8. Spectroscopic ellipsometry

Transcription

1 8. Spectroscopic ellipsometry 8.1. Introduction In this chapter we investigate the use of spectroscopic ellipsometry to monitor the thickness and optical properties of ultra-thin films deposited by filtered cathodic vacuum arc. In particular we are interested in controlling thin film deposition on insulating substrates for the purpose of providing a thin conductive film to remove charge accumulated during a PIII pulse. In addition, an investigation of the mechanisms behind the conductivity changes discussed in the previous chapter is performed utilising real time in-situ spectroscopic ellipsometry to probe the morphological changes of ultra-thin silver films immediately after the end of the deposition process Fundamentals of Ellipsometry Polarised light reflected from a surface provides a powerful non-invasive means for probing surface properties. When linearly polarised light interacts with a surface, the parallel and perpendicular electric-field components usually experience different absorption and phase modifications, resulting in elliptically polarised reflected light. The study of the reflection characteristics of polarised light is subsequently termed ellipsometry. If multiple photon energies are used the technique is termed spectroscopic ellipsometry (SE). 142

2 Paul Drude was the first to conduct fundamental experiments on ellipsometry in the 1880 s and is also responsible for deriving the equations that are still used to this day for analysis of ellipsometric data [1]. It is the ability of ellipsometry to detect changes in reflection characteristics of a surface due to the presence of thin over-layers that makes it such a powerful and widely used technique. It is utilised extensively for characterisation of inorganic, organic and biological films on flat surfaces. In theory, ellipsometry can resolve subatomic changes in film thickness and similarly small variations in optical constants. Whilst the precision of ellipsometric data is usually extremely high, it is often the inaccuracy of the model used to extract the desired information that limits the effectiveness of ellipsometry Data representation Ellipsometric data is generally represented by the ellipsometric parameters and Ψ. These are defined by TanΨe i = R p / R s (8.1) where R p and R s are the complex Fresnel reflection coefficients for parallel (p) and perpendicular (s) polarised states (figure 8.1). R p and R s can be acquired with relatively standard optical equipment. A simple experiment may consist of merely a light source and collimator, a rotating polariser, and a photodiode and amplifier that can detect the amplitude variations of the reflected light. If spectroscopic capability is required a refracting prism may be included before the detector. 143

3 E s-plane Linearly polarised light p-plane Plane of incidence Sample p-plane s-plane Elliptically polarised light E Figure 8.1: Schematic detailing ellipsometric measurements Modelling With the correct experimental equipment it is not difficult to collect vast amounts of data describing the reflection characteristics of a surface. What makes SE a vastly under utilised technique is the difficulty in using this data to confidently and unambiguously determine the surface structure that results in such reflection characteristics. Traditionally, an optical model is developed using parameters such as layer thickness and optical constants. The expected reflection characteristics are then calculated from the model and compared with experimental data for confirmation. If the match between experiment and theory is poor, the model has to be refined and the process repeated. This is often a slow and laborious task. 144

4 Iterative computer programs have improved the speed and accuracy of this process in recent years. It is not surprising that a surge in interest and application of SE has coincided with considerable increases in computing power. However, irrespective of the computing power at hand, it is still important for the researcher to be able to accurately model the system that is under investigation to obtain sensible unambiguous results. Since vastly different optical models can produce essentially indistinguishable reflection characteristics, it is necessary to possess good knowledge of the substrate optical characteristics, and at least some knowledge of surface film properties. An inaccurate choice of the initial values for the iteration algorithm may result in divergence far away the correct solution or, if the solution is not unique, convergence to an incorrect solution Uncertainties A number of sources may contribute to the inaccuracy of a model. The most common are errors in the thickness of one or more of the layers in the model, and/or incorrect values of the optical constants of the layers. Optical constants describe the response of a material to electromagnetic perturbation, providing information about, for example, the absorption, dispersion and reflection characteristics of the material. Optical constants are generally expressed as a complex dielectric function, ~ ε = ε 1 + iε 2, (8.2) or as a complex refractive index, n ~ = n + ik = ~ ε. (8.3) 145

5 Errors may arise when published values of material optical constants are used to model layers of the same material that are morphologically different. Visible and near-infrared light does not penetrate more than a few hundred nanometers into a metal. As a result, ellipsometric analysis of a bulk metal is essentially one of the surface regions only. In contrast, metal films less than 100nm thick are ideal for study by SE, and important information, such as interface roughness and mixing, can be obtained from such an analysis. However, in devising a model from which to determine unknown parameters, complications arise from the fact that the optical properties of thin films are markedly different from those of the bulk material, as will be shown below. These changes are due in part to the same processes that affect the electrical characteristics of thin films, as discussed in the previous chapter. Therefore, optical constants from the literature, typically determined from bulk materials, give erroneous results when used to determine, for example, the thickness of an ultra-thin film. A further source of uncertainty arises from the fact that thin films grown by physical vapour deposition almost always contain voids and defects and exhibit surface roughness of the order of a few nanometers. Some materials, such as TiN and polycrystalline silicon, exhibit a range of optical constants that depend on the method of deposition. Additionally, since the substrate usually exhibits surface roughness, there exists a layer, of thickness the order of the surface roughness, composed partially of substrate and partially of deposited material. To accurately predict the ellipsometric data, any model must include such effects. Effective medium approximations (EMA) have been developed to predict the effect of inclusions of a given material within a host medium and have been successfully applied to 146

6 ellipsometric models. The two most commonly used are the Maxwell-Garnet [2] and the Bruggeman [3] effective medium theories. The validity of these theories to ultrathin films will be discussed below Ellipsometer Hardware The ellipsometer used for this study was a J.A. Woollam Co. M-2000 rotating compensator ellipsometer capable of collecting 390 wavelengths in a spectral range from nm. A Quartz Tungsten Halogen (QTH) lamp broad-wavelength light source is linearly polarised before being passed through a rotating compensator. The rotating compensator converts the linearly polarised light in circularly polarised light. This circularly polarised light is then reflected from the sample surface, passed through a fixed monochromator and the component wavelength amplitudes are detected by a fast CCD array. The CCD allows multiple wavelength data to be collected simultaneously and the collection time of the system is limited primarily by the rotation frequency of the compensator. To improve the signal to noise ratio multiple data sets are usually averaged. Calibration of the system must be performed to account for the spectral properties of the light source. Data is fed to a computer and the complex reflection coefficients are analysed by a regression analysis program, WVASE32. A physical model is created, specifying the angle of light incidence, thickness and optical constants of various layers. WVASE32 then calculates the mean squared error (MSE), which is essentially the sum of the 147

7 squares of the differences between the measured and calculated data for each (,Ψ) pair. The MSE is related to the statistical indicator chi-squared, χ 2, by MSE 1 2N M = 2 χ (8.4) A regression algorithm is then used to minimize the MSE by adjusting the values of one or more nominated parameters. If the final MSE is small and the parameter values are deemed acceptable, the model may be considered correct Experiments Variable-angle ex-situ spectroscopic ellipsometry Variable-angle spectroscopic ellipsometry (VASE), as the name suggests, records reflectance data at multiple angles of incidence. The use of multiple data sets in the regression analysis results in increased confidence in the uniqueness of the output parameters. In this introductory experiment, titanium films were deposited by the DC cathodic arc described in chapter 3. Silicon wafers with a thermal silicon oxide surface layer were used as substrates. Substrates were plasma cleaned by applying 1kHz, 20µs, 4kV pulses to the sample holder in 17.7mtorr argon for 5 minutes. Initially, titanium was deposited at an arc current of 60A for 5 minutes in a background of 0.4mtorr argon. The sample was then removed from the sample chamber and the thickness of the film measured by profilometer. An average of ten measurements determined the film to be 46.8nm, with a standard deviation of 2.6nm. 148

8 Figure 8.2: Ψ as a function of wavelength for four incident angles, 50-80, for a titanium film of thickness 46.8nm as determined by profilometer. VASE was then used to determine the film thickness at angles of 50, 60, 70 and 80 degrees. First the substrate was modelled using an uncoated sample to accurately determine the thickness of the oxide layer. Optical constants for the silicon and silicon oxide were taken from the Woollam database, originally sourced from [4]. The oxide layer was determined to be 509.3nm, which compared well with the manufacturers nominal value of 0.5µm. Bulk titanium optical constants from the Woollam database [5] were used to model the titanium film and the film thickness was determined by linear regression analysis. The fits to the Ψ data for the four angles are shown in figure 8.2. It is immediately obvious that the model does not provide an exact fit to the experimental data. The reason for this stems from the use of bulk optical constants to model a thin metal film. 149

9 The film thickness determined from the above analysis was 43.5nm. This is outside the limits of experimental uncertainty of the profilometer measurements. Further analysis was performed for a number of different film thicknesses, the results of which are presented in figure 8.3. The graph suggests that there is a systematic underestimation of the thickness determined by the ellipsometer. If the two methods were consistent the data points would all lie close to the diagonal line, yet almost all are outside of the limits of experimental uncertainty in the profilometer readings. It is concluded that measurements using the two methods, ex-situ VASE and profilometry, do not agree well for experiments of the type presented above. In general the ellipsometer gives thickness values less than those measured by profilometry. The source of this systematic difference is in primarily due to the use of bulk optical constants from the literature applied to very thin films. Figure 8.3: Comparison of thickness measurements by profilometer and variable angle spectroscopic ellipsometry. 150

10 In-situ spectroscopic ellipsometry In-situ data acquisition provides a convenient means of monitoring film growth during the deposition process. A number of variables, such as differences in substrate properties and deposition parameters, are eliminated, providing more accurate information about the film growth processes. Due to the non-destructive nature of SE, it is ideally suited to monitor film growth in industrial applications. Further, the absence of complex equipment within the deposition chamber makes it straightforward to obtain in-situ SE data. In this section, results of in-situ SE analysis of thin metal films, deposited by the pulsed cathodic vacuum arc described in chapter 5, are presented. A technique to determine the deposition rate without detailed knowledge of the film optical properties is presented and explored. Effective medium approximations are also explored. The results are compared with in-situ conductivity measurement obtained simultaneously Pulsed cathodic vacuum arc deposition of titanium A silicon wafer with a thermally grown oxide of nominal thickness 500nm was used as a substrate. The substrate was plasma cleaned by applying 20µs, 4.5kV pulses at a frequency of 1kHz, to the substrate holder, initiating a glow discharge plasma in 5mtorr of argon gas. The high voltage was then removed and titanium was deposited using the pulsed cathodic arc. A 99.99% pure titanium cathode was used with an arc bank voltage of 200V, corresponding to a peak arc current of around 3kA. The arc pulse frequency was set at 0.1Hz and the background gas pressure was less than 1 x 151

11 10-6 torr. The magnetic filter was powered using a separate power supply. A deposition rate of around 0.05nm per pulse was expected from previous calibration with a profilometer. The ellipsometer heads were mounted on the deposition chamber at a nominal angle of incidence of 75 degrees. Fused silica vacuum-sealed windows were used as entrance and exit ports for the incident and reflected light. The substrate was modelled as a 1mm silicon base layer with a SiO 2 layer on top. Optical data for both layers was taken from the Woollam database, originally sourced from [5]. The angle of incidence and the oxide film thickness were determined from this model to be and 506.0nm respectively. Ellipsometric data was collected every ten arc pulses for 350 arc pulses. The deposition process was not stopped during the data acquisition. and Ψ values are shown in figure

12 Figure 8.4: and Ψ values for pulsed FCVA titanium deposited on SiO 2 /Si in increments of 50 arc pulses. 153

13 Modelling using the method of Arwin and Aspnes Modelling the film growth using the optical constants for bulk titanium gave extremely poor results, for the same reasons as described above. The film thickness and dielectric function of the thin films were subsequently determined using a method described by Arwin and Aspnes [6]. The method takes advantage of sharp features in the optical properties of the substrate. If the substrate is characterised perfectly in terms of its surface optical properties, a dielectric function determined for the deposited film will show evidence of this sharp feature if the assumed thickness of the film is incorrect. If the chosen film thickness is correct, the pseudodielectric function determined for the film will show no signs of the substrate features. The pseudodielectric function describes the optical constants for the specified region of the model, in this case a combination of the void and rough titanium film optical constants. The substrates used in this experiment exhibit a sharp minimum in the Ψ data and a sharp increase in the data at wavelengths near 400 and 570nm. These features appear in the pseudodielectric function if the film thickness choice is incorrect. 154

14 ε 2 ε 1 Figure 8.5: Pseudodielectric functions determined for different guesses of film thickness. The 10nm guess shows the smallest deviations at the location of the minima in the Ψ data from figure 8.4. An example of the pseudodielectric functions for a number of assumed different film thicknesses is shown in figure 8.5 for data obtained after 100 arc shots. The wavelength region between 500 and 600nm exhibits a considerable change for the range of chosen thickness values. A smaller change is also observed near 400nm. A thickness choice of 10nm shows a minimum influence of the substrate features. Further iterations of the film thickness showed a film thickness of 9.7nm to be the best choice. When the film thickness is close to the correct thickness the pseudodielectric functions exhibit a smooth transition across the wavelength range under investigation, as would be expected for a metallic film in this wavelength region. 155

15 Discussion The method described was used to determine the thickness of the growing titanium film from the data in figure 8.4. Film thickness as a function of the number of arc pulses is shown in figure 8.6. The results show a very good approximation to a linear deposition rate, determined from a linear regression straight line fit to be 49 +/- 0.2 pm per arc pulse. The data points between zero and 100 arc pulses were excluded from the set of fitted points for reasons described below. The statistical analysis shows the fit is a particularly good one, and comparison to the expected deposition rate of 0.05nm per pulse suggests that the results are realistic. Figure 8.6: Film thickness as a function of the number of arc pulses. Note the deviation from constant growth rate below 100 arc pulses. 156

16 Careful observation of the data points for film thickness below 3nm reveals a weighting toward increased thickness values. This is consistent with the film at low coverage growing as discrete islands. As more material is deposited the area between the islands must be filled before the film thickness can increase and after around 100 arc pulses the deposition rate becomes constant. Figure 8.7 shows the pseudodielectric functions for the film thicknesses determined by the above method, compared with the dielectric function for bulk titanium from the Woollam database (sourced from [5]). One of the obvious features is the increase in noise as the film thickness decreases. This is due to an increase in sensitivity to the substrate when the film thickness is of the order of the surface roughness of the substrate. Both ε 1 and ε 2 tend toward the bulk values for titanium from the literature as the film thickness increases, although at longer wavelengths there is significant deviation, particularly in ε

17 Figure 8.7: Pseudodielectric functions for thin titanium films determined using the method of Arwin and Aspnes. 158

18 Between 2.8 and 4.9nm the ε 1 values drop below zero. Nguyen, An and Collins report this as the transition from a dielectric film to a metallic film [7]. This is perfectly plausible considering electrically isolated dielectric islands in the early stages of film growth, followed by percolation and in-filling resulting in a continuous metallic film. This is a very important point as we now have an independent non-destructive method for determining the percolation threshold in-situ. Not all values of ε 1 are below zero in the wavelength range available until the film thickness reaches 17.1nm. It is therefore not possible to determine an exact value of film thickness for the percolation threshold using the condition that percolation occurs when ε 1 drops below zero. We can, however, intuit a range of film thickness by using this condition for ε 1 at longer wavelengths, say greater than 600nm. Using this criterion the percolation threshold was determined to be between 3.0 and 3.5nm. 159

19 1E-4 Resistivity, ρ, (Ω.m) 1E Film thickness (nm) Figure 8.8: Film resistivity as a function of film thickness for pulsed vacuum arc deposited titanium. Figure 8.8 shows the resistivity of the titanium film measured simultaneously with the SE data used for the above analysis. The resistivity curve flattens out as the film thickness increases, to a value of 3.2 x 10-6 Ω.m at a thickness of 17nm. This is an order of magnitude higher than the value of 4.3 x 10-7 Ω.m published in the literature [8]. As discussed in the previous chapter, metal films with thicknesses less than the mean free path of conduction electrons exhibit increased resistivity due to enhanced contribution from electron surface scattering. The mean free path for titanium at room temperature is of the order of 40nm and we would therefore not expect the resistivity to approach the bulk value until the film reaches such a thickness. 160

20 The graph shows that there is a dramatic decrease in the rate of change of the resistivity above a thickness of 3nm. As discussed in the previous chapter this is due to the conduction processes becoming increasingly dominated by classical conduction mechanisms as the film approaches the percolation threshold. A study by Maroof and Evans [9] on the determination of the percolation threshold for thin nickel and platinum films reports that the percolation threshold can be determined by finding the minimum value in a plot of thickness, t, against resistance, R, multiplied by the square of the thickness (i.e. t vs Rt 2 ). Such a plot is shown in figure 8.9 using the data from figure 8.8. A derivative curve of this plot revealed the minimum to occur at 3.3 (+/- 0.1) nm, which is exactly in the range predicted previously by determining where ε 1 drops below zero. The excellent agreement between these results provides good confidence in the ability of both techniques to determine the percolation threshold. Figure 8.9: Rt 2 as a function of film thickness from the data in figure 8.8. The minimum at 3.3nm indicates the percolation threshold. 161

21 The difference between the measurements presented here and those presented in the previous chapter is the confidence levels of the film thickness. In contrast to calibration of the deposition rate by ex-situ profilometry, in-situ SE determines the film thickness during the deposition process without affecting the film properties. Crystal monitors, whilst capable of in-situ measurements, do not directly measure the film of interest and require complicated calibrations. As we saw in the previous chapter, the substrate is critical in determining the film properties, particularly in the early stages of film growth, and consequently, crystal monitors are subject to large errors in this region. We can conclude, therefore, that in-situ SE is a far superior method for determining the thickness of ultra-thin films when compared with the other methods considered here. The percolation threshold can be accurately determined by measuring the film resistivity in-situ and determining the minimum point in a plot of t vs Rt 2. Alternatively it can be determined with less precision by noting where the values of ε 1 fall below zero. The distinct advantage of the latter technique is that it is non-invasive Effective Medium Approximations Theories The method of Arwin and Aspnes determines the pseudodielectric function for the growing films. As was demonstrated above it is particularly useful for determining the thickness of the total film layer. However it gives no quantitative information on the 162

22 film morphology or the dielectric constants of the constituent materials. Effective medium approximations provide a means to determine the optical constants and morphology of the materials that constitute the film layer. The simplest EMA is a linear interpolation between the constituent optical constants. The effective complex dielectric function (pseudodielectric function) ε ~ is given by ~ ε f ~ ε + f ~ ε + f ~ ε +... (8.5) = A A B B C C where f A, f B, and f C and are the volume fractions of the constituent materials with dielectric functions ~ ε A, ~ ε B and ~ ε C. The volume fractions must total unity. A more accurate model is the Maxwell-Garnett EMA, which is derived assuming spherical inclusions of materials B and C in a host matrix of material A, described by ~ ε ~ ε A ~ ε + 2 ~ ε A = f B ~ ε B ~ ε A ~ ε 2 ~ + + ε B A f C ~ εc ~ ε A ~ ε + 2 ~ ε C A (8.6) for three constituents. If only two constituent materials are present f C is set to zero. The original derivation of the Maxwell-Garnett EMA assumed that material B consisted of spherical inclusions within the host matrix composed of material A. The Maxwell-Garnett EMA is exact in the limit of small spherical inclusions well separated from each other. The small diameter compared to the wavelength enables the use of the quasistatic approximation to describe the interaction of the spheres with the incident field. The separation enables the use of the isolated sphere case, in which only the induced dipole moment need be considered. In practice, volume fractions of less than 30%, and diameters of less than one fifth of the wavelength, are normally acceptable. 163

23 An extension of the model (for two constituents only) uses a parameter known as a depolarisation factor (DF) that weights the contribution from material B. A depolarisation factor of 1/3 assumes that the material B is spherical; a DF of 1 represents flat disks or a laminar microstructure; whilst a DF of 0 assumes material B is composed of needle-like or columnar inclusions. In all cases here the DF has been fixed to assume spherical inclusions. Unlike the Maxwell-Garnett EMA, the Bruggeman EMA (sometimes referred to as the coherent potential approximation) does not assume a host material, but rather equally weights the constituent materials according to their volume fractions and dielectric functions. It is therefore not subject to the volume fraction restriction described above for the Maxwell-Garnet EMA. The Bruggeman EMA is expressed mathematically as ~ ε ~ ~ ~ ~ ~ A ε ε B ε εc ε f A ~ ~ + fb ~ ~ + fc ~ ~ = 0 (8.7) ε + 2ε ε + 2ε ε + 2ε A B C Analysis In general it has been observed that the Maxwell-Garnet EMA is best suited to modelling the initial stages of film growth when the film is discontinuous, whilst the Bruggeman EMA better describes film roughness and intermixed layer effects [7, 10]. Figure 8.10 shows the predicted volume fractions for titanium thin films using the Bruggeman, Maxwell-Garnet and Linear EMA s. The thicknesses of the titanium films were determined using the method of Arwin and Aspnes. The volume fraction was set as a variable parameter in the regression analysis and the titanium optical constants were those of the bulk material sourced from reference [5]. 164

24 Figure 8.10: Titanium volume fraction as a function of film thickness using three different effective medium theories. The Maxwell-Garnet EMA suggests a very sharp increase in the volume fraction of titanium at the beginning of the deposition, to a value above 0.6. As mentioned above, the Maxwell-Garnet EMA is not acceptable when the value of f B exceeds 0.3. We are inclined therefore to conclude that the Maxwell-Garnet EMA cannot be used to analyse the data here. The Bruggeman EMA is not subject to the same limitations and indicates a smooth increase in f B up to a value of 0.83 at 5nm. This is consistent with the notion that the 5nm thick film is continuous, with a number of defects, such as voids, and a surface roughness layer, which contribute to the reduction in titanium volume. The linear EMA provides a similar result to the Bruggeman EMA with a noticeable deviation in the early stages of film growth. 165

25 Figure 8.11: Mean squared error for the regression fits to the ellipsometric data from figure 8.4 for three different EMA s. Figure 8.11 shows the mean square error (MSE) values for the three EMA s. The MSE is an indication of the ability of the generated data to approximate the experimental data, higher values indicating a poorer fit. The Maxwell-Garnett EMA shows an initially low MSE before quickly jumping to a much higher value. After 2nm the Maxwell-Garnett EMA provides a considerably poorer approximation to the data than the other two EMA s. In contrast, the Bruggeman MSE initially rises, before dropping back to a lower value and flattening out after around 3nm. This suggests the Bruggeman EMA is indeed a better approximation at thicknesses above 3nm, precisely where the percolation threshold is predicted to occur for these films. As mentioned above, the Maxwell-Garnett EMA is not valid for the analysis here since the volume fraction exceeds 0.3 for the first measurement. It is expected that the 166

26 Maxwell-Garnett EMA would provide a valid approximation in the early stages of film growth, with a lower MSE than the other EMA s, if the depolarisation factor were modified to account for the island morphology. Figure 8.12: Film thickness from figure 8.7 scaled with the volume fraction from figure 8.11 to represent the total material deposited as a function of the number of arc pulses. The straight line represents a constant deposition rate. Figure 8.12 shows the amount of material deposited as a function of the number of arc pulses. This data was produced by multiplying the film thickness by f B obtained using the Bruggeman EMA. There is a deviation from a constant deposition rate, as indicated by the straight line, in the early stages of film growth. A constant deposition rate is achieved after around 20 arc pulses. Whilst we would expect a constant deposition rate from the beginning we can attribute the initial deviation to a number of factors. 167

27 Firstly, the roughness of the substrate has not been taken into account. We could reasonably expect a mixing layer of metal and oxide of the order of 1nm, distorting the relative calculated volume fractions. Secondly, we saw in chapter 5 the imperative to condition the cathodic arc to avoid type 1 arcing. Between depositions there may be a build up of adsorbed particles on the cathode surface. This would act to reduce the amount of cathode material ablated per arc pulse in the early stages. Finally, the desorption rate of adatoms on the oxide surface may be higher in the initial stages of film growth resulting in a decreased effective deposition rate Real-time in-situ spectroscopic ellipsometric study of post deposition morphological changes In this section we utilise in-situ spectroscopic ellipsometry to probe pulsed arcdeposited ultra-thin silver films after the end of the deposition process. As was seen in the previous chapter, ultra-thin film electrical resistance exhibits considerable changes immediately following the deposition. Real-time in-situ spectroscopic ellipsometry is a recent extension of in-situ SE, allowing fast data acquisition during and after the deposition process. It is made possible by advances in ellipsometer hardware, specifically, the use of fast mechanically rotating polarisers and compensators, and CCD arrays for simultaneous measurement of multiple wavelengths. Data acquisition times are primarily set by the frequency of the rotating components and are limited by the increase in signal-to-noise as the acquisition time is reduced. In contrast to studies of morphological changes of thin films using high-resolution microscopy, SE probes a comparatively large area of the sample. Since the resistivity changes are observed on 168

28 a 25mm square sample the study provides information on the macroscopic origin of the changes Experimental In this experiment, thin silver films were deposited on silicon substrates with a 0.5µm thermal silicon oxide layer. Silver cathodes of 99.99% purity were vaporized in the pulsed cathodic vacuum arc, described in chapter 5, with a pulse length of 1ms and a peak current of 3kA. The pulse frequency was 0.1Hz and the background pressure was 2 x 10-7 Torr. A magnetic solenoid macroparticle filter was used to remove micron-sized droplets, creating a pure silver plasma. A J.A. Woollam M-2000V spectroscopic ellipsometer was used to take in-situ measurements during and after the film deposition. The ellipsometer software was used to automatically acquire realtime data sets. The nominal angle of incidence of the polarised light was 75 o. This was more accurately determined to be 75.5 o +/- 0.1 o by fitting a substrate model previously generated using ex-situ VASE Results Figure 8.13 shows the thickness of the silver film determined using the method of Arwin and Aspnes. It is apparent that film thickness does not increase linearly with the number of arc pulses. This suggests the growing film has not in-filled to completely cover the substrate surface up to a film thickness of 16nm. This is in contrast to the thin titanium film results in figure 8.6, which suggest complete coverage of the substrate above 5nm. This result is not surprising considering the 169

29 difference in surface energy between silver and titanium. Silver films on NaCl have been observed to exhibit incomplete substrate coverage up to a thickness of 90nm [11]. Figure 8.13: Silver film thickness as a function of the number of arc pulses. After 240 pulses the growth rate still has not reached a constant value. Ellipsometry measurements were made during the deposition at intervals of 1 minute. After a deposition period of 10 minutes the arc was switched off and measurements were made at 7-second intervals. Figure 8.14 shows the change in height and wavelength of a substrate interference peak in the tanψ data at around 760nm as metal is deposited on the oxide surface. The arrow indicates the approximate location of the peak at increasing time intervals. Other spectral regions of the ellipsometric data did not reveal changes after the end of the deposition. Nor were the changes observed for titanium films, a result which suggests that the effect is not due to 170

30 adsorption of gases on the film surface. Additionally, we would expect titanium to oxidise at a faster rate than silver, suggesting the effect is not due to oxidation. Figure 8.14: Changes in the interference peak height and peak location in the tanψ ellipsometric data. Dashed lines were taken at 1-minute intervals during the deposition. The thick dashed line was taken immediately following the deposition. Solid lines were taken at subsequent 7-second intervals. The arrow indicates increasing time Discussion Movement of the peak to longer wavelengths during the deposition is consistent with an effective increase in the total optical thickness of the oxide and metal films on the silicon substrate [12]. Reduction in the peak height is consistent with a decrease in the reflectivity of the surface [12] due to absorption or surface scattering by roughening of the film surface. After the deposition process is terminated, the peak slowly moves back to a lower wavelength suggesting that the effective optical thickness decreases. 171

31 More prominent is the increase in the height of the peak consistent with a decrease in absorption or scattering by the film. The film thickness was determined using the method of Arwin and Aspnes. At the end of the deposition it was found to be 6.8 (+/- 0.05) nm. After 2 minutes the film thickness had increased to 7.0 (+/- 0.05) nm. After 4 minutes there was no discernable change in the ellipsometric data. From figure 8.13 we can conclude that a silver film of this thickness is not yet continuous and still consists primarily of islands. The results suggest that the islands are growing in height for a number of minutes after the end of the deposition due to cluster migration and Ostwald ripening. After a few minutes the system has relaxed to a lower energy state. During this time the surface would also have cooled, reducing the energy available for atoms to overcome activation potentials. It would be valuable to utilise the EMA s to determine the void content of the films, however the results of such an exercise were unrealistic or outside the limits of application for the theory. It should be noted that in all cases the void content of the films increased marginally during the relaxation period, indicating a constant volume of silver with island structures increasing in height. Further analysis of the results with extended EMA theories to account for island shapes may give valuable results. Comparing the above results with those presented in the previous chapter we may conclude that the morphological changes observed here are responsible in part for the observed changes in resistivity after the end of the deposition process. The timescale of the changes observed here is such that we cannot link the morphological changes to 172

32 the resistance changes at times greater than a few minutes. Observed resistance changes at times in excess of one hour must be concluded to be due to alternative processes. Based on the arguments presented in the previous chapter we may conclude that short term changes are primarily due to morphological changes in island morphology, whilst longer term changes are caused by slow cooling of the surface in vacuum, resulting in temperature dependent resistance changes. Finally, a recent publication by Shimuzu et al. reported a change in the in-situ single wavelength ellipsometric parameters over a period of 24 hrs for a magnetron sputterdeposited silver film of average thickness 20nm [13]. A similar observation concerning the relaxation of a 30nm rhodium film over a period of 2 hours was reported by Liu et al. [14]. It is difficult to relate these results with those presented here since the film thicknesses are much greater than the 7nm films considered here. We would expect 20-30nm films to be past the percolation threshold. It is, however, worth noting the complexities associated with the dynamic nature of ultra-thin films are not restricted to films below the percolation threshold Conclusions For the production of an ultra-thin film conductive film to remove charge during PIII of insulators, it is vital that we possess control of the film thickness and morphology, to provide a film that is conductive yet essentially transparent to incident high-energy ions. Spectroscopic ellipsometry has been shown here to be capable of accurately monitoring film thickness in-situ with accuracy of around 0.1nm. The method of Arwin and Aspnes [6] was shown to be invaluable in obtaining such a result, and has 173

33 the added advantage of being able to determine the percolation threshold without direct contact to the growing film. The results suggested a percolation threshold for titanium grown on oxidised silicon at a film thickness between 3.0 and 3.5 nm. This was more accurately determined by comparing the percolation threshold predicted by the method of Maroof and Evans [9], which was shown to be 3.3 (+/- 0.1) nm. The concurrence of these results lends excellent support to the validity of both methods. If control over the final structure of ultra-thin films is to be achieved it is important to understand not only the film structure during the deposition but also changes in the structure after the condensation phase is complete. In-situ spectroscopic ellipsometry is a powerful, non-destructive technique capable of monitoring growth phases of thin films with sub-angstrom resolution. We have shown here that it is also possible to monitor changes in film morphology in real-time, during and after the deposition process. The results suggest that observations of post-deposition resistivity changes are due to a combination of short-term morphological changes in island structure, and also longer-term effects due to cooling of the film and substrate surface References 1. Drude, P., Ann. Phys., : p Maxwell-Garnett, J.C., Phil. Trans. R. Soc. London, : p Bruggeman, D.A.G., Ann. Phys., : p Herzinger, J. Appl. Phys., : p Palik., E.D., Handbook of optical constants of solids. 1985, Orlando: Academic Press,. 174

34 6. Arwin, H. and D.E. Aspnes, Unambiguous determination of thickness and dielectric function of thin films by spectroscopic ellipsometry. Thin Solid Films, : p Nguyen, H.V., I. An, and R.W. Collins, Physical Review B, (7): p Kittel, C., Introduction to solid state physics. 7th ed. 1996, New York: John Wiley & sons. 9. Maroof, A.I. and B.L. Evans, J. Appl. Phys., (2): p Kawabata, S., et al., Thin Solid Films, : p Vook, R.W., Int. Metals Rev., : p Instrument_manual, A short course in ellipsometry. 2001, J.A. Woolam co., Inc. 13. Shimizu, H., Y. Hoshi, and S. Kawabata, Consideration on the initial growth stage of sputtered Ag thin films observed by ellipsometry. Transactions of the institute of electrical engineers of Japan, A(8): p Liu, C., et al., Thickness determination of metal thin films with spectroscopic ellipsometry for X-ray mirror and multilayer applications. Journal of Vacuum Science and Technology A, (5): p