Studying surface diffusion processes with time resolved RHEED

Transcription

1 Low Temperature Division Studying surface diffusion processes with time resolved RHEED author: A.E. Molag supervisor: dr. A.J.H.M. Rijnders Graduation committee: Prof. D.H.A. Blank Dr. A.J.H.M. Rijnders Prof. H. Rogalla Dr. H. Zandvliet

2 Studying surface diffusion processes with time resolved RHEED Summary In order to study the surface diffusion energy strontium ruthenate (SRO) and strontium titanate (STO) thin films were grown with pulsed laser deposition. By varying ambient gases the oxidation state of ablated material was modified in order to influence surface chemistry. Surface diffusion time measurements were carried out using an in-situ high-speed time resolved RHEED system. By fitting a double exponential intensity decay model to the RHEED intensity measurements a time constant was extracted. The theoretical analysis of time-dependent ad atom diffusion predicts the following relation between diffusion coefficient Ds, relaxation time constant τ and the terrace length: L D s (.17) τ By plotting τ versus absolute temperature in an Arrhenius plot the surface diffusion energy was calculated. The theoretically predicted dependence of ad atom concentration on oxygen partial pressure was not observed. Physical justification to the double exponential intensity recovery model is given by calculating the diffusion energy in a case where the single exponential decay model fails. The change in the ratio parameter d of this model indicates a change in growth mode. Growth experiments of SRO films in ozone prove that ozone reacts with the TiO terminated surface of the STO substrate, resulting in etch pits and increased film roughness. This problem can be overcome by activating the ozone supply after deposition has started. Acknowledgements I would like to thank the entire low temperature group, in particular the members involved in materials science, for the good atmosphere and useful comments during the group meeting and in the coffee room. First of all I would like to thank my direct supervisor Guus for the discussions on surface diffusion, the comments on my report and his explanation on how to do AFM measurements. Mark explained me everything about the RHEED system and also gave useful critical remarks on this thesis. I would also like to thank Frank R. for keeping the RHEED system, the laser and of course the diamond saw operational. Ans en Inke were very helpful during the final stages of creating this thesis. Dragana provided help with using the dipping station, Matthijn on STO substrate treatment and XRD and Martijn also with XRD. Ideas and experiments on the role of ozone in film growth, especially etching, were discussed with Joska and Mark. Last but not least Frank V. for his PDF assistance.

3 Studying surface diffusion processes with time resolved RHEED 3 Contents Introduction Experimental Pulsed Laser Deposition Laser ablation Plasma expansion Surface diffusion and growth Reflective High Energy Electron Diffraction Basic operating principles Intensity oscillations High pressure RHEED Substrate treatment and analysis Deposition conditions PLD thin film growth theory Thermodynamics versus kinetics Burton Cabrera Frank theory of crystal growth Mobility of adsorbed molecules on a crystal surface Supersaturation BCF without re-evaporation BCF as a starting point for PLD growth modelling Chemical reactions on the surface Data analysis RHEED response to a single laser pulse Single exponential RHEED intensity decay model Double exponential RHEED intensity decay model Reduced single exponential RHEED intensity decay model Reduced double exponential RHEED intensity decay model Single exponential RHEED intensity decay model with RHEED drift correction or ozone etching effect Arrhenius plots obtained with different models Calculating surface diffusion energies Single exponential RHEED intensity decay model results Results double exponential RHEED intensity decay model Numerical aspects of determining relaxation times Curve-fitting in Origin or Labview Dependence on fitting length Dependence on filtering Conclusion and recommendations Homo-epitaxy of Strontium Titanate Surface diffusion energy Previous surface diffusion energy studies Calculated surface diffusion energies Trends in surface diffusion energy Manipulating the growth mode by varying the partial oxygen concentration Slowly increasing the amount of oxygen Slowly decreasing the amount of oxygen Determining a rate-limiting element Conclusion and recommendations... 33

4 Studying surface diffusion processes with time resolved RHEED 4 5 Hetero-epitaxy of strontium ruthenate Initial growth transition Interval experiments Ozone surface effects Eliminating the ozone reaction with TiO Effect of ozone on crystal structure Effect of ozone on Residual Resistivity Ratio Conclusion and recommendations Conclusion Literature Picture front cover: The PLD system with in-situ RHEED that was used to grow the films described in this thesis and to measure all relaxation time constants.

5 Studying surface diffusion processes with time resolved RHEED 5 Introduction Tremendous progress has been made in thin film materials science over the last 5 years. The development of new in situ analysis techniques such as Reflective High Energy Electron Diffraction (RHEED) made it possible to grow high purity thin films in a controlled fashion. Analysis of these layers also underwent a revolution with the invention of various scanning probe methods, primarily the atomic force microscope and scanning tunnelling microscope. Scientists had wondered for ages exactly what happens when atoms descend from a vapour to attach to the surface of a crystal. Even today it remains popular to think of film growth in terms of marbles rolling around a table 1. Figure 0-1 Surface diffusion of atoms along different paths, each with a different energy barrier. On the right a detailed STM image showing the kinks and steps on a real surface. From [1] The problem with using concepts, such as marbles to describe film growth, is that marbles on a table will tend to move in a straight line, while an atom on a surface will display random hopping. The aim of this project is to gain further insight in the surface processes that occur during thin film growth. The main interest is in surface diffusion times, the time it takes for a deposited ad atom to reach its nucleation site. The experimental techniques used to measure diffusion times are treated in chapter. In this thesis diffusion processes, during growth of complex oxides with Pulsed Laser Deposition (PLD), are studied using time resolved RHEED. PLD is a deposition technique in which deposition and film growth are intrinsically separated in time. This property allows one to deposit material on a clean surface and then wait for it to diffuse and incorporate in the growing film before depositing more material. The in situ tool used to measure the time scale of such diffusion processes is Reflective High Energy Electron Diffraction (RHEED). The intensity of the diffracted beam is modulated by the step density on the surface. Measuring the time dependence of this diffracted beam during growth allows you to watch the evolution from a rough surface immediately after the laser pulse to an atomically smooth surface. In chapter 3 the basic theory of surface diffusion of mobile ad atoms incorporating at step edges is described. This theory (BCF theory) is then modified to examine time dependent diffusion since this is very important in our interrupted pulsed laser deposition process. Using this result typical diffusion times can be coupled to surface diffusion lengths with the diffusion coefficient. The temperature dependence of the diffusion coefficient makes it possible to calculate the surface diffusion

6 Studying surface diffusion processes with time resolved RHEED 6 energy, an important parameter from BCF theory that can be used to simulate film growth processes or to predict optimum growth conditions. By varying the ambient gases during deposition, in this case oxygen, argon and ozone, we can influence surface chemistry. A detailed model that relates the oxygen partial pressure to the amount of mobile ad atoms can also be found in chapter 3. The model systems studied in this thesis are homo-epitaxy of strontium titanate and heteroepitaxy of strontium ruthenate on strontium titanate. In order to fix the diffusion length we tried to grow all films in a step flow growth mode. These materials are easy to grow with PLD and are model systems for other complex oxides such as YBCO. This is the most reliable way to determine the surface activation energy since no assumptions have to be made on surface structure nor does it require growing films in the ill defined limit between step flow and layer by layer growth modes. Theoretically the RHEED intensity should follow an exponential decay model during this transition from rough to smooth. Experiments show that this model is sometimes too simple. For instance an extra exponential decay function is needed if two rate processes are occurring on similar timescales. Another problem is the occurrence of drift in the RHEED signal. The benefits as well as the risks of using more complicated models to analyse RHEED data are discussed in chapter 4 Measurements of surface diffusion time constants and energies in different ambient gases for homoepitaxy are presented and discussed in chapter 5. Especially the dependence of relaxation time on partial oxygen pressure was studied in order to understand the chemistry of thin film grwoth. A more open, explorative approach was used to study hetero-epitaxy of strontium ruthenate as described in chapter 6. Not only the relaxation times were studied but also the characteristic growth transition from layer by layer to step flow observed in SRO and the etching effects of ozone.

7 Studying surface diffusion processes with time resolved RHEED 7 1 Experimental As described in the introduction we want to study surface diffusion in order to gain a fundamental understanding of thin film growth. In this chapter the main reason for choosing our deposition technique Pulsed Laser Deposition (PLD, its instantaneous deposition, will be discussed. The main aspects of PLD will be briefly introduced; particular interest will be given to the parameters that control surface diffusion processes such as background gas pressure. To measure surface diffusion times we used a high pressure Reflective High Energy Electron Diffraction set-up compatible with PLD. The measurement of RHEED intensity oscillations allows the determination of surface diffusion times needed for calculating the surface diffusion energy. The next critical parameter to grow in a controlled fashion is the substrate choice. A well-defined substrate is necessary to fix the diffusion length to a single terrace length. This chapter is concluded with a summary of the different PLD deposition conditions used for the experiments described in chapters 4& Pulsed Laser Deposition All films in this thesis were grown using pulsed laser deposition. The unique property of PLD is that deposition takes places during a very short interval immediately after the laser pulse. This instantaneous deposition makes it possible to study time dependent surface diffusion because no new material arrives during the diffusion and growth stage. This means that there is no risk of nucleation on the terrace; the deposition can take place without changing the surface morphology. This growth process called step flow is discussed in detail in the next chapter. PLD can be split in three steps; in each step it will be indicated which parameters control surface diffusion processes Laser ablation A mask and lens system is used to create a homogeneous laser spot on the target. The short laser pulse almost instantaneously evaporates a fixed amount of material. Measurements before and after deposition allow the laser energy to be kept constant by adapting the laser operating voltage. The amount of material ablated from the target is proportional to the laser fluency times the spot size. The necessary amount of material to be deposited in each pulse is optimised to get maximal effect on the RHEED intensity and a minimal chance of nucleation on a terrace Plasma expansion The evaporated material from the target is ablated into the chamber. This material will partly dissociate and form a bright plasma due to the low pressure inside the chamber. The colour of the plasma will change depending on the background gas and/or target used. The higher the background pressure, the slower the velocity of the particles in the plasma becomes, simply because they undergo more collisions with gas molecules (kinetic effect). Changing the background gas from oxygen to ozone or argon has the effect of changing the oxidation state of the ablated material. In order to do measurements on surface chemistry, depositions are carried out under a constant total pressure, but with different partial oxygen pressures. This makes it possible to maintain a constant kinetic energy of the particles arriving on the surface while varying their oxidation state. Using argon instead of oxygen will decrease oxidation, using ozone will give the opposite effect. We will measure the dependence of diffusion time constants on ambient gas in order to verify chemical models for thin film growth as discussed in section.3.

8 Studying surface diffusion processes with time resolved RHEED Surface diffusion and growth The two processes described before determine how much material is deposited on the surface of the substrate, in which oxidation state and with how much kinetic energy. After this instantaneous deposition the surface diffusion processes start. Surface diffusion and film growth is quite comparable to other deposition techniques like molecular beam epitaxy (MBE) and evaporation. The main difference with these other techniques is that in PLD all particles arrive on the surface at the same time creating a very high supersaturation. The resulting diffusion behaviour can be measured without interference from newly arrived ad atoms, since the next deposition pulse is only given after diffusion has been completed. Varying the substrate temperature will change the speed of surface diffusion processes. Using the measured temperature dependence of diffusion times in combination with surface diffusion theory (chapter ) makes it possible to calculate a surface diffusion energy, provided the surface diffusion length is known. 1. Reflective High Energy Electron Diffraction RHEED is a powerful non-destructive tool to examine the surface structure of a growing film. In the case of PLD the intensity of the RHEED signal provides a direct measure of the step density on the surface of the growing film. The measured variation of step density with time after a laser pulse can be used to calculate surface diffusion time constants by fitting a RHEED intensity model (chapter 5) Basic operating principles An electron beam (0-35 kev) hits the sample under a grazing angle of incidence. This grazing incidence makes it possible to use RHEED during film growth since it does not block the sample. The beam only penetrates the topmost layers and is diffracted due to the interaction of the electrons and the periodic potential of the surface. Because of the strong interaction between electrons and the atomic nucleus the resulting diffraction pattern cannot be quantified using kinematical theory. The diffracted electrons are collected on a phosphor screen close to the sample. The incidence of an electron on the screen causes a flash of light, these light flashes are collected using a CCD detector. The position of the diffraction spots can be predicted using an Ewald sphere construction as is explained elsewhere. 1.. Intensity oscillations The most interesting feature of RHEED is not the diffraction information, but the oscillations observed during growth. In case of layer-by-layer growth the intensity of the RHEED signal will oscillate with a period of one monolayer. During PLD these oscillations can best be explained using the step density model. In this model the electron beam scatters diffuse at step edges and the intensity of the diffracted beam is therefore lowest when the number of step edges is highest. The step density for layer-by-layer growth is given by 3 : S = πn 1 θ ln 1 θ (1.1) s with: N s : number of nuclei per unit area θ: surface coverage factor ( ) ( )

9 Studying surface diffusion processes with time resolved RHEED High pressure RHEED Normally RHEED can only be used in UHV systems to avoid scattering. In case of PLD the mean free path of electrons is only a few cm in the 3-0 Pa regime commonly used for complex oxides. The electron gun filament must be operated in high vacuum in order to increase its lifetime. The use of a differential pumping set-up makes it is possible to minimize the path electrons travel through the high pressure deposition chamber, while still keeping the electron gun under high vacuum. The current system allows the use of RHEED at deposition pressures up to 100 Pa. 1.3 Substrate treatment and analysis As mentioned before a surface diffusion study can only be carried out with reasonable accuracy if the surface structure is known and remains constant during deposition. This is necessary to ensure a constant surface diffusion length. In the step flow growth mode the diffusion length is governed by the substrate miscut and the surface quality. The miscut is defined as the angle between the surface and the closest crystallographic axis. After proper thermal treatment this angle results in a surface containing straight, equidistant steps of unit-cell height. To avoid nucleation on the terrace a perfect and single terminated surface is needed, since deposited material will tend to nucleate at defects. Because an as received STO substrate is not atomically flat and does not have a single termination it is necessary to clean and etch them. In essence the cleaning and annealing procedure described by Koster 4 is followed. To avoid step bunching of the higher miscut substrates (0.40 and above) thermal treatment was reduced to 15 minutes at 850 C instead of an hour at 950 C. To improve the straightness of the surface steps thermal treatment was lengthened to two hours at 950 C for the lowest miscut substrates (0.1 ). After the thermal treatment substrates were checked with Atomic Force Microscopy (AFM) for straight stepedges and single termination. Examples can be seen on the next page in figure 1-1. Since the miscut of some substrates was equal to or higher then 0.4 it is difficult to obtain good AFM pictures.

10 Studying surface diffusion processes with time resolved RHEED 10. Figure 1-1Example of quality decrease in AFM scan because of higher miscut substrate, note the different scan size. Spots on the right are caused by surface contaminations It is possible to see straight stepedges for substrates up to 0.77 degrees miscut. The friction method normally used to determine single termination does not work for these substrates. Some surface steps appear less visible than others and give a too low step height. The cleaning and annealing treatment always yields single termination substrates for substrates with low miscuts. The spots on the right part of figure 1-1 are characteristic for a sample that is not cleaned properly 1.4 Deposition conditions All results in this thesis were obtained using the deposition conditions indicated below. Surface miscut was varied to change the surface diffusion length, substrate temperature was altered to change the diffusion coefficient and the ambient gas was manipulated to influence kinetic surface processes. Deposited Material Laser fluence (J/cm ) Mask Aperture (mm ) STO *1 rectangular SRO elliptic Table 1-1 Laser and substrate parameters Spotsize on target (mm ) Substrate miscut ( ) ; 0.6; 0.77; 0.89; (x); 0.5; 0.7 Substrate temperature ( C) Targetsubstrate distance (mm) Deposited material Background gases used Deposition pressure (Pa) Total gas flow rate (ml/min) Argon concentration (%) STO O, Ar SRO O, O3, Ar* , 90* 0-8 Ozone concentration (%) Table 1- Background gas parameters. If the argon or ozone concentration is less than 100 % the remaining part is oxygen. *only 1 experiment was carried out in argon

11 Studying surface diffusion processes with time resolved RHEED 11 PLD thin film growth theory Thermodynamic film growth theory does not predict any time dependencies such as surface diffusion times or growth rates. It just predicts an equilibrium condition that in many cases cannot be reached within a finite time. Both thermodynamic and kinetic effects are explored in section.1.1. The distribution of ad atoms on a film surface can be predicted using BCF theory as is described in section.. By expanding the theory to include time dependent diffusion (section..4) the PLD step flow growth process can be analysed. Theory then provides a direct coupling between terrace length, relaxation time and surface diffusion constant (formula.17). Section.3 of this chapter deals with approximating chemical reactions during growth of complex oxides by assuming rate limiting elements. This results in predictions for the ad atom concentration as a function of the partial oxygen pressure. Experiments to verify this model are found in section Thermodynamics versus kinetics Depending on whether the film has a strong bond to the substrate or to deposited material it can grow in three different thermodynamic growth modes 5. Depending on the interaction between film and substrate the result will be layer-by-layer (Frank-van der Merwe), island growth (Volmer-Weber) or Strankski-Krastanov growth. These growth modes are observed during growth near equilibrium, which requires low supersaturation and high temperatures. For homo-epitaxy only layer-by-layer growth is predicted by this theory. In reality layer-by-layer growth will only occur if the temperature is high enough. For most deposition techniques kinetics will determine the growth mode. Kinetic processes are determined by the energy of newly arrived particles, their oxidation state and the number of ad atoms per unit area or supersaturation. A special kind of layer-by-layer growth occurs if the energy of the ad atoms is high in combination with a low enough supersaturation. This so-called step flow growth mode is characterized by the absence of nucleation on the terrace. All diffusing ad atoms will diffuse along the surface until they are finally incorporated at a step edge. In order to achieve step flow it is necessary to increase the distance travelled by ad atoms by increasing the diffusion constant or by decreasing the surface diffusion length. A required condition for the occurrence of step flow is: l d > L (.1) With: l d : surface diffusion length L: terrace length In our case the surface diffusion length is coupled to the substrate miscut, on a substrate with high miscut ( degrees) and small terraces step flow will be much easier to achieve than on low miscut substrates (0.1 degrees). For the fundamental study of the relaxation phenomena observed by RHEED in thin film growth, step flow is the only useful regime. In principal layer-by-layer growth is usable provided the actual surface morphology during deposition is known. Since this is not measurable surface diffusion measurements using this technique rely on assuming a known island distribution during growth 6.. Burton Cabrera Frank theory of crystal growth In 1951 Burton, Cabrera and Frank published a paper 7 with a model for crystal growth, which became widely accepted as the standard model. The theory describes how mobile ad atoms diffuse on the surface until they get attached to a kink in an advancing step edge. BCF theory was able to describe growth of crystals without the necessity of two-dimensional nucleation on the terraces, which can only occur if the supersaturation is sufficiently high. The theory requires a thermal equilibrium of ad atoms on the surface with the vapour above it. It is therefore best suited to describe evaporation

12 Studying surface diffusion processes with time resolved RHEED 1 growth, but in principle it can describe any PVD process. Since in PLD such a vapour, the plasma, occurs only briefly the theory will require some adjustments to accurately describe this process...1 Mobility of adsorbed molecules on a crystal surface The equilibrium concentration n s0 of mobile adsorbed molecules will be given by a formula of the type: W n = n s s0 0 exp k BT (.) With: W s :energy of evaporation from the kinks onto the surface n 0 :of the order of number of molecular positions per unit area k B Boltzmanns constant T: absolute temperature The mean displacement x s of adsorbed molecules is given by Einstein s formula: xs = D s τ s (.3) With: D s :diffusion coefficient :mean lifetime of adsorbed molecule before re-evaporation τ s For simple molecules: U D = a s s exp kt (.4) W 1/ τ = s s ν exp kt (.5) With: U s :activation energy between two neighbouring equilibrium positions a :distance between two neighbouring equilibrium positions υ,υ :atomic vibration frequency factor (~10 13 s -1 for monatomic substances) W s :evaporation energy from the surface to the vapour Calculating x s gives typical values of at least two or three magnitudes larger than a. More important is the result that x s increases rapidly with decreasing T, since the re-evaporation chance will decrease. Also interesting is the fact that x s depends on the crystal facet, since W s is in first order proportional to the number of nearest neighbours an atom has on the surface... Supersaturation The supersaturation σ in the vapour is given by: σ = p 1 (.6) p0 With: p :actual vapour pressure :saturation vapour pressure p 0 In PLD growth σ will be very high during the laser pulse and will drop rapidly after the laser pulse when the plasma is disappearing.

13 Studying surface diffusion processes with time resolved RHEED 13 A similar equation can be written down for the supersaturation σ s of adsorbed molecules on the surface: n σ = s s 1 (.7) ns0 With: n s actual concentration of adsorbed molecules The current of ad atoms j s on the surface towards a step edge is controlled by the gradient of the concentration between position x and position 0. js = Ds ns = Dsns0 ( ψ ), ψ = σ σ s (.8) With: ψ relative supersaturation The current j v from vapour to surface is given by: n j s v = ( σ s σ ) 0 = n ψ τ s0 (.9) s τ s Applying the continuity equation, assuming constant D s in all directions and immobile step edges reduces the problem to the following differential equation: x s ψ =ψ (.10) The boundary conditions are as follows: ψ ( 0) = σ s0 concentration of ad atoms near step is equal to n s0 ψ ( ) = 0 supersaturation of surface and vapour are equal far from the step Solving for ψ and transforming the answer into n s gives the following expression for the concentration of mobile ad atoms on a terrace. y ( ) n s = ns0 + n ns0 1 exp (.11) xs With: y distance across the terrace from a step edge concentration of ad atoms far from a step edge n d..3 BCF without re-evaporation For the temperatures used in PLD experiments re-evaporation is not expected to play an important role. This can be expressed by a sticking coefficient of 100 %, i.e. all material that is deposited from the vapour on the surface will stay there. This results in a constant j v =F. Moving the origin to the middle of a terrace instead of on a step edge can make another simplification of the general BCF expression.11. The position of the step edges is then given by y=±l/. This removes the plus/minus from the expression for n s. FL Fy ns ( y) = ns0 + (.1) 8Ds Ds With: F average flux of atoms from vapour to film during the deposition pulse L average terrace length

14 Studying surface diffusion processes with time resolved RHEED BCF as a starting point for PLD growth modelling In most of the experiments carried out in this thesis the fact that PLD is a non continu deposition process was exploited. The BCF result of an ad atom density that is time independent is therefore incorrect. If diffusion on the surface is fast, PLD can be modelled by a two step process. The first step is then a continu PVD process as described by BCF theory in the previous section. The second step is one in which no deposition (j v =0) takes place and the ad atom density on the terrace decays because ad atoms will attach to the stepledge and become immobile. If we assume that the assumptions made in the previous section are valid during the laserpulse we can take the result of the last section as an initial condition for new calculations. Since the trivial solution n(y,t)=n s0 is a valid solution of the diffusion equation the factor n s0 can be removed from the problem because of the principle of superposition. This gives the following partial differential equation, initial and boundary conditions: n n = D s y t FL Fy ns ( y,0) = (.13) 8Ds Ds n ( y = L ) = n ( y = + L s ) = 0 s The full solution of this problem requires Fourier analysis 8. Because the solution must be even only fourier cosines are necessary. Separation of variables and applying the boundary conditions gives the following general expression: k π D = st kπy ns ( y, t) α k exp cos (.14) k L L With: k integer greater than zero In order to determine α k the initial condition must be written as a Fourier cosine series. = + F L / L kπs α k ( s )cos ds LD L / s 4 L (.15) L F kπ kπ α k = sin kπ cos 3 3 k π Ds In order to get a feel for the values of α k the first four are given here: 4L F 4L F α1 = ; α = 3 3 π Ds 8π Ds (.16) 4L F 8L F α 3 = ; α 3 3 = 3 7π D 64π D s The most important result is the characteristic relaxation time τ, the time at which the concentration in the middle of the terrace has dropped by 37 %. This relaxation time is given by: L τ = (.17) k π D s s Given the values of the coefficients α 1 is expected to dominate the relaxation behaviour, since it is already 8 times greater than α

15 Studying surface diffusion processes with time resolved RHEED 15.3 Chemical reactions on the surface The growth process of a thin film has been treated without chemical reactions until this point. In PLD thin film growth of complex oxides these chemical reactions play an important role, this is for instance obvious from the effects of growing a film in different ambient gases. In this section a model 9 will be described in which the dependence on oxygen partial pressure of thin film growth is described. The central idea is, that the deposition of a complex oxide, like YBCO, can be described in terms of a rate-limiting element, for instance Cu +. Only the chemical reaction of this rate-limiting element with oxygen is needed to describe film growth, the other reactions are occurring fast enough not to limit the film growth. In this paragraph I will focus on the essential steps in the derivation of the model, in particular the assumptions that can cause problems, due to the non-equilibrium nature of PLD. The full derivation can be found in the original article. The chemistry of the complex oxide is simplified to a chemical reaction of rate limiting element A with gas B. k A B ja B j k + (.18) This reaction has a Gibbs free energy given by: G = naµ A + nb µ B + n AjB µ k Aj B (.19) k With: µ chemical potential of the particular compound or element Under equilibrium conditions (constant T and constant p) the Gibbs-Duhem relation 10 can be used to obtain: µ + Adn A µ B dn + = 0 B µ AjB dn k AjB (.0) k This assumption of constant temperature presents the first problem, since the temperature in the plasma is far from constant. As long as the process we are studying is occurring on the surface constant temperature may be used. Using conservation of mass the above equilibrium condition can be simplified to: k µ = jµ + (.1) µ A j B k A B Because of the low pressure during deposition the vapour can be described by an ideal gas and the chemical potential of A j B k becomes: p A jbk µ = + A ( T, p ) ( T, p0 ) k T ln jbk Aj B µ k AjBk b (.) p0 With: p AjBk partial pressure of element A j B k p 0 : equilibrium vapour pressure Assuming equilibrium between A j B k in the vapour and in the solid phase gives an expression for p A,eq as a function of p B. Some manipulation allows this equation to be written in terms of the Gibbs energy of formation g and the vaporisation enthalpy h of A j B k : ( ) 0 1 g h 0 1/ j f, Aj Bk AjBk p A, eq = p k A B exp (.3) j k p jk T B B The next equilibrium condition is that the flux of ad atoms from the vapour to the surface is equal to the evaporation flux of ad atoms from the surface. The flux from vapour to surface is calculated by assuming a Maxwell-Boltzmann velocity distribution in the vapour: pa Fv s = (.4) πm k T a B

16 Studying surface diffusion processes with time resolved RHEED 16 The flux from solid to vapour follows from equation.5 for the surface lifetime: na Ws, A Fs v = = n Aν exp (.5) τ k BT s Combining both equations and ignoring the constants gives the following result: k j, eq B n A p (.6) Applying this theory to strontium titanate predicts the following pressure dependencies: 1 n Ti, eq p O (.7) If the deposition is limited by TiO or: 1 n Sr, eq p O (.8) If the deposition is limited by SrO. Using RHEED it is not possible to measure directly the equilibrium concentration of mobile ad atoms, instead the step density is measured. The equilibrium equation n s is coupled to the step density via equation 1.1.

17 Studying surface diffusion processes with time resolved RHEED 17 3 Data analysis The increase in step density after a laser pulse will give a sudden decrease in RHEED intensity. Surface diffusion then reduces the step density again until the RHEED intensity has recovered to its original value (only for step flow growth). More details about this recovery mechanism are found in the first section. Depending on the complexity of surface diffusion processes the recovery data can be fitted to a single or double exponential decay model in order to yield a time constant. By plotting the dependence of the time constant on the temperature in a so-called Arrhenius plot values for the surface diffusion energy can be calculated. Theory, examples and interpretation of the Arrhenius plot are given in section 4.. Efforts to decrease the error in the time constant tau are described in section RHEED response to a single laser pulse After the laser pulse the intensity of a diffraction spot will immediately (within 0.0 seconds) drop. This immediate drop is caused by the formation of many small clusters, which causes a great increase of the step density. This intensity drop can vary from 5 to 50 percent of the original value, depending on the amount of material deposited and the configuration of the substrate surface. After the initial drop these clusters will diffuse to step edges and coalesce to form larger islands if sufficient thermal energy is present. This results in a smoothening of the surface, a reduction of the step density and a slow exponential increase of the RHEED intensity. Typical time constants of this exponential recovery range from 1 to 300 seconds for homo-epitaxy of strontium titanate intensity (a.u.) t(s) Figure 3-1 Example of a RHEED recovery

18 Studying surface diffusion processes with time resolved RHEED Single exponential RHEED intensity decay model The RHEED recovery signal can usually be described a single exponential decay model. This model is usually adequate for describing fast recoveries measured with a RHEED signal without drift. The best physical explanation for this model is diffusion limited growth of a single species. t y = y0 + A* exp (3.1) τ1 With the following initial values: y 0 = steady state value of the RHEED intensity A= intensity minimum-y 0 τ 1 = relaxation time, initial value between.1 and 100 All three parameters in this model are varied to obtain the best fit of model and data. The initial value of τ 1 is arbitrary, the model will converge rapidly due to the accuracy of the other initial values. For some recoveries this model has a tendency to increase the value of A. This means that the model will start above the actual minimum measured RHEED intensity. This tendency can be suppressed by using a more sophisticated model that takes multiple processes into account, such as the double exponential decay model Double exponential RHEED intensity decay model The difference of this model with the previous one is the second exponential decay function. This can be physically justified by assuming two time dependent processes on the surface. One of the processes can again be attributed to surface diffusion, the other can be due to chemical reactions on the surface or surface diffusion of another species. Another good explanation is that the fast process corresponds to diffusion along a step edge, while the process with greater time constant is caused by diffusion across the terrace. The intensity model then becomes: t t y = y A* exp B * exp (3.) τ1 τ With initial parameters: A+B= intensity minimum-y 0 A<0 B<0 τ 1 = 10 * τ The first three constraints are necessary for stability of the curve-fitting algorithm. Also A and B are required to remain negative throughout the fitting procedure to avoid A going to plus infinity and B to minus infinity. The last initial values serves to make sure that the curve-fitting algorithm tries oscillations with different time scales in order to avoid the result τ 1 =τ. Divergence problems of A and B can be avoided by rewriting this model in a different form. ( ) t t y = y A* d exp 1 d * exp (3.a) τ1 τ With: A= intensity minimum-y 0 0 d 1 The five parameters in this model make it computationally expensive. The resulting models show excellent agreement with measurement data. The many degrees of freedom in this model reduces the convergence of the time constants, many combinations of ratio parameter d and both time constants τ can give similar recovery curves. Fixing model parameters before curve fitting can improve model convergence and also speeds up all calculations.

19 Studying surface diffusion processes with time resolved RHEED Reduced single exponential RHEED intensity decay model In the form as described before the single exponential model 3.1 has three free parameters. For maximum convergence and computation speed it is better to use a model with a reduced set of free parameters. This can be accomplished by fixing the values of y 0 and A before the curve-fitting routine. The steady state intensity y o is chosen as the average over the last 100 points in the RHEED data. For A the minimum RHEED intensity after the laser pulse is used. A coordinate transformation starting from (3.1) gives: ( y y ) t z = 0 = exp (3.3) A τ 1 This results in a model with only τ as a free parameter. This removes the unwanted effect of increasing B that is often encountered with the single exponential model. RHEED recoveries calculated with this model tend to increase faster than measurement data, the model intensity line lies above the measurement. During the second part of the recovery the situation reverses and the model is below the measurement until it is close the steady state intensity y Reduced double exponential RHEED intensity decay model This model can be created by again fixing the steady intensity and the minimum RHEED intensity of the double exponential before the curve fitting. Applying the same transformation as before to 3.a gives: ( y y ) t t ( ) z = 0 = d exp + 1 d exp (3.4) A τ 1 τ Results obtained with this mode show excellent agreement with measurement just like the standard double exponential model, only in a quarter or less of computation time Single exponential RHEED intensity decay model with RHEED drift correction or ozone etching effect When the alignment of the RHEED beam is not fully optimised or the e-beam filament is too old the RHEED signal shows a continuous decrease of its steady state level. When it is not possible to remove this effect by adjusting RHEED beam parameters such as deflection, grid voltage and focus, it is necessary to account for it in curve fitting. Similar effects to the RHEED signal can be seen if too much ozone is present during deposition. This will result in etching of the surface and a linear decrease in intensity due to the formation of holes and the roughening of step edges. These effects can be modelled by an extra linear term: t y = y0 + A*exp + C * t (3.5) τ with: C slope of the steady state signal Results of this model are poor if C is a free parameter, since the computer has problems to balance an increasing exponential decay function with a decreasing lineair function. When C is fixed before curve fitting good agreement of model and theory can be observed. Although the effect of ozone etching can be fitted using this model, it is not advisable to use the resulting relaxation times. This is because the surface is roughening and therefore the surface diffusion length is no longer constant.

20 Studying surface diffusion processes with time resolved RHEED 0 3. Arrhenius plots obtained with different models In order to examine the changes in τ and especially in E a models were tested on the same RHEED data. These data looks very good at 850 degrees and have a moderate drift at lower temperatures. The main problem with this data is that the initial decrease of RHEED intensity after a laser pulse is only about 10% compared to the over 0% observed in other runs. The film was grown on 0.77º miscut substrate, under a pressure of 10 Pa in a ml/min oxygen, 18 ml/min argon flow. Full recoveries are obtained from 850 down to 800 degrees. Below this temperature the recoveries have sudden steps in intensity, which makes it hard to fit this data to an exponential model. To examine which model provides the most accurate determination of diffusion energy an Arrhenius plot was drawn for most models described in section 3.1. The reduction of the number of free parameters of the models before curve-fitting is not expected to have much influence on the calculated relaxation time. The reason is that the two parameters, which are fixed, have a clear meaning in the model. The reduced double exponential decay model is expected to give better Arrhenius plots, since it usually provides a better fit to a single RHEED recovery. By plotting the ratio parameter d of the double exponential model versus the temperature we can measure the relative importance of the two exponential decay function used by the RHEED intensity model. The double exponential decay model Arrhenius plot was not calculated due to its excessive computation time 3..1 Calculating surface diffusion energies In the field of chemistry rate constants are routinely used to describe how the chemical kinetics of a reaction depend on the concentration of the reactants 11. In 1889 Arrhenius developed an expression for the temperature dependence of rate constants. E a RT with: k rate constant E a activation energy k = Ae (3.6) The idea behind this theory is that molecules can react after they have attained a critical activation energy E a, the Boltzmann factor gives the fraction of molecules that has attained this energy. The relaxation time τ we measure is inversely proportional to the rate constant k. For the diffusion coefficient D s a similar expression can be given. D s Es kbt = υ a e (.4) To calculate the surface diffusion energy E s an Arrhenius plot is drawn. This plots -ln(τ) versus 1000/T. The slope of this plot then gives the diffusion energy 1 since τ is proportional to D s according to formula.17.

21 Studying surface diffusion processes with time resolved RHEED Single exponential RHEED intensity decay model results /T tau (s) Figure 3- Arrhenius plot single exponential decay model 1000/T tau (s) Figure 3-3 Arrhenius plot reduced single exponential decay model When comparing the two models on their Arrhenius plpots shown in figure 3- and 3-3 their general behaviour is quite similar, just as expected. Reducing the model does not have a significant effect on the τ values calculated in the region from 850 to 80 degrees. RHEED relaxation times in the lower temperature region (810 and 800 C; 0.93 and 0.93 in the Arrhenius plot) were calculated more accurately by the single exponential decay model. There is a decrease in relaxation time with

22 Studying surface diffusion processes with time resolved RHEED decreasing temperature. The increasing slope of the Arrhenius plot in both graphs corresponds to unrealistic negative diffusion activation energy E a. Obviously the single exponential model is too simple for an accurate representation of the surface processes during this run. Results obtained with the more complicated reduced double exponential model indicate a radically different behaviour as can be seen below. The change in the ratio parameter d as a function of temperature observed in the double exponential decay model suggest that this data was measured in a transition region from one growth mode to another Results double exponential RHEED intensity decay model /T [1/K] ln (tau) Figure 3-4 Reduced double exponential RHEED intensity decay model; slow component 1000/T [1/K] ln(tau) Figure 3-5 Reduced double exponential RHEED intensity decay model; fast component

23 Studying surface diffusion processes with time resolved RHEED 3 Figure 3-4 shows the expected increase in relaxation time with decreasing temperature. The surface diffusion energy is 1.5 ± 0.6 ev. In most cases the fast recovery part can almost be represented by a step function, instead of a fast exponential function. Time constants of this fast exponential function give rise to Arrhenius plot 3-5. Since most time constants generated by this model are of the order of the sampling time, this data is therefore not reliable and the Arrhenius plot meaningless. The third parameter in the reduced double exponential decay model is the relative importance of the two exponential functions given by the ratio parameter d. The temperature dependence of d shows whether the slow or fast process dominates the recovery function. A d value independent of temperature could mean the existence of two similar diffusion processes with a different path, one along the terrace and one with a smaller time constant along a step edge. 1000/T [1/K] d Figure 3-6 Temperature dependence of model parameter d This characteristic is very interesting. Obviously the fast relaxation becomes more and more important at lower temperatures. This can be caused by a transition from a diffusion limited growth regime to a chemical reaction speed limited regime. In the first regime the speed of the process is determined by the speed of the diffusing particles and in the second regime by some sort of chemical process for example the formation of a titanium oxygen bond. In order to determine if the observed dependence of d is a numerical artefact or has physical significance it is necessary to perform a full analysis of the double exponential model with d as a parameter. Because of the symmetry in the model d only needs to be varied between 0.5 and 0.9, preferably with 0.1 increments.

24 Studying surface diffusion processes with time resolved RHEED Numerical aspects of determining relaxation times It can clearly be seen in all the Arrhenius plots of the previous section that the spread in time constants at a certain temperature is large. In this section it is investigated how this spread can be reduced. Results obtained with different computer programs, Origin and Labview, are examined. The next part is an investigation of the dependence of τ on curve fitting length, in other words the number of data points used in the curve fit. The relaxation time is not expected to change with fitting length as long as sufficient measured points are taken into account. Finally the effect of filtering by averaging over a number of data points before performing the curve-fit is analysed Curve-fitting in Origin or Labview Curve-fitting RHEED intensity can be done using various commercial programs, the most important of which is Origin. The main disadvantage of using a spreadsheet-based program such as Origin is its inconvenient interface. To overcome this a program to do similar curve fitting was written in Labview. The main advantage of using the Labview environment is that the graphical interface of this program makes it much easier to select which RHEED intensity data points have to be fitted to a model. Both programs use the same algorithm to perform non-lineair curve fitting, the Levenberg- Marquandt algorithm. This algorithm minimizes the error between model and dataset by varying all parameters of the model. In order to do that, both programs internally calculate partial derivatives for all the values of the input variables. For built-in functions (only available in Origin), all the derivatives are computed using analytic expressions. For user-defined functions, the partial derivatives are computed numerically. The computation is thus faster for built-in functions than for user-defined functions. This effect is speed-effect is clearly visible when performing the calculations. A double exponential model (3.) curve fit carried out on the same 1 minute dataset can take 10 seconds in Origin and 5 minutes in Labview (calculation time on a Pentium II 300 MHz). The advantage of using Labview is that the user selects a RHEED recovery by moving two cursors along a graph of measured intensity s. It is also automatically uses optimal initial values for RHEED recovery analysis resulting in a high stability of the algorithm. In comparison the data selection process of Origin is very time consuming and will take about one to two minutes per pulse, independent of the model used. This is due to the less convenient spreadsheet interface of the program. Both programs yield the same time constants for the same dataset, which indicates they really use the same algorithm.

25 Studying surface diffusion processes with time resolved RHEED Dependence on fitting length In itself it is not hard to fit an exponential decay model to RHEED data. The resulting fit and original data usually show good agreement. More problematic is the variance in relaxation time constants from laser pulse to laser pulse. For instance the first pulse may give.5 seconds, while the next one yields 1.5 seconds. One of the factors contributing to this problem is that the time interval used in fitting relaxation time data is usually variable. Traditionally all data points between two laser pulses were selected. Since most laser pulses were given manually, this time is not constant. In order to investigate this phenomenon a good RHEED recovery will be fitted to a single exponential model with a variable number of seconds after the laser pulse tau (s) curve fitting length (s) Figure 3-7 Dependence of tau on curve fitting length. Curve fitting length of zero corresponds to t=6.3 seconds in figure 4-1 Figure 3-1 shows that the relaxation time is constant in the regime where the intensity is constant. It also shows that the single exponential model should not be used before the intensity has reached an almost constant value. This means that the effect of fitting a pulse for 30 or 50 seconds is negligible as long as the intensity has reached a steady value. Therefore the effect of fitting pulses with different lengths of time data is not responsible for the spread in relaxation time data Dependence on filtering Filtering by running an average over a fixed amount of data points has the advantage of strongly reducing high frequency noise. The main disadvantage is that the RHEED intensity minimum will be raised. This results in a slower increase of the signal immediately after the pulse and correspondingly a larger relaxation time.

26 Studying surface diffusion processes with time resolved RHEED 6 The effect can easily be seen in the following figure 3-8 which was calculated on the pulse given in figure tau (s) # filterpoints Figure 3-8 τ as a function of the number of filterpoints This systematic increase is obviously undesired, especially since it will increase more if the RHEED intensity increases faster than this example. The use of filtering will reduce the spread in RHEED intensity data points. These points will appear closer to the model line and therefore look much better when plotted. However the quality of the curve fitting itself is not influenced. The model generated by a curve fitting procedure does not change depending on the number of filter points apart from the systematic increase in τ mentioned before. The only proper use of filtering is to examine which intensity recovery model fits a given set data points best. Otherwise the effects of different models can easily be obscured in the large standard deviation. Therefore all data analysis in this report was performed on unfiltered data, unless mentioned otherwise. 3.4 Conclusion and recommendations Only in certain cases a single exponential decay model will generate good agreement with measurement. This case is the limiting case of the double exponential decay model, with the ratio parameter d close to 0 or 1. When using a double exponential decay model the ratio parameter d will indicate whether a fast or a slow process is dominant at a given the temperature. It also can be used to determine the temperature limits of an Arrhenius plots since E s cannot be determined if two exponential processes are not clearly separated. Such separation problems are likely to occur on the thermal boundary of two growth regimes The other work in this chapter concludes that filtering does not improve the determination of E s. Accurate determination of τ can only be made if the steady state intensity has been reached, this is due to the curve fitting routine. The algorithm will minimize the slope of the model at the end of the dataset, even if the intensity is still slowly increasing. For future relaxation time measurements it is recommended to: - Carefully examine if single exponential decay models can be used. If this is not possible the reduced double exponential RHEED intensity decay model should be used - Avoid to use filtering - Perform curve-fits with the end point well within the steady state intensity region - Use reduced models by fixing the parameters related minimum and steady state RHEED intensity in order to improve model parameter convergence and computation speed

27 Studying surface diffusion processes with time resolved RHEED 7 4 Homo-epitaxy of Strontium Titanate The step-flow growth mode of Strontium titanate provides an ideal model system to measure the surface diffusion time and energy. The first section describes previous surface diffusion energy studies on strontium titanate (SrTiO 3 or STO) and on how to improve their results. Calculated surface diffusion energies are given in section Surface diffusion energy Previous surface diffusion energy studies Only a few studies have been done on surface diffusion energy determination of STO films grown with PLD. This is primarily because only a couple of PLD systems worldwide are equipped with the necessary high pressure time resolved RHEED. Koster et al. carried out the first experiments in a layer by layer growth regime. The activation energies obtained were 0.48±0.05 ev at 3 Pa and. ±0. ev at 0 Pa. The value of 0.5 ev seems to be too low, most likely caused by the inconvenient growth regime for diffusion studies. Rijnders et al. performed a study of the oxygen pressure dependence of the diffusion energy using substrate miscuts of around degrees and a growth temperature of degrees. Step flow is easily accomplished in this region and gives the following diffusion energies:.6 ± 0.3 ev (3 Pa), 3.0 ± 0.3 ev (1 Pa), 3.5 ± 0.3 ev (0 Pa). Lippmaa et al. 13 used a very low pressure of 1.33 e-6 mbar, but a wider temperature range from ºC. The disadvantage of Lippmaa s work is that the pressure used does not correspond to the pressure regime in which most complex oxides materials are normally grown. Their surface diffusion energy values are 3.8 ± 0.3 ev on a TiO terminated and 3.3 ± 0. on a SrO terminated surface, calculated with a different method based on the transition from layer-by-layer to step flow. Compared to the earlier work depositions are carried out under typical PLD growth conditions with medium miscut substrates. The minimum miscut of 0.4 is necessary to obtain step flow, while this range still allows AFM analysis. To determine the dependence of film growth on chemistry various gas mixtures of argon and oxygen were used Calculated surface diffusion energies In most cases the RHEED intensity recovery was not complete due to a slow decrease of the RHEED signal. All relaxation times were calculated using the single exponential decay model with the exception of rs006 that was calculated using a reduced double exponential decay model. There is usually a large difference between the temperature range in which the deposition was carried out and the data points that were actually used to calculate E a. This discrepancy is caused by the transition from step flow to layer-by-layer growth that is not always immediately obvious in the RHEED signal. In an Arrhenius plot the discrepancy can immediately be noticed, since points at low temperature do not follow the linear trend observed at high energy. The missing entries in the table are depositions in which the Arrhenius plot did not produce a linear relation between ln(τ) and 1000/T or in which step flow growth was not achieved. The exact value of E a in electron volt is calculated by multiplying the slope of the Arrhenius plot with the conversion factor 1000 k B /e.

28 Studying surface diffusion processes with time resolved RHEED 8 Run substrate miscut angle deposition pressure (Pa) oxygen flow (ml/min) Argon flow (ml/min) deposition temperature (C) Temperature interval of diffusion measurement (C) E a (ev) rs ± rs ±.6 rs ±.6 rs004! or ±1 1.4 ± 0.1 rs rs ±0.6 rs rs ±0.5 rs009* ±0.5 rs rs ±1 rs01* Table 4-1 Activation energies using different gas mixtures and substrate miscuts. *: Runs in which pulses were accidentally given before the RHEED signal acquisition had started. The surfaces of these substrates were therefore not ideal when the actual experiment was started.! The typical shape of the Arrhenius plot of rs004 allows two different values of the activation energy. One based on the high temperature region and one based on almost the complete dataset. Since the second one is based on a larger temperature range its error is much smaller, although it does not fit with the data at 750 and 740 degrees C. This may be explained by a re-alignment of the RHEED signal carried out at 750 degrees /T ln(tau) Figure 4-1 Arrhenius plot used to calculate E s. Deposition was carried out on a 0.77 miscut substrate at 10 Pa total pressure, 10 ml/min O and 10 ml/min Ar.

29 Studying surface diffusion processes with time resolved RHEED Trends in surface diffusion energy In several experiments problems with RHEED or the lack of step flow prevented a determination of the activation energy. It is still possible to extract quite a lot of information from table 4-1. The dependence of activation energy on substrate miscut and oxygen partial pressure will be described Dependence of surface diffusion energy on substrate miscut The longer the terrace length the longer the relaxation time will be, since material has to travel over longer distances. The effect of increasing the substrate terrace length will be to shift the arrhenius curve down while the slope remains the same. Therefore similar gas pressures should result in activation energies independent of substrate miscut. Comparing measurements done at 10 Pa with a 50%/50% oxygen/argon mixture on substrates with a miscut of 0.6 and 0.77 gives excellent agreement in E a. The 0.6 miscut substrate has an activation energy E a =1.5±0.6 and the 0.77 miscut substrate has an activation energy of E a =1.4 ± 0.1eV Dependence of surface diffusion energy on partial oxygen flow Diffusion energy data were obtained for the 0.77 miscut substrates in different ambient gas mixtures. The data suggests a diffusion energy that is almost independent of partial oxygen concentration. The results are given in figure 4- below. 3.5 Ea (ev) % oxygen in ambient gas flow Figure 4- Surface diffusion energy versus % oxygen in gas flow

30 Studying surface diffusion processes with time resolved RHEED Manipulating the growth mode by varying the partial oxygen concentration It has advantages to a surface diffusion time experiment on a single substrate in a single deposition. This should help to eliminate the effects of using different substrates, since their surfaces are never completely identical, and the small day-to-day variations in deposition conditions. A new experimental scheme was created to investigate the direct influence of partial oxygen pressure on differences in relaxation times Slowly increasing the amount of oxygen It was noticed in the Arrhenius type experiments of section 4.1 that it was hard to obtain step flow growth if the oxygen partial pressure was too low. In order to examine this partial pressure effect further, depositions were done at a fixed high temperature of 850 degrees on a relatively low miscut STO substrate of 0.4º and at a low pressure of 4 Pa. Only the oxygen and argon flow rates were modified, the total flow rate was kept constant. The run was started with an oxygen flow rate of 0.5 ml/min and an argon flow rate of 3.5 ml/min. After giving -3 pulses the oxygen flow rate was increased by 0.5 while the argon flow rate was correspondingly decreased. The procedure was repeated until RHEED recovery was complete, which occurred at.5 ml/min O and 1.5 ml/min Ar. A clear improvement in the RHEED recoveries was visible upon increasing the oxygen flow. The best way to quantify this result is by looking at the recovery factor R, which is defined as: I beforelaser pulse I minimum R = (4.1) I I after laser pulse minimum Full recovery or R=1 corresponds to step flow growth, a lower value indicates formation of islands on the terraces recovery factor Oxygen flow (ml/min) Figure 4-3 Recovery factor as a function of O flow

31 Studying surface diffusion processes with time resolved RHEED 31 The increase in recovery factor in figure 4-3 can indicate an increasing surface diffusion length, the material travels further on the terrace and has sufficient energy to reach the step edge. The figure can also be explained by the increasing roughness during the depositions with low oxygen content. The larger number of islands on the surface has the effect of reducing the surface diffusion length, which makes increased recoveries possible since more material can reach the edge of an island. Another interesting phenomenon is the change in relaxation time during this experiment. However, accurate relaxation time determination is hindered by the lack of recovery at low oxygen flow rates. 5 average relaxation time (s) Oxygen flow (ml/min) Figure 4-4 Relaxation time versus oxygen flow Based on the data from figure 4-4 there is no clear effect of the partial oxygen pressure on the relaxation time. The changing pulse shape that makes it hard to compare relaxation times could have caused this. 4.. Slowly decreasing the amount of oxygen In order to improve the result of the previous experiment, a similar experiment was done which started in an oxygen environment. This has the advantage that the first layers will grow perfectly, until the partial oxygen pressure is reduced to below the value necessary for step flow growth. This should eliminate potential surface roughening that can occur during initial growth in argon environment. The experiment also serves to check the reproducibility of the previous experiment. To maximize the control over the relative oxygen pressure, this experiment was started with 100% oxygen with a total flow rate of 5 ml/min. The oxygen and argon flow rates were modified with 1 ml/min increments.

32 Studying surface diffusion processes with time resolved RHEED 3 A realignment of the RHEED was necessary after the experiment had started in order to find an optimal diffraction spot, i.e. one with a larger intensity decrease after a laser pulse. Recoveries in this experiment were complete (R=1), there is no dependence on oxygen flow rate. Using a single exponential model on the RHEED intensity data yields the following variation of relaxation time with oxygen flow rate. 6 5 relaxation time (s) Oxygen flow (ml/min) Figure 4-5 Relaxation time versus oxygen flow at fixed total pressure and temperature Figure 4-5 shows that the relaxation time is almost constant under variation of partial oxygen pressure. It is however remarkable that relaxation times are much faster in this case, about 1- seconds instead of the 10-0 seconds observed previously in figure 4-. Given the lack of any change in the recovery percentage with oxygen flow in this run deposition conditions were probably not similar to those in the previous section. Most likely causes are the decreased quality of the RHEED signal in this run and a variation in the total pressure. The different growth behaviour observed in this run can also indicate a history effect. If during the initial depositions the surface is roughened as can be expected from figure 4-1 the surface diffusion length for the next experiment will be different Determining a rate-limiting element Modification of the YBCO result of Stäuble-Pümpin, as done in section.3, gives the following predicted pressure dependencies of the ad atom concentration: n eq (Ti) evenredig met.po -1 for Ti 4+ (.7) -0.5 n eq (Sr) evenredig met. po for Sr + (.8) The amount of material grown in step flow, given by the recovery factor R, is an indication of the amount of mobile ad atoms, since step flow is only possible if sufficient mobile ad atoms are present. The results from graph 4- therefore indicate an increase in the mobile ad atom concentration with increasing oxygen pressure. The theory of Stäuble-Pümpin, that predicts a decrease in the number of mobile ad atoms with increasing oxygen pressure, does not hold in this case. Using relaxation times provides a more direct method of determining the number of mobile ad atoms, the longer the relaxation time, the higher the number of mobile ad atoms. Since the data from graph 5-3 shows relaxation time to be constant under variation of oxygen pressure the idea of a rate-limiting element does not hold.

33 Studying surface diffusion processes with time resolved RHEED Conclusion and recommendations The results of various STO experiments show that it is difficult to grow STO in a step flow growth mode at the temperature range we can use (below 850C). In most experiments step flow only occurs above 800 degrees, although this improves for lower deposition pressures. This creates a larger error in activation energy than desired. The experiments in this chapter do not prove dependence of relaxation time and surface diffusion energy on oxygen partial pressure. The chemical processes occurring during growth are therefore not rate-limiting. Experiments from section for 4. indicate a history effect. Similar deposition conditions give different RHEED recoveries, because of the effect of earlier experiments effects on surface roughness. The experiments do indicate a number of critical system parameters to obtain good Arrhenius plots. 1) High quality substrates. Substrates with holes in the surface do no have the fixed diffusion length that is required for the Arrhenius plot. Instead the diffusion length will increase after a number of pulses, because the holes will be the first to fill up. The substrate must also be single crystalline, otherwise there will be multiple interfering diffraction spots, which decrease the effect of a change in surface roughness on the intensity. ) Fully optimised RHEED system. Preferably the electron beam filament and the phosphor screen should be clean and not too old. Only qualified operators should be allowed to change the electron beam deflection, grid and focus values. All changes should also be documented, to make it easier to revert to old values. Using a RHEED system that is not fully optimised can still provide great results for purposes such as counting the number of pulses per monolayer, or sub unit cell epitaxy, but will definitely give problems in obtaining good RHEED intensity recoveries. The main problems are increased noise and especially RHEED intensity drift, which makes it very hard to determine where a recovery stops and also influences the shape of the recovery. 3) Achieving extremely good temperature stability. In order to create a meaningful Arrhenius plot it is necessary to keep the temperature constant within one degree during deposition, since T is sometimes only varied 10 degrees per measurement sequence. Normally temperature is controlled by a PID controller, which can achieve this stability. To reach this stability the controller continually varies the heater current that directly influences the RHEED signal. To avoid this effect temperature was controlled manually, which means long waiting every time the temperature was varied in order to achieve stability. Manual temperature controlling also prevents automation of the process, so the operator must remain near the system during the entire experiment. In future it could be possible to use automatic temperature control if the heater current fluctuations can be minimized. Alternatively the heater could be redesigned by using shielded cable or twisted pair configurations to minimize magnetic fields. 4) Increasing the amount of material deposited per laser pulse by increasing the laser energy or using a different mask. The more material deposited in one pulse, the bigger the increase in surface roughness and the decrease in RHEED intensity. A deep minimum intensity reduces the relative noise level and improves the convergence of fitting to an exponential function. 5) Decreasing the deposition pressure. Unfortunately this decreases the accuracy with which the ambient gas concentration can be controlled, but the main advantage is an increase in surface mobility and an increase in the amount of material deposited in a single laser pulse. Higher surface mobility leads to lower temperatures at which step flow still can occur, and therefore a longer x-axis in the Arrhenius plot. 6) Increasing the substrate temperature. The step flow experiments should be started at the highest temperature possible. The maximum temperature of 850 degrees used is a quite conservative value, 900 or even 950 degrees with a special heater would be much better. This corresponds to a doubling or tripling of the useful 1000/T range and improves the accuracy of determining the slope with at least a factor. 7) Stopping the deposition immediately when recovery is incomplete. A history effect can change the surface diffusion length and make determining E s impossible.

34 Studying surface diffusion processes with time resolved RHEED 34 5 Hetero-epitaxy of strontium ruthenate The main advantage of growing STO on a STO substrate as done in the previous chapter is that almost all chemistry can be ignored when trying to interpret data. It does however severely limit the analysis techniques that can be used after deposition, since the layer and substrate cannot be distinguished. In fact AFM is the only technique that can still be used and this is very hard on the high miscut substrates that are necessary for the diffusion studies. The second problem is that STO is not very mobile, which creates the need for very high temperatures. Therefore strontium ruthenate (SrRuO 3 or SRO) is used, which can be grown in a step flow growth mode at much lower temperatures (down to 550 degrees C), because it has a much higher surface mobility. The RHEED signal also shows a much stronger decrease after a laser pulse (usually about 50%), which is ideal for curve fitting and would give smaller error bars in the Arrhenius plot. It would probably be a lot easier to get interesting results on oxygen partial pressure dependence with this material, although the interpretation will be more difficult. After deposition X-ray Photoelectron Spectroscopy (XPS) can be used to give more insight in the oxidation of the layer and X-ray Diffraction (XRD) to determine structural changes. The fast alternative to XPS is doing a residual resistivity measurement by dipping the sample in liquid helium, the better the oxidation, the better the residual resistivity ratio (RRR). In this chapter the phenomena observed during SRO growth, such as the initial growth transition due to the termination conversion and ozone surface effects will be discussed in relation to the surface diffusion time. The quality of the deposited films, especially of their surface, is analysed with AFM and Residual Resistance Ratio measurements. The growth of SRO is characterized by layer-by-layer growth for the first layers followed by a transition to step flow growth 14. Characteristic for the step flow regime is the disappearance of oscillations and the stronger decrease of intensity after every laser pulse. This results in a RHEED intensity graph characterized by two or more oscillations, followed by a constant intensity. The oscillations are caused by a termination conversion from the B-site terminated STO to A site terminated SRO. By varying ambient gases we expect to modify this initial growth conversion as well as the later stages of film growth. Increasing the oxidation power through the use of ozone can help to preserve the B-site termination during growth, which will yield a completely different RHEED intensity profile. Experiments have shown that at 600 degrees C it takes about one and a half time more pulses to grow the first monolayer then the following monolayers. Since the amount of pulses necessary for the first layer increases with substrate temperature this behaviour can be explained by evaporation of volatile RuO x phases 15. RuO is stable at our deposition temperature while other phases are not. There have also been reports of RuO films grown on LaAlO 3 with PLD at substrate temperatures up to 800 degrees C, the authors report single crystalline RuO up to 700 C Initial growth transition Deposition conditions are given in table 1-1 and 1-. All depositions in the table below were done on 0.5 miscut substrates. experiment background gas #oscillations before step flow quality of RHEED signal rs % O good 7:17 rs018 5% O3, 95 %O 8 good 30:0 rs019 8% O, 9% O 1 noisy, drift 45:1 rs00 8% O, 9% O >13* good 39:0 rs01 3% O3, 97% O None* drift NA rs0 90 % Ar, 10% O, striped spots 8:4 rs03 3% O3, 97% O striped spots 31:19 Table 5-1 Initial growth transition of SRO ratio pulses of first layer to next layer

35 Studying surface diffusion processes with time resolved RHEED 35 * a step flow growth mode was not established during the experiment The growth transition from B-site to A-site termination as observed by the RHEED during depositions in three different ambient gases is given in the figure below. For clarity the intensity curves were shifted. Shifted intensity (a.u.) t (s) 100% oxygen 95% oxygen 5% ozone 10% oxygen 90% argon Figure 5-1 Influence of ambient gas on the pulse ratio between the first and subsequent layers Intensity maxima occur sooner for the 100 % oxygen curve due to a larger amount of ablated material per laser pulse. Ozone does not have an effect on the ratio between the number of pulses for the first layer and the subsequent layer. This remains around 1.5 to 1, the same as for pure oxygen. The termination conversion is therefore not expected to be fundamentally different. It is not possible to stabilize the B-site configuration with ozone. The most pronounced effect is the increased surface roughness at higher ozone levels (8 %), causing the disappearance of the step flow growth mode. With ozone small oscillations are visible longer than the two oscillations observed in oxygen. For argon the ratio is only 1.13 to 1. The smaller ratio suggests that too much oxygen is present during deposition of the first layer, resulting in evaporation of oxygen rich ruthene compounds such as RuO 3. Intensity (a.u.) t (s) 100% oxygen 95% oxygen 5% ozone 10% oxygen 90% argon Figure 5- Detail of RHEED intensity in the step flow regime The individual peaks after every laser pulse in the step flow regime as shown in figure 5- are hard to distinguish in any environment apart from pure oxygen. The surface diffusion in the ozone/oxygen and argon/oxygen mixture appears to occur much faster than in pure oxygen, since individual laser pulses are no longer visible. The alternative explanation is increased roughness that decreases the surface diffusion length and therefore speeds up the relaxation. However, this is

36 Studying surface diffusion processes with time resolved RHEED 36 expected to lead to a continuous decrease in the RHEED signal due to the increasing roughness and therefore does not hold. 5. Interval experiments All SRO films grown with PLD show a transition in the growth behaviour after the first monolayer as described in 5.1. In order to stabilize the first layer we increased the deposition rate by setting the laser frequency to 100 Hz. The number of pulses in run A is equal to the number of pulses needed for a monolayer of SrRuO3, the number of pulses of run B corresponds to a doublelayer of SRO. By performing such as fast deposition the B site termination may be preserved since RuO x evaporation time and surface diffusion are reduced. These films were grown in oxygen ambient. The initial fast deposition was followed by an interval with no deposition after which the run was resumed at Hz experiment Number of pulses at 100 Hz Recovery time after first sequence (s) pulses 1 st maximum: nd maximum A :1 B 4 no recovery 149:9 C deposition at Hz NA 8:18 Table 5- Deposition conditions of interval experiments. The choice for the number of pulses at 100 Hz is given by the number of pulses needed to deposit a mono layer or a double layer. The RHEED intensity time of A still resembles the familiar profile of two maxima followed by step flow growth as seen in the standard deposition C. While the shape of the intensity of B is similar, the difference is however in the time scale. It takes more pulses to reach the first RHEED intensity maximum. The effect of depositing a single monolayer within 0. seconds had no effect on changing the termination. This can be expected for an initial growth stage in which surface diffusion is very limited. Comparing the AFM contact mode scans (not shown in this report) of run A and B yields more information. It shows that for the monolayer experiment (0 pulses) the surface still has monatomic steps that are no longer straight. Depositing a double layer (4 pulses) also fails to preserve the B-site termination. Instead the surface roughness is increased as can be seen in the large number of pulses needed to reach the first RHEED maximum, as well as in the AFM scans. The number of steps per micron looks reduced, indicating the occurrence of step bunching. The steps in C are perfectly straight with 4-6 nm high islands on top. The exact step height is hard to determine because of islands on the steps. The first interval deposition experiment A shows a RHEED pattern that is identical to a film grown under continuous deposition, apart from the interruption. This can only mean that for the first layer the growth properties are independent of the arrival rate of new material. Recovery after the deposition interruption is very small and fast. This indicates diffusion on a rough surface covered with small islands. Either evaporation of RuO x takes places on a time scale smaller than a 0.01 seconds or it is does not play a role at all.

37 Studying surface diffusion processes with time resolved RHEED Ozone surface effects When ozone is let into the deposition chamber the RHEED intensity will drop by at least 5% depending on ozone concentration. There are two factors that can be responsible for this phenomenon. The first factor is a chemical reaction of ozone with TiO which can create etch pits that increase diffuse scattering and therefore decrease RHEED intensity. The second explanation is that ozone molecules have a different and larger scattering cross section that increases diffuse scattering of the electron beam and therefore reduces RHEED intensity. At low ozone levels (1%) the intensity drops around 5% and then recovers to a steady state value. At higher ozone levels (3% and above) the RHEED intensity level keeps decreasing. These measurements are carried out on a bare TiO terminated substrate. The continuously decreasing RHEED intensity is exemplary of increasing surface roughness. The increased roughness for higher ozone concentrations can also be observed in the AFM pictures made after deposition. (figure 5-3) Figure 5-3 Increase in surface roughness for increasing ozone concentration. The z-scales of these x micron contact mode scans are, 4, and 40 nm for respectively the 0, 3, 5 and 8 % ozone depositions