Langmuir 1994,lO,3727-3729
3727
Uniaxial Ellipsometry of Langmuir-Blodgett Films J. P. Cresswell Molecular Electronics Group, School of Engineering and Computer Science, Durham University, Durham DHl 3LE, U.K. Received January 27, 1994. In Final Form: July 27, 1994@ An ellipsometric technique is described for measuring the uniaxial birefringence of Langmuir-Blodgett films. Through the use of certain assumptions about the film properties, it is found that only a small number of samples are required. The results for fatty acids are compared with those for an earlier method, and good agreement is obtained. It is also shown that the use of a uniaxial model leads to a significant improvement of the accuracy of fit. The birefringences of two dyes are also measured.
1. Introduction The Langmuir-Blodgett technique1 is a well-established means for fabricating thin organic films. The nature ofthe process is such that a degree ofmolecular alignment is expected, resulting in anisotropy between in-plane and perpendicular properties. Further anisotropy is possible within the plane, with distinct properties along and perpendicular to the dipping direction. The paper describes a simple ellipsometric technique of measuring anistropy in the refractive index of LB films. A high-quality LB film may be considered as an arrangement of molecules all aligned in the same direction (Figure 1) with a preferred angle of tilt relative to the substrate normal. The molecular axes would be generally expected to lie in a plane containing the dipping direction and the substrate normal, although other situations have been observed. The macroscopic consequence of this arrangement for molecules with axial symmetry is that the film is uniaxially isotropic with the principal axes along and orthogonal to the molecular axis. Reference 2 has shown that fatty acid films are in fact slightly biaxial due to a small differencebetween the two refractive indices perpendicular to the axis of the molecule. The difference is, however, only 0.004 and would be smaller for films which lack the excellent ordering of fatty acids. Biaxiality is therefore neglected in the analysis given in this paper. Before the use of ellipsometry is considered, i t is important to consider the implications for the reflection of polarized light of the idealized version of an LB film described above. Light of s-polarization will have its electric field vector lying within the plane ofthe substrate but that for p-polarization will be coming out of the plane. Unless the direction of propagation is along the dipping direction, polarization mixing will occur, which breaks one of the conditions for nulling ellipsometry. Real LB films will contain less order than the ideal case. For example, the single tilt angle will have to be replaced by a n expectation value surrounded by a distribution of orientations. The ordering relative to the dipping direction may also be lost, giving a film with the molecular axes pointing along the surface of a cone. It has previously been recognized that such a film will be uniaxial with the optic axis along the substrate normal (normal ~ n i a x i a l ) . ~ Abstract published in Advance A C S Abstracts, September 1, 1994. (1)Roberts, G.G. Langmuir-Blodgett Films; Plenum Press: New York, 1990. (2) Barnes, W.L.; Sambles, J. R. Surf. Sci. 1986,177, 399. (3)Scheelen,A.;Winanat, P.; Persoons,A. In Organic Materials for Nonlinear Optics and Photonics; Messier, J., et al., Eds.;Kluwer Academic Publishers: Dordrecht, The Netherlands, 1991;p 497. @
0743-7463/94/2410-3727$04.50/0
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Principal axes
Dipping direction
Figure 1. Uniaxial LB film showing molecular alignment, principal axes, and p and s polarizations. Despite the obvious desire to know the degree of ordering in LB films, there have been few studies of the anisotropic refractive index of LB films. Two notable exceptions to this have been detailed investigations using waveguiding2 and ellip~ometry.~ Ellipsometry provides a convenient method for measuring the permittivity and thickness of thin layers, but unfortunately, as generally applied to LB films, it has one major drawback. This is that the films are usually assumed to be isotropic, which is clearly not the case if any molecular order exists. A method of dealing with anisotropic films has been described by Den E n g e l ~ e n ; ~ here the films are assumed to be normal uniaxial. Unfortunately a large number of samples (typically up to 20) of different thicknesses were needed, which has resulted in this technique being rarely employed. The method of this paper shows how this can be reduced to as few as three samples by making a simple approximation. 2. Theory
Following Den Engelsen, the LB film is assumed to be uniaxially birefringent with the optical axis perpendicular to the substrate. As explained in the previous section, this is a simplification if there is any order relative to the dipping direction. In that case the film could be slightly biaxial and would certainly be non-normal uniaxial. However, provided the plane of incidence is chosen to contain the dipping direction, a good fit between experiment and theory will still be obtained. This is because the optic axes of the molecules will not be tilted out of the plane of incidence. (4) Den Engelsen, D. J . Opt. SOC.Am. 1971,61,1460.
1994 American Chemical Society
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3728 Langmuir, Vol. 10, No. 10, 1994
Substrate Figure 2.
If there is no order relative to the dipping direction, then no approximation is involved-the film really is normal uniaxial. Figure 2 shows the sample arrangement, the light is incident from a region of index NO,the film has ordinary and extraordinary indices Nl0 and Nle, and the substrate index is N z . The (amplitude) reflection coefficients are designated by roppwith the first two subscripts identifying the interface and the last two the input and output polarization states. The angles 40and 4 2 are measured in the incident medium and the substrate, respectively. It is now possible to write down expressions for the amplitude reflection of the two polarization^.^
+
rolpp rlzppe-j2~P RPP
=1
+ rolppr12ppe-j2B~
Each of the refractive indices is a complex quantity, therefore there are potentially a large number of unknowns. If a lossless film is assumed and the refractive indices of substrate and ambient are known, the unknowns are reduced to the real parts of N1, and Nle, and the film thickness d l . The problem is still underspecified for solution by ellipsometry of a single sample, but the use of multiple samples can provide results. Den Engelsen assumes only that each sample has the same refractive indices. A variation on his technique is to apply a further constraint: that the film thickness is proportional to the number of layers deposited. There are now only three unknowns for the whole range of samples, Nl0,Nle, and the thickness per monolayer. Thus, the number of samples needed is reduced, in principle to as few as two. This new assumption does not reduce the validity of the model in any way, as a variation in the thickness of individual LB layers would also lead to a refractive index change. Practically, it is likely that the layers nearest the substrate will have slightly different properties from the rest of the film. This is neglected in order to simplify the solution. A computer program was written to analyze ellipsometric results by this method. The number of layers, A, and y j were input for each sample and the results numerically fitted for monolayer thickness, NI,,, and N1,. The function minimized was the root mean square difference between the experimental and theoretical ellipsometric angles. 3. Experimental Section
where
To allow comparison between uniaxial and isotropic models, films of the fatty acid 22-TA were used. This material deposits well up to several hundred layers, and figures for refractive index and layer thickness are available in the literature.2 A stepped structure of 10, 20, 30, 40, 50, and 60 layers was deposited on hydrophobic silicon a t a surface pressure of 30 mN m-l and a subphase temperature of 20 "C. These conditions ensure that the controlled monolayer is in the L'z phase.6 The ellipsometric angles A and were then measured on a Rudolph Auto-El-IVfor the substrate and for each step a t a wavelength of 633 nm and a 70" angle of incidence. The plane of incidence was chosen to include the dipping direction. The substrate index was calculated using a program built into the ellipsometer. The ellipsometer also has a program for lossless isotropic layers; this was used to fit each step (see Table 1). It can be seen that the results vary a great deal; this is an indication that the model used is incorrect. It was clearly demonstrated by Den Engelsen4that the error is in assuming the films to be isotropic. A fit was also produced using an isotropic model by minimizing the root mean square differencebetween theory and experiment for the ellipsometric angles of all six samples. This gave an index of 1.5125 and a layer thickness of 2.89 nm. The six sets of ellipsometric angles were also fitted by the uniaxial model of section 2 (Le. assuming that the total film thickness is proportional to the number of layers). This gave an ordinaryindexof 1.5125& 0.002, anextraordinaryindexof 1.554 =k 0.003, and a layer thickness of 2.89 f0.01 nm. The molecular length is quoted in ref 4 as 3.24 nm; this leads to a figure of 26.9" for the molecular tilt (relative t o the film normal). The dominant source of error is the uncertainty in the measurement of the two ellipsometric angles. For the Rudolph Auto El-TV,this is 0.1" for A and 0.05" for.)I In order to study the accuracies of the isotropic and uniaxial models, the root mean square errors in A and + for all six samples were calculated for each fitted result. These are tabulated in Table 2. The use of a uniaxial model is shown to lead to a
+
r01ss
- I$ sin240)1'2 - N , cos 4o - (go N , cos 4o+ (No - I$ sin240>1w
and from Snell's law
No sin 4o = N2 sin 42 The reflection coefficients are related to the ellipsometric angles (A and y j ) by
~~~
( 5 ) Azzam,R.M. A.;Bashara,N.M.Ellip,somtryandPolariaedLight;
North Holland: Amsterdam, 1977.
~~
(6)Peterson,I. R.; Russell,G. J.;Earls, J. D.; Girling,I. R. Thin Solid Films 1988,161, 325.
Langmuir, Vol. 10, No. 10, 1994 3729
Uniaxial Ellipsometry of Langmuir-Blodgett Films. Table 1. Ellipsometric Angles and Isotropic Fit for 22-TA ~~
no. of layers 10 20 30 40 50 60
A (deg) 112.94 85.84 74.44 72.93 287.17 281.55
(deg) 16.83 26.47 37.31 58.06 73.46 42.32
n 1.483 1.514 1.527 1.518 1.505 1.481
d (nm) 2.84 2.87 2.84 2.81 2.83 2.91
Table 2. Root Mean Sauare Errors for Fitted Results fitting method isotropic isotropic isotropic isotropic isotropic isotropic isotropic uniaxial
samples used for fit 10 layers 20 layers 30 layers 40 layers 50 layers 60 layers all samples all samples
RMS error (deg) 7.5 2.5 3.6 5.6 5.3 6.7 2.1 0.6
significantly better fit to experiment. In the case ofthe isotropic fits on a single sample, the error is reduced by a factor ofbetween 4 and 10; the improvement on the all-samples isotropic fit is by a factor of 3. This provides conclusive evidence of the uniaxial models superiority. The overall form of the results is found to be very similar to that reported by Den Engelsen in his experiments on arachidic acid.4 Whichever model is used, the layer thickness varies only slightly, and the isotropic refractive index is found to be close to the ordinary index of the uniaxial model. As in the case of arachidic acid, the extraordinary index is found to be larger than the ordinary; for 22-TA the birefringence is approximately 0.04. Reference 2 describes the measurement of the permittivity, molecular tilt angle, and layer thickness of 22-TA by optical waveguiding. Although the permittivities are quoted in molecular axes, these are readily transformable to film axis refractive indices. At 633 nm this gives an ordinary index of 1.5113, an extraordinary index of 1.5710, a layer thickness of 3.02 nm, and a tilt angle of 21.3". The deposition conditions for these films (17 "C, 37 mNm-l) suggest that the floating monolayer was in the more compressed S phase. When compared to the films in this paper, it is clear that they exhibit a slightly smaller tilt angle, a larger birefringence, and a greater thickness. This is exactly as would be expected for a more highly compressed layer. Organic dye materials would be expected to show a greater birefringence than a fatty acid, as they typically contain a highly polarizable n-electron system which is believed to be aligned a t a small angle to the substrate normal in a Langmuir-Blodgett film. Two such dyes were studied: (i) a functionalized diarylalkyne' and (ii) an oligomer containing azo groupss (Figure 3). In each case there was no order relative to the dipping direction, so the choice of a normal uniaxial model is correct. A stepped film of 10,20, and 30 layers was prepared of i, and (7)Tsibouklis,J.; Cresswell,J. P.; Kalita, N.; Pearson,C.; Maddaford, P. J.;Ancelin, H.; Yarwood, J.; Goodwin, M. J.; Cam, N.; Feast, W. J.; Petty, M. C. J. Phys. D: Appl. Phys. 1989,22,1608. ( 8 )Allen, S.; Ryan, T. G.;Devonald,D. P.; Hutchings,M. G.;Burgess, A.N.;Frogatt,E.S.;Hamilton,M.;Swart,R.M.;Ashwell,G. J.;Malhotra, M. Proc. Organic Materials for Nonlinear Optics 1990; Royal Society of Chemistry: London, 1990; p 50.
N
HN
/ N-
NCHO-
HN
N
N-
CONH-
CH3
N\
ci-13
ii) Figure 3. a uniaxial ellipsometric fit gave an ordinary index of 1.496 f 0.005, an extraordinary index of 1.642 f0.014, and a monolayer thickness of 3.65 nm. For ii, steps were prepared of 19,29,39, and 49 layers. The deduced results werel\r, = 1.625 f O.OOl,N, = 1.86 f 0.02, and 2.73 f 0.01 n d a y e r . In each case the birefringence was much greater than for 22TA and was in the direction expected from the molecular design. It is also noticable that the uncertainty in the refractive index results is greater than for the fatty acid. This is because the minimumerror point ofthe fitted functionis less abruptly defined. This may be tentatively linked with the error implicitin assuming that the dye materials are lossless a t the wavelength of measurement.
4. Conclusions A simple technique to measure the thickness and uniaxial refractive indices of an LB film has been described. Only a small number of samples are required. Experimental results on 22TA and two dye materials demonstrate the validity of the approach.
Acknowledgment. The author thanks Dr. M. C. Petty for helpful discussions. Dye i was supplied by Dr. John Tsibouklis, Chemistry Department, Durham University, and dye ii by Dr. Simon Allen of IC1 Wilton Materials Research Centre. The receipt of a n SERC Molecular Electronics studentship is also gratefully acknowledged.
