the TiO.sub.2 acting as a seed layer for {111} Pt nucleation with a full width half maxima (FWHM) between 1.7°-2.3°.
16. The device of claim 15 wherein the first electrode comprises an approximately 50 nm to 500 nm Pt film deposited at around 500° C. using a sputter deposition process with a substrate heater to produce highly {111} textured Pt providing a TiO.sub.2/Pt template for {111} textured PZT film growth.
17. A method of making a piezoelectric device comprising: providing a substrate; coating the substrate with an amorphous coating; growing a crystalline textured layer on the amorphous coating; the textured growth resulting in granular regions; epitaxially growing a first electrode comprising a thin layer of metallic material having a crystal lattice structure divided into granular regions; the granular regions of the textured layer and the first electrode being in registration; epitaxially growing a seed layer; the seed layer being epitaxially deposited so as to form a column-like structure on top of the granular regions of the first electrode and textured layer; epitaxially growing at least one ferroelectric material layer exhibiting spontaneous polarization on the seed layer; the ferroelectric material layer, the seed layer, and first electrode each having granular regions in registration with the preceding granular region; the ferroelectric material growth resulting in a high degree of polarization normal to the growth plane.
18. The method of claim 17 further comprising growing a second electrode on the ferroelectric material layer, the second electrode having a thickness in the range of approximately 10 nm to 500 nm and wherein the second electrode comprises one or more of Pt, Ir, Ru, Pd, Ni, Au, Cu, Ag, IrO.sub.2, RuO.sub.2, LaSrCoO.sub.3, SrRuO.sub.3, LaNiO.sub.3, In.sub.xSn.sub.1-xO.sub.2(0≦x≦1.0).
19. The method of claim 17 wherein the step of epitaxially growing at least one ferroelectric layer comprises maintaining the crystal planes within column-like structure of the ferroelectric material substantially parallel to the growth plane to provide optimum spontaneous polarization perpendicular to the growth plane and wherein the granular regions of the seed layer, at least one ferroelectric layer and first electrode are in registration such that the columns in the ferroelectric layer extend from the granular regions of the seed layer, and the granular regions of the seed layer extend from the granular regions of first electrode, and wherein the crystallographic planes within the granular regions and the column-like structures are substantially planar to the growth plane with a tilt of less than or equal to approximately 10 degrees from the growth plane, and wherein the crystal orientation within the ferroelectric material layer is predominately {001}.
20. A ferroelectric device comprising: a substrate; a textured layer; a first electrode comprising a thin layer of metallic material having a crystal lattice structure divided into granular regions; at least one PZT layer exhibiting spontaneous polarization epitaxially deposited on the first electrode and resulting in a PZT stylo-epitaxy; the ferroelectric material layer, and first electrode each having granular regions in which column-like structures form; the granular regions of the ferroelectric material producing a high degree of polarization normal to the growth plane.
21. The device of claim 20 wherein epitaxial depositing of the at least one PZT layer on the first electrode results in a {111} PZT stylo-epitaxy.
22. The device of claim 20 wherein epitaxial depositing of the at least one PZT layer on the first electrode results in a {001} PZT stylo-epitaxy.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) The embodiments herein will be better understood from the following detailed description with reference to the drawings, in which:
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DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
(73) The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. However, this invention should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, the thickness of layers and regions may be exaggerated for clarity. Like numbers refer to like elements throughout. As used herein the term “and/or” includes any and all combinations of one or more of the associated listed items.
(74) The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the full scope of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
(75) It will be understood that when an element such as a layer, region or substrate is referred to as being “on” or extending “onto” another element, it can be directly on or extend directly onto the other element or intervening elements may also be present. In contrast, when an element is referred to as being “directly on” or extending “directly onto” another element, there are no intervening elements present. It will also be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present.
(76) It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the present invention.
(77) Furthermore, relative terms, such as “lower” or “bottom” and “upper” or “top,” may be used herein to describe one element's relationship to other elements as illustrated in the Figures. It will be understood that relative terms are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. For example, if the device in the Figures is turned over, elements described as being on the “lower” side of other elements would then be oriented on “upper” sides of the other elements. The exemplary term “lower”, can therefore, encompass both an orientation of “lower” and “upper,” depending of the particular orientation of the figure. Similarly, if the device in one of the figures is turned over, elements described as “below” or “beneath” other elements would then be oriented “above” the other elements. The exemplary terms “below” or “beneath” can, therefore, encompass both an orientation of above and below. Furthermore, the term “outer” may be used to refer to a surface and/or layer that is farthest away from a substrate.
(78) Embodiments of the present invention are described herein with reference to cross-section illustrations that are schematic illustrations of idealized embodiments of the present invention. The layers and/or regions illustrated in the figures are schematic in nature and their shapes are not intended to illustrate the precise shape of a region of a device and are not intended to limit the scope of the present invention. The layers are not drawn to relative scale. Moreover, variations from the shapes are to be expected. Thus, embodiments of the present invention should not be construed as limited to the particular shapes of regions illustrated herein but are to include deviations in shapes. For example, a region illustrated as a rectangle may have a variety of configurations without deviating from the present invention and/or may have tapered, rounded or curved features.
(79) Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
(80) It will also be appreciated by those of skill in the art that references to a structure or feature that is disposed “adjacent” another feature may have portions that overlap or underlie the adjacent feature.
(81) A substance which has a natural charge separation in the absence of a field is called a polar material. As used herein, the terminology “polar” in conjunction with material relates to the orientations of the polar material. Specifically,
(82) A piezoelectric develops a voltage (or potential difference) across two of its faces when compressed (useful for sensor applications), or physically changes shape when an external electric field is applied (useful for actuator applications). The dielectric constant of PZT can range from approximately 300 to 3850 depending upon orientation and doping.
(83) Lead zirconate titanate, Pb(Zr.sub.xTi.sub.(1-x))O.sub.3, (also known as PZT) exhibits piezoelectric properties and is used to create large force, large displacement actuators and sensors. PZT is one of the most economical ceramics that exhibits a high piezoelectric coefficient, allowing for the use of lower voltages to achieve the same actuator performance metrics. It is highly desired to achieve highly {001} textured PZT (52/48). Proper control of the crystalline texture allows an increase in the piezoelectric stress constant as shown by N. Ledermann, et. al. “Textured, piezoelectric Pb(Zr.sub.x,Ti.sub.(1-x))O.sub.3 thin films for MEMS: integration, deposition, and properties.” Sensors and Actuators A 105, 162 (2003), with random order PZT (52/48) −e31,f of ˜7 C/m.sup.2 and (100) oriented PZT (52/48) exhibiting 12 C/m.sup.2, close to 60%. These improvements will result in substantial improvements in device performance including lower actuation voltages, higher force actuation, and lower power consumption. Through the use of a chemical solution derived PbTiO.sub.3 seed layer based on the work of Paul Muralt et. al. “Texture Control of PbTiO.sub.3 and Pb(Zr,Ti)O.sub.3 Thin Films with TiO.sub.2 Seeding.” Journal of Applied Physics Vol. 83, Issue 7, pp. 3835-3841 (1998), combined with optimal processing conditions for the solution chemistry, platinum (Pt) electrode texture, and rapid thermal annealing (RTA) conditions of the PZT films, PZT (52/48) thin films having a {001} texture in excess of 95% are achievable.
(84) The piezoelectric coefficient of PZT is inherently linked to its crystalline structural quality. The highest magnitude piezoelectric coefficients are observed at the PZT morphotropic phase boundary (MPB), shown diagrammatically in
(85) Highly beneficial results have been obtained from achieving highly {001} textured PZT (52/48). Proper control of the crystalline texture provides a 30-50% increase in the piezoelectric stress constant as shown by Ledermann et. al. with random order PZT (52/48) −e31,f of ˜7 C/m.sup.2 and (100) oriented PZT (52/48) exhibiting 12 C/m.sup.2, close to 60%. These improvements result in substantial improvements in device performance including lower actuation voltages, higher force actuation, and lower power consumption.
(86) Experiment/Calculations
(87) Sample Preparation
(88) As an example of a preferred embodiment preparation, a 100 mm diameter, (100) silicon (Si) wafer 11 is coated with 500 nm of thermally deposited silicon dioxide (SiO.sub.2) thin film 12. Next, a bottom electrode 13 can be sputter deposited onto the silicon dioxide using a Unaxis Clusterline 200 deposition system. Initial testing involved a bottom electrode comprising a bi-layer of (200 Å) Ti/(850 Å) Pt (referred to hereon as Ti/Pt) where both metal layers may be sputter deposited at approximately 500° C. (see layers 13, 15 in
(89) After the Ti deposition, an oxygen anneal was performed at approximately 750° C., which may be performed, for example, in a Bruce Technologies tube furnace, to convert the Ti to TiO.sub.2. The TiO.sub.2 (shown as 14 in
(90) Chemical solution deposition (CSD) of the PbTiO.sub.3 seed layer 16 and PZT (52/48) were used to deposit the piezoelectric thin films onto the metalized silicon substrates. CSD processing allows for stoichiometry control, reduced processing temperatures, and is relatively cost effective for development and mass production. The CSD solutions were prepared using a process modified from that originally described by K. D. Budd, S. K. Dey, & D. A. Payne. “Sol-Gel Processing of PbTi03, PbZr03, PZT, and PLZT Thin Films.” Electrical Ceramics, Br. Ceram. Proc., 107-121, (1985) (hereby incorporated by reference).
(91) A 30% lead (Pb)-excess PbTiO.sub.3 (labeled as PT seed layer 16) was prepared by mixing Lead (III) Acetate Trihydrate from Puratronic with 2-Methoxyethanol (2-MOE) from Sigma Aldrich. It was then refluxed for 20 minutes at 120° C. with flowing nitrogen (N.sub.2) in a Heidolph Laborata 4000 rotary evaporator. A vacuum distillation step was performed to remove impurities, lowering the pressure of the rotary evaporator to between 280-330 mbar, depending on humidity levels, until a white foam appears. Titanium (IV) n-Isopropoxide (70 weight % in n-propanol) from Alfa Aesar was mixed with 2-MOE and allowed to stir on a magnetic spinner while the Pb solution was refluxed and distilled. Once the Pb solution finished the vacuum distillation step, the Ti solution was combined with the Pb solution and was allowed to reflux for 210 minutes. A second vacuum distillation at 925 mbar was performed followed by a N.sub.2 purge. The solution was transferred to a storage container where 4 volume % formamide was slowly added to the solution to act as a drying control agent. The final solution was stirred overnight using a magnetic stirrer.
(92) For preparation of the PZT solution, a similar process may be used as that used to make PbTiO.sub.3. The difference is the addition of the Zirconium (IV) n-propoxide precursor from Alfa Aesar to the Titanium (IV) n-Isopropoxide and 2-Methoxyethanol solution. This mixture was allowed to stir while the Pb solution was refluxed and distilled. Both solutions were then combined in the glovebox and the procedure described in the foregoing was followed.
(93) The PbTiO.sub.3 16 and PZT 17 films were deposited via a chemical solution deposition process using combinations of liquid dispensing the solution, wafer spinning, pyrolysis, and annealing (see
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(95) Results and Discussion
(96) PbTiO.sub.3 Tests Using a Ti/Pt Bottom Electrode—
(97) The procedure to test the PbTiO.sub.3 required two different solutions, one with acetic acid and one without. Other researchers have reported improved properties in PbTiO.sub.3 solutions with an added 7 volume % acetic acid. The acetic acid acts as a catalyst during the fabrication of the PbTiO.sub.3 solution and also compensates for the lead loss during thermal treatments.
(98) Upon deposition of the PbTiO.sub.3 solution, with or without the addition of acetic acid, the RTA conditions were examined. Temperatures of 600° C. and 700° C. with dwells of 60 seconds in an atmosphere of flowing O.sub.2 with a rate of 5 sccm were studied to ensure full crystallization of the film. Following the PbTiO.sub.3 layer crystallization step, 5000 Å of PZT (52/48) (labeled as 17 in
(99) The initial seed layer tests involved coating PZT (52/48) thin films onto 25 cm square substrates. After deposition, simple 500×500 μm square capacitors were fabricated to measure the electrical properties as a function of the different PbTiO.sub.3 seed conditions tests. After examining the results, the two best PbTiO.sub.3/PZT (52/48) conditions were chosen to fabricate cantilever arrays and thus determine the effective piezoelectric coefficient, e.sub.31,eff, by measuring the quasi-static piezoelectric induced deformation of thin film cantilevers. Initially, the different processing conditions were characterized by examining the crystallographic structure of the PZT thin films by using x-ray diffraction (XRD) collected on a Rigaku0 Ultima III Diffractometer with Bragg-Brentano Optics.
(100) X-ray crystallography is a method of determining the arrangement of atoms within a crystal, in which a beam of X-rays strikes a crystal and causes the beam of light to spread into many specific directions. From the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. X-ray diffraction results in an x-ray beam scattered off the planes of a crystal which creates an interference pattern. To measure an interference maximum, the angle of incidence must be equal to the angle of reflection and the difference in the beam's path from a source to an observer for neighboring planes has to be equal to an integer multiple of the wavelength, the path difference being:
2d sin(θ)=mλ for m=1,2 . . . .
where d is the spacing between diffracting planes, θ is the incident angle, n is any integer, and is the wavelength of the beam. These specific directions appear as spots on the diffraction pattern called reflections. Thus, X-ray diffraction results from an electromagnetic wave (the X-ray) impinging on a regular array of scatterers (the repeating arrangement of atoms within the crystal). An x-ray diffraction scan is shown in
(101) The XRD results revealed a mixed texture of (001) and random grain orientations in a 2500 Å PbTiO.sub.3 thin film (
(102) Even with the random orientation and mixed texturing in the PbTiO.sub.3 layer, the resulting PZT XRD data shows significant improvement in {001} PZT (52/48) orientation. Lotgering factor (f) calculations (equation 1) were performed that demonstrated an improvement from f(001/100)=59.24% texturing to 86.67% (001/100) texturing with the PbTiO.sub.3.
(103) For the different growth conditions, very small changes in the polarization-voltage hysteresis loops were observed. Small subtle changes in the saturation polarization, remnant polarization, and coercive fields are attributed to sample variances and are within the assumed standard deviation for these measurements. In contrast, the dielectric properties for the different films shows more significant changes between the processing conditions. The two PbTiO.sub.3 solutions that were selected for additional testing were the 700° C. and 600° C. annealed samples with acetic acid due to their higher dielectric constants of 1299 and 1354, respectively.
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(106) TABLE-US-00001 TABLE 1 Cantilever displacement values (m) and the effective piezoelectric coefficient data (e.sub.31,eff). Ti/Pt/ Ti/Pt/ Ti/Pt/PZT 600° C. 700° C. Volts (52/48) PbTiO.sub.3/PZT PbTiO.sub.3/PZT (V) Y (μm) e.sub.31,eff Y (μm) e.sub.31,eff Y (μm) e.sub.31,eff 20 15 −4.4 32.3 −8.9 33.8 −9.3 10 12.6 −7.4 24.8 −13.7 21.4 −11.8 5 8.7 −10.2 14.9 −16.5 15.6 −18.2 2 6.3 −18.4 11.8 −32.7 12.1 −33.3 0 2.7 N/A 7.9 N/A 7.5 N/A
(107) After selecting the PbTiO.sub.3 conditions, additional 100 mm wafers were processed with the abovementioned seed layer conditions to form cantilever arrays to measure the piezoelectric induced displacement from the three smallest cantilevers (83 μm, 107 μm, and 132 μm lengths, respectively). In previous studies, higher piezoelectric coefficients have been noted in PZT (45/55) compared to PZT (52/48) due to the random crystalline texture in the PZT thin film.
(108)
(109) The Lotgering factor (f) is defined as follows:
(110)
where
(111) P.sub.O is the XRD intensity values based upon a standard
(112) P.sub.1 is the XRD intensity values based upon a standard
(113) I.sub.(001/100) is the intensity of (001) and/or (100) peaks
(114) ΣI.sub.(hkl) is the sum of all PZT peaks
(115) TABLE-US-00002 TABLE 2 Comparison of PZT (52/48) with (001)/(100) Lotgering Factors Annealing Temperature Lotgering Factor (f) % 680° C. 66.87% 700° C. 54.79% 720° C. 10.97% 740° C. 64.86%
PbTiO.sub.3 Tests Using a Ti/Pt Bottom Electrode-PZT RTA Conditions
(116) Changes in the RTA conditions will have a major impact on Pb-loss during thermal treatment that significantly affect PZT orientation. A study was performed with 9 samples of Ti/Pt/PZT and the final RTA temperature was varied by 20° C. between 580° C.-740° C. with a RTA ramp rate of 4° C./sec. At temperatures below 680° C., the pyrochlore phase is constantly present. The Pb-deficient pyrochlore phase reduces the piezoelectric properties of PZT thin films when present by pinning ferroelectric domain centers and opposes the dominating polarization.sup.i. The best orientations were observed at 700° C. and 720° C. For these two temperatures of interest, 700° C. shows a diminished (110) and larger (111) PZT peaks, whereas at 720° C. the reverse is observed.
(117)
(118) PbTiO.sub.3 Tests Using a TiO.sub.2/Pt Bottom Electrode
(119) To further improve the PZT texture, the bottom electrode metallization was changed from Ti/Pt to TiO.sub.2/Pt. The higher quality Pt results in significant improvements in the PZT orientation with the highly {111}-texture Pt. See, for example, Provisional Application No. 61/547,879 entitled “Thermally Oxidized Seed Layers for the Production of {001} Textured Electrodes and PZT Capacitors,” by Dr. Glen Fox, et al., hereby incorporated by reference. Furthermore, as shown in
(120) TABLE-US-00003 TABLE 3 Lotgering factors (f) of the varying thin films using PZT (52/48). Lotgering Factor Lotgering Factor Sample Layers (f.sub.(001)/(100)) % (f.sub.(111)) % Ti/Pt/PZT 59.24% 8.07% Ti/Pt/PbTiO.sub.3/PZT 86.67% 14.62% TiO.sub.2/Pt/PZT 10.33% 50.38% TiO.sub.2/Pt/PbTiO.sub.3/PZT 96.17% 16.02%
(121)
(122) RTA Ramp Rate PZT with TiO.sub.2/Pt Bottom Electrode Studies
(123) With improved conditions for the PbTiO.sub.3 and TiO.sub.2/Pt identified, optimization of the thermal treatment of PZT was studied. It is known that slow RTA ramp rates of 4° C./sec can be performed as well as fast ramp rates of over 100° C./sec or even furnace annealing of the PZT to acquire high orientation control. The effect of fast ramp rates was studied as well as the effect of varying Pb-excess in PZT solutions. PZT films deposited from solutions with 8, 10, and 15% Pb-excess were analyzed under the following RTA ramp processes. The two RTA ramp processes selected were “Rapid Ramp” (RR) and “Double Ramp” (DR). In the rapid ramp process, the sample temperatures were ramped up and down as fast as possible using a A.G. Associates Heatpulse 610 RTA. For these experiments, the temperature ramp (up and down) was 199° C./sec with a dwell at 700° C. for 60 seconds. Similarly, in the double ramp process, the temperature ramp (up and down) was 199° C./sec with a dwell 1 at 550° C. for 2 minutes followed by a ramp and dwell 2 at 700° C. for 30 seconds. The anneal at 550° C. allows the PZT to crystallize at low temperature under conditions that result in reduced PbO evaporation from the sample surface but still provide the definition of the crystalline texture. The 700° C. portion of the anneal allows grain growth and removal of other growth defects. In both cases, the software control of the RTA was terminated once the samples cooled to 350° C. XRD data was gathered to determine the best orientation in PZT films under the conditions described.
(124) TABLE-US-00004 TABLE 4 Different RTA processes studied. Ramp Hold Temp. and Ramp RTA Process Rate Up Time Rate Down Slow Ramp 4° C./sec 700° C. for 60 sec 4° C./sec Rapid Ramp (RR) 199° C./sec 700° C. for 60 sec 199° C./sec Double Ramp 199° C./sec 550° C. for 120 sec Second Ramp Up (DR) 199° C./sec 700° C. for 30 sec 199° C./sec
(125)
(126) Performing the rapid ramp and double ramp anneals on samples with the optimized bottom electrode and PbTiO.sub.3 seed layer, it was determined that the 10% Pb-excess using a rapid ramp and 8% Pb-excess using a double ramp showed the highest (001) orientation and the greatest reductions in both the (110) and (111) PZT peaks. As illustrated in
(127)
(128)
(129) Similar to earlier experiments, electrical data was recorded on simple capacitors fabricated using wafers coated with PZT processed using the 10% Pb-excess DR and RR annealing conditions on the TiO.sub.2/Pt bottom electrodes. From these 500×500 μm square capacitors, the dielectric constants were calculated for samples processed under both annealing conditions. As show in Table 7, the 10% Pb-excess under the DR conditions showed an approximately 13% higher dielectric constant compared to the RR conditions. The values in Table 7 are average values taken on 6 different capacitors on 8 samples (4 samples under the DR conditions and 4 under the RR conditions) to demonstrate reproducibility.
(130) TABLE-US-00005 TABLE 7 Dielectric Constant Determination in 10% Excess PZT (52/48) with PbTiO3 seed layer 52/48 Double Ramp w/Seed 10% Pb Excess 700C RTA Thickness Capacitance Dielectric Pr+ Pr− (μm) (nF) tan δ Constant 17.21 15.65 0.5 5.943 0.070 1343 16.87 15.37 0.5 5.27 0.066 1190
(131) Initial cantilever displacement data revealed promising results in the efforts to achieve high displacement with lower actuation voltage devices. Comparing 10% Pb-excess PZT (52/48) under Double Ramp and Rapid Ramp annealing conditions with and without the PbTiO.sub.3 seed layer, one can clearly see tremendous improvements from one another (
(132)
(133) In summation, the PbTiO.sub.3 seed layer has shown substantial improvements in {001} texturing in PZT (52/48) thin films. Improvements in the quality of the bottom Pt allows for proper nucleation of the PZT thin films and further improves orientation by 12.7% compared to using the PbTiO.sub.3 seed layer on a Ti/Pt electrode.
(134) The Pb-excess study provided valuable data on the effects of Pb-excess on PZT orientations. At 15% Pb-excess concentrations, (111) orientations begin to resurface compared to 10% Pb-excess concentrations. This shows that after annealing 10% Pb-excess, the PZT (52/48) is at or near stoichiometry compared to previous solutions of 8% Pb-excess. With the 10% Pb-excess we are accounting for lead loss during thermal treatments but don't have an over abundance to allow of random order phase PZT nucleation to dominate which is consistent with research from R. Burmistrova et. al., “Effect of Lead Content on the Microstructure and Electrical Properties of Sol-Gel PZT Thin Films.” Ferroelectrics 271.1 (2002): 51-56, hereby incorporated by reference.
(135) The investigation of the annealing conditions of PZT (52/48) with the PbTiO.sub.3 seed layer provided insight on preferred conditions for proper orientation control. The use of the fast ramp does not allow sufficient time for complete transformation of the PZT film. Instead, surface nucleation processes dominate film texture. The PbTiO.sub.3 allows the PZT film to nucleate along the [001] direction which propagates through subsequent PZT layers. The improved Pt limits nucleation of (110) and (111) PZT thus allowing even greater 001/100 orientation in the film when combined with the PbTiO.sub.3 seed layer.
(136) Comparison studies of cantilever deflections using the optimized bottom electrode and PbTiO.sub.3 seed layer in comparison to the non-textured Ti/Pt bottom electrode with and without PbTiO.sub.3 seed layers are of interest. Using the pyrolysis conditions of PZT (52/48) raises an option to further suppress the (111) orientation in PZT. Between 300° C. and 500° C. the pyrolysis conditions of sol-gel PZT films greatly influences the (111) and (100) orientations. At temperatures above 400° C., (100) orientations are expected to dominate, whereas at temperatures below 400° C., (111) orientations are observed. In accordance with the principles of the present invention, a stylo-epitaxial structure produces a PZT capacitor structure with a high degree of remanant polarization normal to the substrate surface resulting in a maximum efficiency of polarization switching and piezoelectric coefficients. Stylo-epitaxy is defined as a polycrystalline columnar (stylo) microstructure that consists of epitaxial crystalline layers within each individual column or grain. Generally speaking, stylo-epitaxy crystallographic structure comprises a plurality of column-like structures or crystallites adjacent to each other, wherein each layer within a column-like structure or crystallite exhibits a specific epitaxial relationship to adjoining layers within the column-like structure. Although one embodiment of the stylo-epitaxial structure is presented, it can be generalized for application to other structures.
(137) A preferred embodiment uses the combination of epitaxially related seed layers to produce a polycrystalline tetragonal PZT piezoelectric and ferroelectric capacitor element with well-controlled {001}-stylo-epitaxy. The preferred structure meets the following criteria:
(138) The substrate can comprise of any material that is thermally stable in an oxygen containing environment up to at least 700° C. In an example, the substrate was (100)-oriented single crystal Si (11 in
(139) As illustrated in
(140) As illustrated schematically in
(141) As illustrated in
(142) Referring now to
(143) Referring now to
(144) Subsequently, an approximately 1 nm to 200 nm thick perovskite stylo-epitaxial layer, namely PbTiO.sub.3, having a tetragonal distortion of >1.03 (approximately) and with 0-50% excess PbO is deposited and consists of a volume fraction of {001}-oriented grains of >90% (approximately) and tilt distribution of {001}-oriented grains FWHM ≦10 deg (approximately). The excess PbO is required in order to produce the stylo-epitaxial relationship. There are at least two ways of describing the expitaxial relationship between the PbTiO.sub.3 and the Pt. The first method is (111)Pt/(001)PbO/(001)PbTiO.sub.3(Ti/O-termination) (depicted in
(145) An approximately 30 nm to 10 um PbZr.sub.1-xTi.sub.xO.sub.3 stylo-epitaxy layer with x=0.40 to 0.60 and with a PbO excess of 0 to 15% is deposited onto the PbTiO.sub.3 layer and consists of a volume fraction of {001}-oriented grains of >90% (approximately) and tilt distribution of the {001}-oriented grains of FWHM ≦10° (approximately). The epitaxial relationship is (001)PbTiO.sub.3/(001)PZT provided that the strain provides a good match of the PbTiO.sub.3 and PZT lattices. If the lattice mismatch is too large, a fraction of the PZT grains will produce a (001)PbTiO.sub.3/(100)PZT epitaxial relationship in order to reduce the strain energy of the structure. At this point in the structure, there are now 4 or 5 stylo-epitaxial layers, depending on complete or incomplete Ti oxidation, respectively, comprising each grain of the structure. The combination of homo- and hetero-epitaxial layers make a complete chain of epitaxial layers within each grain, but each columnar grain has an undefined rotation about axes normal to the epitaxial plane. (This analysis can be extended to the tetragonal/rhombohedral case.)
(146) The final layer of the structure (which may form a capacitor) is an approximately 10 nm to 300 nm thick Pt top electrode, as shown in
(147) In the preferred embodiment of
(148) The stylo-epitaxial structure can be generalized to include a wide range of materials. The substrate 11 can consist of any material that is thermally stable under the conditions used for processing the stylo-epitaxial structure. Thermally stable means that the material does not substantially oxidize or deform in a manner that does not allow the formation of the overlying amorphous layer and stylo-epitaxial structure. Substrate materials can include, but are not limited to, Si, Ge, GaAs, Al.sub.2O.sub.3, ZrO.sub.2, MgO, spinel (MgAl.sub.2O.sub.4), Yttria Stabilized Zirconia (YSZ), ZrO.sub.2 Cu, Ni, Ti, SOI, stainless steel, quartz, silicate glasses, low expansion glasses, AlN, SiC, SiN.sub.x.
(149) Optimally, the substrate 11 may be coated with an amorphous material that does not crystallize or deform plastically when exposed to the processing required to form the stylo-epitaxial structure and the amorphous coating has a surface roughness (excluding purposely formed topogaphy) of ≦10 nm rms. The amorphous coating 12 can include, but is not limited to, SiO.sub.2, silicate glass, AlOx (1<x<2), SiNx (1<x<2), SiC, AlN, SiON, RuOx (1<x<2), ZrOx (1<x<2), and MgAl.sub.2O.sub.4.
(150) A textured polycrystalline metal 13 (or 14) is deposited to form a self-seeding layer with a thickness of approximately 1 nm to 200 nm, volume fraction of oriented grains is preferably >90% (approximately) and a textured tilt distribution FWHM of preferably less than 7° (approximately). The textured metal is the first layer in the stylo-epitaxy structure and provides a textured base for each columnar or stylo-epitaxial grain. Metals can include, but are not limited to, Ti, Al, Mg, Ca, Cr, Fe, Ni, Sr, Ba, Zn, V, Mn, Ce, Co, Sn, Ru.
(151) The textured metal is thermally oxidized, nitrided or fluoronated to form a textured compound 14 that grows epitaxially on the textured metal. Materials include TiO.sub.2, SnO.sub.2, MgO, CaO, SrO, FeO, ZnO, NiO, CeO, CoO, TiN, AlN, CrN, CaF.sub.2. These crystallographically textured compound layers can also be deposited directly on the amorphous substrate coating provided that the orientation and misalignment specifications are met. The volume fraction of oriented oxide, nitride, or fluoride grains is >90% (approximately) and textured tilt distribution FWHM is less than approximately 7°. Oxidation or nitridation of the textured metal results in forming a crystalline structure that provides an epitaxial surface for growth of the subsequently deposited electrode layer and provides a base for the entire stylo-epitaxial structure. Example compounds and textures include {100}-textured rutile structure layer or {0001}-textured wurtzite structure. If oxidation or nitridation of the metal film is complete the textured compound layer becomes the initial layer in the stylo-epitaxial structure.
(152)
(153) The stylo-epitaxial Pt electrode layer 15, approximately 10 nm to 300 nm thick, may be grown by sputter deposition or any other deposition technique that can result in stylo-epitaxial growth on the textured compound layer. Electrode materials include, but are not limited to Pt, Ir, Ru, Pd, Ni, Au, Cu, Ag. The stylo-epitaxial electrode layer exhibits a volume fraction of crystallographically oriented grains >90% (approximately) and a stylo-epitaxial misalignment distribution FWHM of ≦7° (approximately). Examples of electrode stylo-epitaxial structures include, but are not limited to (100)TiO.sub.2/(111)Pt, (100)TiO.sub.2/Ir, (100)MgO/(100)Pt, (0001)AlN/(111)Pt.
(154) With reference to
(155) In the specific case of layer 16 comprising PbTiO.sub.3, the PbTiO3 may be deposited by metalorganic solution spin-on or other process, with Pyrolysis at 450° C. and crystallization at 700° C. The PbTiO3 has perovskite structure with {100}-texture RC-FWHM≦10°. The volume of {100}-textured grains >90%, and volume of {001}/({001}±{100})>80%.
(156) It is important to note that the A-site species of this first perovskite stylo-epitaxial layer is predominantly the same as the A-site species in the subsequently deposited second perovskite layer. This first perovskite stylo-epitaxial layer can be deposited by any technique such as spin-on chemical solution deposition, rf sputter deposition or MOCVD. The layer can be crystallized by a post deposition anneal or by depositing onto a heated substrate. Examples of stylo-epitaxial structures processed to this point include (100)TiO.sub.2/(111)Pt/(001)PbTiO.sub.3, (100)TiO.sub.2/(111)Pt/(001)PbNiNbO.sub.3.
(157) As depicted in
(158) Examples of stylo-epitaxial structures processed to this point include (100)TiO.sub.2/(111)Pt/(001)PbTiO.sub.3/(001)PbZr.sub.0.52Ti.sub.0.48O.sub.3, (100)TiO.sub.2/(111)Pt/(111)PbZr.sub.0.4Ti.sub.0.6O.sub.3. It should be noted that the first perovskite stylo-epitaxial layer PbTiO.sub.3 was not included in the second structure resulting in a (111)PZT stylo-epitaxial structure. It can be seen that the stylo-epitaxial approach can be extended to a range of perovskite orientations and can also be extended to include crystal structures other than perovskite. At this point the combination of homo- and hetero-epitaxial layers make a complete chain of epitaxial layers within each grain, but each columnar grain has an undefined rotation about axes normal to the epitaxial plane.
(159) The structure (which may be, for example, a capacitor) preferably has an approximately 10 nm to 300 nm thick top electrode 18. It is preferred that the top electrode is a stylo-epitaxial layer, but it is not required. If the top electrode is formed as a stylo-epitaxial layer, the epitaxial relationship to the PZT depends on the termination of the PZT layer. With Ti/O-termination, one epitaxial relationship is (001)PZT/(100)Pt. Top stylo-epitaxial electrode materials include, but are not limited to Pt, Ir, Ru, Pd, Ni, Au, Cu, Ag, IrO.sub.2, RuO.sub.2, LaSrCoO.sub.3, SrRuO.sub.3, LaNiO.sub.3,InSnO.sub.2. The stylo-epitaxial electrode layer exhibits a volume fraction of crystallographically oriented grains >90% (approximately) and a stylo-epitaxial misalignment distribution FWHM of ≦10° (approximately). Examples of stylo-epitaxial structures processed to this point include (100)TiO.sub.2/(111)Pt/(001)PbTiO.sub.3/(001)PbZr.sub.0.52Ti.sub.0.48O.sub.3/(100)Pt.
(160) The stylo-epitaxial structure can be extended to include any combination of layers or repeat units and can further be extended to include a barrier layer that encapsulates the ferroelectric/piezoelectric stylo-epitaxial capacitor structure.
(161) This stylo-epitaxy structure results in a property figure of merit, such as for d.sub.33,film of
d.sub.33,film=d.sub.33,ideal(AV.sub.001+BV.sub.100+CV.sub.111+DV.sub.Rnd)
d.sub.33,film=d.sub.33,ideal(AV.sub.001+BV.sub.100+CV.sub.111+DV.sub.Rnd)
The value d.sub.33,ideal is the piezoelectric coefficient for an ideal single crystal with epitaxial electrode interfaces and V is the volume fraction of the 001, 100, 111, and randomly oriented grains of the PZT film. The coefficients of this equation can be divided into orientation components, denote by subscript 1, and interface components, denoted by subscript 2.
A=α.sub.1α.sub.2
B=β.sub.1β.sub.2
C=γ.sub.1γ.sub.2
D=δ.sub.1δ.sub.2
Since epitaxy is not achieved at the PZT/electrode interface for the randomly oriented PZT volume fraction, it is expected that δ.sub.2<1, but since measurements of the interface coefficients are not readily available and V.sub.Rnd is generally small (<20%) it will be assumed that δ.sub.2=1 is sufficiently accurate in the first approximation. For the common case of pinning of 90° domains, δ.sub.1≈0.46 which gives D=0.46. The 001, 100 and 111 PZT/electrode interfaces are expected to be epitaxial in most cases and it will therefore be assumed that the interface coefficients α.sub.2, β.sub.2, and γ.sub.2 equal 1. The value of γ.sub.2≈0.58 for the common case of a symmetric tilt distribution of the 111 oriented grains; thus, C=0.58. Since we are assuming the case of pinned 90° domains, β.sub.1=0 resulting in B=0. The final coefficient that needs to be determined is α.sub.1, which is determined by the tilt distribution of the {001} grains. In the case that all {001} grains are ideally aligned normal to the substrate, α.sub.1=1, But in real materials, the {001} domains are distributed over a range of angles close to the normal. Any tilt away from the normal reduces the value of α.sub.1. Summarizing, the figure of merit can be calculated to a good approximation by using the equation
d.sub.33,film=d.sub.33,ideal(α.sub.1V.sub.001+0.58V.sub.111+0.46V.sub.Rnd)
Note that the induced in-plane strain x.sub.3 resulting from an in-plane electrical field E.sub.3 is expressed by the piezoelectric effect: x.sub.3=d.sub.33E.sub.3 where d.sub.33 is the longitudinal piezoelectric coefficient of PZT. Further description can be found in Zhang, Q. Q, et al., “Lead Zirconate Titanate Films for d33 Mode Cantilever Actuators,” Sensors and Actuators A 105 (2003) 91-97, hereby incorporated by reference.
Advantages
(162) Stylo-epitaxy structures provide a means for controlling the crystallographic orientation of layers without placing demands for epitaxial requirements on the substrate. In effect, the substrate is decoupled from the electrode and PZT orientation and therefore, a wide range of substrates can be employed that would be excluded from use if a standard epitaxial approach were used. Unlike the {001}-textured PZT on Ti/Pt, stylo-epitaxy preserves the epitaxial relationship between the electrode and PZT layers on a grain-by-grain basis. This ensures that the highest efficiency and reliability of the PZT properties are obtained. Stylo-epitaxy also can allow the separation of {001}-orientation development from the use of seed layers such as PbTiO.sub.3, thus allowing the use of a broader range of electrode materials and processing conditions.
(163) The epitaxial interfaces of all layers within the structure (which may be for example a capacitor) provide enhanced, electrical and reliability performance including improved, switchable polarization, remanant polarization, piezoelectric coefficients, polarization retention, and polarization cycling endurance.
(164) Stylo-epitaxy can be used to produce a variety of ferroelectric/piezoelectric crystal orientations with epitaxial electrode interfaces on the grain-by-grain level.
(165) The stylo-epitaxial structures can be produced by chemical solution deposition (CSD), sputtering and Metalorganic vapor phase epitaxy (MOVPE), also known as organometallic vapor phase epitaxy (OMVPE) or metalorganic chemical vapor deposition (MOCVD), deposition methods. The crystallographic orientations within a columnar grain are always fixed relative to each other so the structure can be used to ensure both orientation and interface quality.
(166) The use of stylo-epitaxy allows the production of capacitor devices with a higher volume fraction of oriented grains and a smaller misalignment distribution than would be achieved by relying on previously reported texturing methods.
(167) Potential Uses
(168) A stylo-epitaxial structure and process as described herein for the fabrication of ferroelectric/piezoelectric {001}-oriented PZT devices (such as capacitors) may be used, inter alia, in piezoelectric MEMS, FRAM and related integrated devices. The stylo-epitaxial structure relies on a series of hetero- and homo-epitaxial relationships between thin films to generate stylo-epitaxial structures with epitaxy on a grain-by-grain basis through the entire device thickness or a majority of the layers composing the device.
(169) Potential uses include, but are not limited to:
(170) 1) Thin film piezoelectric actuators in PZT MEMS.
(171) 2) Thin film piezoelectric sensor in PZT MEMS.
(172) 3) Non-volatile ferroelectric random access memories (FRAM).
(173) 4) Resistive memories that use conductive oxides, such as TiO.sub.2, NiO, etc.
(174) 5) Electrodes for biological and medical applications. Electrodes with different textures will likely have different activities and interactions with bio-molecules and structures.
(175) 6) Solar cells.
(176) Indicies used herein relate to Miller indices that are used in accordance with a crystallography notation system for planes and directions in crystal (Bravais) lattices. A family of lattice planes is determined by three integers h, k, and l (the Miller indices). They are written (hkl), and each index denotes a plane orthogonal to a direction (h, k, l) in the basis of the reciprocal lattice vectors. By convention, negative integers are written with a bar, as in hkl
denotes the set of all directions that are equivalent to [hkl] by symmetry. Further information can be obtained in Wikipedia.
(177) As used herein the terminology “register” in relation to a crystallographic structure means, with respect to two adjacent granular layers, the grains in a first granular layer are in registration with and contacting grains in the adjacent layer. For example, in a preferred embodiment, each ferroelectric grain is in registration with one electrode grain.
(178) The terminology perovskite structure is any material with the same type of crystal structure as calcium titanium oxide (CaTiO.sub.3), known as the perovskite structure, or XIIA2+VIB4+X2−3 with the oxygen in the face centers. The general chemical formula for perovskite compounds is ABX.sub.3, where ‘A’ and ‘B’ are two cations of very different sizes, and X is an anion that bonds to both. The ‘A’ atoms are larger than the ‘B’ atoms. The ideal cubic-symmetry structure has the B cation in 6-fold coordination, surrounded by an octahedron of anions, and the A cation in 12-fold cuboctahedral coordination. The relative ion size requirements for stability of the cubic structure are quite stringent, so slight buckling and distortion can produce several lower-symmetry distorted versions, in which the coordination numbers of A cations, B cations or both are reduced.
(179) As used herein, Piezoelectric coefficient or Piezoelectric Modulus, also known as d.sub.33, quantifies the volume change when a piezoelectric material is subject to an electric field, or the polarization on application of a stress:
(180)
where P is polarization, and σ is the stress.
(181) As used herein, texture measurements refer to measurements used to determine the orientation distribution of crystalline grains in a polycrystalline sample. A material is termed textured if the grains are aligned in a preferred orientation along certain lattice planes.
(182) As used herein epitaxy refers to the deposition of a crystalline overlayer on a crystalline substrate, where the overlayer is in registry with the substrate at a preferred orientation of the overlayer with respect to the substrate for epitaxial growth. The overlayer is called an epitaxial film or epitaxial layer. Epitaxial deposition of a layer on a substrate matches the crystalline order of the substrate.
(183) As used herein the terminology “growth plane” refers to the epitaxial growth planes. Growth planes and their crystallographic axes may be expressed as, for example, [112] (111) X/[1100] (0001) Y, where X and Y are crystal materials and the (111) and (0001) are faces and the brackets [ ] indicate crystallographic axes. For example, the perovskite crystal orientation having a {001} orientation means that the {001} planes of the perovskite crystal lie parallel to the growth plane.
(184) As used herein, the term “stylo” means, in combination with epitaxy, “column,” “pillar,” “tube,” or column-like crystal growth as shown for example in
(185) As used herein the terms columns or column-like structures refer to the column-like structures grown on top of granular regions. The column-like structures and granular regions are substantially coextensive.
(186) As used herein the terminology thin film is a layer of material ranging from fractions of a nanometer (monolayer) to several micrometers in thickness.
(187) As used herein the terminology “rutile” refers to a mineral composed primarily of the preferred polymorph of titanium dioxide, TiO.sub.2. Rutile is the most common natural form of TiO.sub.2.
(188) As used herein the terminology “perovskite” means is the crystal structure, as depicted in
(189) As used herein, the expression full width at half maximum (FWHM) is an expression of the extent of a function, given by the difference between the two extreme values of the independent variable at which the dependent variable is equal to half of its maximum value.
(190) As used herein the terminology “crystallites” refer to small, microscopic crystals that, held together through highly defective boundaries, constitute a polycrystalline solid. Crystallites are also referred to as grains.
(191) The foregoing description of the specific embodiments are intended to reveal the general nature of the embodiments herein that others can, by applying current knowledge, readily modify and/or adapt for various applications such specific embodiments without departing from the generic concept, and, therefore, such adaptations and modifications should and are intended to be comprehended within the meaning and range of equivalents of the disclosed embodiments. It is to be understood that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Therefore, while the embodiments herein have been described in terms of preferred embodiments, those skilled in the art will recognize that the embodiments herein can be practiced with modification within the spirit and scope of the appended claims.