X-Ray Specular Reflection Studies of Silicon Coated by Organic Monolayers ( Alkylsiloxanes )

X-ray specular reflectivity has been used to characterize the structure of silicon--silicon-oxide surfaces coated with chemisorbed hydrocarbon monolayer films (alkylsiloxanes). Using synchrotron radiation the reflectivity was followed over 9 orders of magnitude, from grazing incidence to an incident angle of {phi}{approx}6.5{degree}, or {ital q}=(4{pi}/{lambda})sin({phi})=0.8 A{sup {minus}1}, allowing a spatial resolution of features approximately {pi}/0.8{approx}4.0 A along the surface normal. Analysis was performed by fitting the data to reflectivities calculated from models of the surface electron density and by calculating Patterson functions directly from the data. Although the measured reflectivities could be equally well described by different sets of model parameters, the electron densities calculated from these different parameters were remarkably alike. Inspection of the electron densities allowed identification of a layer of SiO{sub 2} ({approx}17-A thick), a layer of head-group region where the alkylsiloxane adsorbs to the SiO{sub 2}, and the hydrocarbon layer. Fitting the data also required that the various interfaces have different widths. The fact that the same local hydrocarbon density of 0.85 g/cm{sup 3} was observed for both fully formed and partially formed monolayers with alkane chains of varying length excluded a model in which the partially formed monolayer was made up of separated islands of well-formedmore » monolayers. Measurements before and after chemical reaction of a monolayer in which the alkyl chain was terminated by an olefinic group demonstrated the ability to use x-ray reflectivity to characterize chemical changes. The effects of radiation damage on these types of measurements are described.« less


INTRODUCTION
Although Compton demonstrated the phenomena of small-angle x-ray specular reflectivity by 1922,' we are not aware of any serious attempts to use the technique to characterize material surfaces before Parratt's measurements on copper surfaces in 1954.2Unfortunately his work was seriously limited by both the low brilliance [i.e., photons,/(sec mm2 mrad2 O.lVo L), /)")l of the x-ray beams that were available at that time as well as by the difficulty in obtaining a sufficiently smooth surface.2Improved surface preparation techniques and modern experimental methods have permitted study of a broad range of surfaces using conventional or rotating anode x-ray sources.Examples include studies of mercury and liquid-metal surfaces,r 6 of both coated and uncoated solid substrates,T e and of surfactant monolayers on the surface of water.l0The use of high-brilliance synchrotron radiation by Als-Nielsen, Christensen, and Pershan to study specular reflectivity from the surface of the nematic liquid-crystal 4-cyano-4'-n-octyloxybiphenol (8OCB) greatly enhanced the utility of x-ray specular reflection as a probe of interface and surface structure by increasing the range of accessible scattering angles.llSince then, a number of studies on surface of liquid crystals,l2-l6 microemulsions,lT simple liquids,l8'le insoluble monolayers on water,20-22 and metallic single crys-tals23'24 have followed.In most cases the methods by which the reflectivity was analyzed to obtain structural information were relatively simple.While these procedures are adequate for many surfaces, they were not adequate for the more complex surfaces to be discussed here.
In this paper we will describe measurements of x-ray reflectivity from silicon wafers coated with various alkylsiloxanes (i.e., alkylsilanes, R(CH2)nSiO3, covalently bonded to the silicon wafer surface by oxygen-silicon bonds at the head of the chain with R being one of severval moeities) using the technique of self-assembly.Specular reflectivity from the air-hydrocarbon, hydrocarbon-silicon-oxide, and the silicon-oxidecrystalline-silicon interfaces interferes to produce a combined reflectivity that is strongly dependent on the angle of incidence and the surface structure.By comparing calculated reflectivities from different models and by comparing the models with Patterson functions calculated directly from the data, we believe that we have been able to establish both the uniqueness and the confidence VOLUME 4I, NUMBER 2 X-ray specular reflection studies of silicon coated by organic monolayers (alkylsiloxanes) 4T limits for a number of features of monolayers at the surface of silicon.These include the thicknesses of the hydrocarbon layer and the layer of silicon oxide between the hydrocarbon and the single crystal substrate, the widths of the interfaces between the various layers and the electron densities within each layer.

Alkylsiloxane coated surfaces
Most synthesis of organic monolayer films follows one of two different approaches.The first high-quality monolayer films, produced by Blodgett and Langmuir, were made by dipping a substrate into a trough of water coated with a monolayer organic film on the surface.25Each pass of the substrate through the surface of the water applies a coat of either one or two monolayers, depending on the specific structure of the monolayer.A second technique, forming generally more rugged monolayers, makes use of certain molecules which, in solution, spontaneously assemble to form uniform monolayer coatings on solid surfaces.A full review of the production, characterrzatron, and technological value of these and other types of organic thin films, together with extensive references to the literature, is given in the review by Srvalen et a\.26 The present studies are concerned with monolayers that form spontaneouslv on the surface of silicon-silicon-oxide substrates on immersion of the sample in dilute anhydrous solutions of alkyltrichlorosilanes of the form Cl3Si-(CH2),-R, with n varying from 9 to 17.In the simplest case, R is the methyl group (-CHr), but rve have also studied molecules in which the terminal groups were -CH -CH, and -CHBr-CH2Br.We also measured the reflectivity of a monolayer prepared from a fluorocarbon of the structure Cl3Si-(CH2 )2-(CF2 )7-CFr.Little experimental data exist on the formation of the alkylsiloxane fi1m.27On immersion of the silicon wafer into the trichlorosilane solution, the silicon-chlorine bonds of the head group on the molecule react with the surface hydroxyl groups of the silicon-oxide surface and with adsorbed water.This reaction results in a network of covalent Si-O-Si linkages that anchor the alkylsilyl moeity to the surface and to other alkylsilyls.The hydrocarbon film is therefore chemisorbed to the surface, in contrast to Langmuir-Blodgett films which are generally bound to the substrate through much weaker hydrogen bonds and van der Waals interactions (physisorption).As a result, alkylsiloxane monolayers are much more rugged and resistant to chemical attack than are Langmuir-Blodgett films.
Studies on alkylsiloxane monolayers, of the form -Si-(CH2)n-CHj with n :12-20, that have been reported by Sagiv in a series of papers over the last de-.u6.8'28-32 confirm their high stability and general resistance to chemical attack.The high contact angles that have been measured for all of these surfaces with water (110"-115') and hexadecane (38"-45') indicate that they have low surface energies and are not prone to contamination through physisorption of airborne hydrocarbons or water.33For comparison, clean silicon oxide surfaces which are wet by water have relatively high surface energy and readily adsorb airborne contaminants.
Ellipsometric measurements of well-formed monolayers are consistent with relatively dense packing of the alkyl groups and a mean thickness that equals (within experimental uncertainty)3a the theoretical length of the fully extended alkane chain.This thickness could, however, also be consistent with a molecular tilt away from the surface normal by as much as 15".Contact angle studies also support the interpretation of relatively dense wellformed monolayers.-10Both the chemical stability and the high surface uniformity make alkylsiloxane monolayers ideal for study.
The limited brilliance from the rotating anode x-ray source used in the previous study of the x-ray reflectivity from alkylsiloxane monolayerso restricted the range over which measurements could be taken to incident ansles below 3" (corresponding to about 0.4 A-t).As a ..rult, only the overall thickness of the adsorbed monolayer could be obtained with any confidence.The length measured was about 13% less than the length of a fully extended layer.This was explained in terms of an average area per molecule of 20 Aand an associated tilt of each molecule of about 30" [e.g., r]os '10.87 t= 30"].An unusualll' small width of 0.25 A was inferred for the alkyl-air and the silicon-oxide-alkyl interfaces, both being assigned the same width.Since these data were taken for a small range of incident angles, determination of narrorv interface width is very' difficult, and rve believe this estimate to be significantly too small.In the studl' reported here, the use of svnchrotron radiation made it possible to measure the reflectivity out to incident angles of the order of 7", allowing a more accurate determination of the interface rvidths.

REFLECTIVITY THEORY
Even though the wavelength L is comparable to atomic dimensions, and consequently comparable to the roughness of the surface, specular reflection of x rays can be described by the Fresnel laws of classical optics.lers The insert to Fig.I shows the kinematics for specular reflection of monochromatic x rays from the surface of a solid.The refractive index of matter for x rays of wavelength /, is given by n : I -6+iB where $=p),!rs/2rr, p is the effective electron density, ro the classical electron radius or the Thompson scattering length, and B=),/4npt where p is the x-ray absorption length.For the x-ray wavelengths of interest, both 6 and B are much less than 1.The effective electron density p for low-Z materials is just the total electron density of the material p7.For materials where some fraction / of the electrons has binding energies that are greater than the incident x-ray energy p=p7(l-f).
Defining a critical angle Q,=/26 --L/ pro/n and using the classical Maxwell's equations yield the expression for the Fresnel reflectivity (from a sharp interface) at small angles /,36 R p($) = o-@t -a|+ i B)t tz tion.Equation (l ) can be reexpressed in terms of the scattering vector q :(4n /)")sin(d) (Fig. 1) as Ro(q): q -(q'-q?*2i /p.)t/2 l', e) q *(q'-q?*2i /p)1/2 where Qr=(4r/)')sin(/.) is the "critical wave vector" in air and is independent of the wavelength Q,:0.0316A-t for silicon.This form for the reflectivity, shown for silicon as the solid line in Fig. 1, includes a slight rounding near the critical wave vector due to the small absorption factor.Away from Q =Q, absorption effects are negligible.For q 1q, the radical is almost pure imaginary and the reflectivity is essentially l00Vo (i.e., total external reflection).Well above the critical angle the reflectivity is given by R p(q)=(q, /2q)4.
For real surfaces the reflectivity can be expressed in terms of the average electron densityl2'te'lr R (q):Rr(q)lo( q)l' , oQ): I where (ap/az ) is the derivative of the electron-density profile averaged over the in-plane coherence length of the x rays and p-is the electron density of the semi-infinite bulk.This form is valid for angles greater than approximately twice the critical angle, where refraction effects are negligible (i.e., when the Born approximation for the scattering is valid).
It is convenient to model the in-plane averaged elec-where o, the root-mean-square average of the surface width, results from both the intrinsic width of the interface and the mean-square average of the roughness of the surface.leThe Fourier transform described by Eq. @) yields an expression reminiscent of the Debye-Waller factor for solids.For q : 0.4 A I the deviations between the measured reflectivity for the "bare silicon-silicon-oxide" wafer and the Fresnel reflection law in Fig.I are well described by a model surface of the forry of Eq. ( 5) with an interface width of approximately 2.8 A. This model does not explain.eitherthe reflectivity of the uncoated silicon for q >0.4 A-'nor the reflectivity from the alkylsiloxane coated samples that are also shown in Fig. 1.As implied above, since the reflectivity predicted by this model falls off with increasing incident angles as the product of a Gaussian and the | /q" term, the intensity becomes the limiting factor in measuring the reflectivity at larger angles.
The simplest physically reasonable model for the surface of the siloxane coated surface consists of a silicon substrate with electron density pst that is covered uniformly with a hydrocarbon layer of length L and electron density psH.If the silicon-alkane and alkane-air interfaces have widths o, and o 2, respectively, the normal derivative is of the form Application of Eqs. ( 3) and (4) to Eq. ( 8) generates ##:to( dtz: For small angles, such that qor.z11l, this expression simplifies to the form Since (psi-pcu)/psi=pcu/psi, this model predicts the observed minimum in the reflectivity (Fig. l) when q :(4r/X)sin(d):rr/L, where l, is approximately equal to the thickness of hydrocarbon film.On the other hand, this model does ngt ,explain the structure in the reflectivity at (t >0.3 A-' that can be seen in Fig. 1.
A more general model, with .n/separate layers, has the form where fr, corresponds to the electron density' rrf the substrate [p, of Eq. ( 5)], which in the presenr exarnple is crvstalline silicc-rn, p.r , l=0 is the density in air, 1., is the thickness of the ith lavcr end D,:>.i,1, is the distancc from the crl'stalline siliccln surface to the interface bclween the ith and the (i -f 1)st layers (i.e., D,,:0i.The Fourier transform for this form vrelds R(q) -., ^ , ,: QIQ)-^F\ql and some of the synchrotron data were taken on the thin substrates, most of the data reported were carriecl out on the 0.125-in waf'ers.
The follolving proceclilre \\'us tirllorved tro minimize surface cr.rntarninatictn.F.llipsonretric nteasurements of the monolayer thicknesst's were rnadc' n'ithllt 5 min of removal of the samplc lront \ratr'r'.'rCtr;rtcd u rrlcrs were lvpically then stcired in iiir for periods as long 3s one u,eek trefore x-ray measurements r,rcre rnade.No charrge \\as noted in the x-rav data between nteasurernents of fresh santples and of samples stored for up to on..j nronth aftcr' preparation.lmmediately prior to taklng the x-rav data.sanri"rlc's were rinsed with dry ethanol to rernove organie contanrination, blown dr) w'ith dry nitrogen, and irnrnediatell transf-erred to the x-ray spectrometer.X-ray photoelectron spectroscopy (XPS) data for the samples were taken some time (generallv about two months) after the x-ray measurement.
Partially complete monolayers were formed by removing the sample front the solution in a time shorter than that required for a full filrn to form.aOEllipsometric measurements were used to obtain one estimate clf the degree of coverage.saThe alkene terminatecl film rvas made by the same method as for the alkane films, but starting with a trichlorosilane with the appropriate alkene tail, namely Cl3Si-(CH2 ) rs-CH -CHr.The brominated sample was made from one of the alkene terminated samples, after the initial x-ray reflection measurement was completed, by immersing the sample in a 27o by volume solution of elemental bromirre in methylene chloride.The fluorocarbon sample was formed in a similar manner to the alkylsiloxane monolayers, again using the relevant precursor (ClrSi-(CH2)2-(CF2)7-CFr). The use of this form was necessitated by chemical restrictions which make the much simpler fluorosilane molecule Clrsi-(CF2 )e-CF-j difficult to synthesize.Further details of the sample preparations are given in other papers.ra'a('

X-ray technique
Most of the data reported here were taken on beam line X-228 at the National Svnchrotron Lieht Source The coherence length for the x rays is a function of the spectrometer resolution, this being a function of the slit rvidths and x-ray path lengths.Typically the coherence length in the plane of the surJace is also a function of the inverse incident angle.At th^e rotating anode, this length is of the order of 4X 101 A at the critical angle and 3 X 10r A at 3".The corresponding lengths at the synchrotron are about 105 and 8 X 10r A.
Surfaces that are inhomogeneous in the plane of the surface give rise to nonspecular surface diffuse scattering (SDS).Although SDS has been observed by us and others,le'rri''re for the silicon substrates used in this study the surface diffuse scattering integrated over the spectrometer resolution at Q =0.04 A' t was less than = 10-2 of the intensity of the specular reflection, and we have not carried out systematic measurements of surface diffuse scattering from these samples.
EXPERIMENTAL DETAILS Preparation of samples (Ref.34) Sample substrates were made from highly polished silicon (100) wafers obtained from Semiconductor Processing Corporation of Boston, Massachusetts.Each sample consisted of a l-in strip cut from a 3-in-diam wafer that was either 0.08, 0.125, or 0.200 in thick.The thinnest 0.08-in wafers were found to be warped with typical surface normal variations of about 0.05' over the central 5 cm of the wafer, compared to 0.005" for the corresponding region of the thicker wafers.Although early studies (NSLS) facility at Brookhaven National Laboratory.Some of the low-angle data were taken on the rotating anode x-rav generator of the Harvard Materials Research Laborator5t in order to locate the position of the lclwestorder destructive interference rninimum and to make prelirninarv judgements of sarnprle quality.
The rotirting anocle measurements were made using the corrfiguration shorvn in Fig. 2(a).The monochromator wzrs either a single-<lr triple-bounce gernlanium (111) crystal [Ge( I I 1 i] sel to accept copper K o, radiation irvavelength l.-s405A ).At small incident angles d, the intersection of a collimated beam of width u) covers a length -rr'./sin({)>>i1',u'ith the size of the beam incident on the sample being defined by slit S. and some preiinrinary collimation provided by.slit S,.For angles below' = i" the dimensions of S, were approximately 100 1lm horizontal width by' 6 mm, and 500 pm X 6 mm for largcr angles, with similar dimensions for 5, .These slit dimensions were chosen to satisfy the conditions of (1) all the beam being incident on the central 50 mm of the sample, (2) avoiding detector saturation, and (3) maximizing the incident flux at large incident angles.The principal purpose of slit S-q was to reduce the background scattering b-vtrirnming the tails of the slit scattering from Sr. S, u as closed symmetrically to the point that it had a measurable effect on the count rate and was then opened slightly, So was opened to dimensions of approximately X 10 rnm' assuring that all the beam reflected off the ta) il"1 1115 sample was detected.The monitor and detector were NaI(Tl) scintillation counters, the monitor being placed at 90" to the beam with a small piece of plastic scattering approximately' 0"03%, of the beam into the detectclr.A reflection intensity dynamic range of about 107 was achieved for a typical series of scans lasting approximatcly 12 h.At the synchrotron a wavelength of 1.7096 A was used the experimental configuration being shorvn in Fig. 2

(b).
A single bounce Ge(l1l) crystal rvas used.Slit S, actually consisted of two slits about 50 mm apart: the first was a triangular slit used to coarsely define the useful part of the beam in the horizontal direction, the second slit defining the vertical definition of the beanr.Although these slits were crudely set, they significantly reduced the background scattering inside the experimental hutch.S., was the beam defining slit, with slit S-, trimming the tails of the slit scattering but not affecting the counts in the main tream.The slit widths were similar to those used at Harvard except that, at the largest angles, a beam width of I mm rvas used.Because of the very intense bearn at very small angles (beloiv l'), the detector was placed at 90' to the beam with a small sheet of plastic scattering about O.O3Vo of the beam into the detector.The detector was switched to a direct position at about 0.8'.51 was opened to I mm at an angle of about 3".Slit So was set to cut down the direct scattering from sources other than the sample, and S. rvas set wide enough to accept all the specular beam reflected from the sample.All data were normalized to the counts recorded in a beam monitor located between the beam defining slit Sr and the trimming slit S,.It consisted of a second plastic sheet that scattered about 0.02V(' of the direct beam into a second scintillation detector at 90' to the direct beam.A reflected intensity dynamic range of 10u was obtained over the period of about 4 h necessary to record a typical set of scans for one sample. For both experimental configurations samples were aligned by using the diffractometer in a nondispersive three-crystal mode in rvhich a singleor triple-bounce Ge(lll) analyzer crystal was placed between the last slit and the detector.With the sample removed the analyzer was in a dispersive orientation; nevertheless, a good measure of the incident angle for the direct beam was obtained by rotating the analyzer crystal to maximize the signal in the detector.In order to obtain an approximate alignment, the sample was then translated into the beam and, by an iterative process in which d was rotated and the sample translated, the sample was aligned parallel to and obscuring half of the beam.Next the sample was rotated to an angle just below the critical angle (typically 0.15") and the detector was scanned through the specular reflection (i.e., a 20 scan) in order to check the alignment and figure error of the sample.Since the initial alignment procedure was prone to errors arising from macroscopic substrate warping (typically from the edges from which no scattering is measured), the final sample alignment was obtained by setting 6 equal to half of 20.The analyzer crystal was then removed and the detector centered on the specularly reflected beam passing through slit Sr.Finally, the sample was translated through the J.6 3.7 J.8 J.9 4.0 4.1 4.2 4.J 9.6 9.7 9.8 9.9 1 0.0 1 0.1 1A.2 1 0.3 2/ (degrees) FIG. 3. Three typical beam profiles obtained by scanning 20 at fixed 6 for the spectrometer shown in Fig. 2(b).The trapezoidal shape is a function of the resolution of the .S* slit and the beam profile, the former being much larger to ensure all of the reflected beam enters the detector.The lines give the best fit for the amplitude of a trapezoid whose shape was fixed and determined by the incoming beam dimensions and the detector slit width.For all specular scans the detector was positioned in the center of the trapezoid.beam parallel to the surface normal in order to ensure that the incident beam was correctly centered on the sample.
Although the angular dependence of the specular reflectivity was rneasured by a series of "d -20" scans in which / is equal to half of 20, the alignment was frequently checked by performing 29 scans at fixed l.This procedure ensured accurate sample alignment to within 0.01" and was also a check that the figure error of a sarnple was acceptable.Since the nonspecular diffuse scattering depended on the incident angle 6, "backgrouncl scattering" was subtracted from the signal I(6,20)t,:, observed in the specular condition, i.e., specular reflection R (d) : I (0,26)-+U @,20-0.3")+1(0,2(b+0.3")l .
The background for three different angles of incidence are illustrated for data taken at NS[,S in Fig. 3 by d scans at fixed 20.The signal reported as the specular reflectivity is obtained by subtracting the background count rate frorn the peak count rate, as described.
Although the experiments were carried out with the samples contained in a sealed cell that was filled with air or helium, the results discussed below demonstrated that airborne organic materials were not fully eliminated from the helium-filled cell.The x rays were incident through Kapton windows, with an angular access of up to 7' and approximately 7 57o transmissivity.

RESULTS
Alkylsiloxanes with ClO,Cl2, and C18 alkyl chains Data and simple interpretations Figure I shows the results of synchrotron measurements of the reflectivity R ( q) (after background subtraction) for alkylsiloxane monolayers of differing length and for the uncoated silicon.This figure also shows the Fresnel reflectivity for an ideal step surface of a material with the bulk density of silicon.Without any sophisticated analysis, there are a number of prominent features that can be immediately interpreted.The reflectivity of all of the alkylsiloxane-covered samples exhibit structure, most notably a sharp minjmum at a scattering vector of between 0.1 and 0.25 A-', and other minima and maxima at larger q.
The most obvious interpretation is that the first minimum is the result of destructive interference between reflections from the front and back surfaces of the alkane layer of thickness L For thin enough films, or for films in which the electron density is not too high, the position of the minimum in this interpretation is given by the condition that qL :n or @:sin I(l/qf).For either thicker or denser films, refraction effects are, however, irnportant and the destructive interference occurs for q'L :L(qt-q!')t'2:n.For a fully formed hydrocarbon layer of the type of interest here, Q,=0.021A I would be the critical rvave vector of a semi-infinite sample with the san'le electron density as the hydrocarbon layer.The positions of the minima for the C]10, C12, and C18 correspond Io q:0.21 and 0.19, and 0.13 A-l, .espe.tively.
Taking the refracton correction into account, the thicknesses of the Cl0, C12, and C18 alkane layers, for this interpretation of the position of minima, correspond to 14.4,, 16.3, and 23.6 A, respectively.These values for the thickness I of the alkane layers should be compared with the published expressio n L == 1.265n + l. 5 A, which gives 14.2, 16.7, and 24.3 L for the maximum extension of an aliphatic chain --(CH.,),,rCH, with n:10, 12, and l8 respect ively.+lA siniiiaritv of the reflectivities from these three sanlples is that they all fall trelow the Fresnel curve.This indicates that tlie reflecting interfaces are not ideally sharp, but have some associated widths.The deep nature of the lninirna (cancellation of between l0 -2 and i0 3) indicates that at the angle of the minimum, the amplitude of the wave reflected from the top and bottom interfaces of the hydrocarbon chain are of almost equal magnitude.Since the known ratio of the electron density of bulk hydrocarbon to that of silicon is approximately 0.38, the expected ratio of minima to maxima wor,rld be approximately """1 0.2s I 0t 0.1 0.06 r 0.8 0.7 0.6 0.4 0.3 0.2 1,1r.2) X 0. 38l2 = 0.06 if interfacial widths were neglected.The fact that this prediction is approximately an order of magnitude larger than the observed ratio implies that the different interfaces have different widths.Closer examination of the reflectivity also reveals that minima at larger angles do not occur at positions that are integral multiples of the positions of the smallest-angle minimum.All of these features can be understood in terms of a more complex three-layer model that will be described in detail below.

Uncoated silicon sample
Evidence of an experimental problem with surface contamination of the uncoated silicon sample during the xray measurements can be seen in the data in Fig. 1.At large scattering vectors, alternate points were measured in scans taken approximately 60 min apart and, as can be seen, the points from the two different scans are offset from one another.We believe this is due to the continuous build up of a contamination layer on the sample.At the time of the measurement this layer was probably about 5 A thick; however, the progressive shifting of the minimum to lower angles in data taken a few hours later confirmed the build up of contaminants on the surface.Some of the contamination is probably caused by the presence of organic materials or water in the helium flowing through the sample cell during the experiment since there was a significantly slower build up on samples left exposed to air for a similar length of time.No such problem was observed with the lower-energy alkylsiloxanecoated surfaces.

Detailed analysis
Detailed analysis of the alkylsiloxane surface electron density was carried out by least-squares fitting of the data to a version of the y'{-layer model for <D(q) that was corrected for the effects of refraction.The correction involved replacing the IqD,J in the factor , -iqD, -q2ol .,/2,Ie 'e I of Eq. ( 12) by 100 where Qj:(q'-qli)t/2 and Qrj rs the critical rvave vector for the 7th layer. in principle, a similar correction is required for the Gaussian term.The corrections are, however, small and were neglected.

C18 alkyl chain monolayer
Figure 4 shows the data for the Cl8-coated silicon wafer in the form of R (q)/Rp.(q).The solid lines display a set of fits for models with 1 , 2, and 3 layers, respectively, i.e., ly':1,2, and 3 in Eq. ( 12).The parameters of these fits are given in the columns labeled try': I , 2, and 3'-' in Table I.The 1/ : 1 and 2 models are obviously inadequate.In addition, for the l/:2 model the fitting algorithm was unable to fix either the width of the 0.3 0.6 0.9 q (A-') FIG. 4. Reflectivity and analysis of an alkylsiloxane monolayer containing an 18-carbon chain using one-, two-, and three-layer models.The data are shown after normalization to the silicon Fresnel reflectivity, and hence the y axis represents lOl'.(a) shows the one-layer model fit to the data at low q.This model accurately fitting only the first minimum; the twolayer fit (b) is quite accurate out to about 0.45 A -' and qualitatively predicts the peak and dip positions at larger angles.The three-layer model (c) reasonably fits the data over the entire range.The best fit parameters for the different models are given in Table I in the r:1.2. and 3' '' columns.
silicon-silicon-oxide interface (o61) or the thickness of the silicon oxide layer (l,l).The values of these parameters appearing in Table I for l{:2 were chosen such that the maxima and minima in the model were at approximately the same positions as in the data, and the depth of the second minimum was also approximately correct.Given the obvious inadequacies, confidence limits for the parameters of these models are not particularly meaningful.
The motivation for the layer I, comes from the wellknown fact that on exposure to 02, crlstalline silicon forms a relatively stable oxide layer that is about 10-20 A thick.a2In addition, it is difficult to see how a hydrocarbon layer on its own could give rise to the nonintegral positions of the high-angle minima.2: iO( -q)l' and using a smooth Gaussian-to extrapolate from the last measured point at q = 0.8 A ' tn the vanishing of Q(q)t ur q: r 8 A I (u,ell be1'ond the measured range, where the reflectivity is essentially zero).For the Cl:i rlkyisiloxane this Gaussian corresponded to a surf'ace harrrig l .1.b-Ainterfacial rvidth.The pea.k at .r =40 ,{ in f ig.,s indicates that, in addition^to the nrairl hydroii,i lrorr lavcr of approximately ?0A thickness, there is a second lay'er.aiso of about 20 A thickness, rvith an interlace that_is either 20 A above the alkane-air interfacc and 40 A above the silicon-oxidc-alkane interf-ace, or ?O L below the silicon-oxide-alkane interface and 40 A below the alkane-air interface.While the former suggestion is unphysical, the latter could correspond to the native silicon oxide layer, the silicon -silicon-oxide interface convoluted with the hydrocarbon-air interface being responsible for the peak at about 40 A. The values of the parameters in Table I for the N:2 model with the electron density p1:0.968 and a layer thickness Lr:11.4A are consisrent with the presence of a silicon oxide layer.
The most important uncertainty associated with the Patterson function is whether or not the structure could be an artifact associated with the way the data are extrapolated past the last measured point.a3The dashed line indicates the result that is obtained from multiplying the data by a Gaussian with o,r:0.3A-'such that the data for q greater than 0.8 A ' make no important contribution to the integral, i.e., expl-(0.8/0.3)2 /2]= 3 X 10-4.The Patterson function calculated is equivalent to viewing the autocorrelation function through a "real-space Gaussian filter" which reduces the amplitudes of the peaks and increases their widths, e.g., X.RAY SPEC{.ILAR REFLECTION STUDIES OF SILICON I119 procedure as used to obtain Since the structure at s=+O A is still preseni (albeit smeared out) it cannot be attributed to a "truncAtion artifact." The lV :3' * ) model that was used to c.nst*tct the solid line in Fig. 4(c) is obtainecl by adding a thi:-d layer (interface in Table I) in the immccliate vicinitl of the silicon-oxide--hydrocarbon interl'ace.Thc reducecl yl for ttris fit, using the 95 clata points above 0.1 A ,,,-..,ppro"imately 80 rvhen *'cighted by poisson statistics, ;ls comparrrd to a yl of approximately 800 ior the trv.-iayc-r fit anci 2000 for the one-layer fit for the same poirrts.In vieu' of the l'acts that (i) the measured reflecti'ity spans eight cir nine orders of rnagnitude, ancr (ii) in sorle cases the statistical weight due to Poisson statistics is less than 0.1%' r'alues of yr .f the rlrder of E0 coulcl arist: from small sy'stematic errors in either the measurccl signal or the rnodel.In any e'vent, the r _-3' +) model cloes account fcrr all of the main features of the data qriite well.The main differences between ttre electron densities of the \---1,' * I model and the hi --2 moclel occur at the silicon-oxide-hydrocarbon interface.rvith the properties of the other interfaces remaining essentiail,v' unchanged.Hon'ever, the width of the silicon-silicon-oxicic interface could still not be determined from the existing data set.the minimun-r value of X2 being obtainel for an infinitesimally small value for the rvidth of this interface.
The fits \\'ere carried out with o,,, arbitrarily set equal to 1 A, the other parameters being relatively independent of the precise value.Similarly, since the data were taken clnly to q <0.8A ', the results for the fine structure of the silicon-oxide-alkane interface are not unique.The solid line in Fig. 4(c) is the best fit for the A.:3, t,model n'hen p:.> pr.The confidence limits listed in Table I for these parameters, as well as the possible variations in the model (i.e., uniqueness) for the silicon-oxide-arkane interface, rvill be discussed below.Figures 6(a)-6(c) display the electron density as a function of cristance from the surface for the lf : I , 2, and 3' t ' models used to calcu_ late the R(q)/Rr(q) inFig.4. Figure 6(d) illustrates that there are only small quantitative differences between the electron densities for the three models by superposing the three offset curves in Figs.6(a)-6(c).
In order to assess the confidence limits for the /y-:3i+ ) parameters, a set of fits was carried out in which the electron density associated with the interface p, was con_ strained to different values and all other parameters in the model, except for the width of the silicon-siliconoxide interface os1, w€re allowed to vary.Since most of the parameters are tightly coupled, this procedure is necessary to estimate the range of the density p, allowed by the data with this model.Figures 7(b) and 7(c) display the results for what we subjectively consider to be values of pz surrounding the local minimum rn X2 at pt=1.25 that yield borderline acceptable reflectivity fits.These correspond to values of y2 that are appro ximately 25vo larger than the minimum.The iy':3(+) fit that senerated the minimum X2,Frg.4(c), is shown again for Jomparison in Fig. 7(a).The parameters obtained from these fits are listed in Table I as r/ :3'*r) and 3(+2).Similarly, the confidence limits in Table I are arbitrarily set at the values that incre ase y2 by approximately z5vo, the fits be-ing completed by the same Figs.7(b) and 7(c).
In order to illusfrate the significance of these variations, the rezrl-space electrcln clensity for all the three 'v:3i ''mocleis are clisplayecr in Figs.g(a)*g(c) with ail oi' the i.terf'ace wiclths set to be zero) and ir Figs.
8(e)-8(g) n'rth thc appropriate interface iviciths.Note that thc verv high peak density that appears for the second layer in thc J -l column is misleaciing since this layer is also rery thirr.The rviclth of the two interfaces for this laycr are si'rilar, resulti'g in two srneared steps n't dp/dz, ctf .ppositesigns, which almost exactly cancel to give the profilr shown in Fig. S(fl.Also, the sharp feature in Fig. 8(g) c61116 be smeared out with no appreciahle change to rhc fit qLrality.In addition to the fit shown in Fig. 7(a), there ls a second local minimum surrounding the value of pz=0.82.The best fit parameters for this minimum are listed in Table I in the column 3'-' and the results for the R(q)/Rp(q\ are illustrated in Fig. 8(d).In this case, the minimum value of X'is about 78 when calculated using the same data as previously.
Although some of the .l{:3(+) and 3( ) parameters are quite different, the real-space densities, as illustrated in Figs.8(e) and 8(h), and superposed in Fig. 8(i), have only small quantitative differences only in the region of the SiO2,/alkane interface.In fact, for all of the models described in Table I [i.e., as shown in Figs.6(d) and 8], the small quantitative differences between the electron densities are much less significant than would appear from the parameters in the table.
That dffirent sets of parameters giue rise lo similar electron-density profiles suggests that the parameters themselues are not the most meanindul way to interpret the reflectiuity data.In the present case, the l{ :3 models were introduced because the reflectivity data clearly indicated that the SiOr/hydrocarbon interface had some structure.However, since the various model electron densities resultant from these different sets of parameters are similar, the procedure used does allow a relatively unambiguous determination of the electron density responsible for the observed specular reflection.If the interfacial widths were small, the thickness of the hydrocarbon layer could be determined graphically from the distance between sharp breaks in the slope of the curve for r(z).The solid lines in Fig. 6 illustrate one possible way to estimate the corresponding positions when the interlaces have finite width.
We expect that the dominant effect giving rise to the observed interfacial widths is the roughness of the outer SiO, surface.Assuming that the substrate roughness is t o-' 1oo 0.i 0.6 0.9 0 0.J 0.6 i.3 q (r ') q (A-') FlG. 7. Comparisons of different fits for the Ci8 sirmple whose pararneters are shown iu Table i.(a) corresponds to column 3't ', {b) to column 3{ , (c) to column 3' ' ", and (d) to column 3r"f li.The parameters are shorvn in Table I. coated by a fixed thickness of hydrocarbon, the solid construction lines in Fig. 6 illustrate a graphical procedure for determining the average thickness.The results obtained on applying this technique to the models in Figs. 6 and 9 are listed in Table I in e) and (fl are the corresponding re:rl-space profiles including the widths of the different interfaces.The sharp f'eature in (g) rs well beyond the resolution limit and a fit thrt is almost as good would have a profile more sirnilar to {c) and {l-1.{i) shor,rs a comparison ol'the 3 and 3 density profiles on the sanle axes (the two best fits).Although the pararrreters corresponding to these three curves are quite different, the only' srgnificant differences in the real-space densities are in the unresolved structure of the resion where the siloxane bonds to the silicon oxide.q (A-') tt2l obtained by consideration of the fits shown in Figs.9(a) and 9(b), for the C10 and ClZ coated wafers.Since the reflectivity fg. the C10 sample was measured only for q=0.65 A-', it was not possible to determine either the parameters appropriate to the SiO, layer or the hydrocarbon electron density from this data set.The fit was thus carried out by assuming that the SiO2 layer for this sample was the same as those of all of the other samples studied.The best parameters for both the C10 and C12 fits are listed in Table II and the real-space densities are shown in Fig. 10.The confidence limits for the parameters listed in Table II were set in the same manner as used for the fits for the C 18 sample.The real-space densities for the i{ :3(+) models that provide the "best fit" for the C10, Cl2, and C18 coated wafers are displayed superposed on one another in Fig. l0(d).The graphs shown in Fig. 10 suggest that the SiO, region for the C10 and C12 samples might be -1 A shorter than that of the C I 8 wafer.However.since the data for q-0.5 A-' u.. of much lower quality for the C10 and Cl2 than for the Cl8 sample, we do not believe 100 1 0-1 1 0-2 ? 1 0-' 1 0-4 0 0.3 0.6 0.9 q (A-) FIG. 9. (a) Three-layer fit and Fresnel normalized reflectivity for a l0-carbon chain alkylsiloxane monolayer.The fit was carried out using 62 data points between 0.18 A t aqS0.65 A-' and, with four adjustable parameters, the Xr was 9.4.The fit parameters are given in Table II.(b) Three-layer fit and Fresnel normalized reflectivity for a l?-carbon chain alkylsiloxane monolayer.^The fit was carried out using 96 data points in the range 0.15 A 'Sq a0.8A I and, with six adjustable parameters, the y2 was 13.The fit parameters are given in Table II.
Although there is some variation between the tr{:1,2, and 3 models, the results for the various .l/:3 models are, within errors, identical.While this technique is somewhat arbitraryr we believe it gives a resonable estimate of the length of the hydrocarbon chain excluding the silicon head group.The mean value of 2L 3+0.4A is shorter than the length obtained from the position of the clip (23.6 A) (dashed urro* in Fig. 6) duelo the specific exclusirrn of the head group from the graphical length determination.
Sincc thc ,&li t) and 3{ ' nrodels give cssentialh' the sanre structure.we u'ill cotrtinr-ie tire analysis of the of her .iri:rplc.r in rerms of the rnodei that gives the best fit fcr" :ltat spec:ific sample (holdine sorlte parameters f;xed if ,recessarv to ubtirin a physicallv reasonable structLlre.i-his is riecessarv fol fh ,se paranreters rvith large unoer tainties: t.IL from these, we obtain a length per carbon atom of 1.3810.2,1.23+0.04,and 1. 18f 0.02 L for the C10, C12, and C18 monolayer, respectively.These can be compared with the accepted value for the 1.265A for the maximum extension of an aliphatic chain in the all-truns configuration.arAlthough the C18 value is slightly shorter, the three results are identical within the quoted errors" This length for the C 18 indicates that there could be either a small degree of gauche isomerization or a tilt in the mean axis of the chains with respect to the surface normal.The result allows the layer thickness to be reduced by no more than 107o from the expected length of an alltrons chain oriented normal to the surface. As a measure of the packing of the monolayers, it is interesting to calculate the area per alkylsiloxane molecule.Given a length per CH2 group of L 20+0.05A for the Cl2 and C18 monolayers, a silicon electron density of 7.04X 1023 electrons/cmr, and a hydrocarbon electron density of 0.42+0.02 of that of silicon, one obtains an area-alkylsiloxane molecule of 22.5f 2.5 A2.This area should be compared to an area of 20.5 Al for long-chain paraffins in bulkaa and between ZO.5 and ZZ.S -L) for Langmuir-Blodgett monolayers of long-chain alcohols.a5 Partially formed C18 alkyl chain monolayer Figure l l shows the reflectivity from an incomplete C18 alkylsiloxane film that we designate as C18P.The position of the minima at q =0.2 L I in comparison with 0.13 A ' for the fully formed C 18 film clearly indicates 't00 t c-1 r0 0 0.r 06 0.9 q (A-,) FIG.11.Three--layer fit and Fresnel normalized reflectivity for a partialll, fcrrmed C18 alkylsiloxiine monolayer.The fit parameters given in Table II were obtained with a yr of 32 for points rvith q > 0. 15 A that this alkylsiloxane fi1m is considerab^lV shorter (i.e., 16.2A ) than the fully formed layc'r t23.6A r. Thc.sample reflectivity also falls off much faster than that of the fully formed C18, suggesting that the alkane-air interface is considerably more diffuse for the partially formed layer.
Detailed analysis of the reflectivity of the C18P monolayer, using the 1/ :3' ' ' model and the silicon oxide layer parameters from previous fits, obtains the fit listed in Table II.The previous obserr,'ation that the alkane-air interface of the C18P monolayer is more diffuse than that of the fully formed C18 is supported by the relative values of o3a in Tables I and IL In addition, since the mean value of o3o:-1.9+0.9A for the partially formed    Cl8P monolayer is noticeably larger than o1a--2.9+0.3A for the fully formed Cl2layer with comparable thickness to the C18P sample, there is a high probability that the alkane-air interface is considerably more diffuse for the partially formed layer than for either of the tLL)o potentially similar systems.The fit for the C18P monolayer is illustrated by the solid line in Fig. 1 1.
'fhat the electron density of the partially formed layer is comparable to the density obtained for the full1' formed la-ver suggests that the alkane chains either tilt, or otherrvidc bend, to fill space in order to maintain a density ckrse to the fully form_ed hydrocarbon density of approximately 0.85 gm/cm'.If the partial monolal,er was comprised of close packed, uniformly tilted, straight C18 chains, the mean tilt rvould be about 45" if one uses the lengths obtained frorn the dip position or 36" using the graphically determined length.f'hese results are not consistent rvith one previously suggested model of' partially f ormed films as islands of close-packed, straight, fully extended molecules that are oriented normal to the surface.46'47The avelage electron clensity for this model w'ould consist of a layer of the same length but a lower eiectron density.Variations of this model, in which the molecules at the boundary of the islands were partially disorienled, would increase the apparent intc'rfacial width o.1*, but would not change the thickness.
Figure 12 shorvs the comparison of the alkylsrloxane lengths as measured by ellipsometrl' anci from 2rr/qn,u, rvhere 4n,in is the position of the first minimum in the xray rellectivity.The ellipsometric measurements rvill be described in more detail in a separate publication.raThe .\-ray' measurements were made using both the rotating anode and synchrotron sources.Assuming a constant 10 15 20 X-roy Lenqth (A) FIG.12.Comparison of the alkylsiloxane length as determined by x-ray reflectivity and by ellipsometry.(o ) are fully formed monolayers, (V) are incompletely formed layers.The solid line corresponds to the expected curve if both techniques gave the same result.The dashed curve is a fit to the fully formed layer results and has the form lcllip-1.02(+0.06)XIxrav+ 1.8(+1.0) A. The two techniques appear to predict the same length per CH, group, but have different sensitivities to the silicon oxide-hydrocarbon interface.lt23 offset, the average difference between the ellipsometrically determined length and 2rr /q ^in corresponds to 1.8+1.0A with the ellipsometric value being larger.Since the graphically determined value for the x-ray determined thickness is of the order of 1.5+0.6A shorter than 2n /Qmirt the eilipsometric values are of the order of 3.0 A larger than the graphically determined values.This difference is slightly outside of the quot^ed errors of approximatell' 0.5 A in the x-ray and *2 A for the ellipsometrically measured lengths and may be systematic, having an origin in factors such as the effects of the interface on eitire r lechnique, size related corrections to the index of reliaction for the e llipsometric technique, etc.
The data, in the form of R (q)/RF(r7), and the calculated results for the 11 :3' -' rnodel are shou n in Fig, 13(a).The parameters for the fit are displayed in Tablc II in the column C17 and the real-space electron density is illustrated by the broken line in Fig. 14.The reflectivity data are substantially the same as for the simple alkane samples except for a somervhat nlore diffuse hydrocarbon-air interface (3.0A versus approxirnatelr' 1.5 A for the simple C18 molecule of similar length), but aside from this variation, there are no systematic differences between the real-space electron densities extracted from this data set and the one for the 100 13. (a) Fresnel normalized reflectivity from the olefin terminated sample together with (b) the reflectivity from the same sample after bromination.The technique used to fit the data is described in the text, with the parameters for the fits given in Table II.The fits for (a) and (b) have y2 values of 33 and 60 for the points above 0.1 A r.The filled points at large q indicate the data taken on a second measurement.The small systematic differences may be indicative of the radiation damage also observed by the contact angle and XPS measurements..tnbromine atoms we calculate the addition of 45+10 electrons per alkylsiloxane group.Assuming that bromination takes place as described above, the fully brominated layer would have 66 effective electrons per alkylsiloxane (the two ls electrons per bromine atom are too tightly bound to contribute to the measured electron density).This measurement thus implies that only fr, or 68Vo of the molecules were brominated.XPS analysis carried out some weeks later than the xray measurement showed that on sections of the sample which were not in the beam 9O% of the molecules were brominated, but on radiated sections this figure was only about 307o.It is clear that the radiation had initiated some chemical change to the monolayer surface.Damage occurred during the x-ray exposure both before and after bromination.This damage is visible in the reflectivity scans shown in Fig. 13 as a systematic shift of data taken 30 min later at large scattering vectors (shown as solid symbols).While this implication of x-ray damage adds uncertainty to the significance of the x-ray determined structure, it does not alter the basic objective of demonstrating that specular reflection can be used for quantitative determination of chemical modifications of the alkane surface.

Fluorocarbon coated samPle
In order to demonstrate the applicability of the technique to samples with a radically different layer density from the hydrocarbon, a wafer was coated with a monolayer of -Si-(CH )2-(CF2)7-CFr.
The reflectivity data for this sample, in the form of R (q)/Re(q), and the calculated results for an N:4 model are shown in Fig. 15(a).Since the difference in electron density between the silicon oxide and the fluorocarbon layers is much less than that between the silicon oxide and the alkane layer in the previous samples, the amplitude of the x rays reflected from the fluorocarbon-air interface is correspondingly stronger than the net amplitude reflected from the composite interface between the fluorocarbon-silicon-oxide interface.As a consequence' the depth of the first interference minimum at q =Q.)A t is much shallower in this sample than the corresponding minimum for the alkane coated samples.On the other hand, since the amplitude of the signal reflected from the fluorocarbon-air interface is greater than the amplitude of the signal from the composite interface, and since that is yet larger than the amplitude reflected from the Si/SiO, interface, the interference pattern is dominated by the two signals from the first two inter{acgs.As a result, the two minima at q:0. 18 and 0.55 A 'in Fig.
!5(a) correspond to roughly qL :rr and 3rr with L = 17.8 A. We suggest that this is the distance between the silicon-oxide/(CH2)2 and the fluorocarbon-air interface.This length should be compared to a length of the 18.1 A obtained from the graphical analysis of the four-layer fit.
The one unfortunate consequence to follow from the fluorocarbon electron density is that the reflectivity is less sensitive to the SiO2 layer and its two interfaces.The solid line in Fig. 15(a) is calculated from a model in which l,{ :4, but using values for the parameters describ- 14.Real-space electron density profile of the surface obtained from the parameters of the fits in Fig. 13 for the alkene sample and the same sample after bromination.Note that the fit to the brominated sample was done by using the parameters of the unbrominated sample (dashed line) for all except the hydrocarbon-air interface.The addition of the peak is due to the addition of one bromine atom to each of the two carbon atoms at the tail of the molecule.

C18 sample.
After the initial x-ray measurement, the same sample was brominated and measured again [Fig. 13(b)].Bromination results, to a first approximation, in breaking the terminal a-bond and attaching two bromine atoms to the two terminal carbon atoms to give the structure -Si-(CH2)r5-CHBr-CHrBr.
Relative to the data in Fig. 13(a), the overall reflectivity has increased, suggesting the presence of additional electron density at the surface, and the position of the first minimum has shifted to a lower angle as would occur if the distance between surfaces were increased.
More detailed fitting was carried out by considering the addition of a single Gaussian to the real-space electron density profile to the ly' :3(*) model that described the Cn(:) data, to account for the bromine electron density.The three new adjustable parameters in fitting the Cl7\-) data were the position LilLs, , the width osr, dfld the area nu, of the Gaussian.The fit was carried out by holding fixed most of the other parameters at the values in column C17(:) of   IL Because of the limited range of data and the complicated nature of the interface, it rvas impossible to obtain accurate values for the parameters, the fit being only a physically reasonable one.(b) Real-space electron density profile of the surface of the sample obtairied from the parameters of (a).Note that the fluorocarbon chain has a much higher density than the hydrocarbon chain resulting in the less pronounced first minimum.The dip in the real-space profile corresponds to the rocation of the two methl'len,-' (CH2 ) groups in the molecule.
ing the SiO, Iayer, its interfaces and other parameters for the h1'drocarbon portion of the molecule as determined f'rorrr the other samples.^In addition, since the data were taken ..rni;; for q < 0.7 A 1 and since the points near 4 =,0.I A I themselves have large error trars, the .:onfidenc,:limits on the fit para',neters are larger than thcse frlr the other fits.In an.v event.the parameters that .-rbtainc'J the be:;t fit and are phy'sically realisiic, are displal,cd in Table II.The real-space electron densitr, :., ;::hown i' iiig.15(b)" l'he sclid line indrcates the 17.8A tliat i.s i;he orisin of the princig,le interference rninima in i;ig.15(a).DTSCUSSION T'he very deep nature of the first interference minirrru'r ftir the hydrocarbon sarnples with well formeci fillns is a Cirect demonstration that organic rronoiayers syrrthesized by the self-assembly process are capabtre of pro-viding microscopically and macroscopically uniform films.In particular, the first sharp minimum in the reflectivity allows an approximate determination of the thickness of the adsorbed film that is in reasonable agreement with the thicknesses predicted by assuming maximally extended aliphatic chains normal to the surface, when the size of the silicon head group is assumed to be included in the length measured.Comparisons between x-ray reflectivities calculated from more detailed models, which included structure in the head region, gave a hydrocarbon thickness that also suggests maximally extended molecules.The principal residual uncertainty of the hydrocarbon thickness is due to the width of the interfacial region between the SiO, layer and the hydrocarbon layer.We suspect that the major contribution to this width is the roughness of the bare SiO, substrate and that a significant improvement could be obtained by preselection of flatter substrates.
The highly sensitive dependence of the reflectivity on details of the monolayer structure is indicated by the much improved fits of the 1/ :3 model as compared to the l[:2 model, the differences being only small changes in the electron-density profile at the silicon oxide-alkylsiloxane interface.The reflectivity is particularly sensitive to the interface width, which must be considered separately for each of the interfaces if a good fit to the data is to be obtained.This sensitivity to interfacial structure has been neglected in most other x-ray studies of similar systems.
Inspection of the various models for the 18 carbon alkylsiloxane real-space electron density (i.e., Fig. 6) suggests the hypothesis that the real-space density might be the result of coating the SiO, surface, rvhich has some roughness, with a fixed thickness of alkane.The variations in the model parameters for the rvidth of the SiO2/alkane and alkane-air interfaces leads to some uncertainty in the thickness to the alkane layer.However, from the graphical inspection of the various models described earlier, we believe that this uncertainty is no more than f0.5 A (1.0 A for the ClO alkylsiloxane).Using the thickness of the hydrocarbon part of the C18 molecule only, the measured tilt angle is about cos r[21.4 /( l.z65x l8 )l:20"+4'.In summary, the x-ray data are consistent with uniform monolayers whose thicknesses are of the order of 957o of the expected values for maximally extended alkane chains normal to the surface.The layer thicknesses determined directly from the dip minimum in the x-ray specular reflectivity also agree within 2 A with those determined by ellipsometric measurement.Since the rvidth of the head group affects the position of the rninimum, rve believe, however, that the thickness of the alkane region alnne may be as much as 4 A thinner than the ellipsometrically determined values.
The structure near the silicon-oxide-hydrocarbon interface is almost cert.linlydue to the silicon-oxygen network formed by the siloxane head groups to neighboring atoms and to the silicon oxide surface.Since the available data are restricted to a region of q < C.8 A l, we did not have sufficient resolution to distinguish between a well-formed head-group layer, at a fixerl distance from the SiOr substrate, or one that is more distorted.From the absence of any chlorine signal in the XPS spectra, we can.however.be confident that the interface structure is not due to chlorine atoms remaining from the prepara-40 non.- The electron density of the fully fornred alkylsiloxane layers was essentially independent of the sample, having values between 0.41 and 0.43 of the silicon electron density.This value is equivalent to a mass density of between 0.83 and 0.87 g/cm' (silicon has a mass density of 2.33 g/cm3).This is somewhat larger than densities of liquicl phases of alkanes containing l2-18 carbon atoms (0.75 and 0.78 g/cm3 ), but it is less than the clensities found for crystalline phases of the same materials Q.93 g/c*t).ooThis is equivalent to the statement that the area per hydrocarbon chain was found to be approximately l0% larger than that of crystalline alkanes.
The width of the hydrocarbon-air interface does varv considerably between the long and shor-t hydrocarbon chains, with values of 3.8, 2.9, and 2.4 A for the ClO, C12, and C18 alkylsiloxanes, respectively (see Fig. 10).This variation may be due to the increased flexibility of the longer chains which are able to deform more easily and thereby quench some of the nonuniformity introduced at the silicon-oxide-hydrocarbon interface.
The most striking feature of the partially formed C18 alkylsiloxane reflectivity data when compared to the fully formed layer is the change in the position of the first minimum, unambiguously indicating a reduced thickness of the incomplete monolayer.Since the average electron density in the alkane layer is essentially the same as that for all of the fully formed layers, this result rules out the previously suggested model of islands of fully extended molecules.32Since, for films thinner than approximately 100 A, ellipsometry is only sensitive to the mean optical thickness, this technique cannot distinguish between the island hypothesis and the uniform layer.The reduced thickness of the partially formed layer could be explained in terms of a homogeneous coating in which the mean molecular tilt was about 45'.However, since the alkane-air interface for the incompletely formed monolayer was also found to be rougher than the same interface for all of the fully formed monolayers, the correct description of the partially formed monolayer must involve some degree of nonuniformity in the coating.
The present set of measurements cannot distinguish between a uniform-diffuse interface and one that was microscopically sharp, but rough.In principle, this distinction could be made by a more systematic study of the line shape as d is tuned off of the specular condition, like those shown in Fig. 3, but using a much finer resolution such as can be obtained using a crystal analyzer.taThe data reported here will not support a value for the parameter os1 that describes the Si/SiO, interface that is greater than 2 A. The fitting algorithm always drives it to zero.
A variation of the technique described here is to study the way the intensity falls off as the spectrometer is tuned away from the condition for Bragg reflection rather than away from the condition for specular reflection.The intensity along the "truncation ro6t"48'4e can be interpret-ed in terms of the width of the termination of the crystal lattice rather than as we have done in terms of the density profile at the interface between two regions of differing average electron density.The data for the surface of crystalline silicon indicate that the silicon lattice termination occurs in a single step, giving an atomically flat silicon-silicon-oxide interface.'r8'4eAnother study using transmission electron diffraction on specially prepared silicon wafers also found perfect termination of the silicon crystal lattice.s0A 5-A layer of ordered silicon oxide crystal was found at the crystalline silicon-amorphous silicon-oxide interface.Our measurements are consistent with these results indicating a very narrow silicon -silicon-oxide interface.This interface and, in particular, its width are of exceptional importance to the silicon-based electronics industry.a2'5 I Using other more intense synchrotron beam lines, it shcluld be straightforward to extend x-ray reflectivity measurements to values of q at least two or three tirnes larger than the maximunr of 0.8 A ' in the present measurements.Provided that neither radiation damage nor diffuse background radiation itre the limiting features, the structure of the various interfaces could be determined to a spatial resolution that could be three times finer than achieved in the present measurement.Furthermore, if the Si/SiO.sample is protected from airborne contaminants, specular reflectivity measurement of the bare Si/SiO2 substrate is the only method of w'hich we are aware that has the potential for fully characterizing the transition from the crystalline silicon region, through the strained crystalline Si/SiO, region, into the region of amorphous SiOr.
In some respects the use of the Si/SiO2 substrate, with its native oxide layer, complicated the analysis and made it more difficult to characterrze the alkane surfaces.On the other hand, the Si/SiO2 substrates have the decided advantages of having a much sharper interface with air than any other solid surface of comparable dimensions that we could obtain.In addition, since the observed diffuse scattering from the SilSiOr Samples, at all angles of incidence, is significantly lower than that observed from highly polished amorphous materials (such as polished or float glass), we believe that the microscopic surface width of the Si/SiO2 surface is also significantly less than that of other possible substrates.
The data on the olefin-terminated C17 sample, together with the study on the effect of bromination, illustrate a powerful tool for study of certain types of surface structures.In this particular example Br, molecules added to the reactive olefin groups attached to the end of the alkyl chains.From the x-ray reflectivity, it was possible to observe the position of the additional electrons and the consequent distribution of the bromine atoms.Although there were some effects of radiation damage that were discovered after the x-ray measurements had been completed, the example suggests that this type of measurement could be carried out using a much larger variety of reactive species.In particular, if the moiety to be attached to the end of the alkane group has some extended structure, this technique would allow for a relatively detailed mapping of its electron density.Since the specular reflection from the substrate provides a reference field, this technique has a built-in solution to the phase problen'r that plagues most other x-ray techniques for struct ural deterntinatiott.
The mclst serious linritation on the potential applicability of specular reflection for the study of organic monolar crs is the problenr of radiation damage.In the present lvork nrost of the samples with well-forrred alkanes had contact ungles with r.l'ater o1approximateiy 110" before s-v-nchrotron reflectivitr rneasurcment and from 75' to 90" afteruarcls dependir)g on the amount of exposure.XPS studies of the irradiated region suggested between 5-10 jc of the alk1l chains hud been oxidized, while sections of the sanrple that rverc not irradiated did rtot shou' thc 1-rrtsr'nce o1-iinr tiriclizecl spccies.laThis clanr.rgewas 111r1 irbsr.r'red on slrniples nreasured dr-rring c'xpcrimettts tusirtg tltt' r't-rtating anodc-rvitli liltered racliaticn (rr'ltere to-1al r-rar c\posLlre ri as rougltlv 17c, of th'--s1'ttclircitron ex-p{r:tire), but rr'lts l-c}-rlivflucetl n'hen a sample tt'as e xposed Itr the polychrornatic i:rt-'am for 24 h.In a ferv cases, there \\'as some evidence that for q >-0.7 A ' radiation clamage rnal' have been obserr cd as changes in the reflectivity of the order of 30o/c.Howevcr, no changes were detected for q <0.5 4 Since only about 0.1 photons per alkyl group fell on the san-rple during the course of a typical series of scans, rvith mosi being transmitted into the silicon bulk, and given that the number of damagecl molecules exceeds this number.the damage cannot be associated rvith the photttelectric effect acting directly on the alkylsiloxanr-nrolecules.One possibility is that the damage is induced by photoelectrons generated b)' x rays in the silicon substrate.These keV energl' electrons interact strongly with other electrons sparvning man\ more secondary electrons u'hich could ionize thc carbon atoms in the alkylsiloxane chain.The final damage rvould then result when the highlr reactive radicals thus formed combine with oxygen in the surrounding air.Alternativell', x-ray induced ozone in the atmosphere might be the source of the damage, ol' there might be free-radical chain reactions mediated by oxygen in the organic monolayers.
There are a number of n'ays that this damage might be reduced.The first and most obvious wa)' \\'ould be to place the sample in an atmosphere free of O.'.The n27 second would be to make the measurements with significantly' less exposure to radiation than was the case in these studies.For example, measurements of background scattering do not necessarily have to be taken with the same statistics as for the main data.In any event, the backgrouncl scans can be taken after the reflectivity datu irarr been completed.Sinr:e the bzickground is nrainll di.rc to air and bulk scattering, it will be little affec:tcc1 l-ri surfircriiarnage.The exposure can also be reducecl bv rrptirnizing the number of data points l(r climinate nrrrcli rrl'thc redundancl'' evident in the data irr Fig.I at lou' anslc's In additiott, since the samples have proven to be higlrli uttiform, data points catr he taken on the diff'erent regions ol'the wafer. Finally, thc e harrgcs in the reflectiiitv r.'ith time that \\'ere nleasurdcl <lri the uncoated silicorr siinrple are prclbahlv clue fo thc huilcl ilp oli the surface of u cont;rntitutiion la1'er u'ith a dcnsitl' lou,er thar: silicon.The strong signal fronr this 1.rr t'r makes it difficult to characterize thc SiO.la-ver fronr tht',llita in f-'ig.1(a), and future tlteaslrrements tlf the uneoa{cct Si/SiO.surfacc tnusf be done under nr()rc rtgoi'ortsl-r cont t'rtlled conditions thatt wcre available for this rt rr<lr .

,
FIG. L Normalized reflectivity data from several samples.Successive data sets are displaced by 100 times and error bars omitted for clarity.( -) Theoretical reflectivity from an ideal step interface with bulk silicon density.(c ) Uncoated silicon sample in helium; the "pairing" of points occurs for two scans taken 60 min apart and is probably due to the build up of contaminants on the surface.(A) 10-carbon chain alkylsiloxane.(V) 12-carbon chain alkylsiloxane.(!) l8-carbon chain alkylsiloxane.The inset shows a schematic diagram of the scattering vectors for the specular reflectivity condition, where 2(6):20.
psi is the density of crystalline silicon.We rvill shorv below that the data for the alkylsiloxane coated silicon wafers shown in Fig.Iare well described by a model in which ,\ _--3.

X
FIG. 2. (a)Schematic of the rotating anode configuration.S, was the beam-defining slit; the monochromator was either triple-bounce or single-bounce germanium.A11 lengths are ln millimeters, with typical slit dimensions given in the text.(b) Schematic of the synchrotron configuration (beamline X-228 at NSLS).S1 defined the coarse horizontal and vertical beam, fine beam definition being obtained from slit 52;the monochromator was a single-bounce germanium crystal.
A more compelling case specific to the present data are the results for the Patterson function --(+?l\*E l" calculated from the data for R(q)/RF(q):l0(q)|2 in Fig.4.The solid line in Fig.5was calculated directly from the data by correcting the critical angle to cor-Parameters for fits ofthe N:1,2, and I layer model described by Eq. 112) to the data lor the Cl8 alkylsiloxane-coated silicon wafer.The results calculated from the columns I{: l, 2, and 3' ' ' arc shorvn in Fig.4.Thc model reflectivities for parameters l' * , l'*r', 3'r r', and 3 are illustrated in Figs.?(a), 7(b), 7(c), end 7(d), respectirell'.and the real-space densities are illustrated in Fig.8.Thenotation3'''distinguishesbetweenmodelsinwhichp.(?)pu.ThcN:1,2,3'',and3 columns are best fits, u hile the r\r :]i +l and 3L+lr columns indicate the boundaries ofacceptabie fits itr:= 1 .'51rminimunr).The sixth line gives the lengths as me;rsured by the graphical technique described in the text.
FIG.5.Patterson function calculated from the data in Fig.4fbr the 18-carbon chain alkylsiloxane monolayer.The solid curve was calculated directly from the Fourier transform of the data; the dashed curve was obtained by multiplying the reflectivity data by a Gaussian of the form exp( -q2 /\o)p), where ap:0.3A r, prior to taking the Fourier transformation.This is equivalent to convoluting the Patterson function with a Gaussian of the formexpl -(,2z'):o1,, /2].The fact that the peak at about 40 A survives the convolution process indicates that it is a real feature of the data and not an artifact of the data termination.
FIG. 6. Real-space profiles of the model surface electron density from the parameters used to obtain fits in Fig.4.(a)-(c) showthemodelprofilesforthely':l(. . ..),N:Z(---), and tr/ :3 ( -) fits.(d) shows the three profiles overlapping for comparison.The hydrocarbon-air interface and hydrocarbon density and length are similar in all the fits, the only region with significant variation being the silicon-oxide-hydrocarbon region.The constructions shown in the three top figures illustrate a graphical technique, which is discussed in the text, for determining the thickness of the hydrocarbon region from these measured densities.The lengths shown as the solid arrows in (a)-(c) are given in Table I.The dashed rine in (d) shows the length of 23.6 A measured directly from the position of the first minimum in the data shown in Fis.4.
FIG. 8. Real-space densities corresponding to the fits of the rellectivity scans shown in Figs.7(a)-7(d).(a)-(d) show the densities with sharp interfaces.(e) and (fl are the corresponding re:rl-space profiles including the widths of the different interfaces.The sharp f'eature in (g) rs well beyond the resolution limit and a fit thrt is almost as good would have a profile more sirnilar to {c) and {l-1.{i) shor,rs a comparison ol'the 3 and 3 density profiles on the sanle axes (the two best fits).Although the pararrreters corresponding to these three curves are quite different, the only' srgnificant differences in the real-space densities are in the unresolved structure of the resion where the siloxane bonds to the silicon oxide.
FIG.10.Real-space profiles for the (a) C10 (. . ..),(b) C12 ( ---), and (c) ClB ( --) samples obtained from the reflectivity fits.(d) shows the same profiles overlapping for comparrison.Note that although the iength of the hydrocarbon layer varies significantly, the silicon oxide layer and layer density are similar for all three samples.The dashed arrows show the length as determined directly from the position of the first minimum.The solid arrows show the construction described in the text used to obtain thc revised estimate of the hvdrocarbon thickness.
Parameters for the /y' :3' ' models that obtain the best representations of the reflectivity for samples as discussed in the text. c10
FIG.14.Real-space electron density profile of the surface obtained from the parameters of the fits in Fig.13for the alkene sample and the same sample after bromination.Note that the fit to the brominated sample was done by using the parameters of the unbrominated sample (dashed line) for all except the hydrocarbon-air interface.The addition of the peak is due to the addition of one bromine atom to each of the two carbon atoms at the tail of the molecule.
FIG. 15.(a) Normalized reflectivity and three-layer fit for a fluorocarbon sample.The parameters are shown in TableILBecause of the limited range of data and the complicated nature of the interface, it rvas impossible to obtain accurate values for the parameters, the fit being only a physically reasonable one.(b) Real-space electron density profile of the surface of the sam- Table II and allowing only | 3, LB, oJ4, ogr, &fld fry, to vary.The values for the parameters that gave the best fit are listed in column glTiBrr of Table II and in the notes below the table.The solid line in