Domain structure and phase transitions in epitaxial KNbO3 thin films ...

Domain structure and phase transitions in epitaxial KNbO3 thin films studied by in situ second harmonic generation measurements Venkatraman Gopalan and Rishi Raj Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853

~Received 24 August 1995; accepted for publication 21 December 1995! Epitaxial thin films of KNbO3 were deposited on SrTiO3 ~100! substrate by laser ablation. In the orthorhombic phase, the four possible domain variants in the KNbO3 ~110! film growth plane were ¯0 # iSrTiO @ 001# , @ 001 ¯# , @010#, and @ 01 ¯0 # denoted as X1, X2, Y1, determined to be KNbO3@ 11 3 and Y2, respectively. Using a fundamental beam of 1064 nm transmitted normal to the film, the second harmonic generation ~SHG! signal at 532 nm was measured and correlated to the area fractions A X1 , A X2 , A Y 1 , and A Y 2 of the four domain variants X1, X2, Y 1, and Y 2, respectively, in the growth plane of the film. At room temperature, the area fractions d A x 5A X1 2A X2 and d A y 5A Y 1 2A Y 2 were determined to be ;3.3% and ;2.2%, respectively. In-situ SHG measurements revealed the phase transitions to be 210610 °C for orthorhombic– tetragonal and 450610 °C for tetragonal–cubic transitions. In the tetragonal phase ~between 210 °C and 450 °C! the KNbO3 ^ 100& iSrTiO 3 ^ 100& . The use of SHG as a sensitive, non-destructive and real-time probe of phase transitions and evolution of domains in ferroelectric thin films is demonstrated. © 1996 American Institute of Physics. @S0003-6951~96!00710-6#

Potassium niobate is of interest due to its large electrooptic coefficient,1 non-linear optical coefficients2,3 and excellent photorefractive properties4,5 making it suitable for applications such as second harmonic generation and optical parametric oscillation. Thin films of KNbO3 have applications in integrated optoelectronic devices such as solid state blue-green laser, optical modulators, and holographic storage. The synthesis of epitaxial and stoichiometric films of KNbO3 by laser ablation has been detailed elsewhere.6,7 KNbO3 film on SrTiO3 ~100! substrate grows with a pseudocube-on-cube geometry at room temperature with KNbO 3 $100%p uu SrTiO3 ~100!, where subscript p denotes pseudo-cubic notation.7 The KNbO3 pseudo-cubic unit cell can also be represented as an orthorhombic cell with a, b, 110# p , and @001#p , respectively, and c axes along @110#p , @ ¯ and the polarization Ps uu b direction of the orthorhombic cell. In the orthorhombic notation, the film shows only ~110! growth plane. In this epitaxial geometry, there are eight possible polarization directions. They have been grouped into four domain variant pairs in the film growth plane in Fig. ¯0 # i SrTiO @001#, @ 001 ¯# , @010#, or 1~a!. They are KNbO3 @ 11 3 ¯ @ 010 # denoted as variants X1, X2, Y1, and Y2, respectively. KNbO3 shows three first order phase transitions.8 It transforms from cubic to tetragonal at 435 °C, tetragonal to orthorhombic at 225 °C, and then to rhombohedral below 210 °C. In the tetragonal phase, the polarization axis of KNbO3 can be parallel to any of the 6x, 6y, or 6z axes ~same as SrTiO3 ^ 100& ) giving six possible variants as shown in Fig. 1~b!. In this work, we shall show how second harmonic generation measurements can be used as a sensitive in situ tool to study domain variants and phase transitions in the film with temperature. Second harmonic generation measurements were done as follows: A fundamental beam of 1064 nm light from a 20 Hz,

Q-switched Nd:YAG laser is passed through a polarizer, half wave plate for rotating incident polarization! and a filter that absorbs 532 nm wavelength. The fundamental beam of 3 mm diameter and 10 mW average power is then transmitted normal to the substrate and the film. The output second harmonic ~532 nm! is passed through an analyzer and detected by a photomultiplier tube, monitored by a gated integrator and boxcar averager, interfaced to a computer. In order to study the phase transitions, a special heater was made for sample mounting with a window cut at the center of the heater for transmitted light to pass through. The sample was clamped over this window. Polar plots of SHG signal from the film were obtained as

FIG. 1. A schematic of the domain variants in a KNbO3 ~110! film in the ~a! orthorhombic phase ~b! tetragonal phase. Bold arrows are possible polarization directions. The substrate SrTiO3 ^ 100& directions are denoted as x, y, and z.

Appl. Phys. Lett. 68 (10), 4 March 1996 0003-6951/96/68(10)/1323/3/$10.00 © 1996 American Institute of Physics 1323 Downloaded¬28¬Aug¬2002¬to¬146.186.113.195.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/aplo/aplcr.jsp

follows: The sample was aligned such that the SrTiO3 @010# and SrTiO3 @001# directions of the SrTiO3 ~100! substrate were aligned with the x and y directions of Fig. 1. The incidence was along 1z ~SrTiO3 @100# direction!. The SHG signal was measured as a function of the rotating incident polarization angle, u with the y axis. The output analyzer was fixed along either y or x polarization directions. The polar plots for this system can be described by the following general equation9 I 2j v 5K 1,j ~ sin2 u 1K 2,j cos2 u ! 2 1K 3,j sin2 2 u 1K 4,j ~ sin2 u 1K 2,j cos2 u ! sin 2 u ,

~1!

where j5x or y represents the polarization direction of the output SHG. There are four fitting constants, K 1 , K 2 , K 3 , and K 4 for each polarization x and y. One can further show that cos2 G5

S

K 24,x 4.K 1,x K 3,x

DS 5

K 24,y 4.K 1,y K 3,y

do 1 5K 2,y 5 , d 32 K 2,x

S D S S D S

d 24 4 K 3,y 5 do K 1,y K 22,y

D

,

~2!

~3!

DS D DS D

dAx 4 K 3,y 5 dAy K 1,y K 22,y

K 3,x , K 1,x K 1,x , K 3,x

~4!

~5!

where G5(2 v l/c) @ n 2c v 2(n o ) 2 v )# is a phase shift in orthorhombic phase and l is the film thickness. The term n o 5 A2/„(1/n a ) 2 1(1/n b ) 2 … where n a , n b , and n c are the principle refractive indices10 along a ~5.69 Å at 25 ° C!, b ~5.71 Å!, and c ~3.97 Å! axes of the orthorhombic cell and d o 5d 151(d 331d 31)/2. The values of non-linear coefficients for bulk orthorhombic KNbO3 at room dij temperature are d 315d 155212.8 pm/V, d 325d 24 5211.3 pm/V, and d 335219.5 pm/V.11 In the tetragonal phase, G5(2 v /c)(n 2c v 2n 2a v ) where c is the polar axis of the tetragonal lattice and a the other two axes. The non-zero coefficients in tetragonal phase are d 31 , d 32 , d 33 , d 15 , and d 24 . The values of these coefficients are temperature dependent. The above equations are valid in the tetragonal phase by replacing (d o , d 32 , and d 24) by (d 33 , d 31 , and d 15), respectively. We assume a two-dimensional microstructure which implies that all domain walls are crystallographically planar and extend through the entire thickness of the film. Hence we define A X1 , A X2 , A Y 1 , and A Y 2 as the area fractions of domains variants X1, X2, Y 1, and Y2, respectively in the growth plane of the film in both orthorhombic and tetragonal phases. We also define the net area fractions of antiparallel domains d A x 5A X1 2A X2 and d A y 5A Y 1 2A Y 2 along the x and y directions, respectively. Since the ^ 100& SrTiO3 directions are crystallographically equivalent, the four domain variants are equally possible. Thus we expect A X1 1A X2 'A Y 1 1A Y 2 and the net polarizations d A x and d A y to be very small ~of the order of a few percent!.

FIG. 2. Polar plots of second harmonic generation signal ~532 nm! vs incident polarization angle ( u ) for normal incidence of 1064 nm light through a 3700 Å KNbO3 ~110! film on SrTiO3 ~100! substrate. Inset schematics show the measurement geometry.

Figure 2 shows the polar plots ~circles! and theoretical simulations ~solid lines! based on Eq ~1! for x and y output polarizations of SHG at room temperature for the orthorhombic phase. Also shown are schematics of the measurement geometries for each output polarization. Using Eqs. ~2!–~5! and the constants K i, j obtained from fitting, the material and microstructural parameters were calculated as shown in Table I. A thickness of 3700 Å was used to calculate cos G. The calculated material constant (d o /d 32 ) is consistent along x and y directions as insisted by Eq. ~3!. It is also close to the value of ;2.4 for bulk crystals of KNbO3 . The calculated material constant (d 24 /d o ) is consistent with bulk KNbO3 crystal value of ;0.42 for all cases. The calculated values of cos G for output along x and y axes are consistent with each other within their error bars as required by Eq. ~2! and are close to theoretical values calculated. The quantity ( d A x / d A y ) represents the ratio of the net area fraction bias (A X1 2A X2 ) in the SrTiO3 @010# direction to the bias (A Y 1 2A Y 2 ) in the SrTiO3 @001# direction. In absolute terms, the SHG intensity along x axis in Fig. 2~a! is proportional to an effective coefficient d 2eff5 d A 2x d 2o . Using d 11 ~0.36 pm/V! of a quartz crystal as the known reference and comparing the SHG intensity of the quartz and the film d eff was measured to be ;1.25 pm/V. Taking values of d o 5238 pm/V,11 we get d A x '6 3.3% at room temperature. Similarly, the SHG intensity along y axis in Fig. 2~b! is proportional to d A 2y d 2o . Using quartz as reference, this corresponds to d eff'0.85 pm/V which gives d A y '62.2%. Figure 3 shows the SHG output as a function of temperature. The incident polarization and the output analyzer were both fixed along SrTiO3 @100# direction ~direction x in Fig. 1, corresponding to u 590°). The second harmonic output shows a steep decrease at the orthorhombic to tetragonal transition and then gradually decreases to zero at the tetragonal to cubic transition. From the theoretical simulation of the pole figures using the above analysis, the material and microstructural parameters of Eqs. ~8!–~11! were obtained and are listed in Table I.

1324 Appl. Phys. Lett., Vol. 68, No. 10, 4 March 1996 V. Gopalan and R. Raj Downloaded¬28¬Aug¬2002¬to¬146.186.113.195.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/aplo/aplcr.jsp

TABLE I. Calculated microstructural and material parameters from Eqs. ~2!–~5!.

System ~temperature! Bulk single crystal KNbO3 25 °C KNbO3 ~110!iSrTiO3 ~100! 25 °C 100 °C 150 °C 190 °C

KNbO3 $100%iSrTiO3 ~100! 250 °C 300 °C 400 °C

~cos G!x , ~cos G!y 0.87 ~60.15, 0.68, 0.71, 0.75, 0.77,

a

Orthorhombic ~d o /d 32 ) x , (d o /d 32 ) y

Phase d 24 /d o

2.15 22.56

0.39 20.45

b

60.05! 0.84 0.84 0.88 0.89

c

b

dAx /dAy c

–

(60.1, 60.3! 2.28, 2.25 2.24, 2.38 2.33, 2.56 2.54, 2.66

(60.1! 0.47 0.44 0.40 0.40

(60.15! 1.50 1.61 1.73 1.67

~cosG) x , ~cosG) y

Tetragonal (d 33 /d 31) x , (d 33 /d 31) y

Phase d 15 /d 33

dAx /dAy

0.94, 0.95 0.82, 0.95 0.71, 0.97

2.43, 2.93 2.54, 2.56 2.35, 2.36

0.37 0.44 0.38

1.80 1.49 1.22

Calculated for thickness t50.37 mm, l50.532 nm, and n o 2n c 50.12. After Uematsu ~Ref. 2!. c W. R. Bosenberg ~Ref. 11!. a

b

Let us first consider the behavior of SHG intensity with temperature in Fig. 3. Substituting u 590° into Eq. ~1!, we get I 2x v } d A 2x d 2o for the observed intensity in the orthorhombic phase. Thus an initial decrease in the SHG intensity in the orthorhombic phase can be attributed to either a decrease in the non-linear coefficients d o or a decrease in the relative bias d A x . The coefficient d 33 in single crystals of orthorhombic KNbO3 has been reported to decrease by about 6% from room temperature to 200 °C.2 Since the domain microstructure is expected to be relatively constant until one gets close to a phase transition, the intensity variation in Fig. 3 from 25 °C up to ;200 °C mainly reflects the change in the term d 2o . The steep drop in the SHG intensity between 200 °C and 220 °C corresponds to a phase transition from orthorhombic to tetragonal structure. Substituting u 590° in the tetragonal phase, we get I 2x v } d A 2x d 233 . Here, the variants Z1 and Z2 in Fig. 1~b! have zero contribution to the SHG output. If we assume that the six variants in tetragonal phase are

equally likely, then the area fraction of each variant would be approximately 0.15. The area contributing to SHG intensity in Fig. 3 will be (A X1 1A X2 )A o '0.3A o , where A o is the total probe area ~9 mm2). Similarly in the orthorhombic phase, all four variants have equal probability of being present. Thus from Eq. ~1!, the total area contributing to SHG signal in Fig. 3~a! is (A X1 1A X2 )A o '0.5A o . Thus the area contributing to the second harmonic signal is reduced from ;0.5A o to ;0.3A o , i.e., by 40% the original probe area. Since the second harmonic power P 2v5I 2 v A o , the SHG intensity also shows a corresponding drop. This is consistent with the observed drop in Fig. 4. The second transition from tetragonal to cubic phase shows a gradual decrease in the SHG intensity until at ;440– 460°C, where it completely disappears as is expected in the cubic phase. As seen from Table I, the microstructural bias ratio remains relatively constant until 400 °C indicating that its origin is related to either defects or steps on the substrate. In conclusion, the area fractions of domain variants in the growth plane of KNbO 3 ~110! thin films on SrTiO3 ~100! substrate have been correlated to second harmonic generation ~SHG! output from the film. Using the correlation model, the ratios of nonlinear d i j coefficients and area fractions of domain variants in the film have been determined. Second harmonic generation as a sensitive in-situ tool to obtain information about domain structure and phase transitions in ferroelectric thin films has been demonstrated. P. Gunter, Opt. Commun. 11, 285 ~1974!. Y. Uematsu, Jpn. J. Appl. Phys. 13, 1362 ~1974!. 3 M. K. Chun, L. Goldberg, and J. F. Weller, Appl. Phys. Lett. 53, 1170 ~1988!. 4 P. Gunter and F. Micheron, Ferroelectrics 18, 27 ~1978!. 5 P. Gunter, Phys. Rep. 93, 199 ~1982! 6 V. Gopalan, H. Xie, W.-Y. Hsu, and R. Raj, Ferroelectrics 152, 55 ~1994!. 7 V. Gopalan and R. Raj, J. Am. Ceram. Soc. 78, 1825 ~1995!. 8 A. W. Hewat, J. Phys. C 6, 2559 ~1973!. 9 V. Gopalan and R. Raj ~unpublished!; V. Gopalan, Ph.D. thesis dissertation, Cornell University, May 1995. 10 I. Biaggio, P. Kerkoc, L.-S. Wu, P. Gunter, and B. Zysset, J. Opt. Soc. Am. B 9, 380 ~1992!. 11 W. R. Bosenberg and R. H. Jarman, Opt. Lett. 18, 1323 ~1993!. 1 2

FIG. 3. The SHG intensity as a function of temperature for incident polarization and output analyzer parallel to x ~SrTiO3 @001#! direction. Inset shows polar plots for rotating incident polarization and output analyzer fixed along x axis. Circles: experiment, Line: theoretical fit.

Appl. Phys. Lett., Vol. 68, No. 10, 4 March 1996 V. Gopalan and R. Raj 1325 Downloaded¬28¬Aug¬2002¬to¬146.186.113.195.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/aplo/aplcr.jsp