Stress Engineering and Optimization of Thick Garnet Crystal Films

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Stress Engineering and Optimization of Thick Garnet Crystal Films Grown by Pulsed Laser Deposition Timothy C. May-Smith,* Katherine A. Sloyan, Rossana Gazia, and Robert W. Eason Optoelectronics Research Centre, University of Southampton, Highfield, Southampton SO17 1BJ, U.K. ABSTRACT: We present here results indicating that stress in films grown by pulsed laser deposition (PLD) may be engineered simply by altering the growth parameters of substrate temperature and laser fluence to balance tensile and compressive stresses. Compositional and structural analysis of Gd3Ga5O12 (GGG) films grown on Y3Al5O12 (YAG) substrates, using three different PLD setups and two different ablating lasers, reveals the effects of different growth parameters on residual stress. Some stress reduction strategies were investigated, including slower heating and cooling ramp rate, and amorphous buffer layers, but changing the growth parameters of substrate temperature and laser fluence was found to have a more significant effect. To characterize the evolution of film stress as thickness increases for different laser fluences, three films were grown in stages to allow substrate curvature measurements and X-ray diffraction analysis to be performed every time the thickness had doubled (from 1 to 16 μm in thickness). The results from these experiments reveal a compressive stress that relaxes with thickness, thought to be due to lattice mismatch, and leads to the conclusion that stress in PLD grown films of GGG on YAG is a balance between lattice mismatch, thermal expansion mismatch, and ion-bombardment.

’ INTRODUCTION Several recent reports have revealed the potential of the technique of pulsed laser deposition (PLD) for the fabrication of high power miniature lasers and other optical devices using the wide range of optical garnet crystals,1-3 a selection of which are detailed by May-Smith et al. elsewhere with some relevant physical properties.3 The merits of utilizing such a material matrix for the growth of multilayered and/or microstructured optical waveguides are numerous. Using materials with the same crystal structure and similar lattice constants for multilayers makes epitaxy relatively easy to achieve and allows high quality crystals to be grown with losses as low as 0.1 dB cm-1 in Gd3Ga5O12 (GGG) films.4 As a further proof of the level of high quality layers that can be produced by PLD, there have been several reports of lasing being achieved in waveguiding films using various different laser host materials and dopants, for example Nd:GGG,5-7 Ti:sapphire,8 and most recently, Nd:(Gd,Lu)2O39 and Yb:(Gd,Lu)2O3.10 The different refractive indices of the various garnet compositions allow advanced refractive index profiles for pump-cladding or large-mode-area structures to be fabricated,11 and, as a particularly promising avenue for demonstration of complex growth capability, it should be possible to make designer index and/or dopant concentration profiles by continuously grading layers using more than one target at a time.12,13 Before such sophisticated growth designs can be realized, however, it is important to analyze the more fundamental aspects of stress associated with growth of thick monolithic garnet films for use in high-power and diode-bar-pumped laser operation. In our r 2011 American Chemical Society

experience with all GGG films whose thickness was above ∼40 μm, residual stress has inevitably led to substrate and/or film cracking or film delamination, either while the sample was cooled or later as a result of necessary postprocessing steps such as sawing and polishing. This places a practical limitation on the thickness regimes required for diode-pumped structures, where relatively large waveguide thicknesses of 50 μm or more are needed for efficient launching of pump light and applications such as selfimaging.11 Residual stress resulting from thermal expansion mismatch will affect any film growth technique that uses heated substrates for the growth of films with significantly differing thermal expansion coefficients. Direct-bonded planar laser waveguide devices can also suffer from thermal expansion mismatch when operated at a temperature that is well above the bonding temperature used. Lattice mismatch problems can be expected to arise whenever epitaxy is inherent to the growth of crystalline layers, and relaxation rates of lattice mismatch will depend upon the crystal structure and composition in use. The tolerance of stress depends on many factors, including material properties (strength, elasticity), structure design, thicknesses involved (substrate and film), and degrees of lattice and thermal expansion mismatches. Residual stress issues have been overcome in the semiconductor industry by using integrated buffer layers as one example.14 Received: September 30, 2010 Revised: February 1, 2011 Published: March 09, 2011 1098

dx.doi.org/10.1021/cg101285r | Cryst. Growth Des. 2011, 11, 1098–1108

Crystal Growth & Design

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Figure 1. Schematic of the different pulsed laser deposition setups used for the growth of films: (a) combined schematic of PLD setups 1, 2, and 3 with the main common and significantly different attributes highlighted in bubbles; (b) expanded view of one tilting target from PLD setup 3.

Alternating the mismatch of properties from positive to negative with each subsequent layer leads to an overall balanced/relaxed structure. Other approaches, some of which have been repeated in experiments here to evaluate their applicability to garnet films, include annealing (to relax lattice defects and correct oxygen concentration), slowing of heating and cooling ramp-rates (to avoid thermal-shock induced cracking), growth on amorphous buffer layers,15 and glass-underlayers16 (to relax lattice mismatch). Yet, there does not appear to be any established or accepted approach equivalent to the semiconductor buffer layer principle for the minimization of residual stress in thick oxide films and layers. The relatively thick films we grow here are atypical of those in the semiconductor industry, however, and layer thicknesses (in our experiments) can approach 5% of the substrate thickness, a critical rule of thumb value for losing the elasticity in the substrate that would otherwise allow bending without cracking.17 It is also worth noting that lattice mismatch relaxation with thickness in garnet is slower than that in semiconductor films, since the energy required to form dislocation defects is relatively higher. Residual stress is not only dependent upon lattice mismatch and thermal expansion mismatch. Factors such as crystal defects

(e.g., dislocations, impurities, oxygen fill-factor), dopant concentration, and off-stoichiometric compositions can also contribute to changing the crystal dynamics and lattice constant, and therefore the residual stress. In particular, oxygen vacancies or an excess of incorporated oxygen have been reported to significantly influence lattice constant and physical properties, for example as observed for the deposition of Y3Fe5O12 films, where the magnetic properties have been found to be critically dependent upon oxygen concentration.18,19 By deliberately decreasing or increasing oxygen concentration, it is possible to respectively decrease or increase the lattice spacing while also changing the valence state of cations from the normal 3þ to 2þ and/or 4þ. In our case, for optical and laser applications, high crystal order is required for low-loss material and the 3þ state is almost always required to avoid any negative spectroscopic effects and maximize efficiency. Tuning of oxygen concentration has therefore not been selected for experiments here. A possible side-effect of PLD, not usually considered as positive, is lattice damage due to high energy ion-bombardment, which can also contribute to residual stress in films.20 This phenomenon has been observed for oxide films grown by PLD,21 and also with other ion-based techniques such as sputtering22 and ion-assisted 1099

dx.doi.org/10.1021/cg101285r |Cryst. Growth Des. 2011, 11, 1098–1108

Crystal Growth & Design deposition.23 There are examples where this approach has been adopted previously for stress/strain engineering,24-26 but the literature appears to be lacking in reports of experimental application and verification of the idea, particularly for PLD. Since the stress contribution due to high energy ion-bombardment is almost always compressive, it may be used to reduce, balance, or override tensile stress in PLD grown films. This is the exact situation for our experiments of GGG and Gd3Sc2Ga3O12 (GSGG) film growth on YAG substrates, where the lattice mismatch and thermal expansion mismatch contributions would otherwise lead to tensile residual stress for thicknesses >10 μm. In fact, we believe that this solution may be applied to all garnets that have a higher thermal expansion coefficient than the substrate in use (e.g., YAG, which conveniently has the lowest thermal expansion coefficient out of the optical gadolinium and yttrium based garnet compositions being studied here). We report here our work to optimize the growth of thick garnet films and ideally eliminate the problem of residual stress. The ensemble of results from samples grown in different chambers and with different laser wavelengths relating to various optimization experiments (in terms of crystal quality, composition, particulate density, and film flatness) have been reanalyzed to reveal the stress behavior that results from different growth parameters. The results from separate optimization experiments performed when using different lasers and PLD apparatus will be used to highlight the effects of different deposition parameters on the residual stress within films. A qualitative description of the effects of gas pressure, target-substrate distance, substrate temperature, and laser fluence is made possible by observing how the relationship between composition and structure changes. We will also present results from a specific study of the effect of substrate temperature and report findings of experiments using potential stress reduction strategies and changing different deposition parameters to see which have the biggest effect on residual stress. Quantification of stress in thin films that results from several related factors, and where the influence of growth parameters on these mechanisms is complex, is less straightforward. Relaxation of some of these stress mechanisms with increasing film thickness presents an even more difficult problem to both analyze and solve. For example, when changing one critical parameter, such as laser fluence, it is possible to change the intrinsic stress produced in films due to ion-bombardment but also have the secondary effect of altering the rate of relaxation of stress induced as a result of lattice mismatch because of a difference in defect formation dynamics and therefore density, leading to a change in the relaxation rate with thickness, and the growth rate will also be affected. It is therefore necessary to look at the stress evolution with increasing film thickness for different fluences, rather than simply studying one thickness. Films have been grown in stages (each stage doubling the film thickness) to allow the stress to be estimated as a function of thickness. The results from three films grown using different laser fluences will be presented, revealing how influential laser fluence is in determining the balance that may be struck between the different contributors to residual stress. Although our results all focus on the growth of GGG on YAG, we expect our findings will also be similarly applicable to other garnet films and substrate combinations with PLD.

’ EXPERIMENTAL SECTION The results reported here encompass films of GGG and Nd:GGG (1-2% at.) that have been grown on YAG substrates (with dimensions

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10.0 10.0 1.0 mm3) using two different lasers (KrF 248 nm excimer and 266 nm frequency-quadrupled Nd:YAG) and three different PLD setups. Figure 1a shows a schematic of the setup used with the common and significantly different attributes highlighted. PLD setup 1 consisted of a custom-built vacuum chamber with a fixed substrate holder and a standard rotating target holder. Gas pressure was controlled by a needlevalve and physical turbo pump throttling, and substrate heating was performed using a raster-scanned CO2 laser.27 PLD setup 2 was similar to setup 1, except the target rotator was driven by an off-center cam to induce side motion as well as rotation, improving the target surface area usage, and a refractive tetraprism was used instead of a scanner for homogenizing the CO2 laser beam shape and intensity profile.28 PLD setup 3 was a commercially manufactured system (Kurt J. Lesker Company) incorporating several enhancements. Computer operated mass-flow controllers set the chamber pressure, and the turbo pump speed could be speed-throttled for high pressures. A new substrate holder design made it possible to rotate substrates while simultaneously heating with a raster-scanned CO2 laser from the rear; the CO2 laser was scanned to a grid of points in a circular area to ensure homogeneous heating at all angles of substrate rotation. All of the different laser heating approaches have been described in more detail elsewhere.28 The most critical difference in PLD setup 3 is the target holder assembly, which was a triple-target arrangement where the targets were symmetrically offset from the substrate axis to allow them to be used alternately, or simultaneously, when multiple lasers are employed. An expanded view of a cross section of one of these tilting targets is shown in Figure 1b. To compensate for the off-axis positioning of the targets, a synchronized variable tilt angle can be induced to direct the plume at the substrate center, and this angle can be changed while the targets are rotating. This combination of substrate rotation and tilting targets is currently a unique system, to the best of our knowledge, and is highly advantageous for producing homogeneous films in terms of composition, particulates, and crystal lattice constant. Continuous tilting allows the plume to be scanned across the substrate and also continuously changes the radius at which ablation occurs on the target surface, vastly improving target utilization and increasing the deposition time between target reconditioning. A further enhancement made possible by this approach was flatfilm growth via continuous target tilt adjustment and dwelling at different angles with an experimentally obtained optimal bias to average out the otherwise uneven growth rate that typically occurs with a PLD plume over large substrate areas. All the chambers used turbomolecular pumps backed by rotary forevacuum pumps. A KrF 248 nm excimer laser (400 mJ per pulse, up to 20 Hz, ∼20 ns pulse duration; Lambda Physik) was used for ablation in PLD setup 1, whereas 266 nm flashlamp-pumped frequency-quadrupled Nd:YAG lasers (100 mJ per pulse, up to 10 Hz, ∼5 ns pulse duration; Continuum) were used in PLD setups 2 and 3. In all PLD setups, the lasers were focused using a single convex or planoconvex lens, and the desired fluence at the target surface was obtained by changing the distance between the lens and the target. Particulate density can increase significantly if target surfaces are overused, so targets were lapped regularly to reveal fresh unablated surfaces. The required frequency of reconditioning was different for each PLD setup: off-center cam-driven rotation and continuous target tilting typically allowed five times more usage between reconditioning compared to when these practices were not adopted. One drawback of remote laser heating is the difficulty of accurately determining substrate temperature without the measurement interfering with the result. Our solution to this problem has been to calibrate heating setups approximately to absorbed CO2 power by observing the melting of small pieces of metal foil balanced on the heated substrate. While this is enough to give us an idea of substrate temperature, perhaps within (50 degrees, and is sufficient for achieving the same experimental conditions from day to day, it is not sufficiently accurate for us to report temperature as a precise parameter. Since we operate without a real-time 1100



Figure 2. Graph to show the lattice spacing measured by XRD for a group of films all grown with the same deposition conditions. The calculated values for the mean and standard deviation of the data are shown inset, and solid and dashed lines have been drawn on the graph to represent them respectively. measurement of substrate temperature, reproducibility is a critical factor so that films grown on different occasions can be compared fairly. To test for this, we grew several films of equal thickness under the same deposition conditions and at the same power setting on the CO2 laser, and we compared the film lattice spacing as measured by X-ray diffraction (XRD). The Ga concentration in laser deposited GGG films is dependent on substrate temperature, so any significant variation would be expected to result in films with different lattice spacings. Figure 2 shows the lattice spacings measured for this reproducibility experiment. The standard deviation is comparable to the error level that is expected due to minor alignment differences that occur with the XRD measurement process itself ((0.005 Å), so we can make the assumption that substrate temperature reproducibility effects are negligible. As a precaution when laser heating substrates, to avoid thermal shock and/or substrate cracking due to a momentary inhomogeneous temperature profile, the CO2 heating power was ramped to the desired final setting over a period of 20 min. Prior experience allowed the optimization of deposition conditions using typical starting parameters for oxide crystal growth: targetsubstrate distance = 40 mm; gas pressure = 2.0 10-2 mbar; fluence = 2.0 J cm-2; substrate temperature ≈ 750 °C. Deposition parameters were changed one at a time in turn until little or no further improvement was obtained. Rather than creating many samples within a high order matrix of deposition parameters, this approach allows for more rapid isolation of optimal conditions using far fewer samples, and it also quickly reveals which parameters are dominant in influencing the various properties by which films can be characterized. Optimization was evaluated in terms of crystal quality (i.e., minimum fullwidth at half-maximum of XRD peaks and maximum counts), stoichiometry (compared to bulk target, measured using energy dispersive X-ray analysis (EDX)), particulate density (observed with optical microscope and/or scanning electron microscope (SEM)), and growth rate (including considering film height profile measured using a stylus surface profiler—flat films are desired). Repeating this process using several PLD setups and different lasers has given us a spread of results from films grown under various different combinations of deposition parameters, and we have compositional and structural data for all of these. The excimer laser setup was also optimized in terms of the quality (sharpness) and aspect ratio of the imaged laser spot on the target surface (i.e., rectangular vs a more square area). All investigatory experiments aside from optimization of conditions were performed using PLD setup 3 and a Nd:YAG laser. Substrate

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temperature was investigated further to see if thermal expansion mismatch could be minimized by reducing the substrate temperature to the lowest possible value that still yielded crystalline growth. Using a previous calibration of CO2 laser heating power vs resulting substrate temperature estimate, a series of heating powers were selected that would produce samples grown at temperatures separated by approximately 50 °C. For this experiment, the absolute temperature is not critical because the effect of incremental temperature change is the key factor. All films were grown under the same conditions (other than temperature) and for the same length of time (which should lead to similar thicknesses). The order in which these films were grown was randomized to reduce any potential influence from progressive-use chamber effects such as window coating and/or target surface degradation. Initial experiments investigating the origins of residual stress were directed toward some practices that have previously been associated with its reduction in laser-deposited films, with an aim of revealing which stress mechanisms may be influenced and to what magnitude. Different deposition parameters were changed in subsequent experiments to reveal the effects on residual stress. Films were grown on substrates that were optically polished on both sides with back-side curvatures measured both prior to and after deposition to detect any difference in the residual stress resulting from different stress minimization practices. A control film of Nd:GGG on YAG (100) was first grown under optimal deposition conditions using the following parameters: target-substrate distance = 35 mm; O2 background pressure = 6.0 10-2; absorbed heating power ≈ 5.0 W, estimated to result in a substrate temperature of about 750 °C; fluence = 1.9 J cm-2. A deposition time of 1 h was used, resulting in a film thickness of 1.5 μm. Substrate curvatures were measured before and after deposition using a stylus-based surface profiler. The premeasured curvature profiles were deducted from the postdeposition curvature profiles for normalization, which was followed by a curve fitting procedure to make the deflection measurement systematic. When fitting polynomial curves to the surface curvature profiles, only the middle 80% of the scan length was considered to eliminate the influence of edge-effects on the results. Films were grown using the following modifications to the control film deposition parameters: 1. Slow Ramp Rate. Previous reports suggest the use of a slower ramp rate for the cooling phase29 for improved thermal relaxation and thermal shock avoidance, and therefore, a film was grown with the same conditions as the control but cooled over 2 h rather than the usual 20 min. 2. Amorphous Buffer Layer. To see if lattice mismatch could be relaxed by an amorphous buffer layer, a 10 nm thick layer was deposited at low temperature followed by overgrowth at the optimal temperature used for the control film, similar to the work of Yamada et al. which described some success with growth of SrTiO3 on LaAlO3 using this two-step approach.12 The amorphous buffer layer growth was performed with the substrate heated using approximately 1.0 W of absorbed power (to avoid adhesion issues which can occur with room temperature deposition). Although the substrate temperature for this absorbed power level is unknown, the important thing is that it would be significantly lower than the cutoff temperature for crystal growth (estimated to be ∼600 °C). The buffer layer was annealed for 30 min at the growth temperature before overgrowth was then performed. 3. Increased Target-Substrate Distance. To investigate the dynamics of ion-bombardment induced stress, a film was grown with a longer substrate-target distance (growth time was changed for this film to make the thickness the same as that of the control film for fair comparison). 4. Undoped GGG. To check the possibility that Nd-doping increases stress (due to the larger ionic radius of Nd3þ, 1.25 Å compared to 1.19 Å for Gd3þ in the dodecahedral crystal site), a film was grown using undoped crystal. 5. GGG Substrate. As a simple way of confirming the existence of stress mechanism(s) other than lattice mismatch and thermal expansion mismatch, a film was grown on a GGG substrate. 1101


Crystal Growth & Design 6. Substrate Temperature. To assess the effect of thermal expansion mismatch relative to other stress influences for the conditions used in these investigations, films were grown at different temperatures with all other parameters unchanged. 7. Laser Fluence. To characterize the effect of fluence on residual stress, three films were grown with different laser fluences. Films were grown to 16 μm in thickness, with deposition being interrupted whenever the film thickness had doubled (starting from 1 μm), allowing the samples to be removed for curvature profiling and XRD analysis. The samples were then meticulously cleaned before being returned to the deposition chamber for further film growth. The limit of 16 μm in thickness was chosen in an attempt to stay within an elastic regime and avoid cracking. XRD analysis was performed using a Siemens D5000 diffractometer with a Cu KR source (λ = 1.5406 Å) operated at 40 kV using slits of width 2 mm before and after the sample, and a 0.2 mm width slit before the detector. Diffraction peaks originating from the YAG substrate were used to normalize out errors due to alignment differences (mainly due to a small misalignment of lattice planes with the substrate faces). Compositional analysis was performed using either a LEO 430 SEM operated at 20 kV with an Oxford Instruments ISIS EDX detector (samples were carbon coated for this device) or a Zeiss EVO 50 SEM operated at 20 kV with an Oxford Instruments INCA PentaFETx3 EDX detector (variable pressure operation at 40 Pa was used with this device, negating the need for carbon coating). Cobalt standards were used to calibrate the EDX detectors, and a piece of unused target crystal was measured to normalize results from analysis sessions at different times and using different instruments. Several regions around the center of each film were analyzed to generate an average composition measurement for the samples. A Tencor SP-16 stylus-based surface profiler was used to measure sample curvature and film thicknesses from corner to corner in both axes.

’ THEORETICAL PREDICTIONS The quaternary garnet crystal unit cell consists of eight A3B2C3O12 formula units with cations located in three different lattice site coordinations: A, dodecahedral; B, octahedral; C, tetrahedral. Ternary garnets are allowable and simply have B and C lattice sites occupied by the same element. Garnet compositions are typified by a larger ionic radius cation that occupies A lattice sites and smaller ionic radius cations occupying B and C lattice sites. It is also permissible for some of the larger cation species to occupy B lattices sites when a deficiency in the stoichiometry occurs, resulting in a larger lattice constant due to the volume required to accommodate the larger cation in this site. This is a common occurrence for PLD grown films, where lighter or more volatile elements can be lost preferentially in the deposition process, and investigations have been made into correcting this problem.30 For bulk crystal, several works report different empirical formulas for predicting the behavior of the lattice constant as the stoichiometry changes.31-34 To define the problem more precisely, the garnet formula can be written as {A3}[AxB2-x](B3)O12 to indicate the higher than normal concentration of the larger cation (different parentheses are used for different lattice sites)—we are interested in what happens to the lattice when 0 e x e 2. Note, it is also possible to have the reverse case, whereby the deficiency occurs for the larger cation, resulting in {A3-yBy}[B2](B3)O12, but this is a rarer problem with the case of GGG growth and is more difficult to model in our experience, so it will not be discussed further here. When GGG has a higher than normal concentration of Gd compared to Ga, eq 1, derived by Strocka et al,31 can be used to predict the lattice constant for

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Figure 3. Graph of expected thermal expansion mismatch induced stress for different growth temperatures. Data from Geller et al.36 was used to produce this graph. Closed circles represent data points, and the solid line is a guide for the eye.

bulk crystals with compositions where 0 e x e 0.5. This will be used as a guide for our experience with films of GGG; deviation from this predicted trend is an indication of residual stress or significant intrinsic defects, impurities in the film, or a combination of these problems (in the case of films here, we are assuming that residual stress is dominant). a ¼ 12:383½1 þ 0:0268xðrGd =rGa - 1Þ

ð1Þ

where a is the lattice constant, rGd and rGa are the gadolinium and gallium ionic radii, respectively, in the octahedral lattice site, and x is an indexing parameter for composition variation as described above. The ionic radii of Gd and Ga were taken from the work of Shannon.35 Stress resulting from thermal expansion mismatch between YAG and GGG will clearly depend on the growth temperature. However, since thermal expansion does not necessarily increase linearly with temperature, simply minimizing growth temperature may not minimize the overall thermal expansion mismatch and the stress it induces once samples have cooled. Extensive studies of high temperature thermal expansion of garnets do not exist in the literature, but one report by Geller et al. details the expansion of YAG and GGG at high temperature.34 Using data from Geller et al., we can produce a graph of expected thermal expansion mismatch-induced in-plane stress for different growth temperatures, as shown in Figure 3. The line between the points has been drawn as a guide to the eye in Figure 3. This graph is limited by the small number of data points available, but it can serve as a useful indicator for minimization of thermal expansion mismatch stress. Equation 2 was used to derive the strain expected to be induced at room temperature as a result of different growth temperatures. εTEM ¼ ðTRT - TG Þ=ðRYAG - RGGG Þ

ð2Þ

where εTEM is the strain resulting from thermal expansion mismatch, RYAG and RGGG are the thermal expansion coefficients for YAG and GGG, respectively, calculated for different growth temperatures, TG, from the data reported by Geller et al., and TRT is room temperature (20 °C). Strain values were converted to stress using eq 5 shown below. 1102



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Figure 4. Graph of composition vs lattice constant for films encompassing depositions performed over the last several years with three different PLD setups and two different lasers using a wide variety of growth conditions. Crosses, closed circles, and open circles represent data points from experiments using an excimer laser with PLD setup 1, a Nd:YAG laser with PLD setup 2, and a Nd:YAG laser with setup 3, respectively. The solid line shows the trend expected from the Strocka et al. model, and the dotted line is an extrapolation of this model.

The limit of lattice mismatch for epitaxial growth to be possible is often reported as about 9% in the literature.37 However, for the crystalline film lattice constant to relax after initial epitaxial matched (strained) growth at the interface, dislocation defects must be generated as the thickness increases. The relatively high energy required for dislocation defects to occur in garnet crystals could be viewed as advantageous from a crystal quality point of view; in fact, this could even be interpreted as an indication as to why high quality garnet crystal with large lattice mismatches can be grown with relative ease using PLD—epitaxy is not effectively compromised early on in film growth by a high defect density, allowing thick crystal films to be grown. However, this means that lattice mismatch relaxes over a relatively large thickness of a few micrometers rather than hundreds of nanometers, which is more typical. Consequently, lattice mismatch stress must be accounted for even when films are several micrometers in thickness. Lattice mismatch-induced in-plane strain, including accounting for a degree of relaxation as a function of thickness, can be given by eq 3 below. The degree of relaxation can be calculated by comparing the strained film lattice constant to the unstrained bulk crystal lattice constant. εLM ¼ ð1 - Rðdf ÞÞððas - af Þ=af Þ

ð3Þ

where εLM is in-plane strain resulting from lattice mismatch, R(df) is the degree of lattice mismatch relaxation (dependent on film thickness, df), and af and as are the film and substrate lattice constants, respectively, out of plane. The use of ion energy as a moderator of film stress has been reported previously for PLD,16 sputtering,17 and other ionassisted deposition techniques.20 Ex-situ postdeposition ion treatment for stress modification has also been reported in the literature.25 Impinging ions with energies of around 100 eV and

Figure 5. Graph to show the effect of changing background pressure on the structure and composition of films. Dashed gray arrows indicate the trends observed with increasing background pressure for different groups of films. Crosses, closed circles, and open circles represent data points from experiments using an excimer laser with PLD setup 1, a Nd: YAG laser with PLD setup 2, and a Nd:YAG laser with setup 3, respectively. The solid black line shows the trend expected from the Strocka et al. model, and the dotted black line is an extrapolation of this model.

above are expected to induce a significant amount of compressive stress.38 There are several reports of experimental work contributing to characterizing the effect of ion energy on generated stress. However, due to the complexity of this problem, which depends on nearly all the deposition parameters in some way as well as critically on the materials in use, there are no simple models to gauge the expectations of laser fluence or ion energy vs induced stress. The Stoney equation is well-known for the calculation of inplane stress from curvature of a thin film bilayer structure and is repeated below as eq 4.39 Stress and strain can be interchanged using eq 5, and curvature can be calculated from measured substrate deflection using eq 6. σS ¼ KEs hs 2 =ð6hf ð1 - vs ÞÞ

ð4Þ

ε ¼ σð1 - vf Þ=Ef

ð5Þ

K ¼ 1=F ¼ 8dc =l2

ð6Þ

where σS is the calculated stress on the film, K is the measured substrate curvature, E is Young’s modulus, h is thickness, ν is Poisson ratio, ε is the calculated in-plane strain in the film, F is the substrate radius of curvature, dc is the deflection of the substrate due to stress induced curvature (dc > 0 = convex/tensile, dc < 0 = concave/compressive), l is the length over which curvature/ deflection is measured, and the subscripts s and f denote substrate and film parameters, respectively. Values for constants have been used as follows:40 (for YAG) E = 291 GPa, ν = 0.265; (for GGG) E = 225 GPa, ν = 0.28. For thick films grown with multiple growth runs, the position of the substrate was deliberately rotated 90° between each growth stage so that opposite corners masked by the holder alternated with each run, making the structure as symmetric as 1103



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Figure 6. Graph to show the effect of changing fluence and spot size (with constant fluence) on the structure and composition of films. The solid and dashed gray arrows indicate trends observed with increasing spot size and fluence, respectively. Open and closed squares represent data points for changing spot size and fluence, respectively. The solid black line shows the trend expected from the Strocka et al. model, and the dotted black line is an extrapolation of this model.

possible as its thickness increased. Also, curvature measurements were taken in two axes so that an average could be taken. Residual stress in crystal films can distort the lattice. Compressive stress leads to shrinking of the lattice out of plane, and expansion of the lattice in plane occurs to compensate for this. Tensile stress leads to expansion of the lattice out of plane while the lattice in plane shrinks. XRD measurements of the crystal lattice constant can therefore be used to estimate stress in films if the expected unstrained lattice constant is known (this can be estimated by using compositional measurements and the Strocka et al. model, eq 1). Equation 7 may be used to estimate the net strain out of plane from the measured lattice constant in plane or directly from the XRD spectrum peak positions. εX ¼ Δd=d0 ¼ - Δθ cot θ0

ð7Þ

where εX is the strain out of plane determined by XRD, Δd is the difference of measured lattice constants to that of unstrained bulk crystal of the same composition, d0 is the unstrained lattice constant, Δθ is the XRD peak shift resulting from strain, and θ0 is the expected XRD peak position for unstrained crystal. The Poisson ratio can be used to convert to in plane strain and to compare directly to stress calculations using curvature measurements (when eq 5 is also used to convert to stress).

’ RESULTS AND DISCUSSION Figure 4 shows a graph of composition vs lattice constant for film depositions performed over the last several years with the three different PLD setups and two different lasers using a wide variety of growth conditions. The composition axis is shown as the indexing parameter x in Gd3þxGa5-xO12 used previously in eq 1 for convenience. It is clear from Figure 4 that there is some significant variation in the relationship between lattice constant and composition.

Figure 7. Graph to show the effect of changing growth temperature on the structure and composition of films. The diamonds represent data points and are labeled with the estimated substrate temperature (°C), and the gray arrow indicates the trend in the midrange of temperatures used. The solid black line shows the trend expected from the Strocka et al. model, and the dotted black line is an extrapolation of this model.

We believe that residual stress is the most significant cause of deviation from the Strocka et al. model line. Data points above the Strocka et al. model line have smaller than expected lattice constants in plane, indicating tensile residual stress, whereas data points below the line have larger than expected lattice constants in plane, indicating compressive residual stress. Data points for films grown with an excimer laser are mostly above the Strocka et al. model line, whereas the data points for films grown using Nd:YAG lasers nearly all lie below this line. Care must be taken when drawing initial conclusions from this observation, as it may be conjectured that laser wavelength, energy, and/or pulse duration strongly determine residual stress, since the specific laser type is the most defining difference between the two sets of experiments. However, since GGG has a high absorption at both 248 and 266 nm,41 laser differences are not thought to be the main source of the difference between these subsets of films. Film thicknesses vary mainly from 0.5 to 10 μm for the data in Figure 4, but it should be noted that films grown with the excimer laser are all at the upper end of this range, partly due to the higher growth rate experienced with the excimer laser and PLD setup 1. Since lattice mismatch-induced compressive stress relaxes with increasing thickness, we can expect thicker films to suffer less from this factor and be more likely to be dominated by thermal expansion mismatch, which leads to tensile residual stress. Over the course of depositing GGG films with three different PLD setups, we have accumulated data that reveals the effects of different deposition parameters on film composition and lattice constant. Parameters fall into two categories: those that do not moderate the residual stress and those that do. Figure 5 shows data points replotted from Figure 4 for films grown using different background pressures, ranging from 2.0 10-2 mbar to 2.0 10-1 mbar. Three different groups of films are shown, from three separate optimization experiments only changing the parameter of background pressure with the three different PLD 1104



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Table 1. Results of Different Techniques for Reducing or Modifying Residual Stress in Films description of test

measured substrate deflection (μm)

calculated stress (GPa)

control

-0.17

-0.59

slow ramp down

-0.15

-0.52

amorphous buffer layer

-0.13

-0.47

longer substrate-target distance

-0.12

-0.42

undoped GGG

-0.19

-0.66

GGG substrate

-0.50

-1.39

lower temperature (ΔT ≈ -100 °C)

-0.09

-0.32

lower temperature (ΔT ≈ -125 °C)

-0.05

-0.18

setups and two different lasers. Dashed gray arrows on the graph are best fits to each group and point in the direction of increasing background pressure. All three groups show composition and lattice constant changing together with trends that are parallel to the expected direction as modeled by Strocka et al., indicating that although background pressure strongly influences stoichiometric transfer (i.e., Ga concentration), it does not strongly affect the film residual stress. Changing substratetarget distance similarly does not affect film residual stress, although it does influence stoichiometric transfer, growth rate, and film thickness profile. Figure 6 shows data points replotted from Figure 4 for specific experiments of changing fluence using PLD setup 3 with an Nd: YAG laser, and changing laser spot size, while keeping fluence constant (i.e., varying incident laser energy), using PLD setup 1 with an excimer laser. The dashed gray line indicates the trend for changing fluence and points in the direction of increasing fluence from ∼1 J cm-2 up to ∼30 J cm-2, indicating that residual stress is more compressive for higher fluences. This may be due to increased ion-bombardment induced stress and/or the lower growth rate experienced with higher fluences, which led to thickness differences and a potential difference in the degree of lattice mismatch relaxation for the films. The solid gray line indicates the trend for the data points relating to changing spot size and points in the direction of increasing spot size (ranging from an area of 0.04 cm2 to 0.10 cm2), indicating that the effect of laser-target interaction on stress is not restricted to the simple parameter of fluence. We can also observe from this graph that care must be taken to ensure the laser is focused or imaged on the target so that the spatial energy profile is well-defined (i.e., top-hat), since the film with the least Ga loss which is closest to the Strocka et al. model line was grown using the most well-defined laser spot in this experiment and, notably, had an aspect ratio the same as that of the unfocused laser beam. Figure 7 shows data points replotted from Figure 4 for a specific experiment investigating the effects of growth temperature using PLD setup 3 with an Nd:YAG laser. The solid gray line indicates the midrange trend and points in the direction of increasing temperature, which was estimated to have varied between 600 and 1100 °C for this experiment, as indicated by the labels shown for specific data points. The trend arrow shows that film composition and lattice constant changed parallel to the Strocka et al. model line in the midrange of substrate temperatures used. The effect of temperature on stoichiometric transfer can be attributed to the increased rate of Ga loss through evaporation that occurs with higher temperatures; however, it is unclear why the increased temperatures do not appear to have significantly affected the residual stress. The two films grown at the lowest temperatures, estimated to be 650 and 700 °C,

Figure 8. Graph to show the evolution of stress with increasing thickness for different fluences used (all other parameters constant apart from growth rate)—calculated from the curvature measurements using the Stoney formula. Squares, circles, and diamonds represent data points for experiments using a fluence of 6.3 J cm-2, 5.5 J cm-2, and 2.4 J cm-2, respectively, and lines are drawn between data points for each group as guides for the eye.

respectively, deviate from the trend followed by the other films and do appear to have a different residual stress. This could be explained by the thermal expansion data reported by Geller et al. and reproduced as expected stress induced by thermal expansion mismatch earlier as Figure 3. There is a significant decrease in expected thermal expansion mismatch between YAG and GGG at a temperature of ∼750 °C. Films grown at temperatures below this minimum would therefore be expected to be less compressively stressed due to the higher tensile contribution from thermal expansion mismatch. It is also notable that the film grown at the highest estimated temperature of 1100 °C is far away from the trend displayed by other films. This is thought to indicate a difference in how the crystal lattice is accommodating the increased Gd concentration, and it suggests that the Strocka et al. model is no longer adhered to for severely Ga deficient films. For the purposes of engineering stress with the conditions used for these experiments, it would actually be preferable not to minimize thermal expansion mismatch but instead elevate it slightly to compensate for compressive stresses by growing at a temperature of around 700 °C. Table 1 shows the results from stress reduction attempts and changing different deposition parameters using PLD setup 3 with 1105



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Figure 9. Optical micrographs of the stress evolution with sample thickness, labeled with respective fluences used.

an Nd:YAG laser to reveal the main stress contributing mechanisms. The normalized postdeposition substrate deflections are displayed along with the calculated values of residual stress for each test. All of the films were found to be under compressive stress. Slowing of the cooling phase, inclusion of an amorphous buffer layer, use of a longer substrate-target distance, and growth of undoped GGG as compared to Nd-doped GGG were all found to have a minimal effect on the film residual stress, not changing it by more than ∼0.15 GPa. The most significant difference has been found for the film grown on a GGG substrate. This film could be expected to have negligible residual stress because of the very small expected thermal expansion mismatch and lattice mismatch between bulk GGG crystal and deposited GGG crystal film. The more than doubling of compressive stress as compared to the control sample is a strong indicator that there is a further contributor to residual stress that must be taken into account. The estimated temperature for the control film growth was ∼750 °C. The two films grown at lower temperatures agree with earlier observations from Figure 7, the lower substrate temperatures have reduced the compressive stress, thought to be due to increased tensile stress as a result of a higher thermal expansion mismatch. It appears, therefore, that for films of GGG on YAG, thermal expansion mismatch can be increased by increasing or decreasing the growth temperature from the optimum of ∼750 °C. Since it is not ideal to increase the growth temperature, due to an increased loss rate of Ga which can occur, decreasing the temperature to increase thermal expansion mismatch may prove to be a useful parameter by which residual stress can be engineered. Figure 8 shows a graph of residual stress evolution with thickness for three different fluences. The samples were all grown using PLD setup 3 with an Nd:YAG laser. The lines plotted with the data points are guides for the eye. All the films show a trend of high compressive residual stress for low thicknesses which then reduces with increasing thickness. This is in line with the theory that lattice mismatch-induced compressive stress dominates for small thicknesses until it is relaxed by defects that can be increasingly accommodated as thickness increases. For the two higher fluences used, 6.3 J cm-2 and 5.5 J cm-2, the films remained under compressive residual stress even up to the final thickness of 16 μm. However, for the lower fluence used, 2.4 J cm-2, the residual stress state changed to tensile and the trend changed direction. From optical micrographs of the three films, shown as Figure 9, we can see that this lower fluence sample has cracks in

Figure 10. Graph to show the evolution of stress with increasing thickness for different fluences used (all other parameters constant apart from growth rate)—calculated from EDX, the Strocka et al. model, XRD lattice constant measurements, and conversion to in-plane stress using the Poisson ratio. Squares, dots, and diamonds represent data points for experiments using a fluence of 6.3 J cm-2, 5.5 J cm-2, and 2.4 J cm-2, respectively, and lines are drawn between data points for each group as guides for the eye.

the surface, suggesting that the tensile stress could not be tolerated, forcing the film to crack to relieve the stress. As can be seen from Figure 9, the other two samples do not display any cracking in their surfaces, suggesting that compressive stresses can be tolerated better than tensile. Fluence appears to be a strong moderator of stress, thought to be due to the consequent changes in ionbombardment dynamics and strength that occur when it is varied. According to Figure 8, it should be possible to find a fluence for a desired film thickness such that the residual stress is zero. It may be noted from Figure 9 that the particulate density is higher for lower fluences. This is in line with previous observations of this behavior for depositions using the 266 nm wavelength pulses from a Nd: YAG laser, and it is thought to be due to poor beam quality. EDX measurements of the three stress evolution samples were taken when they were all 16 μm in thickness. Using the 1106



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Fluence and therefore ion-bombardment may have an influence on oxygen concentration, and this could be the mechanism by which residual stress is being changed.

Figure 11. Graph of composition vs lattice constant with a highlighted group of films for which an unusually high fluence was used (∼30 J cm-2 compared with 1-5 J cm-2 for the rest of the films). Crosses, closed circles, and open circles represent data points from experiments using an excimer laser with PLD setup 1, a Nd:YAG laser with PLD setup 2, and a Nd:YAG laser with setup 3, respectively. The solid line shows the trend expected from the Strocka et al. model, and the dotted line is an extrapolation of this model.

procedure described in the previous section, these compositional measurements were used to estimate in-plane stress using eq 7 and the Poisson ratio. Figure 10 shows the stress evolution with thickness for the three samples when this secondary approach of stress estimation was employed. The lines on the graph are shown as guides for the eye. This approach has reproduced similar overall stress with thickness evolution behavior to the curvature-based approach of estimation. However for two of the fluences used, the data points produced by this approach have deviated from the overall trend. For the 2.4 J cm-2 fluence case, this approach has reiterated that the film was indeed under intolerable tensile stress, and it appears that significant relaxation occurred during or after the growth phase that took the film to 8 μm in thickness. The trend for the 5.5 J cm-2 fluence case is the hardest to interpret. For this film, compressive stresses seem to have increased, as determined by this estimation approach, after a thickness of 2 μm was reached. A separate investigation will be required to determine the exact mechanism by which increased fluence is increasing compressive residual stress in laser deposited films. However, our experimental data can offer one clue for the case of very high fluence (∼30 J cm-2). EDX analysis was used to measure the oxygen concentration of all the films discussed here; however, this data was not reported because of the limited accuracy of the EDX technique for such a light element. For films where the fluence used was 1-5 J cm-2, typical for many materials grown by PLD, the oxygen concentration was always measured to be 60-64% and no correlation was found with deposition conditions. For a group of films where the fluence used was ∼30 J cm-2, the oxygen concentration was measured to be ∼80%. The data points for these films are highlighted below in Figure 11 on a composition vs lattice plot. It is interesting to note that these are all the films for which the highest residual stress was found.

’ CONCLUSIONS The experiments reported here were devised to find a way of engineering the residual stress in PLD garnet crystal films. We have presented a graph of composition vs lattice constant using data from films grown over the last several years using three different PLD setups and two different lasers for ablation. The data indicated that the differing deposition parameters used for films had an effect on the relationship between composition and lattice constant, and tthey allowed data points to stray from the predicted bulk crystal behavior modeled by Strocka et al. We have attributed this effect to residual stress, which is dependent on the deposition parameters used. In an investigation into possible stress minimizing techniques, we found that slowing the postdeposition cooling phase, use of an amorphous buffer layer, and increasing the target-substrate distance did not have a significant impact on the residual stress. Temperature and fluence were found to be the two most influential parameters for moderating the residual stress. Experiments to track the evolution of stress with increasing film thickness showed that there is a relaxing compressive stress contribution at work, which has been attributed to lattice mismatch. Results showed that the lattice mismatch relaxation mostly occurred within the first 4 μm of film growth. Fluence was proven to have a significant effect on the residual stress. Two films deposited with a fluence of ∼6 J cm-2 were found to be under compressive stress even up to 16 μm in thickness, whereas a film deposited with a fluence ∼2.4 J cm-2 was found to be under compressive stress initially but reverted to tensile stress when the thickness exceeded ∼2 μm. This latter film also appeared to suffer some stress relaxation due to cracking, as confirmed by direct observation of cracks using optical microscopy. The results all lead us to the conclusion that the residual stress state of films is a balance of lattice mismatch (compressive), which relaxes with increasing thickness, thermal expansion mismatch (tensile), which changes with growth temperature, and fluence (compressive), whose magnitude determines the severity of ion-bombardment-induced lattice damage. Fluence can be used to effectively hold the film under compressive stress at the growth temperature so that the tensile contribution from thermal expansion mismatch is canceled out when the sample is cooled. The balance is illustrated by eq 8: σ net ¼ σ LM ðhf Þ þ σTEM þ σ F

ð8Þ

where σF = ion-bombardment-induced stress. While the compressive stress contribution from lattice mismatch is not easy to control, the contributions from thermal expansion mismatch and fluence can be modified by changing deposition parameters. We therefore propose that a possible stress engineering solution for these films is to carefully select growth temperature and fluence such that resultant stress contributions cancel for the desired film thickness. Since changing these parameters also has other impacts on film quality such as compositional deficiency, particulate density, and growth rate, it is important that both parameters are changed to find the best compromise. This technique needn’t be restricted to stress engineering of the active layer, since it should be possible to deposit such a layer as normal and then apply a stress engineered layer on top to 1107


Crystal Growth & Design balance the residual stress in the overall structure. This particular approach is attractive for optical films, where the different parameters required for the stress-relieving cap may be unfavorable in terms of optimal conditions for minimal particulates, for example, and therefore minimal loss. One possible drawback could be the intermediary stress films are placed under, which may be highly compressive at the growth temperature before the sample is cooled and the tensile stress from thermal expansion mismatch is activated. However, since the only sample that suffered from cracking was in fact the low fluence, tensile stressed sample, it appears as if high compressive stresses while the film is growing are tolerable.

’ AUTHOR INFORMATION Corresponding Author

*Telephone: þ442380593177. Fax: þ442380593149. E-mail: [email protected].

’ ACKNOWLEDGMENT The authors acknowledge the support of the Engineering and Physical Sciences Research Council (EPSRC) for funding under Grant Nos. GR/R74154/01, EP/C515668, and EP/F019300/1. The authors thank Prof. Mark T. Weller and Dr. Mark E. Light for access to X-ray diffraction facilities in the School of Chemistry. T.C.M.-S., K.A.S., and R.G. acknowledge the receipt of EPSRC studentships for part or all of their time spent working toward the results reported here. ’ REFERENCES (1) May-Smith, T. C.; Shepherd, D. P.; Eason, R. W. Thin Solid Films 2007, 515, 7971–7975. (2) Gazia, R.; May-Smith, T. C.; Eason, R. W. J. Cryst. Growth 2008, 310, 3848–3853. (3) May-Smith, T. C.; Eason, R. W. J. Cryst. Growth 2007, 308, 382–391. (4) May-Smith, T. C.; Grivas, C.; Shepherd, D. P.; Eason, R. W.; Healy, M. J. F. Appl. Surf. Sci. 2004, 223, 361–371. (5) Grivas, C.; May-Smith, T. C.; Shepherd, D. P.; Eason, R. W. Opt. Commun. 2004, 229, 355–361. (6) Anderson, A. A.; Bonner, C. L.; Shepherd, D. P.; Eason, R. W.; Grivas, C.; Gill, D. S.; Vainos, N. Opt. Commun. 1997, 144, 183–186. (7) Gottmann, J.; Wortmann, D.; Vasilief, I.; Moiseev, L.; Ganser, D. Appl. Surf. Sci. 2007, 254, 1105–1110. (8) Grivas, C.; Shepherd, D. P.; May-Smith, T. C.; Eason, R. W.; Pollnau, M. Opt. Express 2005, 30, 210–215. (9) Kahn, A.; Heinrich, S.; K€uhn, H.; Petermann, K.; Bradley, J. D. B.; W€orhoff, K.; Pollnau, M.; Huber, G. Opt. Express 2009, 17, 4412–4418. (10) K€uhn, H.; Heinrich, S.; Kahn, A.; Petermann, K.; Bradley, J. D. B.; W€orhoff, K.; Pollnau, M.; Huber, G. Opt. Lett. 2009, 34, 2718–2720. (11) Shepherd, D. P.; Hettrick, S. J.; Li, C.; Mackenzie, J. I.; Beach, R. J.; Mitchell, S. C.; Meissner, H. E. J. Phys. D: Appl. Phys. 2001, 34, 2420–2432. (12) Sloyan, K. A.; May-Smith, T. C.; Zervas, M. N.; Eason, R. W.; Huband, S.; Walker, D.; Thomas, P. A. Opt. Express 2010, 18, 24679–24687. (13) Eason, R. W.; May-Smith, T. C.; Grivas, C.; Darby, M. S. B.; Shepherd, D. P.; Gazia, R. Appl. Surf. Sci. 2008, 255, 5199–5205. (14) Sugo, M.; Yamaguchi, M. Appl. Phys. Lett. 1989, 54, 1754–1756. (15) Yamada, T.; Astafiev, K. F.; Sherman, V. O.; Tagantsev, A. K.; Muralt, P.; Setter, N. Appl. Phys. Lett. 2005, 86, 142904.

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Stress Engineering and Optimization of Thick Garnet Crystal Films

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