- Email: [email protected]
Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond and faster
Thin Solid Films 313]314 Ž1998. 40]46
Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond and faster K. Hemmesa,U , M.A. Hamstraa , K.R. Koopsa , M.M. Winda , T. Schramb , J. de Laet b , H. Bender c a
Delft Uni¨ersity of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands b Free Uni¨ersity Brussels, Pleinlaan 2, B-1050 Brussels, Belgium c Interuni¨ersity Micro-Electronics Centre, Kapeldreef 75, B-3001 Leu¨en, Belgium
Abstract An interferometric ellipsometer based on a Zeeman laser has been developed. The so-called Zeeman]LePoole ellipsometer ŽZLE. is a single wavelength ellipso-reflectometer with a time resolution of 1 m s. The light source used is a Zeeman Žtwo-frequency. He]Ne laser, operating at the 632.8 nm wavelength with a frequency difference of 1 MHz between the two modes. The optical system of the ZLE is based on an interferometric configuration. Two photo-diodes transform the light carrying the optical information from the sample into electrical signals with a frequency of 1 MHz, which are processed with high speed data-acquisition equipment. This new type of ellipsometer was designed for studying fast processes. As a test of the dynamic capabilities of the ZLE, we measured the optical response of a LCD and a Pockels cell, that were externally stimulated with time-dependent voltages. We also report on in-situ electrochemical experiments monitored with the ZLE. The advantages and disadvantages of the ZLE are discussed. The application of two coupled lasers in an interferometric ellipsometry set-up is a novel approach that allows for a variable time resolution and avoids the problem of frequency mixing. This new set-up also has a high potential for application in optical recording. Q 1998 Elsevier Science S.A. Keywords: Ellipsometry; Interferometer; Zeeman laser; Optical recording
1. Introduction Approximately 25 years ago Hazebroek and Holscher successfully demonstrated the feasibility of interferometric ellipsometer systems. In their set-up they used a conventional He]Ne laser as a light source w1x. Using essentially a Michelson-interferometer optical configuration, the laser beam was split into two branches, a measurement beam and a reference beam. The measurement beam picked up the ellipso-
U
Corresponding author.
0040-6090r98r$19.00 Q 1998 Elsevier Science S.A. All rights reserved PII S0040-6090Ž97.00766-9
metric information on the sample simply by reflection. The optical frequency of the reference beam was slightly altered by means of a moving mirror ŽDoppler shift.. Recombining the two beams generated an interference pattern. The constant terms in the pattern could be discarded, but the beat-signal, oscillating with the frequency difference of the two beams, carried the ellipsometric information on the sample. Photodiodes transformed the light to electric signals having the beat-frequency. The signals were sampled, stored and finally analysed. As an alternative approach the use of a Zeeman Žtwo-frequency. laser was suggested w2x. This way the two frequencies, necessary for creating the beat-signal, would already be present
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
from the start. Thus the weakest component of the first interferometric ellipsometer Ži.e. the moving mirror. could be omitted. In a theoretical study several optical configurations for a Zeeman interferometric ellipsometer were analysed and the most feasible configuration was found which we called the LePoole set-up w3,4x. In these references and in other publications we also used the term UFE ŽUltra Fast Ellipsometer.. However, to avoid confusion on the meaning of fast and ultra fast we will call our interferometric ellipsometer the ‘Zeeman]LePoole Ellipsometer’ or ZLE. 2. Experimental 2.1. Optical set-up and operating principles of the ZLE The principles of the ZLE will be explained briefly here but are described more completely elsewhere w3]5x. The ZLE is schematically shown in Fig. 1. It is a modified version of the LePoole set-up as described by Wind and Hemmes w3x and Hemmes et al. w4x. Essentially it consists of a Zeeman He]Ne laser that produces two laser beams of 632 nm, with a relatively small frequency difference of about 1 MHz and mutually orthogonal polarisations. The two beams, called the measurement and reference beams, are separated by a polarising beamsplitter. The measurement beam is directed towards a sample via a second beamsplitter and redirected by a retro-mirror. In general the sample changes the polarisation state of the light beam. Since the beam is reflected twice by the sample, this
41
effect is doubled. The reference beam is directed around the second beamsplitter by two mirrors and a pentaprism. A pentaprism is used here instead of a third mirror in order to preserve the correct left]right symmetry of the beam which improves the interference of this reference beam with the measurement beam in the second Žnon-polarising. beamsplitter. The polarisation state of the interfering beams is analysed by separating the p and s components in the third polarising beamsplitter subsequently followed by detection in a ‘p’ and an ‘s’ detector. Since the light frequencies of the two interfering beams differ by approximately 1 MHz, two sinusoidal signals with a so-called beat frequency of 1 MHz are generated in the two detectors. It can be shown that, apart from a constant, which can be determined separately in a reference measurement, the amplitude ratio and phase difference of these 1-MHz signals are related one-to-one to the amplitude ratio and phase difference of the optical p and s components, i.e. the polarisation state of the light beam after its reflection from the sample. Hence any change in the optical properties of the sample leads to a change in the amplitude ratio and phase difference of the two 1MHz signals. These two parameters must be determined. Since the signal frequency of approximately 1 MHz can be determined accurately, one can filter with a narrow band around this value and thus remove almost all noise. In fact we can regard the 1-MHz signals as the information carriers, and the measurement principle is analogous to the modulation principle as frequently used in ellipso- and re-
Fig. 1. Optical lay-out of the Zeeman]LePoole ellipsometer ŽZLE..
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
42
flectometers. However, in the ZLE no explicit modulators Žsuch as Pockels cells or acousto-optic modulators. are necessary. The high accuracy of the ZLE is mainly obtained by making use of this modulation principle, i.e. the information is carried by two sine waves with a well known high frequency. This allows for a very effective noise filtering, either analog or digital. 2.2. Two laser set-up Two commercially available stabilised He]Ne lasers ŽMelles Griot type 05 STP 901. were used to realise an optical mixer with a tuneable mixing frequency according to the set-up depicted in Fig. 2. The lasers are supplied with a control unit providing amplitude or frequency stabilisation. Since the frequency can be regulated by supplying an external signal, we constructed a third control unit that regulates the frequency difference between the two lasers to a fixed and tuneable value, at present limited only by our available low-cost electronics to about 10 MHz. This way of controlling the frequency difference has also been described in a patent by Hitachi Ltd. w6x. As shown in Fig. 2, this system can be used to replace a single Zeeman laser in our ZLE w7x. The availability of stabilised laser diodes which are much smaller, offer the possibility of applying this two laser set-up in optical recording. The main advantage is that with this set-up, changes in phase difference caused by the written data bits on a optical disk can be read out, instead of amplitude changes.
2.3. Possibilities for spectroscopic interferometric ellipsometry. In principle it is possible to construct a spectroscopic interferometric ellipsometer. In the set-up of Fig. 1, the Zeeman laser can be replaced by a tuneable dye laser and one or two acousto-optic modulators can be placed in the reference beam to generate a frequency difference. Of course, the original Hazebroek]Holscher ellipsometer with a moving mirror also can be modified by using a laser source with variable wavelength or by using a laser emitting more wavelengths at the same time. In the latter case diode arrays can be used to measure simultaneously a number of wavelengths in a spectrum. 2.4. Data analysis We developed two ways of analysing the two 1-MHz signals from the ZLE. A real time option is provided by using one Žor two. lock-in amplifiers ŽLIAs, PAR EG & G model 5302.. However, in this work a second and more accurate analysis method is used. The two signals are digitised and stored, followed by an off-line analysis using dedicated software. Digitising is performed by a four-channel digital storage oscilloscope ŽDSO, LeCroy. which provides 8 bits resolution and a large memory depth of 1 Mbyte per channel. Hence, at the standard sampling rate of 100 MSrs, a 10-ms transient can be recorded. For slower processes, sampling is interrupted by dead periods so as to prevent overflow of the memories. Channels 3 and 4 can be
Fig. 2. Interferometric ellipsometer with two coupled lasers having a variable time resolution.
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
43
used to digitise simultaneously the voltage perturbation andror the electrochemical current for later off-line analysis and comparison with the optical response. 2.5. Electrochemical cells The electrochemical part of the set-up consists of an electrochemical cell with one optical window that allows for perpendicular incidence laser light on the sample and two windows for the in and outgoing laser beam in in-situ ellipsometry. A fourth window is placed opposite to the front window to allow for transmission measurements Žsee Fig. 3.. The angle of incidence on the sample is approximately 708. The anodic oxidation of aluminium in 20 vol.% H 2 SO4 at 208C was studied in order to test the possibilities of the ZLE for in-situ measurements of an important industrial process w8x. Prior to the actual measurement, the cell was oriented for use at perpendicular incidence. Afterwards the cell was rotated by 708 using a stepping motor-driven rotation table. The anodic oxide layers were formed on a 3-m m thick evaporated aluminium film on a SiŽ111. wafer. An aluminium counter electrode was used. The current was controlled by an EG & G model 274 potentiostat, used with a saturated calomel reference electrode. 3. Results and discussion The ZLE is especially suitable for measuring fast optical changes. To test the capabilities and limitations of the ZLE, we measured the time-dependent response of a liquid crystal device ŽLCD. and a Pockels cell. Experiments under in-situ electrochemical conditions suffered from large fluctuations in D and C even under stationary conditions. Also the speed of most electrochemical processes was found to be much slower than the 1 m s time resolution of the ZLE, yet an example of the formation of an oxide film on aluminium is given in the last sub-section.
Fig. 3. Electrochemical cell for in-situ optical measurements.
3.1. Liquid crystal de¨ice We note that the ZLE can easily be used in the transmission mode as well. So in order to study the response of the ZLE to fast optical changes, we have used the test set-up shown in Fig. 1 without the electrochemical cell and with the sample used in transmission mode. The optical properties of a LCD depend on the applied voltage. The LCD studied was designed to respond to square wave voltages with a frequency up to 60 Hz. A faster response is obtained, however, by using an additional high frequency Ž20kHz. carrier wave modulated with a 60-Hz square wave signal. In the first experiment the digital storage oscillos-
Fig. 4. ZLE measurement of a modulated liquid crystal device.
44
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
Fig. 5. ZLE measurement of a modulated liquid crystal device over an extended time period of 1 s.
cope was set to perform a single shot measurement at the maximum sample rate of 100 MSrs for 10 ms. The resulting data set was analysed in consecutive blocks of 100 points to obtain a time resolution of 1 m s. The results in Fig. 4 show that the response of the LCD to the driving voltage is not instantaneous but that the LCD shows a considerable rise time of approximately 50 ms. Secondly a sequential measurement was performed. In Fig. 5 the result is shown for a sequential measurement lasting 1 s, in which 1000 blocks of 1000 sampling points each were stored with a time interval of 1 ms. Since the sampling rate was 100 MSrs each data block covers a time span of 10 m s. So in order to be able to measure over the long period of 1 s, dead periods of 990 m s must be accepted. Therefore the accuracy is a factor 10 Žnamely 6100. smaller than what could have been obtained with a larger memory of 100 Mbytes instead of 1 Mbyte. Nevertheless, the accuracy of the ZLE is
sufficiently high to study details in the response of the sample. This is clearly demonstrated by the smaller graphs in Fig. 5 for this specific test sample. 3.2. Pockels cell A Pockels cell is a well known electro-optical element. Two electrodes are used to produce a potential difference over the element that changes the refractive index in one direction. The change in refractive index in response to the applied voltage is very fast and also precisely proportional to the applied potential difference over the cell. For a light beam, the change in refractive index causes a phase difference between the two orthogonal polarisation states. Hence a Pockels cell can be used as a tuneable phase retarder. With the Pockels cell now taking the place of the LCD, we performed a potential step experiment. An
Fig. 6. ZLE measurement of a Pockels cell modulated at 100 kHz.
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
45
instantaneous step response was observed, both in the two amplitudes and in the phase difference. This is not surprising, since the response time of a Pockels cell is approximately 1 ns. Next we applied a sinusoıdal ¨ perturbation of 5 V Žrms. with a frequency of 100 kHz. The results in Fig. 6 clearly show a 100-kHz modulation, both in the amplitudes of s- and ppolarised light and in their phase difference. We note that the variations in C and D are only on the order of 18, yet the response is accurately Ž"0.158. recorded by the ZLE with a time resolution of 1 s. 3.3. In-situ electrochemical measurements Under the applied galvanostatic conditions of 6.7 mArcm2 the porous oxide layer on aluminium grows linearly with anodising time. The fluctuating curve in Fig. 7 shows the measured C and D transients during the anodising experiment. Periodic behaviour is observed in both C and D, in accordance with theory for a growing transparent layer w1x. Based on previous studies using TEM and ex-situ spectroscopic ellipsometry ŽSE., and based on complementary ex-situ SE measurements on the in-situ grown film, the expected transient was simulated. Morphological data were extracted from the SE spectra using a simulation and regression analysis procedure w8x. The optical model used in this regression procedure consists of a two-layer structure, in which the upper layer of the optical model represents the porous part of the anodic coating, while the lower layer of the optical model represents the scalloped substrate surface covered by the compact oxide layer. The thicknesses of both layers for the sample measured with the ZLE were determined as 2.19 m m and 0.020 m m, respectively. The volume percentage of air Žvoid. in the top layer and the percentage of aluminium in the lower layer, which are necessary for the determination of the optical constants of both layers, were determined as 25% void and 40% Al using the Bruggeman effective medium theory w9x. Considering the anodising time of 480 s and a final thickness of the top layer of 2.19 m m, the layer growth rate was determined as 0.00463 m mrs. The smooth curve in Fig. 7 represents the simulated transient as an overlay on the measurement results. The agreement is reasonable except for a small deviation in the oscillation period and a small shift in the absolute value for D. These deviations can possibly be explained by the fact that the pores in the porous part of the anodic film are not completely filled with water, as we assumed in our model. 4. Conclusion Our measurements demonstrate that the ZLE and its software ŽOPTIMA. are capable of measuring and
Fig. 7. In-situ ZLE measurement of the anodic oxidation of aluminium.
analysing fast optical phenomena. A relative accuracy of 0.158 in D and C could be obtained at a time resolution of 1 m s. However, due to the interferometric principle the ZLE is very sensitive, and the D and C obtained in in-situ electrochemical experiments show fluctuations of several degrees. Using two coupled stabilised lasers, one can obtain a simple interferometric ellipsometer with a tuneable time resolution that can possibly be used in optical recording.
Acknowledgements
This work is supported in part by the European Commission DGXII-BCR under contract No. MATICT-94002.
46
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
References w1x R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarised Light, North-Holland Publishing Company, Amsterdam, 1986. w2x Private communication with Prof. R. LePoole, Leiden University, the Netherlands. w3x M.M. Wind, K. Hemmes, Meas. Sci. Technol. 5 Ž1994. 37. w4x K. Hemmes et al., ‘Zeeman-ellipsometer’, Dutch patent application No. 9202303. w5x K. Hemmes et al., Ultra Fast Ellipsometry, Final report for the European Committee, BCR contract no. MATI]CT 940029.
w6x S. Sasaki et al., Frequency seperation stabilization method for optical heterodyne or optical homodyne communication, US Patent No. 53963613. w7x K. Hemmes, K.R. Koops, ‘Twee-laser ellipsometer’, Dutch patent application No. OA 1006016, May 1997. w8x J. De Laet, J. Vanhellemont, H. Terryn, J. Vereecken, Thin Solid Films 233 Ž1993. 58. w9x D.A.G. Bruggeman, Annalen der Physik 5 Ž1935. 636.
Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond and faster K. Hemmesa,U , M.A. Hamstraa , K.R. Koopsa , M.M. Winda , T. Schramb , J. de Laet b , H. Bender c a
Delft Uni¨ersity of Technology, Rotterdamseweg 137, 2628 AL Delft, The Netherlands b Free Uni¨ersity Brussels, Pleinlaan 2, B-1050 Brussels, Belgium c Interuni¨ersity Micro-Electronics Centre, Kapeldreef 75, B-3001 Leu¨en, Belgium
Abstract An interferometric ellipsometer based on a Zeeman laser has been developed. The so-called Zeeman]LePoole ellipsometer ŽZLE. is a single wavelength ellipso-reflectometer with a time resolution of 1 m s. The light source used is a Zeeman Žtwo-frequency. He]Ne laser, operating at the 632.8 nm wavelength with a frequency difference of 1 MHz between the two modes. The optical system of the ZLE is based on an interferometric configuration. Two photo-diodes transform the light carrying the optical information from the sample into electrical signals with a frequency of 1 MHz, which are processed with high speed data-acquisition equipment. This new type of ellipsometer was designed for studying fast processes. As a test of the dynamic capabilities of the ZLE, we measured the optical response of a LCD and a Pockels cell, that were externally stimulated with time-dependent voltages. We also report on in-situ electrochemical experiments monitored with the ZLE. The advantages and disadvantages of the ZLE are discussed. The application of two coupled lasers in an interferometric ellipsometry set-up is a novel approach that allows for a variable time resolution and avoids the problem of frequency mixing. This new set-up also has a high potential for application in optical recording. Q 1998 Elsevier Science S.A. Keywords: Ellipsometry; Interferometer; Zeeman laser; Optical recording
1. Introduction Approximately 25 years ago Hazebroek and Holscher successfully demonstrated the feasibility of interferometric ellipsometer systems. In their set-up they used a conventional He]Ne laser as a light source w1x. Using essentially a Michelson-interferometer optical configuration, the laser beam was split into two branches, a measurement beam and a reference beam. The measurement beam picked up the ellipso-
U
Corresponding author.
0040-6090r98r$19.00 Q 1998 Elsevier Science S.A. All rights reserved PII S0040-6090Ž97.00766-9
metric information on the sample simply by reflection. The optical frequency of the reference beam was slightly altered by means of a moving mirror ŽDoppler shift.. Recombining the two beams generated an interference pattern. The constant terms in the pattern could be discarded, but the beat-signal, oscillating with the frequency difference of the two beams, carried the ellipsometric information on the sample. Photodiodes transformed the light to electric signals having the beat-frequency. The signals were sampled, stored and finally analysed. As an alternative approach the use of a Zeeman Žtwo-frequency. laser was suggested w2x. This way the two frequencies, necessary for creating the beat-signal, would already be present
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
from the start. Thus the weakest component of the first interferometric ellipsometer Ži.e. the moving mirror. could be omitted. In a theoretical study several optical configurations for a Zeeman interferometric ellipsometer were analysed and the most feasible configuration was found which we called the LePoole set-up w3,4x. In these references and in other publications we also used the term UFE ŽUltra Fast Ellipsometer.. However, to avoid confusion on the meaning of fast and ultra fast we will call our interferometric ellipsometer the ‘Zeeman]LePoole Ellipsometer’ or ZLE. 2. Experimental 2.1. Optical set-up and operating principles of the ZLE The principles of the ZLE will be explained briefly here but are described more completely elsewhere w3]5x. The ZLE is schematically shown in Fig. 1. It is a modified version of the LePoole set-up as described by Wind and Hemmes w3x and Hemmes et al. w4x. Essentially it consists of a Zeeman He]Ne laser that produces two laser beams of 632 nm, with a relatively small frequency difference of about 1 MHz and mutually orthogonal polarisations. The two beams, called the measurement and reference beams, are separated by a polarising beamsplitter. The measurement beam is directed towards a sample via a second beamsplitter and redirected by a retro-mirror. In general the sample changes the polarisation state of the light beam. Since the beam is reflected twice by the sample, this
41
effect is doubled. The reference beam is directed around the second beamsplitter by two mirrors and a pentaprism. A pentaprism is used here instead of a third mirror in order to preserve the correct left]right symmetry of the beam which improves the interference of this reference beam with the measurement beam in the second Žnon-polarising. beamsplitter. The polarisation state of the interfering beams is analysed by separating the p and s components in the third polarising beamsplitter subsequently followed by detection in a ‘p’ and an ‘s’ detector. Since the light frequencies of the two interfering beams differ by approximately 1 MHz, two sinusoidal signals with a so-called beat frequency of 1 MHz are generated in the two detectors. It can be shown that, apart from a constant, which can be determined separately in a reference measurement, the amplitude ratio and phase difference of these 1-MHz signals are related one-to-one to the amplitude ratio and phase difference of the optical p and s components, i.e. the polarisation state of the light beam after its reflection from the sample. Hence any change in the optical properties of the sample leads to a change in the amplitude ratio and phase difference of the two 1MHz signals. These two parameters must be determined. Since the signal frequency of approximately 1 MHz can be determined accurately, one can filter with a narrow band around this value and thus remove almost all noise. In fact we can regard the 1-MHz signals as the information carriers, and the measurement principle is analogous to the modulation principle as frequently used in ellipso- and re-
Fig. 1. Optical lay-out of the Zeeman]LePoole ellipsometer ŽZLE..
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
42
flectometers. However, in the ZLE no explicit modulators Žsuch as Pockels cells or acousto-optic modulators. are necessary. The high accuracy of the ZLE is mainly obtained by making use of this modulation principle, i.e. the information is carried by two sine waves with a well known high frequency. This allows for a very effective noise filtering, either analog or digital. 2.2. Two laser set-up Two commercially available stabilised He]Ne lasers ŽMelles Griot type 05 STP 901. were used to realise an optical mixer with a tuneable mixing frequency according to the set-up depicted in Fig. 2. The lasers are supplied with a control unit providing amplitude or frequency stabilisation. Since the frequency can be regulated by supplying an external signal, we constructed a third control unit that regulates the frequency difference between the two lasers to a fixed and tuneable value, at present limited only by our available low-cost electronics to about 10 MHz. This way of controlling the frequency difference has also been described in a patent by Hitachi Ltd. w6x. As shown in Fig. 2, this system can be used to replace a single Zeeman laser in our ZLE w7x. The availability of stabilised laser diodes which are much smaller, offer the possibility of applying this two laser set-up in optical recording. The main advantage is that with this set-up, changes in phase difference caused by the written data bits on a optical disk can be read out, instead of amplitude changes.
2.3. Possibilities for spectroscopic interferometric ellipsometry. In principle it is possible to construct a spectroscopic interferometric ellipsometer. In the set-up of Fig. 1, the Zeeman laser can be replaced by a tuneable dye laser and one or two acousto-optic modulators can be placed in the reference beam to generate a frequency difference. Of course, the original Hazebroek]Holscher ellipsometer with a moving mirror also can be modified by using a laser source with variable wavelength or by using a laser emitting more wavelengths at the same time. In the latter case diode arrays can be used to measure simultaneously a number of wavelengths in a spectrum. 2.4. Data analysis We developed two ways of analysing the two 1-MHz signals from the ZLE. A real time option is provided by using one Žor two. lock-in amplifiers ŽLIAs, PAR EG & G model 5302.. However, in this work a second and more accurate analysis method is used. The two signals are digitised and stored, followed by an off-line analysis using dedicated software. Digitising is performed by a four-channel digital storage oscilloscope ŽDSO, LeCroy. which provides 8 bits resolution and a large memory depth of 1 Mbyte per channel. Hence, at the standard sampling rate of 100 MSrs, a 10-ms transient can be recorded. For slower processes, sampling is interrupted by dead periods so as to prevent overflow of the memories. Channels 3 and 4 can be
Fig. 2. Interferometric ellipsometer with two coupled lasers having a variable time resolution.
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
43
used to digitise simultaneously the voltage perturbation andror the electrochemical current for later off-line analysis and comparison with the optical response. 2.5. Electrochemical cells The electrochemical part of the set-up consists of an electrochemical cell with one optical window that allows for perpendicular incidence laser light on the sample and two windows for the in and outgoing laser beam in in-situ ellipsometry. A fourth window is placed opposite to the front window to allow for transmission measurements Žsee Fig. 3.. The angle of incidence on the sample is approximately 708. The anodic oxidation of aluminium in 20 vol.% H 2 SO4 at 208C was studied in order to test the possibilities of the ZLE for in-situ measurements of an important industrial process w8x. Prior to the actual measurement, the cell was oriented for use at perpendicular incidence. Afterwards the cell was rotated by 708 using a stepping motor-driven rotation table. The anodic oxide layers were formed on a 3-m m thick evaporated aluminium film on a SiŽ111. wafer. An aluminium counter electrode was used. The current was controlled by an EG & G model 274 potentiostat, used with a saturated calomel reference electrode. 3. Results and discussion The ZLE is especially suitable for measuring fast optical changes. To test the capabilities and limitations of the ZLE, we measured the time-dependent response of a liquid crystal device ŽLCD. and a Pockels cell. Experiments under in-situ electrochemical conditions suffered from large fluctuations in D and C even under stationary conditions. Also the speed of most electrochemical processes was found to be much slower than the 1 m s time resolution of the ZLE, yet an example of the formation of an oxide film on aluminium is given in the last sub-section.
Fig. 3. Electrochemical cell for in-situ optical measurements.
3.1. Liquid crystal de¨ice We note that the ZLE can easily be used in the transmission mode as well. So in order to study the response of the ZLE to fast optical changes, we have used the test set-up shown in Fig. 1 without the electrochemical cell and with the sample used in transmission mode. The optical properties of a LCD depend on the applied voltage. The LCD studied was designed to respond to square wave voltages with a frequency up to 60 Hz. A faster response is obtained, however, by using an additional high frequency Ž20kHz. carrier wave modulated with a 60-Hz square wave signal. In the first experiment the digital storage oscillos-
Fig. 4. ZLE measurement of a modulated liquid crystal device.
44
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
Fig. 5. ZLE measurement of a modulated liquid crystal device over an extended time period of 1 s.
cope was set to perform a single shot measurement at the maximum sample rate of 100 MSrs for 10 ms. The resulting data set was analysed in consecutive blocks of 100 points to obtain a time resolution of 1 m s. The results in Fig. 4 show that the response of the LCD to the driving voltage is not instantaneous but that the LCD shows a considerable rise time of approximately 50 ms. Secondly a sequential measurement was performed. In Fig. 5 the result is shown for a sequential measurement lasting 1 s, in which 1000 blocks of 1000 sampling points each were stored with a time interval of 1 ms. Since the sampling rate was 100 MSrs each data block covers a time span of 10 m s. So in order to be able to measure over the long period of 1 s, dead periods of 990 m s must be accepted. Therefore the accuracy is a factor 10 Žnamely 6100. smaller than what could have been obtained with a larger memory of 100 Mbytes instead of 1 Mbyte. Nevertheless, the accuracy of the ZLE is
sufficiently high to study details in the response of the sample. This is clearly demonstrated by the smaller graphs in Fig. 5 for this specific test sample. 3.2. Pockels cell A Pockels cell is a well known electro-optical element. Two electrodes are used to produce a potential difference over the element that changes the refractive index in one direction. The change in refractive index in response to the applied voltage is very fast and also precisely proportional to the applied potential difference over the cell. For a light beam, the change in refractive index causes a phase difference between the two orthogonal polarisation states. Hence a Pockels cell can be used as a tuneable phase retarder. With the Pockels cell now taking the place of the LCD, we performed a potential step experiment. An
Fig. 6. ZLE measurement of a Pockels cell modulated at 100 kHz.
K. Hemmes et al. r Thin Solid Films 313]314 (1998) 40]46
45
instantaneous step response was observed, both in the two amplitudes and in the phase difference. This is not surprising, since the response time of a Pockels cell is approximately 1 ns. Next we applied a sinusoıdal ¨ perturbation of 5 V Žrms. with a frequency of 100 kHz. The results in Fig. 6 clearly show a 100-kHz modulation, both in the amplitudes of s- and ppolarised light and in their phase difference. We note that the variations in C and D are only on the order of 18, yet the response is accurately Ž"0.158. recorded by the ZLE with a time resolution of 1 s. 3.3. In-situ electrochemical measurements Under the applied galvanostatic conditions of 6.7 mArcm2 the porous oxide layer on aluminium grows linearly with anodising time. The fluctuating curve in Fig. 7 shows the measured C and D transients during the anodising experiment. Periodic behaviour is observed in both C and D, in accordance with theory for a growing transparent layer w1x. Based on previous studies using TEM and ex-situ spectroscopic ellipsometry ŽSE., and based on complementary ex-situ SE measurements on the in-situ grown film, the expected transient was simulated. Morphological data were extracted from the SE spectra using a simulation and regression analysis procedure w8x. The optical model used in this regression procedure consists of a two-layer structure, in which the upper layer of the optical model represents the porous part of the anodic coating, while the lower layer of the optical model represents the scalloped substrate surface covered by the compact oxide layer. The thicknesses of both layers for the sample measured with the ZLE were determined as 2.19 m m and 0.020 m m, respectively. The volume percentage of air Žvoid. in the top layer and the percentage of aluminium in the lower layer, which are necessary for the determination of the optical constants of both layers, were determined as 25% void and 40% Al using the Bruggeman effective medium theory w9x. Considering the anodising time of 480 s and a final thickness of the top layer of 2.19 m m, the layer growth rate was determined as 0.00463 m mrs. The smooth curve in Fig. 7 represents the simulated transient as an overlay on the measurement results. The agreement is reasonable except for a small deviation in the oscillation period and a small shift in the absolute value for D. These deviations can possibly be explained by the fact that the pores in the porous part of the anodic film are not completely filled with water, as we assumed in our model. 4. Conclusion Our measurements demonstrate that the ZLE and its software ŽOPTIMA. are capable of measuring and
Fig. 7. In-situ ZLE measurement of the anodic oxidation of aluminium.
analysing fast optical phenomena. A relative accuracy of 0.158 in D and C could be obtained at a time resolution of 1 m s. However, due to the interferometric principle the ZLE is very sensitive, and the D and C obtained in in-situ electrochemical experiments show fluctuations of several degrees. Using two coupled stabilised lasers, one can obtain a simple interferometric ellipsometer with a tuneable time resolution that can possibly be used in optical recording.
Acknowledgements
This work is supported in part by the European Commission DGXII-BCR under contract No. MATICT-94002.
46
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