Properties of TiOx Thin Films

8/3/2019 Properties of TiOx Thin Films

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Chapter 2:Properties of TiOx thin films

2.1 IntroductionIn this chapter we would like to report about our attempt to make TiO xthin films, with x varying between 0.71 and 1.28. The aim was to study themodification of the properties due to the lattice mismatch between layerand substrate. Therefore we grew our titanium oxide layers on differentkinds of substrates, i.e. MgO and MgAl2O4, with different amounts ofoxygen. We analyzed our samples with a number of techniques. RHEED isprobably the most important one followed by X-Ray Diffraction (XRD). Wealso performed resistivity measurements and compared them with literaturedata for bulk samples. We also observed superconductivity in our samples.

2.2 Properties of TiOx single crystals

The titanium oxides, as well as the vanadium oxides, have been underinvestigation for a long time already. This is mainly because of the richphase diagram and the accompanying variation in physical properties.Already in the 1940s several detailed studies were performed into thestructure of TiOx [1, 2]. At that time a most remarkable property of TiOx

was recognized. At temperatures larger than 990

C, a sample near thelower limit of the stoichiometry range, x = 0.70, was stable even though theoxygen lattice had almost 30% vacancies. The titanium lattice, however,was almost perfect. Near the opposite limit of the stoichiometry range, i.e.for a stable sample of TiO1.25, the oxygen lattice was almost perfect and thetitanium lattice had about 25% vacancies. For the ideal stoichiometric case,i.e. x = 1, the amount of vacancies was about 15% for both lattices. Fortemperatures lower than 990C it was found that the stoichiometry rangeis a little smaller, but nevertheless runs from x = 0.90 to 1.25. Althoughthe vacancies are distributed at random in the samples at temperaturesabove 990C, at temperatures below this equilibrium temperature some

5


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6 Chapter 2: Properties of TiO x thin films

vacancy ordered phases exist. Watanabe et al. [4] performed a detailedstructure analysis of the low temperature forms of TiOx using electron

diffraction, electron microscopy and X-Ray powder diffraction methods.They propose a vacancy structure for TiOx where in every (110) plane ofthe original cubic cell half of the titanium and half of the oxygen atoms aremissing alternately. They claim this structure to be valid for TiOx, with0.9 x 1.1, indicating a tolerance for some disorder. They also recognizethat this structure is not applicable over the whole stoichiometry range.Denker [3] carefully prepared polycrystalline samples over the stoichiometricrange from TiO0.55 to TiO1.30. While preparing his samples he was verycautious not to introduce impurities into his samples. He used the preparedsamples to study the electronic properties of titanium monoxide. He

however only presents results for TiOx with x varying between 0.80 and 1.25.His conclusions are, amongst others, that titanium monoxide is metallic,even though TiOx has a high resistivity as compared to conventional metals,and exhibits weak paramagnetism. The high resistivity is attributed to thelarge concentration of randomly disordered lattice vacancies.Like TiOx, VOx also exists over a wide stoichiometry range with similarlysized vacancy concentrations. The two materials were often mentionedtogether [6, 7]. Mott [5] tried to explain the conduction properties of VOxby assuming that the electrons form a highly correlated electron gas andthat, in addition, the random field due to the high concentration of vacantlattice sites produces so-called Anderson localization. His theory might alsoapply to TiOx. Goodenough [7] also studies the effect of vacancies on theproperties of the TiOx and VOx transition metal oxides. He concludes thatin the case of TiOx the variation of the conductivity with x is compatiblewith itinerant d electrons and the mobility decreases as the number of cationvacancies increases. Banus et al. [6] performed a range of experiments onprepared ingots of TiOx and VOx and compared their results to the workof others. They present experimental results for the stoichiometric rangeof 0.71 x 1.28. They find that the lattice parameter a0 and thedensity of TiOx decreases linearly with increasing x. They also find thatthe resistivity of cubic TiOx is essentially independent of both temperature

and composition. A series of pressure annealed samples showed an overallincrease in lattice parameter and density and a 12% 22% decrease ofvacancies. The series also showed an increase in superconducting transitiontemperature with increasing x.Through the years there were some other investigations into the bandstructure of TiOx and some theory with respect to why there are so manyvacancies and what are the consequences of this for the electronic structure[8, 9, 11, 12, 15, 20, 34]. The area of thin films of TiOx is fairly new andthe techniques of producing the films are also very diverse. Oxygen ionassisted physical vapor deposition was used by Martev [28] to grow TiO x


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2.3. Experimental 7

films with 0.95 x 1.15. After growth, the films, which usually had verysmall grain sizes, were annealed to obtain poly-crystalline fcc-TiOx. Typical

deposition rates were 60 A min1 and MgO was used as a substrate. Suzukiet al. [26] deposited titanium oxide films using an electron-beam evaporatorat room temperature. The titanium deposition rate was 0.5 A min1 andthe thickness of the samples varied between 10 A and 50 A. Their filmswere grown in a vacuum chamber with an oxygen background pressure ofabout 1 106 Pa. After deposition the films were annealed for 10 minutesat 1000K in vacuum. In their follow-up paper [29] they found it was alsopossible to grow TiOx films without supplying oxygen to the system. Theincorporation or diffusion of oxygen from the MgO substrate into the Tifilm during the annealing at 1000K took care of the oxidation. They also

report a MgO-(2 2)-TiO superstructure found after a heat treatment ofthe film and substrate of 1270K.We have employed the Molecular Beam Epitaxy technique with typicaldeposition rates of 1 A min1 and MgO and MgAl2O4 as substrates.We would like to refer to the work of D. Rata on VOx who used the samesystem and technique [36, 37] in her work. The reason for growing thinfilms of TiOx on different kinds of substrates is a simple one. The latticemismatch between the lattice of the substrate and the lattice of the filmimposes strain on the film. This strain will modify the properties of thefilm, since atoms will lie closer to or further apart from each other andelectronic bands might or might not start to overlap. We expect the strainto modify the number of vacancies present in the film, because in order toget TiOx with x = 1 and a small amount of vacancies, people have growntitanium oxide crystals under high pressure [6]. As we will show, the straincan also modify the structure of the film and be responsible for vacancyordering.

2.3 Experimental

All the samples mentioned in this chapter were prepared in the UHV-system described in Appendix B. The substrates we used were polishedor cleaved MgO or polished MgAl2O4 crystals. The MgO crystal wascleaved outside the system and then inserted as quickly as possible throughthe load-lock into the system. The substrates were mounted on stainlesssteel or tungsten sample holders by spot-welding stainless steel, tungsten ortantalum strips over the corners of the substrates (figure 2.1 B). This hadseveral advantages over the old way the samples were mounted (figure 2.1A). Some of the samples still had to have contacts evaporated on top of themfor conductivity measurements. By mounting the samples in this way it was


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Figure 2.1: Here we show the two different ways to mount the substrate onthe sample holder. A) Sample fixed on the sides B) Sample fixed on the corners.

Black are the strips used to fix the substrate, dotted is the substrate and whiteis the sample-holder

Figure 2.2: This figure showsA) a RHEED pattern of a film of TiOx grown ona MgO substrate at Room Temperature (RT) and B) a RHEED pattern of a filmof TiOx grown on a MgAl2O4 substrate at RT.

easier to evaporate the contacts in situ in our system. Secondly, in this way

the free sample area became larger. This allowed us to make RHEED-rotation movies over a larger range. The substrates were cleaned in situ byheating them to 1000K in the preparation chamber (see Appendix B.They were not exposed to oxygen or any other type of gas during heating.In the beginning of the cleaning the pressure in the chamber would rise.The heating or cleaning was stopped when the background pressure wasat the level of 107 Pa, the same level as before the heating began. Nocontaminants could be detected on the surface of the substrates using XPS.The substrates always showed good RHEED patterns but we needed to usea flood gun to compensate for the charging of the substrates.MgO has a rocksalt like structure with space group Fm3m (O5

h) giving it


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2.3. Experimental 9

the selection rules hkl : h + k, k + l, h + l = 2n. MgAl2O4 has a spineltype structure and space group Fd3m (O7

h) with the same selection rules

as for Fm3m (O5h) but with an additional condition for possible reflectionshkl : h+k, k+ l, h+ l = 4n if the third index is zero. XRD of the substratesusually showed very sharp peaks, indicating a good quality. The latticeparameter found in these measurements for MgO was a = 4.2110.005 A ingood agreement with tabulated values. For MgAl2O4 this was different. Onebatch of substrates turned out to have slightly different lattice parameters.The c-parameter found in this batch was c = 7.986 0.008 A insteadof the expected value of 8.082 A indicating a slight off-stoichiometricmagnesium-aluminum ratio. The substrates from the other batches did havea comparable c-parameter ofc = 8.083 0.006 A, but the effects describedin this chapter do not seem to be affected much by this difference, becauseall phenomena described here occur on both batches.The samples were usually grown at a substrate temperature of 400C. Wealso tried to grow at RT. This was successful for samples grown on MgOsubstrates (figure 2.2 A), but not on MgAl2O4 substrates (figure 2.2 B). At 400C good films were obtained for both kinds of substrates.The titanium flux used was normally 1 A min1. It was calibrated in situusing the flux monitor of the e-gun evaporator itself, through the quartz-balance present inside the system and ex situ by XRD (Philips XPert).A more accurate way would be if we had observed RHEED oscillations,but we unfortunately rarely did so. This was probably caused by the factthat the flux monitor of the electron-beam evaporator turned out to benot very reliable. Its readings changed from rod to rod, although we keptthe current through the filament, the emission current and the acceleratingvoltage the same. We also found that at some point it was impossible toincrease the flux. This was because the titanium rod in the electron-beamevaporator melted. A droplet of titanium would form at the end of therod and increasing power or voltage wouldnt result in a flux increase. Thequartz-balance was also not a very accurate means to calibrate the fluxbecause the device is meant to measure flux rates much higher than 1 Amin1. However in some cases this method was the only option to get a

reasonable direct estimate of the flux. A very accurate indirect method isto use XRR curves to determine the layer thickness. When this thickness isdivided by the time it took to grow the sample, a number is obtained whichwe will call the TiOx flux. This number is equivalent to the deposition rate.Although very precise, a drawback of the XRR method is that it is an exsitu method. If the sample is taken out of the system the sample surfaceis contaminated and a few nanometers are usually added to the thickness.Another problem is that in this way not the titanium flux is determined butthe TiOx flux. To derive the titanium flux, assumptions have to be madeabout the vacancy concentration. The RHEED oscillations are in our case


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the only way to determine the deposition rate directly. See figure 2.3 andaccompanying text for an explanation.

The distance between the gas-inlet tube, or, in our case, the oxygen inlettube, to the sample was 8 cm and the diameter of the inlet was 1.0 cm.First we grew the samples with 2 50 mV of baratron pressure, whichis equivalent to 0.02 0.50 Pa. During the preparation of the films wefound that titanium was very reactive with oxygen in contrast to vanadium[37, 36]. Even at 0.02 Pa of oxygen baratron pressure it turned out wewere still able to grow TiOx, which was later confirmed by RutherfordBackscattering Spectroscopy (RBS) measurements, because we could stillfind a relatively strong oxygen peak in these measurements. This indicatedthat we still had not reached the lower limit of TiO0.71. At 0.02 Pa it was

quite difficult to keep the gas flow constant, so to decrease the baratronpressure in this arrangement was out of the question. The solution wasfound in changing the diameter of the gas inlet. The amount of particlesarriving at the sample (f) is, in the molecular flow regime, proportional tothe diameter of the tube to the power three (d3) and the length of the tube(l)

f d3

l(2.1)

provided we keep the distance of the end of both tubes to the sampleconstant. If we now halve the diameter of the delivery tube, i.e. make

it 0.5 cm instead of the previous 1.0 cm, it results in an eightfold decreaseof particle flux arriving at the surface of the sample. This allowed us todecrease the oxygen flux while keeping it stable at the same time.The samples used for conductivity measurements were capped in situwith a MgO cap-layer after the chromium contacts were deposited. Themagnesium, 99.999% purity, was evaporated from a Knudsen-cell with atemperature of 155C. The oxygen baratron pressure used was 1 Pa, makingthe background pressure inside the system in the order of 102 Pa. Duringthe evaporation of Mg the substrate was kept at RT.

2.4 Results and Discussion

In this section we will show our results categorized by the technique used.We will start with RHEED, from which especially the so called rotationmovies are interesting. To our knowledge the rotation movie technique isnot used very often. We believe this is a pity because as we will show, itis in fact a very powerful tool for determining the crystal structure. Wethen continue with XRD. In the past there have been studies in whichthe relation between oxygen content of the titanium oxide versus latticeparameters for bulk samples was established [6]. We repeat this research


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2.4. Results and Discussion 11

for epitaxial thin films. Finally, we will present resistivity data obtainedusing the four point probe method. We wanted to determine whether or

not our layers are metallic or semiconducting, and whether their resistivityis comparable to bulk data.

2.4.1 RHEED

During the growth of every sample we recorded a RHEED movie not only formonitoring the growth but also for doing post-growth analysis of the growthof the sample. During growth we would like to see RHEED oscillations andafter growth we can analyze the evolution of the recorded RHEED patterns

and determine the lattice parameters. Along with the RHEED movie wemeasured the baratron pressure, the substrate temperature and the titaniumflux as displayed by the e-gun evaporator. So, for every frame of the RHEEDmovie we also have information about these three parameters, giving anaccurate account of growth conditions. At the end of the growth we made aRHEED rotation movie, which enabled us to determine the structure of thelayer. In Appendix A the different uses of RHEED are discussed in moredetail.

RHEED oscillations

RHEED oscillations are commonly observed during sample growth if thegrowth is layer-by-layer like. They are a useful tool for determining growthrates, because one oscillation-period is equal to the time needed to grow asingle atomic layer. They will also give useful information about the growthconditions. RHEED oscillations do not appear if there is no layer by layergrowth. If samples become rough very soon the oscillations will damp outfast. This indicates that the growth conditions are not optimal. If there areonly a few oscillations, the determination of the flux rate is evidently more

difficult and inaccurate, but it still gives a rough estimate.In figure 2.3 we show the RHEED oscillations obtained from one of oursamples. Displayed are the fist twelve oscillations. These oscillations aremeasured in about 315 5 time units. The oscillation period is therefore3 (315 12) = 78 seconds and is equal to the time it took for one layerto grow. The thickness of one titanium oxide layer is half that of the cubicunit cell, so 4.19 2 = 2.095 A, making the TiOx flux 1.62 A/min. Wekept growing this layer for 125 minutes, so we expect the layer to have athickness of 1.62 125 = 202.5 A. From XRD measurements a thickness of204.9 A is obtained, which is in very good agreement. From the RHEEDwe can also see that the oscillations are damping out. This is an indication


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Figure 2.3: Here a plot of RHEED oscillations of the specular spot is shown.In total there are twelve oscillations visible in 315 5 time-units. This means

the oscillation has a period of about 26 time-units, each time-unit being threeseconds. Every oscillation is equal to 1 ML of TiOx, having a thickness of 2.10A. Our growth rate is therefore (2.10 (3 26)) 60 = 1.62 0.05 A/min.

of roughening of the sample surface.

RHEED images

In RHEED we can distinguish between two general patterns. These two

patterns appear for both substrates. We start off with the TiOx

samplesgrown on MgO substrates. In figure 2.4 A) we show the RHEED patternof a clean MgO substrate and in figure 2.4 B) the RHEED pattern of thedeposited TiOx layer. The pattern looks the same and it is the same exceptfor the distance between the RHEED lines, which is directly related to thelattice spacing. In figure 2.5 we show the evolution of the separation ofthe two outermost RHEED streaks. At t = 0 seconds the distance betweenthe lines is equivalent to the lattice parameter of MgO. When the shutteris opened at t = 60 seconds the distance between the lines first decreasesfrom 210.4 to 208.6 pixels and then increases to about 211.5 pixels. Thisis the in-plane lattice parameter of the strained TiOx thin film with a


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Figure 2.4: Shown areA) the RHEED pattern of a clean MgO substrate and B)

the RHEED pattern of the resulting TiOx thin film on top of the MgO substrate.

lattice parameter of (210.4 211.5) 4.212 = 4.190 A. When the filmreaches the critical thickness after t = 1450 seconds, the lattice parameterrelaxes to the films intrinsic value which is not affected by the substrateanymore. We can now calculate the in plane lattice parameters. Its valueis (210.4 212.2) 4.212 = 4.176 A, which is a reasonable value for TiOx.The lattice of MgO is larger than that of TiOx, by approximately +0.5%.This means that the titanium oxide will have tensile strain, i.e. the in-

plane lattice parameters are increased with respect to the bulk value. Thisis exactly what we see happening in figure 2.5.

In figure 2.6 A) we again show a RHEED pattern of a MgO substrateand in figure 2.6 B) the RHEED of the layer grown on this substrate. Thesample from figure 2.4 and the sample from figure 2.6 have comparablethicknesses, 205 5 A and 226 5 A respectively. They were also grown atthe same temperature of 400C. The deposition rate was different for thetwo (3.42 0.05 A/s and 1.88 0.05 A/s) as well as the oxygen baratronpressure (0.05 Pa and 0.08 Pa). In other words, the sample from figure2.6 had more oxygen available per titanium atom. If we now look at the

RHEED pattern, it is clear that this image is different from the previoussample, and it is the second general TiOx RHEED pattern observed. Therenow have appeared pairs of lines between the MgO streaks. In figure 2.7we show a transverse scan through the RHEED pattern, taken at the endof growth (line of intermediate thickness). Also shown are the RHEEDintensities of the substrate (thin line) and the difference between these two(thick line). The peak positions are indicated by arrows. They divide thearea between the two outermost peaks in six equal sized parts. Since thetwo outermost peaks are almost at the same position as the MgO peaks,the titanium oxide unit cell has become about three times that of MgO.We have performed the same analysis on samples grown on MgAl2O4. In


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Figure 2.5: Plot of the evolution of the separation between the two outermoststreaks in the RHEED pattern of figure 2.4. In the beginning we have MgO (asindicated) with a distance between the two streaks of 210.4 pixels. Immediatelywhen the shutter is opened the intensity of the RHEED pattern decreases, andthe determination of the peaks positions is more difficult, hence a dip in the plot.

When the RHEED stabilizes again we observe an intermediate phase of strainedTiOx. After reaching the critical thickness, in the plot after 1350 seconds, weagain see a small dip before the rest of the film grows relaxed. The relaxed TiOxis also indicated and there the separation is 212.2 pixels. If we now divide thesetwo values and multiply with the (in-plane) lattice parameter of MgO we get asin-plane lattice parameter for TiOx, a = b = 4.178 A.

figure 2.8 A) the RHEED pattern of a clean MgAl2O4 substrate and in figure2.8 B) the RHEED of TiOx grown on this substrate is shown. MgAl2O4

has a unit cell which is about twice that of natural TiOx

. It is therefore notsurprising that the final TiOx layer has streaks which are separated by twicethe amount of the distance between the RHEED lines of the substrate.

On MgAl2O4 also TiOx with a superstructure can be grown (figure 2.9).The pattern is similar to the one of TiOx on MgO. When we look atthe RHEED evolution of this film (figure 2.10) we see that two of thesubstrate streaks disappear immediately after growth has started. Aftersome time (about 750 seconds) there appear pairs of streaks between theremaining streaks. The RHEED image is now similar to that of TiOx witha superstructure on MgO (figure 2.6). The pattern is also divided into sixequally spaced peaks. If we plot the in-plane parameters against oxygen


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Figure 2.6: FigureA) shows the RHEED pattern of the clean MgO substratebefore growth and B) shows the RHEED pattern of the resulting TiOx thin film.The white line indicates the position where the scans in figure 2.7 were taken.

Figure 2.7: A line taken from both images in figure 2.6. On the x-axis the pixelsare displayed and on the y-axis their intensity. The thin line is the RHEED fromthe substrate showing the three lines as three peaks. The thicker line is the TiOxfilm with the superstructure showing in total 7 peaks. The thickest line is thedifference between the two, the arrows marking the positions of the peaks.

content of the TiOx layer and compare these to the MgO case, we can seethey are different.


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Figure 2.8: Displayed in A) is the RHEED pattern of the clean MgAl2O4substrate and in B) the RHEED pattern of the resulting TiOx thin film. Thereis no superstructure visible.

Figure 2.9: Here we present A) the RHEED and transmission pattern of TiOxwith a superstructure grown on a MgAl2O4 substrate and B) RHEED pattern ofa different TiOx sample grown on MgAl2O4 also with a superstructure but witha different roughness, so no transmission. Also have a look at Appendix A for anexplanation about the patterns.

The results for our TiOx samples on MgO and MgAl2O4 are displayed infigure 2.11 A) and B). In this graph the black squares and triangles representthe samples on MgO and the white squares and triangles represent those onMgAl2O4. For both substrates the squares represent data obtained from theRHEED pattern and the triangles represent data obtained from XRD. Inthe visualization of our results we make use of the thickness of our samples.Because the flux of titanium was not the same for all the samples and thetime we grew was different for different batches, we use the thickness of thesamples, determined by XRD, to scale them. This scaling turned out tobe much more fruitful than scaling with oxygen baratron pressure alone.


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Figure 2.10: The RHEED pattern evolution of a TiOx sample with asuperstructure grown on a MgAl2O4 substrate. Indicated in black at thebeginning and the end of the scan are the positions of the peaks of the RHEEDlines. Indicated in white is the position from where the superstructure clearlyappears.

We are however aware that this scaling need not to be continuous, due tophase transitions of the titanium oxide. In our scaling this will cause someoverlap between points, i.e. the titanium oxide phases with and withoutsuperstructure coexist for some values. Figure 2.11 A) shows the in planelattice parameters of TiOx without superstructure for both substrates andfigure 2.11 B) shows the same for TiOx with a superstructure. The valuesare similar for both substrates suggesting that in both cases we are lookingat relaxed samples. It was shown in figure 2.5 that the film relaxes (inthat case) after 1450 seconds. We usually grew for more than 1 hour,

so the above conclusion is probably correct. The trend seems to be thatthe in-plane lattice parameter is increasing with oxygen content for thenormal titanium oxide and the in-plane lattice parameter is decreasingwith increasing oxygen content for the reconstructed titanium oxide. Thisresult is quite surprising, because for bulk samples the lattice parameteralways decreases with increasing x. We should mention that determiningthe lattice parameter from RHEED is error sensitive, because of the varyingquality of the RHEED patterns. The area-scans are more accurate, and theyshow a lattice parameter for TiOx of a = b = 4, 20 0.01 Angstrom, eventhough x is different for the samples.

RHEED rotation

We would like to have more information about the two kinds of samples,i.e. the ones with and without a superstructure, in order to find out whatthe origin of the superstructure is. RHEED rotation movies are a powerfulltool for determining the crystal structure in situ. Especially the samplesthat show a transmission and a RHEED pattern are very useful, becausethat pattern does not only provide us with the in-plane lattice parameter,but also with out of plane information. Furthermore, we can do simulationsof this pattern for a specific structure which we can then compare with


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Figure 2.11: Lattice a- and b-parameters for titanium oxide layers on MgOdetermined from the area-scans (black squares) and RHEED (black triangles),and on MgAl2O4 from the area-scans (white squares) and RHEED (white

triangles). In A) we show the samples without a superstructure and in B) theones with a superstructure. The scaling we use (mV/(A/sec)) is defined in thetext.

our measurement. See Appendix A for an explanation of how we obtain aRHEED rotation movie and how to do the simulations.If we make a rotation movie of a TiOx sample grown on MgO we get figure2.12. From this figure we can see the lattice is cubic, as it should be fora relaxed rocksalt-like material. The resemblance is striking if we comparethis to the same kind of rotation picture from a simulation of the rocksalt


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Figure 2.12: RHEED rotation image of a TiOx thin film grown on a MgOsubstrate. For an explanation about RHEED rotation images have a look atAppendix A. The heights at which these slices are taken are at the bottom andhalfway the reciprocal space unit cell.

structure (figure 2.13).The next structure to treat is the TiOx with a superstructure. In


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Figure 2.13: RHEED rotation image of a simulated MgO substrate. The heightat which this slice is taken is comparable to the bottom slice of the previous figure,figure 2.12.

figure 2.14 we show the rotation movie of a film grown on MgAl2O4. Itis clear this rotation movie is different from that of figure 2.12, althoughthe basic square lattice is still apparent. When we analyze the RHEEDrotation movie at different heights with respect to the sample surface, weobtain the threedimensional picture of the reciprocal unit cell. By carefullyexamining the positions where the intensity of the RHEED spots are a

maximum we can conclude that theTiOx is growing in a rocksalt lattice,

but one out of three titanium sites is vacant. We will now explain how wecome to our conclusion. From the careful examination of the positionsof maximum intensity, looking along the c-direction, we were able todistinguish six different levels in the reciprocal lattice. It also indicatedwe were dealing with a body-centered reciprocal unit cell. Using this as abasis, we constructed an orthorhombic unit cell with unit cell parameters|a| = 1

3|a

c|2, |b| = |a

c| and |c| = |a

c|2. This makes the volume of the

reciprocal cell V equal to 23Vc

.The reciprocal lattice just described and the accompanying cell are

depicted in figures 2.16 and 2.17. In real space we have a face-centered unit


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Figure 2.14: RHEED rotation image of a TiOx sample with a superstructuregrown on a MgAl2O4 substrate.

Figure 2.15: RHEED rotation image of a simulated TiOx sample with asuperstructure.

cell with a volume of one and a half times that of the rocksalt unit cell.The total number of atoms and vacancies in the rocksalt unit cell is 4 sofor our face-centered cell this is six. Since we are dealing with TiOx the


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Figure 2.16: The reciprocal space proposed TiOx structure. Only one domainis shown.

Figure 2.17: The reciprocal space proposed TiOx structure. Only one domainis shown.

basis consists of 3(TinVac1nO) if x in TiOx is greater than one. If thematerial is stoichiometric, we can form Ti2O3 + VacTi or TiO3 +2VacT i.From this Ti2O3 + VacTi is the most probable one, which was also ourprevious conclusion. The real space cell is drawn in figures 2.19 and 2.20.

The observed complex mix of transmission and RHEED patterns (figure2.9) are obtained if the lattices of all equivalent domains which may beobtained by a fourfold rotation of the body centered orthorhombic latticeof figure 2.18 are superimposed. When we simulate this structure and makea rotation movie we get figure 2.15.

Here we would also like to mention a peculiar effect we saw in some ofour samples. In figure 2.21 we show the RHEED rotation movie of a TiOxsample grown on MgAl2O4. As can be seen, the resulting figure consists of asquare grid of lines. The points where the lines intersect are the positions ofthe RHEED rods. The lines are caused by the phenomena that the vacanciespresent in the sample order in a certain direction, but are disordered with


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Figure 2.18: Two of the four identical unit cells in reciprocal space of the

proposed TiOx superstructure indicated in grey in the reciprocal unit cell ofrocksalt. All the possible domains are drawn in this figure, that is why it seemsthe unit cell has more than four atoms in it. Attention should only be paid tothe atoms at the corners of the unit cells.

respect to each other in the two perpendicular directions. Because of this,

the lattice sum

Rn

eiQRn is only discrete in one direction. These diffuse

planes cause lines like we see in figure 2.21. The fact that the lines are atevery plane perpendicular to the c-direction also supports this idea.The effect was previously observed in LEED [24]. Our RHEED rotationimages are actually comparable to LEED images, only for the latter it isnot always possible to obtain an image, especially for rough samples. In thethesis of F.C. Voogt [24] the effect is described for a MgO substrate. Therecalcium segregation causes (110) planes of diffuse intensity. This indicateslong range order in one [110] or [111] direction, but disorder in the [111] or[110] direction perpendicular to it, i.e. they correspond to one-dimensionalline features. The streaking in LEED was accompanied in RHEED by asplitting of the diffraction rods, just like the RHEED pattern of the streakyrotation movie was split up (figure 2.6).

2.4.2 XRD

A known property of TiOx is the decrease of lattice parameters withdecreasing oxygen content [6]. Since the epitaxially grown thin films are(partially) strained in the in-plane direction, probably the best way toobserve the dependency of the lattice parameter on oxygen content of thefilm is in the out of plane direction. Through the Poisson-ratio we couldalso relate this to a volume change of the unit cell. With X-rays we canalso determine the critical angle c, i.e. the angle below which there is


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Figure 2.19: The real space proposed TiOx structure.

Figure 2.20: The real space proposed TiOx structure.

total reflection and above which part of the photons is absorbed. This is anumber directly related to the electron density, i.e. the number of electronsper unit cell, of the material. This gives us information about the phase ofthe material under investigation.

Reflectivity

In analyzing the samples using XRD, the first measurement we usuallyperformed was a reflectivity scan, i.e. a 2 scan near c. Because theobtained curve is mostly a result of kinematical processes, we can accuratelysimulate these scans. By fitting the obtained curve we can in this waydetermine several important properties of our thin film. The properties areelectronic density, thickness and roughness of interface and surface. Fromthe critical angle c (in radians) we can deduce the electron density ethrough the relation

e

re

22c

(2.2)


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Figure 2.21: RHEED rotation image of a TiOx sample with a superstructuregrown on a MgAl2O4 substrate, seemingly showing lines connecting the rocksaltlattice points.

where is in our case equal to the Cu-K radiation wavelength and re isthe classical electron radius. For a typical value for the critical angle ofc = 0.31 /180 we get an electron density ofe = 1.376 e/A3.In figure 2.22 we show our results for the electron density of our samplesversus the previously defined scaling of oxygen baratron pressure (in mV)divided by the deposition rate. As can be seen there are two separate regions

of points for both kinds of substrates. One region with an electron densityof about 1.62 1.67 A3 corresponds to the calculated electron density ofstoichiometric TiO, which is 1.663 A3. The other region with an electrondensity of about 1.30 1.36 A3 seems to correspond to the calculatedelectron density of Ti2O3, which is 1.314 A

3.In the ideal case, the deposition rate would be kept constant and only theoxygen flux would be varied. In our case, however, during growth we hadproblems keeping the deposition rate constant between different samples,although there was no problem keeping the deposition rate constant for onesample. This was caused by problems with the e-gun evaporator describedbefore in section 2.3. Therefore we followed another method. We kept


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Figure 2.22: Electron density versus our scaling, defined in the text, of baratronpressure in mV divided by the deposition rate in Angstrom per second for MgO(white circles) and MgAl2O4 (black squares). The lines indicate the error bar ofeach point. They only point in one direction because the error depends on theobserved oxygen baratron pressure, which is an upper limit to the real baratron

pressure.

the amount of oxygen, i.e. the baratron pressure, constant and changed thedeposition rate. By determining the layer thickness, the effective depositionrate could be determined after growth, and the sample would get its placeon our scale. By increasing the deposition rate and keeping the oxygen fluxconstant, we move towards zero in our scaling. If we have a constant oxygen

pressure and a relatively large deposition rate, we grow TiOx

. If we have arelatively low deposition rate, we grow titanium oxide with a superstructure.There is some overlap, probably because of a phase transition. This overlapis in the region of our scaling of about 2.5 3.0 mV/(A/min).It is clear that for TiOx the electron density increases with increasingamount of oxygen. This means that the volume of the unit cell is decreasingwith an increasing amount of oxygen, in agreement with experimentalobservations. The electron density of Ti2O3 seems to be decreasing slightly,implying an increase in unit cell volume with an increasing amount ofoxygen.


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Figure 2.23: Overlay of two 2 scans, also called wide-scans, of TiOx layerson MgO. The normal TiOx, at a 2 value of about 43.0, has a plane spacingof 2.099 A. The TiOx with a superstructure can be found at a 2 value of about45.3, and a plane spacing of 1.991 A.

Figure 2.24: Overlay of two 2 scans, also called wide-scans, of TiOx grownon a MgAl2O4 substrate. The normal TiOx, at a 2 value of about 41.0, has a

plane spacing of 2.191 A. The TiOx with a superstructure can be found at a 2value of about 42.5, and a plane spacing of 2.120 A.

Wide-scans

Wide-scans are 2 scans like reflectivity scans but far away from c.They typically run over about 100 in 2. From these scans the distancebetween crystallographic planes can be determined through the Braggrelation 2dhkl sin = n. For our samples grown on MgO and MgAl2O4


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Figure 2.25: Lattice parameter versus x in TiOx for bulk crystals, taken fromreference [6].

we used this type of scan to determine the lattice c-parameter. In figure

2.23 an overlay of wide-scans of the two different types of TiOx grown onMgO is shown. In figure 2.24 we show the same for MgAl2O4 as a substrate.As can be seen, it is easier to distinguish between the two different types inthe case of MgAl2O4 as a substrate.

In figure 2.25 we show a plot of the lattice parameter versus x in TiOx forbulk samples, taken from reference [6]. The lattice parameter and thereforealso the unit cell volume linearly decreases with increasing oxygen content.

Since we can determine from the RHEED patterns if there is asuperstructure present or not we can already divide our data into twosets. In figure 2.26 A) and B) we show the data collected for the c-

parameters of our films on both MgO (black points) and MgAl2

O4

(whitepoints) substrates plotted against the previously defined scaling. For bothsubstrates the squares represent data obtained from the wide-scans andthe triangles represent out of plane data obtained from area-scans. Thein-plane data obtained from area-scans was already shown in figure 2.11.Figure 2.26 A) shows the out-of-plane lattice parameters of TiOx withoutsuperstructure for both substrates and figure 2.26 B) shows the same forTiOx with a superstructure.As can be seen, the c-parameter for both substrates decreases withincreasing oxygen content, as expected. However, the values for titaniumoxide on MgAl2O4 are larger than those on MgO. For MgO the tensile strain


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Figure 2.26: Lattice c-parameters for titanium oxide layers on MgO from thewide-scans (black squares) and the area-scans (black triangles), and on MgAl2O4from the wide-scans (white squares) and area-scans (black triangles).

imposed by the lattice mismatch does not modify the lattice parameters toomuch, but for MgAl2O4 this is different. The compressive strain seems toincrease the out of plane lattice parameter by about 4% with respect to thebulk.When we compare our scale with the one from figure 2.25, we can see thatour scale runs from about 1 mV/(A/min)to about 5 mV/(A/min) comparedto an x that runs from 0.72 to 1.28. Since the c-parameter changes from4.20 A to 4.17 A in our measurements and from 4.20 A to 4.17 A in reference


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Figure 2.27: Area-scan of the reciprocal plane spanned by the MgO(004) andthe (202) reflection, also showing the TiOx(002) and (202) reflections.

[6], we believe the two scales are comparable, i.e. they illustrate the same

phenomena.For the titanium oxide with a superstructure the magnitude and behaviorare also different for both kinds of substrates. For the samples on amagnesium oxide substrate the lattice parameter decreases with increasingoxygen content, just like the titanium oxide without superstructure. Forthe samples on MgAl2O4 however, the lattice parameter seems to stay moreor less constant. The c-parameter is larger than that of samples on MgO.

Area-scans

Area-scans made with XRD are very helpful if the crystal structure of thethin film is more or less known. There are different kinds of area-scans thatwe can perform with our XRD apparatus. One of them, the one where arange in 2 is divided into discrete steps and at every step a -scanis measured, is the most used area-scan. These scans produce an imagelike figure 2.27. We are growing TiOx in the rocksalt structure, so weexpect the same reflections as for MgO. In figure 2.27 we show an imageof the reciprocal plane spanned by the (004) and the (202) reflections ofMgO and in figure 2.28 we show the reciprocal plane spanned by the (004)and the (222) reflections of MgO. These reflections are indexed in bold


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Figure 2.28: Area-scan of the reciprocal plane spanned by the MgO(004) andthe (222) reflection, also showing the TiOx(002), (004) and (113) reflections.

Figure 2.29: Area-scan of the reciprocal plane spanned by the MgAl2O4(008)and the (404) reflection, also showing the TiOx(002) and (202) reflections.


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Figure 2.30: Area-scan of the MgO(113) reflection, also showing the strainedTiOx(113) reflection.

Figure 2.31: Area-scan of the MgAl2O4(226) and the TiOx(113) reciprocallattice points. There is also a powder line visible, originating from the aluminumsample holder.

in the figures. Since MgO also has a NaCl type of structure all the MgOreflections are accompanied by TiOx reflections, indicated in italic in bothfigures. In figure 2.29 we show the reciprocal plane spanned by the (008)and the (404) reflections of MgAl2O4. It also shows the TiOx (002), (004)and (202) reflections. The substrate reflections are again indexed in boldand the ones from the film in italic.If we zoom in on certain reflections, the area-scans provide us withinformation about the strain or relaxation of the thin film. In figure 2.30we have zoomed in on the (113) reflection of MgO. Also visible is the (113)


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A B

Figure 2.32: A) a side-view of a sample with contacts evaporated beforefilm deposition B) a side-view of a sample with contacts evaporated after filmdeposition. In black are the contacts, striped is the substrate and dotted is thefilm.

reflection of TiOx. It appears as a streak right above the MgO reflection.

This means the film is fully strained, i.e. it did not take on its own a-and b- lattice parameters. The strain is caused by the lattice mismatch,which in the case of MgO is +0.5% and in the case of MgAl2O4 is 3.5%.Measuring area-scans of off-specular reflections will thus provide us witha- and b- lattice parameters as well as the out of plane c-parameter. Thec-parameters obtained in this way were already shown in figure 2.26 andin figure 2.11 we show a plot of the in plane lattice parameters versus ourscaling. For MgAl2O4 we expect the TiOx (113) reflection to lie next to thesubstrates (226) reflection. In figure 2.31 we show this is indeed observed.What is immediately clear from this picture is that it is completely different

from that of the TiOx (113) reflection on MgO. The titanium oxide layer ofthis sample is completely relaxed, hence there is no streak visible.

2.4.3 Resistivity

In order to perform conductivity measurements on our samples there hadto be contacts on the samples. These contacts can either be deposited exsitu on the dirty substrate after which it is introduced into vacuum andcleaned by heat treatment or in situ on top of the freshly grown sample.

We chose to follow the latter procedure after experiencing problems withthe first one. We used chromium for contact material. One of the problemswe encountered with evaporating contacts before cleaning the substrate isthat they would oxidize to Cr2O3 during the substrate cleaning process orthe sample growth process. We conclude this from the drastic decreaseof conductivity and the change of color from silvery to transparent of thecontacts. By evaporating the contacts after the cleaning process and afterthe film was grown, the contacts will not oxidize by these steps. Anotherreason for putting on the contacts in situ is illustrated by figure 2.32. Thecontacts evaporated on the substrate ex situ are much thicker than our film.This will result in macro-steps in our film (figure 2.32 A). Shadowing will


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Figure 2.33: Resistivity versus 1000/T curves of different samples on MgO(white) and MgAl2O4 (black). On top or on the left the curves ar shown fornormal samples. In the middle picture we show the digitized curves fromreference [6], i.e. resistivity curves for bulk samples. In the figure on the bottom oron the right we show the resistivity curves for the samples with a superstructure.


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make the contact of our film with the metal strips poor. The interfacebetween the contacts and the film is not well defined and dislocations

and defects are present at the boundary. The resistivity measurementsmay therefore give unrealistic results. In the case where we evaporatethe contacts after film growth (figure 2.32 B) most of these problems arecircumvented. In some cases we were even able to grow epitaxial Cr-contacts on the film. This means the interface is well defined and resistivitymeasurements are much more reliable. For these reasons we preferredmethod B over method A.We performed resistance measurements from 5K - 300K on our samples.We did this to be able to compare available bulk data with our samples. But,to be able to compare these resistance measurements, we have to convert the

resistance into the resistivity. For this we need four ingredients, namely themeasured resistance (R), the distance between the contacts (d), the lengthof the contacts (l) and the thickness of the film (t). Since we used the fourpoint probe contact method for measuring the resistance we dont have toworry about contact resistances or interface resistance. Now, through therelation

= (td

l)R (2.3)

we can calculate the resistivity. We note that the thickness of the film hasthe largest uncertainty of the measured parameters. This is because thecontacts and MgO cap-layer complicate the determination of the thicknesswith XRD. With typical measured values for R = 30 , d = 1, 25 mm,l = 10 mm and t = 100 A we get a resistivity of = 3 105 cm, whichis about the same as for bulk titanium oxide.The bulk data is displayed in the center pane of figure 2.33 using the samescaling, log() vs. 1000/T, as the other two panes. In our resistivitymeasurements we observe two types of behavior. In one case the resistancevaries only a little with temperature, not even one order of magnitude. In

the other case it changes considerably, more than two orders of magnitude.These two cases are shown in the left and in the right panel of figure2.33, respectively. We attribute these different behaviors to two differentstructures. The points measured in the left pane of figure 2.33 were obtainedfrom TiOx samples without a superstructure, like the one from figure 2.4.They are quite similar to the resistivity measurements of bulk samples. Themeasured points from the right panel were obtained from titanium oxidewith a superstructure, like in figure 2.9. This behavior is quite differentfrom that of the bulk, again showing we are dealing with another phase ofTiOx.


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Figure 2.34: Resistivity versus temperature curve showing the superconductingtransition of our TiOx thin film. The apparent hysteresis is caused because theteperature sensor is not measuring the temperature exactly on the position of thesample.

Superconductivity

TiOx is also superconducting with a transition temperature varying withx. In literature values have been reported of 0.47K for a sample underpressure with an x of 0.8 6 u p t o 2.07K for a single crystal underpressure with an x value of 1.22 [6]. We also tried to measure thesuperconducting transition temperature in one of our samples. We observeda transition at about 0.65K (fig 2.34). The measurement was performed ina He3 refrigerator that could reach a minimum temperature of 0.3K. Theapparent hysteresis loop is caused by the difference in location of sample

and temperature sensor. This caused the sample to, during cooling, reachthe superconducting transition temperature before the temperature sensormeasured that temperature. During heating, the sample would reach thetransition temperature again before the temperature sensor, and in this waythe hysterisis loop is formed. Although the resistance of the sample doesnot entirely drop down to zero, we still believe this is the superconductingtransition we observe. This is because the resistance decreases exactly inthe range where we would expect it.One of the reasons why the resistance did not become zero could be thelayout of the contacts. Under influence of the chromium contacts, whichremained in a normal state, parts of the thin film remained in the normal


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stoichiometry of the TiOx thin film. With this extra information we can alsodiffer between the number of oxygen and titanium vacancies. A comparison

between c-parameters of our thin films and those of single crystals suggeststhat we are covering the whole known range of x in TiOx.

2.6 Outlook and Recommendations

For future research we have a few recommendations. We for instance showedwhy we believe it is favorable to deposit electrical contacts in situ. Werecommend this method and suggest to experiment with different layouts ofthe contacts. The superconductivity measurements were a time consumingbut interesting thing to do. We believe the Tc of our films can be increasedto higher values than known for bulk crystals. Since bulk crystals obtaina higher transition temperature when pressure is applied upon them, wethink that by imposing a pressure up on a film through lattice mismatchwill modify the Tc of the film. By choosing the right substrate a film witha higher Tc than that of the bulk can be obtained.We recommend evaporation of titanium from a Knudsen cell instead offrom a e-gun evaporator. The flux control is much more stable because thepower input is more constant. It also makes the calibration more easy andreproducible. We saw in our experiments with an e-gun evaporator that

settings had changed when we had replaced the titanium rod. The onlyproblem we see with the Knudsen cell is the high temperature needed toevaporate titanium. This could cause other materials to start evaporating aswell. Good shielding and a tungsten insert in the Al2O3 cruicible probablyovercome this problem.Titanium is very reactive with oxygen. In further research this property hasto be recognized. We solved this by decreasing the diameter of the deliverytube. The samples should also be made thinner. For a lot of the sampleswe passed the critical thickness, where strain effects due to the substrateare already lost or at least much smaller than below dcr.

We tried to determine the stoichiometry by growing our films with18

O andmeasure them with RBS. The attempt failed, mainly because of choosingthe wrong thickness of the films, capping of the samples and channellingeffects. When we made our calibration samples we were also not aware of thegreat reactivity of titanium with oxygen. The measurements we performedmainly resulted in an x of about 1.5 in TiOx. We suggest to redo thesemeasurements with the smaller delivery tube and titanium evaporated froma Knudsen cell. Make sure there are no channelling effects in the measuredRBS spectra because this makes fitting of the spectra impossible.

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Properties of TiOx Thin Films