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An alternative micro-area X-ray diffraction method for

residual stress measurement of Pb(Zr,Ti)O3 film

F. Yang a,b,, W.D. Fei b, Z.M. Gao c, J.Q. Jiang a

a School of Materials Science and Engineering, Southeast University, NanJing 211189, P.R. Chinab School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, P.R. China

c School of Chemistry, Jilin University, Chang Chun 130012, P.R. China

Received 25 March 2007; accepted in revised form 29 April 2007

Available online 10 May 2007

Abstract

An alternative X-ray diffraction method for micro-area residual stress measurement was proposed by means of the analysis of a single

diffraction ring, which was performed on a laboratory X-ray microdiffraction system equipped with a 2D planar detector. The microdiffraction

experiments were employed to evaluate the residual stress in solgel-derived Pb(Zr,Ti)O3 film before and after Ag electrode deposition. The

tensile stresses of about 2.3 GPa and 1.2 GPa were calculated in the micro-area of film without and with electrode, which was related to a top

electrode stress relaxation effect.

2007 Elsevier B.V. All rights reserved.

Keywords: XRD2; Solgel; Residual stress; Ag electrode

1. Introduction

Residual stress is one of the important features that deter-

mine the performance of structural and functional materials [1].

For solid films, residual stress is especially obvious due to great

thermal mismatch and/or lattice mismatch between film and

substrate. Excessively large residual stress in the films may

cause delamination and/or cracking. Residual stress plays such

a significant role in film behavior that many researches have

been initiated to measure and modulate it in the films.

In particular, the advantage of Pb(Zr,Ti)O3 (PZT) thin filmsin favorable piezoelectric and ferroelectric properties has made

them good candidates for the Micro-electromechanical Systems

(MEMs) and nonvolatile ferroelectric random access memories

(FRAM). It has been pointed out that residual stress could have

crucial influence on PZT films structure and properties. Shaw

et al. reported that the degradation of permittivity and remanent

polarization was ascribed to the presence of residual stress in

PZT film [2]. Another example of the effect of residual stress on

ferroelectric properties of solgel derived PZT film was

discussed by Garino et al. [3], in which an increase of the

dielectric constant (by 2%) and remanent polarization (by 11%)

in film was observed, while the residual tensile stress was

lowered by about 30%. Therefore, it is essential to understand

the role of residual stress in PZT films in order to improve film

performance.

Indeed, the effect of the residual stress in micron scale on the

resulting dielectric and ferroelectric properties of PZT filmsshould also be considered in view of the reducing planar

dimension in the microfabrication and FRAM applications. In

recent years, there have been lots of researches on the residual

stress in PZT films [4,5]. And a growing attention has fell into

the category of micron scale structure and residual stress in the

films, especially in the areas of top electrode. It has been found

that the difference of stress state in micron scale area of PZT

films led to the obvious discrepancy of ferroelectrics [6].

Moreover, the study of surface treatment effects on thickness

dependence of Pb(Zr0.52Ti0.48)O3 capacitors has indicated that

it is not intrinsic but extrinsic effect, such as interfacial or

Available online at www.sciencedirect.com

Surface & Coatings Technology 202 (2007) 121125

www.elsevier.com/locate/surfcoat

Corresponding author. School of Materials Science and Engineering,

Southeast University, NanJing, 211189, P.R. China. Tel./fax: +86 25 52090630.

E-mail address: yang_fan@seu.edu.cn (F. Yang).

0257-8972/$ - see front matter 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.surfcoat.2007.04.125

mailto:yang_fan@seu.edu.cnhttp://dx.doi.org/10.1016/j.surfcoat.2007.04.125http://dx.doi.org/10.1016/j.surfcoat.2007.04.125mailto:yang_fan@seu.edu.cn

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strain effect related to electrode that provides a reasonable

interpretation on the degradation of the remanent polarization

[7]. As the top electrode would exert considerable effect on the

micro-area stress state, the evaluation of stress state in top

electrode areas would thereafter help to understand electrode

effect on the properties of Metal/PZT/Metal structure.

Many experimental techniques have been developed tomeasure the amount of stress/strain in thin films, amongst

which X-ray diffraction (XRD) is a well-known non-destructive

method that is routinely employed to determine the level of

residual stress in the films [810]. But the conventional XRD

technique can only allow determining the average stress

throughout the entire film as the illuminated area is millimeter

scale. The curvature method using Stoney's equation is also

mentioned in the residual stress analysis of films [11]; never-

theless, it fails to evaluate the local stress in micro area. Addi-

tionally, due to the effects of both underlying layers and

interdiffusion among layers, residual stress of the films depo-

sited on the heterostructure substrate could not be determinedfrom the wafer curvature.

Recently, a bidimensional (2D) X-ray diffraction technique

(XRD2) has developed and theoretically shed light on the so-

called mesoscale (0.1 m100 m) stress analysis in thin film

and coatings [12]. By combining the use of X-ray microdiffrac-

tion with the fast large-area two-dimensional-detector technol-

ogy, this technique allows for the orientation and strain/stress

mapping of polycrystalline thin films with micrometer/sub-

micrometer spatial resolution. When the monochromatic beam

is used, the resulting diffraction patterns recorded in 2D detector

are Debye-Schereer ring patterns, resulting from the scatter-

ing of thousands of grains. Because the presence of residual

stress in the film will result in the deformation of Debye rings,the strain/stress can be evaluated through the Debye ring

analysis [13]. To obtain the stress/strain information, Debye

ring is taken and analyzed at each point of map, in which each

part of Debye ring has to be assigned to another orientation of

the diffraction vector with respect to the sample reference

system. In the research given by Gelfi et al. [14,15], X-ray

diffraction Debye ring analysis for stress measurement

(DRAST) based on XRD2 diffractometer was demonstrated,

by combining a collimator with a diameter of 300 m with a

cylindrical image plate(IP) detector, and the residual stresses in

TiN and LaCoO3 films were well determined.

In this article, an alternative micro-area residual stressmeasurement method is described based on the XRD2 dif-

fractometer, equipped with a planar 2D detector instead of the

cylindrical 2D detector mentioned in Ref. [14]. By using this

method, the residual stress in PZT film prepared by the solgel

route is explored, and the influence of top electrode on the

micro-area residual stress is discussed as well.

2. Experimental procedure

The Pb(Zr,Ti)O3 thin film of nominal morphotropic phase

boundary (MPB) composition was prepared on Pt/Ti/SiO2/Si

substrate by a modified solgel route, in which Zr/Ti ratio of 50/

50 was verified by EDS analysis. The as-derived film with the

thickness of about 200 nm was crystallized at 650 C under

ambient atmosphere. The elaborate procedure of fabricating

PZT film has been previously published [16]. The Ag top

electrode was deposited by DC sputtering on the condition of

the sputtering pressure of 0.5 Pa and the sputtering current of

0.1 A, where the base pressure was 1.010E3 Pa. The thick-

ness of Ag electrode is 200 nm, with diameter of 0.3 mm.The XRD2 experiments with a fixed incidence angle of 18

and exposure time of 60 s were performed in a Bruker AXS D8

Diffractometer, operated at 40 kV and 35 mA using CuK

radiation. The microbeam with illuminated spot size of 100 m

was carried out through a long collimator, and meanwhile

diffraction rings were collected as XRD2 images by a rec-

tangular planar detector. For comparison, four micro-areas of

PZT film were analyzed (see Fig. 1), hereafter denoted as A1,

A2, A3 and A4, of which A1 and A2 referred to the illuminated

areas with Ag electrode, while A3 and A4 represented the areas

without Ag electrode. The Debye rings of the 111-diffraction in

PZT film were taken into account in the residual stress mea-surement based on XRD2 images.

3. Results and discussion

3.1. XRD2 geometry definitions

To describe the relationship between residual stress and

XRD2 measurement, it is necessary to build two coordinate

systems (O-XYZ and O-XYZ), the configuration is shown in

Fig. 2. In the scattering geometry of XRD2 measurement

(Fig. 2b), the pointO represents the X-ray illuminated zone, O

is the center of Debye rings. For convenience, O-XYZ co-

ordinate is fixed on the sample, O -XYZ coordinate is fixedon the Debye ring. The direction of vector

YOO 0 is that of the

incidence beam, withYOZ axis direction is film normal di-

rection,YOY,YOZ and

YOO 0 are in the same plane.

YO 0Y0 axis is

YOO 0 , and

YO 0X0 axis is parallel to

YOX axis.

YO 0Z0 axis lays in

the plane that is determined byYOO 0 and

YOY axis. The vector

YO 0P is parallel to

YON which defines the normal direction of the

diffraction plane. The angle between the vectorYON and

YOZ is

angle. The angle between the vectorYOY andYOO 0 is incidence

angle (), and that between the vectorYOP and

YOO 0 is

diffraction angle (2)(in O-XYZ coordinate), describing the

rotation ofYO 0P on the diffraction ring. The point P is the

Fig. 1. Top view of PZT sample, white dots show the areas illuminated by X-raymicrobeam with diameter of 100 m, while black dots are Ag top electrode.

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projection of P on the planar detector, in this case, the position

P can be determined by the two parameters, and 2.

The diffraction vectorq is defined with respect to the O-XY

Z system by 2 and angle. It is figured out from Fig. 2b thatthe principal cosines ofq vector in this reference system are:

cosv 0 sinv 1

To determine the residual stresses, nevertheless, it is necessary

to explore the deformation of interplanar spacing with respect to

the OXYZcoordinate system (sample reference system). Based

on the above coordinate system configuration, the coordinate

change can be implemented by a clockwise rotation aroundYO0X0

axis, in which the rotation angle equals to incidence angle .

Then the resulting rotational matrix is

1 0 00 cos x sin x

0 sin x cos x

0@

1A

: 2

The principal cosines of diffraction vectorq with respect to the

O-XYZcoordinate system (sample reference system) can thereof

be derived as

cosv sinx sinv cosx sinv : 3

Hereby, the inclination angle between the diffraction vector and

the surface normal, angle can be given by the following

equation:

w arccos cosx sinv : 4

3.2. Residual stress measured by micro-area XRD2 method

Firstly, the relationship between residual stress and XRD2

measurement parameters is provided as follows. If the in-plane

stress possessed a symmetry so that11=22=; assuming the

presence of a biaxial stress state in PZT film, and the normal

direction (33) as well as the shear stresses (ij) (fori orj= 1, 2,3 where ij) are zero, we have

e11 r11

E

m

Er22 r33

1 m

Er;

e33 m

Er11 r22

2m

Er;

5

where, ii and ii are the principal components of stress and

strain, v and E are the Poisson's ratio and Young's modulus of

the film. Thus, the lattice strain in direction ( ) can be

written as

ew e33 cos2w e11sin

2w

rE

1 m cos2w 1 m

6

Using differentiation of Bragg's equation, the following

equation can be obtained for the strain in the direction of:

ew 1

2coth0 2h 2h0 ; 7

where, 0 is the Bragg angle of (hkl) plane in stress-free sample.

Subsequently, combining Eq. (6) with (7), the general

equation for the residual stress calculation can be given as

2h 2tanh0r

E

1 m cos2w 1 m 2h0

2tanh0r

E1 m cos2x sin2v 2tanh0

r

E1 m 2h0

8

For brevity, the above equation can be rewritten as

2h m sin2v D 9

here,

m 2tanh0r

E1 v cos2x 10

D 2tanh0r

E1 m 2h0 11

2 versus sin2plot will be linear according to Eq. (8). The

residual stress can be obtained by determining the slope of the

linear fits between the fractional change in diffraction angle and

the term sin2.

3.3. Micro-area residual stress in PZT film

Fig. 3 displays a typical XRD2 image of the PZT film, and

meanwhile the XRD pattern of film by integrating all Debye

Fig. 2. Schematic diagram of XRD2 apparatus (a) panorama view; (b) scattering

geometry.

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rings in XRD2 image is shown as well. Among the (100), (110)

and (111) diffractions, the intensity of (111) diffraction is

highest, thus the fact indicates that there would be moderate

(111) preferred orientation in PZT film. Here, {111} diffraction

ring of PZT film is adopted for the stress measurements

according to the consideration in three perspectives. First,

intensity of 111-diffraction is comparatively high to assure the

precision. Second, the 111-diffraction is single peak withoutsplitting effect when PZT film is in ferroelectric state. At last,

the use of the (hhh) diffraction will be helpful to minimize the

crystallographic texture effect on the linearity of 2sin2

curves [17,18].

To determine the 2 value corresponding to a certain angle

( value is automatically provided during the integrate

operation in XRD2 analysis software, GADDs), the integration

within the range of two degree is performed on XRD2 image,

and the middle value of is chosen as value for the following

analysis. To derive 2sin2 plot of {111} diffraction,

interspacing of 5 is adopted on integrating the {111} Debye

ring. The resulting diffraction patterns of {111} diffraction inevery angle are corrected for Lorentzian Polarization Ab-

sorption effects and then the (111) peaks are fitted by Pseudo-

Voigt function. Consequently the residual stress is calculated by

fitting the 2 versus sin2 plots.

Fig. 4a shows the linear fits of 2sin2 in PZT film with Ag

electrode, while the linear fits of 2sin2 in PZT film without

Ag electrode are depicted in Fig. 4b. It can be seen that

satisfactory linear fits are achieved and the simulations give the

fitting slope (m) values of about 0.013 and 0.025, for the areas

with and without Ag top electrode, respectively. Moreover, the

fitting slopes of 2sin2 plots are coincident within error in

different areas with identical circumstance, e.g., A1 and A2

spots, experimentally exhibiting that residual stress measure-

ment with the alternative micro-area XRD2 method proposedabove is reliable.

According to Eq. (10), the residual stresses in micro-areas of

PZT film were obtained and shown in Fig. 5, where the isotropic

Young's modulus ofEPZT=75.5 GPa and Poisson's ratio v=0.3

are used for PZT with a composition close to the morphotropic

phase boundary [19]. It is clear from Fig. 5 that there is sig-

nificant difference in the residual stress of PZT film with and

without Ag electrode. The area without Ag electrode exhibits

larger residual tensile stress (2.30.1 GPa), while for the area

with Ag electrode, there is lower residual tensile stress (1.2

Fig. 5. Residual stresses of sol

gel-derived PZT film with and without Agelectrode.

Fig. 4. Linear fits of 2 sin2 in solgel-derived PZT film (a) with Ag

electrode; (b) without Ag electrode.

Fig. 3. Typical XRD2 image of solgel-derived PZT film, the arrows represent

the increasing direction of the angle and diffraction angle, meanwhile the

XRD pattern of PZT film by integrating all Debye rings in XRD2 image is

shown as well.

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0.1 GPa). The calculated residual stress might be overestimated,

but the variation trend of stress between the PZT film with and

without Ag electrode should be credible, that is, a Ag-electrode-

related stress relaxation effect exhibits in the film. It can be

inferred from the value of residual stress that the top electrode is

tensile, partially sharing the residual tensile stress in PZT film.

4. Discussion

According to previous analysis, the linear fits of 2sin2 in

PZT film, measured by the alternative micro-area residual stress

measurement method, are considerably satisfactory. The stress

measurement on the different zones with identical circumstance

gives the consistent results within error; and the stress mea-

surement errors are below 15%, both of which suggest that the

proposed method is credible and valuable in the micro-area

residual stress measurement. Furthermore, the method needs

only one exposure and the analysis of single Debye ring in

combination of the use of microbeam, which makes it beneficialto measure the residual stress on the surface with complex

geometry.

It is worthwhile noting that an obvious residual stress

relaxation effect takes place in PZT film after Ag top electrode

is deposited on the surface. The Ag top electrode is deposited at

room temperature with a low pressure, so the microstructures of

micro-areas of PZT film with and without Ag electrode should

be identical, namely, the evolution of microstructure in PZT

film should not be the key reason for stress relaxation.

Two factors are assumed to explain the residual stress

relaxation in PZT film with Ag top electrode. First, it is related

to the stress evolution during the growth of Ag electrode. The

growth stress in Ag electrode during sputtering would affect theunderlying PZT layer due to constraint effect, which may re-

duce the residual stress in PZT film. Second, it is supposed that

residual stress relaxation in PZT film could be ascribed to the

effect of mechanical boundary condition [20]. Other than the

free surface case in PZT film without Ag electrode, the depo-

sition of Ag electrode accounts for the variation of mechanical

boundary condition of PZT film and thereof results in the stress

redistribution in the heterostructure, i.e., Ag/PZT/Pt. As a result,

residual tensile stress in PZT film decreases by means of partial

balance between electrode and film.

It has to be figured that there is still blemish in the proposed

micro-area residual stress measurement method, since someexperimental data are a little away from the linear regression

fits, and the sin2 ranging from 0.82 to 1 is not adequately broad

compared with the traditional sin2 method. It should be

whereas considered that the shortcoming results from the usage

of the rectangular planar detector with limited size. Unlike the

cylindrical 2D detector that is able to record the full Debye ring,

planar 2D detector can only collect parts of the Debye ring in

limited range, where 2 ranges from 18 to 50 and angle is

restricted within 65 to 90.

To obtain better precision of stress measurement, alternative

ways could be considered. Debye ring in higher 2 would better

be used in the analysis for better accuracy and wider range. In

the case of (111) Debye ring, using radiation with longer

wavelength, for instance, FeK radiation, would shift the

diffraction line to a higher angle. In addition, it is beneficial to

reconfigure the set-up of 2D detector to obtain broader 2 and

range. The above mentioned improving approaches are under

investigation.

In summary, the exploration of electrode effect is necessary

for a better understanding on stress state of ferroelectric films.Additionally, it is of importance to take top electrode effect into

consideration when discussing the residual stress of piezo-

electric or ferroelectric film, as top electrode is almost always

present in practical application of the film.

5. Conclusions

Based on the XRD2 diffractometer, an alternative X-ray

diffraction method is proposed and performed in the micro-area

residual stress measurement of solgel-derived PZT film. The

mentioned technique can implement the evaluation of the

micro-area residual stresses within short time, as only oneexposure and the analysis of single Debye ring are needed. The

effect of Ag top electrode on the residual stress of PZT film is

also investigated and the XRD2 results indicate that the residual

tensile stress of 1.2 GPa in PZT film with Ag electrode is much

lower than that of 2.3 GPa in the film without Ag electrode,

which suggests that top electrode has effect on the relaxation of

micro-area residual stress.

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