Appl. Phys. A 63, 207—216 (1996)

Invited paper

Fluorescence interference-contrast microscopy on oxidizedsilicon using a monomolecular dye layer

Armin Lambacher, Peter Fromherz*

Department of Membrane- and Neurophysics, Max-Planck-Institute for Biochemistry,D-82152 Martinsried Munchen, Germany(Fax: #49-89/8578-2822, E-mail: fromherz@biochem.mpg.de)

Received: 9 May 1996 / Accepted: 22 May 1996

Abstract. A silicon chip is covered by a monomolecularfilm of a fluorescence dye with silicon dioxide used asa spacer. The fluorescence depends on the distance of thedye from the silicon. The modulation of the intensity isdescribed quantitatively by an optical theory which ac-counts for interference of the exciting light and of theemitted light. The effect is used to obtain a microscopicpicture of the surface profile with a precision of a fewAngstroms. The perspectives for an application in wetsystems such as neuron-silicon junctions and lipid mem-branes on silicon are pointed out.

PACS: 42.80; 68.55; 78.65

A living cell in close contact to a surface formsa twodimensional electrical cable with the cell membraneas a capacitive coat and the narrow cleft between mem-brane and surface as a resistive core [1, 2]. The electricalproperties of that cable can be studied by field-effecttransistors if the cell is attached to a silicon chip [3, 4, 5].In the future such hybrid systems of cells and oxidizedsilicon may allow the assembly of integrated circuits ofnerve cells and silicon microstructures and the develop-ment of technical devices such as drug sensors. A criticalpoint in the investigation of cell-silicon junctions is theunknown distance of the membrane from the surfacewhich may be in the range of tens of nanometers [5]. Herewe propose a method which is suitable to solve thisproblem. We take advantage of the modulation of fluores-cence of dye molecules in front of the reflecting surface ofsilicon.

Distance dependent excitation and emission is knownsince the classical experiments of Wiener [6], Drude andNernst [7], Selenyi [8] and Kossel [9]. It was studied inparticular by Kuhn and Drexhage in their elegant experi-ments with fluorescent dyes on metal mirrors spaced byLangmuir-Blodgett films [10, 11, 12]. The effect was ob-served also in soap lamellas [13]. A change of fluorescence

*correspondence author

was noted on oxidized silicon [14, 15] and assigned tooptical interference [15].

In the present paper we investigate the fluorescence ofa cyanine dye embedded in a Langmuir-Blodgett filmwhich is spaced from silicon by a layer of silicon dioxide(Fig. 1). The observations are made in a microscope. Wedescribe the modulation of fluorescence intensity by clas-sical optics. On that basis we show that changes of fluores-cence intensity on a microscopic scale can be used todetermine small changes of the surface profile with a pre-cision of a few Angstroms. At the end the perspectives foran application in cell-silicon junctions are pointed out.

1 Theory

In this section we derive how the observed fluorescenceintensity depends on the distance of a dye molecule froma silicon surface. The spatial structure of the electromag-netic field is described by the classical electrical fieldstrength. We study the processes of excitation and ofemission and combine the results to obtain the fluores-cence intensity . First we consider only the light reflectionat the interface silicon to silicon dioxide ( Fig. 2a). Then wetake into account reflection and refraction at the surfaceof the system and at the interface between silicon dioxideand the lipid film (Fig. 2b). Although the basis of theoptical approach is described by Born and Wolf [16] andsome aspects are discussed by Drexhage [12], we presentthe theory in some detail to avoid any misunderstanding.

1.1 Excitation

A dye molecule is embedded in silicon dioxide (refractiveindex n

1) on silicon (complex refractive index n

0) at a dis-

tance d from the interface (Fig. 2a). The orientation of thetransition dipole of excitation is described by the unitvector e6

%9. This system is illuminated by light of

a wavelength j*/

with an amplitude of the electrical fieldE0

at an angle of incidence h*/1

with respect to the normaland an angle of polarization c

*/with respect to the plane

Fig. 1. Structure of a silicon chip coated with silicon dioxide anda monomolecular film of Cd-arachidate with the cyanine dye S9

Fig. 2a, b. Optical models. a Silicon with an infinitely extendedphase of silicon dioxide on silicon. The complex refractive indices aren0

and n1. A dye molecule is located at a distance d from the

interface. The direct and the reflected components of the illumina-ting wave at an angle hin

1in the plane of incidence are drawn at the

left. The direct and the reflected components of the emitted wave atan angle hout

1in a second plane of incidence are drawn at the right.

b Silicon with a layer of silicon dioxide (thickness d, refractive indexn1) and a layer of lipid (thickness d, refractive index n

2) in air

(refractive index n3). The dye is located in the lipid close to the

interface. Some of the partial waves of illumination and of emissionare drawn as they occur by reflection. The effect of the opticallyweak interface between silicon dioxide and lipid is disregarded inthis diagram

of incidence. The probability of excitation per unit time isproportional to the squared projection of the local electri-cal field E

*/of the incident wave on the direction of the

transition dipole. To describe the modulation of excita-tion by the interface we calculate the normalized projec-tion of the field DF

*/· e

%9D2 with F

*/"E

*//E

0as a function

of the distance from the surface of silicon.At a given direction two coherent light waves arrive at

the dye, one directly from the source and the other oneindirectly after reflection at the silicon surface (Fig. 2a).Their phase difference U

*/is given by

U*/"

4nn1d cos h*/

1j*/

(1)

To compute the normalized local electrical field wesplit the incident wave into its TE-component (E-fieldperpendicular to plane of incidence) and its TM-compo-nent (E-field parallel to the plane of incidence). With theFresnel coefficients of reflection rTE

10and rTM

10(see appendix)

we obtain for the Cartesian components of the normalizedfield (x-axis along the plane of incidence in the direction ofincidence, z-axis normal to the interface)

F*/"sin c

*/

0

1#rTE10

ei'*/

0

#cos c*/

cos h*/1

(1!rTM10

ei'*/ )

0

sin h*/1

(1#rTM10

ei'*/)

(2)

The orientation of the dipole is given by its inclinationh%9

to the normal and the azimuthal angle /%9

in thexy-plane with respect to the plane of incidence

e%9"

cos/%9

sin h%9

sin/%9

sin h%9

cos h%9

(3)

The squared projection DF*/

· e%9

D2 for a set of para-meters h

%9, /

%9, c

*/, h*/

1and j

*/is obtained from (1), (2) and

(3).Usually we use incoherent light of different directions

and polarizations and we observe an ensemble of dyemolecules with different orientations. The probability ofexcitation is then proportional to an average of thesquared projection DF

*/· e

%9D2. In an uniaxial lipid film the

orientation of the transition dipoles is described by a dis-tribution function O(h

%9) per unit space angle which is

independent on the angle /%9. For unpolarized illumina-

tion through an objective with its optical axis along thesurface normal we describe the relative intensity by anaperture function A(h*/

1) per unit space angle.

We compute the average of DF*/

· e%9

D2 for a givenwavelength in two steps. First we integrate analyticallyover the azimuthal angle /

%9and the angle of polarization

c*/. Then we average numerically over the inclinations h

%9of the dye and the angles of incidence hn1. Disregarding

208

normalization factors we obtain

SDF*/

· e%9

D2TJP sinh*/1

dh*/1

A*/

(h*/1)

]Psinh%9

dh%9

O(h%9)º

%9(j

*/,h*/

1,h

%9) (4)

º%9"sin2h

%9D1#rTE

10ei'

*/ D2#sin2h%9cos2h*/

1D1!rTM

10ei'

*/ D2

#2 cos2h%9

sin2hin

1D1#rTM

10ei'

*/ D2

The total probability of excitation per unit time P%9results from integration over the wavelength. We take into

account the intensity of illumination I (j*/) (quanta per

area, time and wavelength interval) and the extinctioncoefficient of the dye e(j

*/) according to

P%9RPdj

*/I (j

*/)e (j

*/)SDF

*/· e

%9D2T (5)

1.2 Emission

The description of emission is homologous to that ofexcitation. The detection system defines a light wave witha wavelength j

065along a plane of incidence at an angle

h0651

with respect to the normal and an angle of polariza-tion c

065. The probability of spontaneous emission into

a certain mode of the electrical field is proportional to theprobability of excitation of the same molecular transitionby the same mode [17]. I.e. it is proportional to thesquared projection of a local electrical field E

065onto the

direction e%.

of the transition dipole of emission. Todescribe the effect of the interface we calculate how thenormalized projection of the electrical field DF

065· e

%.D2

with F065

"E065

/E0

depends on the distance from thesilicon surface.

For a given direction two coherent waves are emittedby the dye, one directly and the other one after reflectionat the silicon (Fig. 2a). Their phase difference U

065is

U065

"

4nn1d cosh065

1j065

(6)

We split the emitted wave into its TE- and TM-com-ponent. With the Fresnel coefficients of reflection rTE

10and

rTM10

we obtain for the Cartesian components of the nor-malized field (x-axis along the plane of incidence oppositeto the direction of emission)

F065

"sin c@065

0

1#rTE10

ei'065

0

#cos c@065

cos h0651

(1!rTM10

ei'065 )

0

sin h0651

(1#rTM10

ei'065)

(7)

The orientation of the transition dipole of emission isgiven by its inclination h

%.to the normal and the

azimuthal angle /@%.

in the xy-plane with respect to thenew plane of incidence

e%.

"

cos/@%.

sin h%.

sin/@%.

sin h%.

cos h%.

(8)

The squared projection DF065

· e%.

D2 for a set of para-meters h

%., /@

%., c

065, h065

1and j

065is obtained from (6), (7)

and (8).We describe the orientation of transition dipoles by

a distribution function O(h%.

) per unit space angle and therelative transmission of the optics by an aperture functionA

065(h065

1) per unit space angle. In the detection is unselec-

tive for polarization and incoherent for different direc-tions we obtain

SDF065

· e%.

D2TJPsin h0651

dh0651

A065

(h0651

)Psinh%.

dh%.

O(h%.

)

]º%.

(j065

,h0651

, h%.

) (9)

º%.

"sin2h%.

D1#rTE10

ei'065 D2#sin2h

%.cos2h065

1

]D1!rTM10

ei'065D2#2cos2h

%.sin2h065

1D1#rTM

10ei'

065 D2

The probability per unit time P%.

to detect an emittedquantum from an excited molecule is given by integrationover the wavelength. We obtain Eq. 10 with the quantumyield U

$%5(j

065) of the detector and with the fluorescence

spectrum far from the interface (quanta per unitwavelength) using the normalized spectrum f (j

065)

P%.

JPdj065

U$%5

(j065

) f (j065

)SDF065

· e%.

D2T (10)

1.3 Detected intensity

Under stationary illumination there is a flow of detectedquanta per unit time. This flow J

&is given by the probabil-

ity that the molecule is in its excited state and by theprobability of detected emission per unit time P

%.. The

population of the excited state is controllable by theprobability of excitation per unit time P

%9and by the total

probability of deactivation which depends on the totaltransition probabilities of fluorescence and of non-radiative decay k

&and k

/3. We obtain

J&"P

%.P

%9

1

k&#k

/3

(11)

Nonradiative decay may be affected by energy transferinto acceptor states of metals [9, 10, 11, 18]. There is noindication that such effects play a role for weakly dopedsilicon. We assume that the nonradiative decay is given byits value far from the interface with k

/3"k=

/3.

The total transition probability of fluorescence ismodulated by the constraint which is imposed onto theelectromagnetic field by the reflecting surface [12, 19]. Wewrite the radiative decay as a modulation of the decayconstant k=

&far from the interface as k

&"k=

&#dk

&. With

209

Fig. 3. Theoretical flow of detected quanta of fluorescence J&versus

the distance d of a molecule from the surface of silicon normalized tothe flow at infinite distance . The dashed line (1) refers to the simpleoptical model which takes into account only the reflection at thesilicon (Fig. 2a). The drawn line (2) is obtained when the reflectionand refraction at the surface of silicon dioxide is taken into accountand- undistinguishable on the scale—if the interface silicon dioxide tolipid film is considered, too (Fig. 2b)

the quantum yield of fluorescence far from the interface

U=&"k=

&/(k=

&#k=

/3)

we obtain

J&"P

%.P

%9

1

k=&#k=

/3

1

1#U=&

dk&

k=&

(12)

The modulation of J&by a change of radiative decay is

small if the quantum yield of the dye is low. In that casethe observed fluorescence intensity is proportional to theprobability of excitation and of detection as

J&JP

%.P

%9(13)

We do not elaborate here the change of lifetime as theexperiments indicate that the effect may be neglected inour system. The approximation (13) is sufficient.

1.4 Silicon mirror

We compute an example for the fluorescence intensityJ&

as a function of the distance d of the dye from thesurface of oxidized silicon (Fig. 2a) using (5), (10) and (13).The result is shown in Fig. 3 (curve 1). The excitation ismonochromatic with a wavelength in vaccumj*/"366 nm. The spectrum f (j

065) is the fluorescence

spectrum of the cyanine dye $9 which is used in theexperiments. It is centered around j

%."430 nm. The

aperture function is A*/"1 up to h*/

1"11.75° for illu-

mination, A065

"1 up to an angle h0651

"11.84° for detec-tion and zero elsewhere. (These values correspond to anaperture of 17.46° of the objective used in the experimentstaking into account the dispersion of refration.) The

transition dipoles of excitation and of emission are parallelto the interface (h

%9"h

%."90°). The refractive indices of

silicon and silicon dioxide are taken from the literature[20, 21]. Any interaction between dye molecules is neglected.

The fluorescence intensity is very low at the surface ofsilicon. Silicon behaves as an rather ideal mirror witha small tangential electrical field at its surface. Just abovethe surface we observe a strong modulation of fluores-cence. Here the interference effects of excitation describedby P

%9and of emission described by P

%.are in register. At

larger distance a pattern of beating arises due to thedifference of the wavelength of excitation and emission.Further away the interference effect of emission levels outdue to a compensation of the different wavelengths in thespectrum. We remain with the modulation of the excita-tion alone. At a very large distance (not shown in Fig. 3)also that effect levels out due to the compensation of raysof different directions within the finite aperture.

1.5 Thin Film System

The finite thickness of the dielectric layer on silicon madeof silicon dioxide and lipid gives rise to refraction andmultiple reflection (Fig. 2b). We assume first that theoptical properties of the lipid and silicon dioxide are equalwith n

2"n

1. The thickness of the dielectric film is d#d.

The dye molecule is located at a distance d from the siliconand at a distance d from the surface.

We account for refraction by evaluating the internalangles of incidence h*/

1and h065

1from the external angles h*/

3and h0653

according to Snellius law. We correct the interfer-ence terms in Eqs. 4 and 9 for multiple reflections andobtain

º%9"sin2h

%9D if TE

*/D2#sin2h

%9cos2h*/

1D if TM,1

*/D2

#2 cos2h%9

sin2h*/1

D if TM,/*/

D2 (14)

º%.

"sin2h%.

D if TE065

D2#sin2h%.

cos2h0651

D if TM,1065

D2

#2 cos2h%.

sin2h0651

D if TM,/065

D2 (15)

The expressions for if TE*/

, if TM,1*/

, if TM,/*/

and if TE065

, if TM,1065

,if TM,/

065with the pertinent Fresnel coefficients of transmis-

sion and reflection t31

, t13

, r13

and r10

are found in theappendix. The fluorescence intensity is given again by (5),(10) and (13).

The result of a computation is shown in Fig. 3 (curve2). The wavelength of illumination, the spectra of fluores-cence and detection and the orientation of the transitiondipoles are chosen as in the model with a single interface.The external aperture angles are h*/

3"h065

3"17.46°. The

thickness of the lipidfilm is d"2.64 nm [12]. Apparentlythe overall pattern of fluorescence intensity remains un-changed. The finite thickness of the dielectric layer intro-duces only slight modifications. The reflecting silicondominates the system.

1.6 Multilayer system

The refractive index of silicon dioxide (n1) is not identical

to that of lipid film (n2). We account for the reflection and

210

refraction in the system with three interfaces by using newinterference terms in (14) and (15). They are obtained bythe matrix technique (see appendix). If we choose all otherparameters as in the previous model we see only littlechange. On the scale of Fig. 3 the pattern of fluorescencecannot be distinguished from the previous model.

2 Materials and methods

In this section we describe the preparation of the siliconchips, the coating with the fluorescent dye and the opticalset-up of fluorescence measurement.

2.1 Chips

We used n-doped silicon with a 100 surface (5-14 Xcm,Wacker, Burghausen). Chips of 31 mm]11 mm were cut.They were cleaned according to the standard RCA-pro-cedure [22.23]. Oxidation was performed in dry oxygenatmosphere at a temperature of 1200 °C in a RTP-oven(AST, Ulm) for oxides up to 100 nm. Thicker oxides weremade in a tube oven (Heraeus, Hanau) in wet oxygen at1000 °C. The thickness of the oxide was measured with anellipsometer (Plasmos, Munich).

The silicon dioxide was structured by photolithogra-phy and etching. The chips were covered with a positivephotoresist (AZ 1514H, Hoechst) by spin coating. Afterillumination through an appropriate mask the exposedphotoresist was developed. The chips were dipped intodiluted HF (0.5% to 10%). The progress of etching waschecked by ellipsometry. Afterwards the photoresist wasremoved with acetone. Three kinds of structures weremade: (i) From oxide films with a thickness of 5 nm to450 nm a few nanometers (2—10 nm) were removed on halfof the chips. Each of these samples was used to obtain twopoints for the dependence of fluorescence on oxide thick-ness. (ii) On chips with about 40 nm oxide rectangles of anarea 5 mm]7 mm were etched to a depth of 2 to 5.5 nm.These samples were used to evaluate the depth of etchingfrom fluorescence data. (ii) On chips with an oxide ofabout 90 nm thickness a step of about 36 nm height wasetched. Microscopic lanes of 25 lm width were etchedacross the step with a depth of 2.5 to 5.5 nm. These chipswere used for thickness measurements from microscopicfluorescence data alone without external reference.

The chips were sonicated for 10 min at 70 °C in an aciddetergent (5% Ultrax 102, KLN, Heppenheim), rinsedwith a jet of Milli-Q water (Millipore Inc.), sonicated for20 min at 70 °C in an alkaline detergent (2% TickopurRP100, Bandelin, Berlin) and rinsed with a jet of Milli-Q.Then the chips were sonicated three times in Milli-Qwater for 10 min at room temperature and rinsed betweeneach stage with a jet of Milli-Q. After sonication each chipwas rinsed separately with a Milli-jet and dried in hot air[24]. It should be noted that the alkaline detergent erodesthe silicon oxide at a rate of about 0.5 nm in 10 min.

The complex refractive indices of silicon are takenfrom ref. [20]. We used the table of refractive index ofsilica from ref. [21]. We scaled the dispersion of the tablesto the refractive index n"1.456 at 632.8 nm of our

thermally grown silicon dioxide as determined byellipsometry.

2.2 Monolayer

The monomethine-oxacarbocyanine S9 (Fig. 1). was syn-thesized as described by Sondermann [25]. Arachidic acidwas obtained from Sigma, Heidelberg. S9 and arachidicacid were dissolved in chloroform (Uvasol, Merck) ata molar ratio 1:10 at concentrations of 5 mM and 0.5 mM,respectively [26]. Monolayers were prepared on a circulartrough [27]. At first the hydrophilic chip was dipped intothe subphase of 5 mM CdCl

2in Milli-Q water. Then

a mixed monolayer was formed by spreading and com-pression up to 35 mN/m [26]. The chips were withdrawnacross the monolayer at a speed of about 0.05 mm/s. Aftercompleting the fluorescence measurement, the monolayerwas removed by successive dips into chloroform, pro-panol and Milli-Q water. Remaining organic material wasremoved with a mixture of hydrogen peroxide (30%) andconcentrated sulfuric acid (volume ratio 1 : 4) and a finalrinsing with Milli-Q water. At this stage the ellipsometricmeasurement of the oxide thickness was made.

We used as a thickness of a monolayer Cd-arachidated"2.64 nm which was determined optically for multi-layers on glass [12] and as a refractive index n

2"1.526 at

all wavelengths (ordinary index) [12]. The birefringence ofthe monolayer was neglected. The fluorescence spectrumof the dye was measured in a monolayer on glass. It was inagreement with the published data [26].

2.3 Fluorescence

Fluorescence pictures were taken with a microscope(Axioskop, Zeiss) through an objective with a magnifica-tion 10x and a numerical aperture 0.3 (Plan Neofluar,Zeiss). The aperture corresponds to an effective angle of17.46° for illumination and detection. For illumination weused a high pressure mercury lamp (HBO 100W/2, Os-ram) with an interference filter of 366 nm and a dichroiticmirror FT400 (Zeiss). The edges of the etched patternswere used to bring the surface in focus. The intensity of thelamp was monitored by a photodiode. We observed thefluorescence above 415 nm using a cutoff filter (LP 415,Schott, Mainz) by a CCD-camera (HRC, Theta System,Munich) using a sensor with enhanced spectral sensitivityin the blue (Sony ICX039AL). Exposure time (40 ms to320 ms) and gain were controlled by a computer. Thepictures were transferred to a frame grabber (ITEX AFG,Stemmer, Munich). Only the odd lines of the interlacedframes of the video norm were transferred. A region of15]15 pixels therefore contains only 120 (15]8) elementsof information. In all cases we subtracted the backgroundmeasured on a area of the chip which was not covered bythe dye.

To evaluate fluorescence intensities we selected areaswhich were free of defects by visual inspection. The sizewas usually 20 lm]20 lm up to 200 lm]200 lm. Insome cases intensity profiles were taken with differentresolutions. In that case we used horizontally a floating

211

average over a certain number of pixels (1—15) and aver-aged vertically over the same numbers of lines (odd lines1—15).

3 Results and discussion

This section has three parts. First we consider the fluores-cence of a monomolecular film on homogeneously oxi-dized silicon with different thickness of silicon dioxide(Fig. 4). The results are compared with the optical theory.Then we evaluate the height of an etched step in silicondioxide from the fluorescence change of a monolayer(Fig. 5). In a third part we consider a shallow microscopicpattern etched into two levels of a step. The depth of thepattern is determined from the fluorescence on the patternalone without an external reference (Fig. 6).

3.1 Fluorescence on oxidized silicon

We deposited a monomolecular film of the amphiphiliccyanine dye on chips of oxidized silicon. 37 samples withtwo different oxide thickness were prepared. In total westudied 74 different thickness values between 5.0 nm and450 nm.

The fluorescence intensity was observed with an aper-ture angle of 17.46°. The wavelength of illumination was366 nm. The detection covered the whole fluorescencespectrum above 410 nm (maximum at 430 nm). The dataare plotted in Fig. 4 versus the thickness of the silicondioxide. The intensity close to the silicon is low. It in-creases to a first maximum at a distance of about 65 nmand drops to a second minimum at about 120 nm. Withinthe range of the measurements three further maxima ap-pear at larger thickness. The estimated maximal error is

Fig. 4. Fluorescence on oxidized silicon. The fluorescence intensityof the cyanine dye S9 in Cd-arachidate (molar ratio 1:10) is plottedin arbitrary units versus the thickness of silicon dioxide. The dye isexcited at 366 nm, the integral emission of the spectrum centeredaround 430 nm is detected. The cross indicates the estimated maxi-mal error. The drawn line is the result of the optical theory. The onlyadjusted parameter is a scaling factor of the intensity

Fig. 5a, b. Thickness measurement with fluorescence. a Profile of thesystem with a step of depth D(0 etched into silicon dioxide ofthickness d

0. The surface is covered by a monolayer with fluorescent

dye. b Fluorescence picture of a monolayer with the cyanine dye S9in Cd-arachidate (molar ratio 1:10) on oxidized silicon. The size ofthe picture is 660 lm]425 lm. The thickness of the oxide in thissample was d

0"36.6$0.14 nm in the bright and

d"33.9$0.14 nm in the dark region as measured by ellipsometry

marked in Fig. 4. The error of the thickness is due toinhomogeneous oxidation. The error of fluorescence isdue to changes in the quality of the monolayer of differentsamples and to inhomogeneous illumination.

We compare now the data with the optical theory. Weassume that the transition moments are parallel to thesurface with random orientation [10, 11,12] and that theillumination is unpolarized and homogeneous over thespace angle defined by the aperture of the objective. Theillumination is monochromatic. We take into account thefluorescence spectrum of the dye, the filters in the emissionpath and the sensitivity spectrum of the detector. Weassume that the detection system is unspecific with respectto polarization. We apply the optical model with twointerfaces (Fig. 2b) as described above using the knownoptical constants of silicon, of silicon dioxide and theknown thickness of the monolayer. We neglect the correc-tion due to a changed lifetime. The only parameter toadjust is the scaling of the intensity. The fit is shown inFig. 4.

It is apparent that the theory matches the complicatedpattern of the fluorescence intensity in most details. Thereare two small systematic discrepancies: (i) The relativeheight of the second maximum is too low as compared tothe first maximum. (ii) The asymmetry of the third max-imum is inverted. The first deviation may be due to theneglect of a changed radiative lifetime using the approxi-mation (13). The range of the minimum of beating around300 nm is particularly sensitive to small changes in theoptical parameters. It may be inadequate to apply thedispersion data of fused silica for thermally oxidizedmicrocrystalline silicon dioxide.

212

Fig. 6a, b. Fluorescence of a monolayer with the cyanine dye S9 inCd-arachidate (molar ratio 1:10) on silicon. a Schematic cross sec-tion. A step of silicon oxide is fabricated with a thickness d

1on the

right and d2

on the left. Microstructures with the depth D(0 areetched in both levels. The surface is covered by a monolayer withfluorescent dye. b Fluorescence picture of a chip with letters etchedacross the step with d

1"36.1$0.5 nm, d

2"89.8$0.5 nm and

D+!2.8 nm. One pixel corresponds to 0.86 lm]0.83 lm. Theletters on the right (level d

1#D) show a lower intensity as compared

to the background. The intensity on the letters on the left (leveld2#D) is enhanced. The vertical black stripe along the step is an

artefact of the CCD-camera caused by excessive intensity due toreflection. The two arrows mark the location of the profiles shown inc. The black squares mark the size of the areas (1]1, 3]3, 7]7 and15]15 pixels) used to obtain those profiles. (c) Profiles of fluores-cence intensity (arbitrary units) at different resolutions. The arrowsmark that part of the traces which is used to evaluate the resolutionof the method

We conclude that the optical model used to fit the datadoes not neglect a major physical mechanism. The modu-lation of fluorescence in front of silicon is dominated bythe interference of the exciting and of the emitted light.There is no significant effect of energy transfer to thesilicon. A possible effect of a changed lifetime is small.

3.2 Distance measurement with reference

We use now the distance dependent fluorescence to deter-mine the height of a step etched in silicon dioxide. Asa basis we use the optical model with two interfaces whichwas shown to be sufficient to describe the experiment dataaccording to Fig. 4.

We prepared an oxide layer with a thickness around40 nm. That thickness is close to the steepest slope on theleft hand side of the first wave of interference (Fig. 4). Weetched shallow rectangle of a size 5 mm]7 mm (Fig. 5a).Then both levels of the chip were coated with a fluorescentmonolayer. The pattern of fluorescence was observed inthe microscope. One corner of a sample is shown inFig. 5b. We evaluated the fluorescence intensity I

0on the

original level and the intensity I on the etched level. Theywere taken from areas 20 lm]20 lm to 200 lm]200 lm, depending on the homogeneity of the film. Thenthe dye was removed and the thickness of the originaloxide d

0and of the etched level d

0#D (D(0) were deter-

mined by ellipsometry (averaged over about1 mm]1 mm).

The fluorescence intensity I0

of the dye at a knowndistance d

0was taken as a reference to scale the optical

theory. From the intensity I the unknown distance d0#D

was evaluated using the scaled theory. In other words weidentified the ratio of the experimental fluorescence inten-sities on the two levels with the ratio of the theoreticalfluorescence

I

I0

"

J&(d

0#D)

J&(d

0)

(16)

The unknown scaling factor of the theory is eliminatedin (16). From the experimental data of intensity and thegiven distance d

0we obtain the unknown value of the

depth of etching D by numerical solution of (16).The results from several samples are presented in

Fig. 7a. The maximal error is estimated on the basis of theerror of the intensity due to inhomogeneous illumination.For comparison we determined the step height by ellip-sometry, too. There the error is due to the inhomogeneousthickness of the oxide. The results of the fluorescencemeasurement agree with the ellipsometric data in mostcases within the error of the data. We assign the deviationsto defects in the monolayers not recognized by visualinspection. We conclude: The fluorescence intensity canbe used as a ruler to measure the location of a dye abovea silicon surface if we know the intensity at a knownlocation as a reference.

3.3 Distance measurement without reference

It is our goal to measure the unknown distance D'0 ofa biomembrane from a surface of oxidized silicon after

213

Fig. 7a, b. Values for the depth of profiles etched in silicon dioxide.a Depth D of a step etched into a layer with a thickness d

0according

to Fig. 5. The ratio of intensities on the etched and unetched area isdetermined. The depth D (black dots) is evaluated with the opticaltheory. For control the depth is determined by direct ellipsometricmeasurement as D"d!d

0(circles). The bars of the fluorescence

data are estimated maximal errors. The error bars of the ellipsomet-ric data mark 3p intervals. b Depth D of the letters etched acrossa step in silicon dioxide with thickness d

1"36.1 nm and

d2"89.9 nm according to Fig. 6. The ratio of fluorescence inten-

sities on the etched areas on both levels is determined. The depthD (black dots) is evaluated with the optical theory without referenceto the surround. For comparison the values are given which areobtained with reference to the surround (circles). The bars of bothsets of data are estimated maximal errors

labeling with a fluorescent dye. If a lipid bilayer or a cell isfloating on a chip with an oxide of thickness d there is noreference where the membrane is at a known distancefrom the surface of silicon. It is not possible to use thefluorometric method as described above. The problem canbe solved, however, if the membrane covers two levels ofsilicon dioxide of different thickness d

1and d

2. We studied

the procedure in a model experiment.As a support of a lipid monolayer we prepared a step

of silicon dioxide with the thickness d1

and d2

(Fig. 6a).The low level was chosen to be on the left of the first waveof the interference pattern (Fig. 4), whereas the high levelwas on the right hand side of the first wave. In ourexperiment we used d

1"36.1$0.5 nm and d

2"89.8$

0.5 nm. We prepared an increment of distance on this

support by etching a shallow pattern of unknown depthD(0 across the step as shown in Fig. 6a and coated thestructure by a lipid monolayer with fluorescent dye.

A photograph of assembly is shown in Fig. 6b. Theincremental pattern leads to an increase of fluorescence onthe high level and to decrease on the low level. We con-sider now the fluorescence intensities I

1and I

2on the

incremental pattern alone with the two unknown thick-nesses d

1#D and d

2#D. We identify the ratio of the

experimental intensities with the ratio of theoretical fluo-rescence as

I1

I2

"

J&(d

1#D)

J&(d

2#D)

(17)

The unknown scaling factor is eliminated by this pro-cedure of internal reference. For given thicknesses d

1and

d2

of the substrate we can evaluate the unknown in-crement D by numerical solution of (17) using the fluo-rescence intensities I

1and I

2. There is no external refer-

ence. The results for a set of samples are shown in Fig. 7b.The maximal errors are estimated from possible in-homogenities of illumination and of the thickness of theoxide.

For comparison we evaluated the depth D of thepattern also by the fluorometric measurement with refer-ence to the surround using (16). As shown in Fig. 7b theresults are in good agreement with the approach of inter-nal reference.

It may be noted here that the agreement of the twoapproaches of fluorometric measurement of distance indi-cates also that the optical model chosen is adequate. Theapproach with external reference relies on a comparison offluorescence changes on a single slope of the primary waveof interference whereas the approach with internal refer-ence relies on changes on both slopes of the primary wave.If an incorrect model would be used we would expecta drastic discrepancy of the two results. The perfect agree-ment confirms the fit of Fig. 4.

Finally we consider the resolution in depth and inlateral distance. We scanned the pattern as marked inFig. 6b. Traces for 1]1, 3]3, 7]7 and 15]15 pixels areshown in Fig. 6c. The increment D+!2.8 nm of theletters is detected even with a single pixel of0.86 lm]0.83 lm. We evaluate the 3p deviation from theoptical trace as marked in Fig. 6c and calculate the errorof the thickness measurements. For the four measure-ments in Fig. 6c with lateral resolutions of about 0.9 lm,2.5 lm, 6.0 lm and 13 lm we estimate 0.31 nm, 0.61 nm,0.06 nm and 0.04 nm for the resolution of depth. At theoptical resolution of the microscope of 1.45 lm the resolu-tion of distance is better than 0.3 nm.

4 Outlook

Our study shows that the modulation of fluorescence onoxidized silicon can be described quantitatively by anoptical approach. Fluorescence quenching by the siliconand changes of radiative lifetime played no significant rolein the system used here. For a more thorough understand-ing it is important, however, to study quantum yield and

214

lifetime of fluorescence and the interaction of dye molecu-les through the electromagnetic field and to vary theorientation of the dye, the refractive index of the spacerand the polarization of illumination and detection.

The experiment with a dry lipid film on an etchedmicrostructure in silicon dioxide shows that the positionof a thin film can be measured with a resolution of 0.3 nmat a spatial resolution of 1.5 lm. The investigation opensthe way to apply fluorescence interface-contrast micro-scopy to a wet system such as a cell attached to the chip.The cell membrane has to be labelled with a fluorescentchromophore. The cell has to cover a microscopic stepetched in silicon dioxide. If parts of the adhesion regionare homogeneous it will be possible to determine thedistance of the membrane from the surface.

Acknowledgements. This work was supported by the Deutsche For-schungsgemeinschaft (grants Fr 349/9 and SFB 239/E2) and by theFonds der Chemischen Industrie. We thank Dieter Braun for criticalreading of the manuscript.

Appendix

Fresnel coefficients. The Fresnel coefficients of reflectionand transmission at an interface between media of refrac-tive index n

*and n

+as a function of the angles h

*and

h+with respect to the normal in those media are given by

(A1) and (A2) for the TE- and TM-mode. The angles h*and h

+with respect to the normal in those media are given

by (A1) and (A2) for the TE- and TM-mode. The angles h*and h

+are related by Snellius law.

rTE*+"

n*cos h

*!n

+cosh

+n*cosh

*#n

jcosh

+

rTM*+

"

n+cosh

*!n

*cos h

+n+cos h

*#n

*cos h

+

(A1)

tTE*+

"

2n*cos h

*n*cos h

*#n

+cos h

+

tTM*+

"

2n*cos h

*n+cos h

*#n

*cos h

+

(A2)

¹wo interfaces. We assume that the optical properties ofthe lipid film are identical to those of silicon dioxide withn2"n

1. The dye is at a distance d from the silicon and at

a distance d from the air. The interference terms forexcitation used in (14) are given by (A3) with the phaseshifts of (A4).

if TE*/"tTE

31

1#rTE10

e i'@*/5

1!rTE13

rTE10

ei'*/

if TM,1*/

"tTM31

1!rTM10

ei'@*/

1!rTM13

rTM10

e i'*/

if TM,/*/

"tTM31

1#rTM10

ei'@*/

1!rTM13

rTM10

ei'*/

(A3)

U*/"

4nn1

j*/

(d#d) cos h*/1

, U@*/"

4nn1

j*/

d cos h*/1

(A4)

The interference terms for emission used in (15) aregiven by (A5) with the phase shifts of (A6).

if TE065

"tTE13

1#rTE10

e i'@065

1!rTE13

rTE10

e i'065

if TM,1065

"tTM13

1!rTM10

ei'@065

1!rTM13

rTM10

ei'065

if TM,/065

"tTM13

1#rTM10

ei'@065

1!rTM13

rTM10

ei'065

(A5)

U065

"

4nn1

j065

(d#d) cos h0651

, U@065

"

4nn1

j065

d cos h0651

(A6)

¹hree interfaces. We distinguish the optical properties ofsilicon dioxide (refractive index n

1) and of the lipid film

(n2). The properties of the interfaces silicon to silicon

dioxide and silicon dioxide to lipid are comprised informal Fresnel coefficients r of a virtual interface at thelocation of the interface silicon dioxide to lipid accordingto (A7) to (A10).

if TE*/"tTE

32

1#rTE

1!rTE23

rTE e i'*/

if TM,1*/

"tTM32

1!rTM

1!rTM23

rTM ei'*/

if TM,/*/

"tTM32

1#rTM

1!rTM23

rTM ei'*/

(A7)

U*/"

4nn2

j*/

d cos h*/2

(A8)

if TE065

"tTE23

1#rTE

1!rTE23

rTE ei'065

if TM,1065

"tTM23

1!rTM

1!rTM23

rTM ei'065

if TM,/065

"tTM23

1#rTM

1!rTM23

rTM ei'065

(A9)

U065

"

4nn2

j065

d cos h0652

(A10)

The effective Fresnel coefficients r are obtained fromthe characteristic transfer matrices MTE and MTM of thelayer of silicon dioxide according to (A11) to (A15).

rTE"(mTE

11#mTE

12p0)p

2!(mTE

21#mTE

22p0)

(mTE11#mTE

12p0)p

2#(mTE

21#mTE

22p0)

(A11)

p0"n

0cos h

0, p

1"n

1cos h

1, p

2"n

2cos h

2(A12)

MTE"AmTE

11mTE

21

mTE12

mTE22B

"

cosA2nn

1j

d cos h1B !

i

p1

sinA2nn

1j

d cos h1B

!ip1sinA

2nn1

jd cos h

1B cos A2nn

1j

d cos h1B

(A13)

rTM"(mTM

11#mTM

12q0)q

2!(mTM

21#mTM

22q0)

(mTM11

#mTM12

q0)q

2#(mTM

21#mTM

22q0)

(A14)

215

q0"

cos h0

n0

, q1"

cos h1

n1

, q2"

cos h2

n2

(A15)

MTM"AmTM

11mTM

21

mTM12

mTM22B

"

cosA2nn

1j

d cos h1B !

i

q1

sinA2nn

1j

d cos h1B

!iq1sinA

2nn1

jd cos h

1B cosA2nn

1j

d cos h1B

(A14)

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216