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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 4 — Feb. 15, 2010
  • pp: 3719–3731
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Digital holographic reflectometry

Tristan Colomb, Stefan Krivec, Herbert Hutter, Ahmet Ata Akatay, Nicolas Pavillon, Frédéric Montfort, Etienne Cuche, Jonas Kühn, Christian Depeursinge, and Yves Emery  »View Author Affiliations


Optics Express, Vol. 18, Issue 4, pp. 3719-3731 (2010)
http://dx.doi.org/10.1364/OE.18.003719


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Abstract

Digital holographic microscopy (DHM) is an interferometric technique that allows real-time imaging of the entire complex optical wave-front (amplitude and phase) reflected by or transmitted through a sample. To our knowledge, only the quantitative phase is exploited to measure topography, assuming homogeneous material sample and a single reflection on the surface of the sample. In this paper, dual-wavelength DHM measurements are interpreted using a model of reflected wave propagation through a three-interfaces specimen (2 layers deposited on a semi-infinite layer), to measure simultaneously topography, layer thicknesses and refractive indices of micro-structures. We demonstrate this DHM reflectometry technique by comparing DHM and profilometer measurement of home-made SiO2/Si targets and Secondary Ion Mass Spectrometry (SIMS) sputter craters on specimen including different multiple layers.

© 2010 Optical Society of America

1. Introduction

Although digital holographic microscopy (DHM) allows the measurement of the entire complex optical wavefront [1

1. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-34-6994. [CrossRef]

], up to now only the phase signal is really exploited for quantitative measurement. Indeed, for reflection configurations, the phase signal is converted into topography under homogeneous material and single reflection interface assumption [1

1. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-34-6994. [CrossRef]

, 2

2. S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, “Surface topography of microstructures in lithium niobate by digital holographic microscopy,” Meas. Sci. Technol. 15, 961–968 (2004). [CrossRef]

, 3

3. J. Kühn, F. Charriére, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074,007–74,008 (2008). [CrossRef]

]; and into thickness and/or refractive index (RI) in transmission configurations [4

4. T. Ikeda, G. Popescu, R. Dasari, and M. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005). [CrossRef] [PubMed]

, 5

5. P. Marquet, B. Rappaz, P. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). URL http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-30-5-468. [CrossRef] [PubMed]

, 6

6. B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry Part A 73a, 895–903 (2008). [CrossRef]

, 7

7. B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, “Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye-enhanced dispersion of perfusion medium,” Opt. Lett. 33, 744–746 (2008). URL http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-7-744. [CrossRef] [PubMed]

, 8

8. H. Wahba and T. Kreis, “Characterization of graded index optical fibers by digital holographic interferometry,” Appl. Opt. 48, 1573–1582 (2009). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-8-1573. [CrossRef] [PubMed]

, 9

9. C. Yelleswarapu, S.-R. Kothapalli, and D. Rao, “Optical Fourier techniques for medical image processing and phase contrast imaging,” Opt. Commun. 281, 1876–1888 (2008). [CrossRef] [PubMed]

]. On contrary, in reflectance measurement systems, like time spectral interferometry, thin film thicknesses and RI are only measured from the reflected wavefront intensities [10

10. C. Moore, “Optical reflectometry elucidates layer thicknesses,” III-Vs Review 12, 34–37 (1999). [CrossRef]

, 11

11. P. Hlubina, J. Lunacek, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Applied Physics B: Lasers and Optics 92, 203–207 (2008). [CrossRef]

]. Recently, Debnath et al. used a spectrally-resolved phase-shifting interferometer to measure thicknesses of thin transparent layers [12

12. S. Debnath, M. Kothiyal, J. Schmit, and P. Hariharan, “Spectrally resolved white-light phase-shifting interference microscopy for thickness-profile measurements of transparent thin film layers on patterned substrates,” Opt. Express 14, 4662 (2006). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-11-4662. [CrossRef] [PubMed]

] thicker than 100 nm [13

13. S. K. Debnath, J. Kothiyal, P. Mahendra, Schmit, and P. Hariharan, “Spectrally resolved phase-shifting inter-ferometry of transparent thin films: sensitivity of thickness measurements,” Appl. Opt. 45, 8636–8640 (2006). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-34-8636. [CrossRef] [PubMed]

]. In this paper, quantitative complex data measured by dual-wavelength DHM allows the measurement of thiner layers in addition to topography and/or RIs for non-homogeneous multiple layer samples. For this purpose, a theoretical complex function (amplitude and phase), describing the reflected wave propagation through multiple layers, is established. In addition to standard models, our function models the sources coherence lengths, usually chosen in the hundreds of micrometers range in order to reduce parasitic interferences contributions. Topography, thicknesses and RIs determination using this function is demonstrated on home-made SiO2 test targets and different types of SIMS sputter craters on multiple layers.

2. DHM setup

Figure 1 presents the basic configuration of the dual-wavelength DHM used for the experimental validation and demonstration of the DHM reflectometry. This DHM (DHM R1100 ® from Lyncée Tec) has two different wavelength sources (682.5 nm and 660 nm, with respective coherence length (Lc) of 300 μm and 600 μm, that can be switched on and off alternately to provide two different 1024 × 1024 pixels holograms recorded on the CCD camera, resulting from the interference between the reference wave and the object wave reflected by the specimen. Usually, dual-wavelength DHM is used to increase the vertical measurement range by an extension of the phase ambiguity-free phase measurement range obtained on homogeneous material and single reflection samples [14

14. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15, 7231–7242 (2007). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7231. [CrossRef] [PubMed]

]. This ambiguity can also appear for multiple reflections. Furthermore, a dual-wavelength DHM doubles the equation numbers for the fitting procedure explained further. A microscope objective (MO) is used to improve the lateral resolution (LR), that is diffraction limited and depends on the numerical aperture (NA) of MO (LR= 0.61λ/NA) as in classical microscopy [15

15. C. Mann, L. Yu, C.-M. Lo, and M. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-22-8693. [CrossRef] [PubMed]

]. All results in this paper are achieved with a 10 × MO (NA= 0.3) that gives a lateral resolution about 1.4μm. The condenser lens (CL in Fig. 1) focalizes the wave near the back focal plane of the MO to deliver a collimated illuminating wave ψ ill. The optical path length (OPL) of the reference wave is adjusted by moving the optical path retarder (OPR). The maximal coherence plane, defined in Fig. 2, is placed on the sample surface at the position x 0 = 0 by calibrating the position of the OPR to have a maximal fringe contrast when the surface of a calibration mirror is focalized.

3. Complex wavefront measurement

For each wavelength λi, the hologram intensities are

IHi=Ri2+Oi2+RiOi*+Ri*Oi,
(1)

where Ri and Oi are respectively the reference and object waves for the wavelength λi. These digital holograms are filtered in the spatial frequency domain by using the technique explained in details in Ref. [16

16. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography.” Appl. Opt. 39, 4070–4075 (2000). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-23-4070. [CrossRef]

], to retain the real image term RiOi * (in reflection it corresponds to the topographic contrast, a hole giving a phase decrease).

Due to the finite coherence length of the source and due to non-perfecting homogeneous reference and object waves intensities on the CCD, the reconstructed amplitude is not homogeneous in the field of view when using a standard reconstruction. Therefore, a spatial amplitude normalization is performed using a reference hologram recorded on a flat reference surface (mirror) as specimen. This hologram is filtered to keep its RiOi,ref * term. The normalization of the phase [17

17. T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14, 4300–4306 (2006). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4300. [CrossRef] [PubMed]

], but also of the amplitude [3

3. J. Kühn, F. Charriére, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074,007–74,008 (2008). [CrossRef]

], is performed using the normalization reference hologram

Fig. 1. DHM R1100® setup. Two lasers sources can be alternatively switched on. The object wave Oi passes through a condenser CL and a microscope objective MO to illuminate the sample with a collimated beam. The reflected wave interferes with the reference wave Ri, whose optical path length can be adjusted with the optical path retarder OPR.
ΓH=1RiOi,ref*exp(iϕi,ref),
(2)

that multiplies the filtered object hologram:

ψi,H=ΓHRiOi,ref*=OiOi,refexp[i(ϕiϕi,ref)].
(3)

ψ i,H is then numerically propagated to the focus plane to obtain ψ i. The numerical propagation is computed in the convolution formalism, with the use of numerical lenses to compensate for possible aberrations, as described in details in Ref. [18

18. T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification and complete aberration compensation in digital holographic microscopy,” JOSA A 23, 3177–3190 (2006). URL http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-12-3177. [CrossRef] [PubMed]

]. The numerical reconstruction of the digital complex wavefront for 1024×1024 pixels hologram is done in less than 1/30 second.

One should note that ψ i can be different from the effective optical object wave. Indeed, for a single reflection on a sample surface, the amplitude of ψ i is clearly dependent on the position of the OPR due to the finite coherence length of the sources. In fact the recorded wave is different from the real wave and corresponds to

ψi,H=g(OPL,OPR)RiOi*,
(4)

where g(OPL,OPR) is the degree of coherence function that is defined by the Gaussian function:

g(OPL,OPR)=exp[-(OPLOPR)22σ2],
(5)
Fig. 2. Multilayer schematic. ψ ill is the illumination wave, (experimentally α = 0), and ψ r (r=0,…) are the multiple reflections of order r. x 0 is the position that corresponds to the Gaussian center of the degree of coherence function g(OPL,OPR).

with the coherence length Lc of the source defined as

Lc=2σ(2In2)12.
(6)

Here with multiple layer samples, as the degree of coherence influences the summation of the multiple reflected wave, it has to be taken into account. It is not the case in usual reflection DHM where the topography is proportional to the phase.

4. General equation of reflected complex wave on a three interfaces sample

Two different equivalent methods are usually used to model reflected wave propagation through multiple layers: the infinite summation of Fresnel amplitudes and the transfer-matrix method. The reader can refer to Ref. [19

19. P. Pereyra and A. Robledo-Martinez, “On the equivalence of the summation and transfer-matrix methods in wave propagation through multilayers of lossless and lossy media,” Eur. J. Phys. 30, 393–401 (2009). [CrossRef]

] to have more details about the two techniques. In this paper, a modified version of the infinite summation is developed to take the influence of the coherence length into account.

Figure 2 presents the schematic principle. The illumination wave ψ ill has a normal incidence because a collimated illumination beam is used (α = 0 ). ψ ill is depicted with an angle for didactic purpose to separate the different multiple reflections on the 3 layers with respective complex RI nk and thickness dk (d 3 = ∞). We deliberately choose to present only a 3 interfaces model to lighten the equations and because we will study sample with a maximum of 3 interfaces. The model can be generalized for more layers.

The reflection and transmission Fresnel coefficients on interface kl are, for α = 0

rkl=(nknl)(nk+nl),
(7)
tkl=2nk(nk+nl).
(8)

The different contributions to the reflected wave are in x = 0

ψ0=r01g(0,OPR),ψ1=t01r12t10exp(i2πλ2d1n1)g[(2d1n1),OPR]=Tg(X),ψ2=t01r12t10r12t10exp(i2πλ4d1n1)g[(4d1n1),OPR]+t01r12t23r21t10exp[i2πλ(2d1n1+2d2n2)]g[(2d1n1+2d2n2),OPR]=ATg(2X)+BTg(X+Y),ψ3=t01r12t10r12t10r12t10exp(i2πλ6d1n1)g[(6d1n1),OPR]+t01r12r10t12r23t21t10exp[i2πλ(4d1n1+2d2n2)]g[(4d1n1+2d2n2),OPR]+t01t12r23t21r10r12t10exp[i2πλ(4d1n1+2d2n2)]g[(4d1n1+2d2n2),OPR]+t01t12r23r21r23t21t10exp[i2πλ(2d1n1+4d2n2)]g[(2d1n1+4d2n2),OPR]=A2Tg(3X)+ABTg(2X+Y)+BCTg(2X+Y)+BDTg(X+2Y),
(9)

where is the complex real part, T = t 01 r 12 t 10, OPR = 2x 0 n 0, g(X)=g[(x),OPR]exp[i2πλ(x)],X = 2d 1 n 1, Y = 2d 2 n 2, A = r 12 r 10, B = t 12 r 23 t 21/r 12, C = r 10 r 12 and D = r 21 r 23. One can note that a simple rule allows deducing the component ψ r+1 from ψ r:

ψrψr+1ATg(mX+nY){AATg[(m+1)X+nY]ABTg[mX+(n+1)Y]BTg(mX+nY){BCTg[(m+1)X+nY]BDTg[mX+(n+1)Y]CTg(mX+nY){CATg[(m+1)X+nY]CBTg[mX+(n+1)Y]DTg(mX+nY){DCTg[(m+1)X+nY]DDTg[mX+(n+1)Y]
(10)

The wavefront in x = x 0 is therefore:

ψ(d,n,x0)=[r=0Nψrexp(i2πλ2x0n0)]*=r=0Nψr*exp(i2πλ2x0n0)
(11)

where d = [d 1,d 2] and n = [n 0,n 1,n 2,n 3]. One can note the complex conjugate operator in the summation, in order to stay consistent with the real image term reconstruction.

5. Models and fitting procedure

5.1. Structured deposition on a single layer

Figure 3 presents the model for a micro-structure of height h(x, y) and RI nd deposited on a wafer composed of a semi-infinite layer (d 2 = ∞) and RI nw. The theoretical function (Eq. 11) is now adapted to this model. For each position (x,y) of the sample, the reflected wavefront is

Fig. 3. Model for structures of height h(x,y) and RI nd deposited on a semi-infinite wafer (d 2 = ∞) with RI nw. The multiple layers function (Eq. 11) is defined from the respective origin 0, 0’ and so on, for each step.
ψ(x,y)=ψ[d(x,y),n(x,y),x0(x,y)]
(12)

where the different parameters depend on the deposit thickness h(x,y):

d(x,y)=[h(x,y),]
(13)
n(x,y)={[n0,nw,0,0]ifh(x,y)=0[n0,nd,nw,0]ifh(x,y)>0
(14)
x0(x,y)=h(x,y).
(15)

5.2. Etching in multiple layers

Figure 4 presents the model for an etching dug in a 3-layers wafer of respective RI and thickness (nk, dk, k = 1 to 3, d 3 = ∞). For each position (x,y) of the sample, the reflected wavefront ψ(x,y) (Eq. 12) is this time defined by the parameters:

d(x,y)={[d1+h(x,y),d2]ifh(x,y)<d1[d1+d2+h(x,y),]ifd1<h(x,y)<d1+d2[,]ifd1+d2<h(x,y)
(16)
n(x,y)={[n0,n1,n2,n3]ifh(x,y)<d1[n0,n2,n3,n3]ifd1<h(x,y)<d1+d2[n0,n3,n3,n3]ifd1+d2<h(x,y)
(17)
x0(x,y)=h(x,y)
(18)

where h(x,y) < 0 is the crater depth.

5.3. Fitting procedure

5.3.1. Normalization

A first normalization to compensate for aberrations and for non-homogeneity of wavefronts intensities, is achieved by the use of a reference hologram recorded in an assumed flat area of the investigated sample, by using the procedure explained in Section 3. But, it is still necessary to compensate for phase offset variations due to external vibrations. This task is achieved by computing the mean phase value ϕexp(h = 0) in an assumed homogeneous Region of Interest (ROI) corresponding to h = 0 (for example dashed rectangle in Fig. 5(b); and to suppress it to the experimental wavefront ψ exp. The theoretical model function ψ(x,y) is also normalized with the complex value computed for h = 0. The normalized experimental and theoretical functions are:

Fig. 4. Etching dug in 3-layers wafer model. The maximum coherence position is x 0 = 0. The etching is delimited by 5 different areas (I,V: outside crater; II and IV crater edges; and III maximum depth). The layers are defined by the RIs nk and thicknesses dk.
ψ̄exp(x,y)=ψexp(x,y)exp[iϕexp(h=0)],
(19)
ψ̄(x,y)=ψ(x,y)ψ(h=0).
(20)

5.3.2. Mean square fitting

MSE=i=12j=1Sψ̄ijψ̄ij,expdn,
(21)

5.3.3. Topographic image

When RIs and layer thicknesses are assumed to be known constants on the entire field of view (known sample characteristics or fitting results), the theoretical complex functions ψ̄i(h) are computed with h = hmin + pΔh, p = 0,Nh defines the precision, hmin the minimal height, N the number of points). Then for each reconstructed pixel (x,y), the height h(x,n) is defined as the abscissa that corresponds to the minimum of the function Σ2 i=1ψ̄i(h) - ψ̄i, exp(h(x,y)∣.

Fig. 5. Test target reconstructed wavefronts (a,c) amplitude and (b,d) phase images for λ 1 (a,b) and λ 2 (c,d). Steps are manufactured to be nominally 375, 525, 975, 1200 and 1275 nm high. The rectangles in (a) correspond to the ROIs used for the spatial averaging of complex data for RIs determination, the dashed rectangle in (b) defines the ROI used for the phase normalization.

6. Results

6.1. Structured deposition on single layer

Two home-made test targets, composed of different thickness steps of SiO2 deposited on a Si wafer, are measured by DHM reflectometry. The first target is composed of low resolution (LR) steps of 375, 525, 975, 1200 and 1275 nm in thickness and the second one is composed of high resolution (HR) steps of 25, 35, 65, 80 and 85 nm in thickness (fabrication precision is about ±3%).

Figure 5 presents the reconstructed complex data achieved with the two wavelengths. One can note that the normalization described in Eq. 19 is achieved by computing exp[-exp(h = 0)] as the averaging phase value acquired in the dashed rectangle area defined in Fig. 5(b).

Fig. 6. Topography of (a) low, and (c) high resolution test targets; (b, d) respective profiles comparison between DHM [8 pixels average profile along red line in (a,c)] and Tencor Alphastep 200 profilometer. The standard deviations between the vertical lines are used to define the uncertainty in Table 1.

6.1.1. Refractive index determination

For these samples, the model defined in Fig. 3 is used with n 0 = nair = 1, nd = n SiO2. As the deposition parameters (temperature, pressure, deposition rate, and so on) influence the RI of wafer and deposit [20

20. C. Cobianu, C. Pavelescu, and A. Paunescu, “The effect of deposition conditions on the refractive index of LTCVD SiO2 films,” Journal of Materials Science Letters 4, 1419–1420 (1985). [CrossRef]

], we will use the first target with the larger height differences to determine the RIs, enabling then the measurement of the step heights for the two targets (the second target was manufactured with same deposition parameters). As the RIs are assumed homogeneous and to reduce the computation time, the least square fitting for the real RI determination (the imaginary RI is neglected) is carried with the average complex data contained in ROIs [white rectangles on Fig. 5(a)] and gives n Si02 = 1.4706 and nSi = 3.8051.

6.1.2. Step heights determination

In order to validate the step height measurements, profiles measured with a Tencor Alphastep 200 stylus profilometer are compared to DHM reflectometry measurements. They are two different ways to measure the step heights: either the mean ROI values are considered (column DHM ROI in Table 1), or the topographic images [Fig. 6(a,c)] are computed as explained in Section 5.3.3. The extracted profiles are compared with profilometer results [Fig. 6(b,d)]. For DHM ROI, no uncertainty is defined as the fit is obtained on the average complex value on the entire step. On contrary, with the profiles extraction, the uncertainty for the profilometer and for DHM is defined similarly by the addition of the standard deviation of the measurement along a profile taken in assumed flat area, and the standard deviation of the profile values between the vertical lines for each step in Fig. 6(b) in an assumed flat area.

Table 1. Comparison between theoretical step height and their measurement with DHM reflectometry and stylus profilometer

table-icon
View This Table

6.2. SIMS sputter crater

Secondary Ion Mass Spectrometry (SIMS) is an outstanding analytical technique for surface characterization and in-depth information with applications in a broad range of scientific and industrial fields [22

22. D. S. McPhail, “Applications of Secondary Ion Mass Spectrometry (SIMS) in Materials Science,” Journal of Materials Science 41, 873–903 (2006). [CrossRef]

]. In this work we used a TOF.SIMS5 instrument (IONTOF, Germany), in order to prepare craters of different depths via sputtering with O+ 2 (Energy: 1 keV, sputter current: 254 nA). For SIMS data treatment, it is of major importance to obtain the accurate depth of sputter craters [23

23. Y. Yamamura and M. Ishida, “Simulation of oxide sputtering and SIMS depth profiling of delta-doped layer,” Applied Surface Science 203–204, 6268 (2003). [CrossRef]

]. Here we demonstrate the capability of DHM reflectometry in order to provide this information even for samples which include thin transparent layers.

Fig. 7. 3-layers (Au/SiO2/Si) SIMS sample reconstructed wavefronts (a,c) amplitude and (b,d) phase images for λ 1 (a,b) and λ 2 (c,d). The dashed rectangle in (a) delineates the ROI used for phase normalization.

The first analyzed crater is sputtered in a 3 interfaces wafer composed of gold (n 1 = 0.161+3.445812i @670.2 nm, d 1 = 40 nm), SiO2 (n 2 = 1.4560 @670 nm, d 2 = 100 nm) and finally a Si substrate (n 3 = 3.815103+0.014041i @673.8 nm). The RIs around 670nm is used as the average RIs for 660nm and 680nm. From Ref. [21], the theoretical RI differences between the source wavelengths and the used RI at about 670nm are below 0.001 for SiO2, 0.02 for Si and 0.004 for Au. As the deposit process can shift the RI with higher magnitude [20

20. C. Cobianu, C. Pavelescu, and A. Paunescu, “The effect of deposition conditions on the refractive index of LTCVD SiO2 films,” Journal of Materials Science Letters 4, 1419–1420 (1985). [CrossRef]

], this difference is negligible for topographic determination.

From the measured complex data presented in Fig. 7, the topographic image [Fig. 8(a)] enables to compare the depths obtained with DHM (-252.8±1.9 nm) and the profilometer (-249.3±5.4 nm).

Fig. 8. (a) Topographic image of SIMS crater sputtered in three layers of 40 nm Au, 100 nm SiO2 and Si; (b) profile comparison between DHM [8 pixels average profile along red line] and Tencor Alphastep 200 profilometer.

Now, two different SiO2 layer thicknesses wafer (certified 35 and 100 nm) with sputtered craters are investigated. The reconstructed amplitude and phase images for λ 1 are presented in Fig. 9.

As for RIs determination, the layer thicknesses are computed by the mean square fitting of average values in ROIs (white rectangles in Fig. 9), with layer thickness and depth as parameters. The fit gives respectively d 1 = 103 nm, hmin = -226.7 nm and d 1 = 33.7 nm, hmin = -148.8 nm. From the computed thicknesses and theoretical RIs, the topographic images [Figs. 10(a,c)], and the respective profiles are computed and compared to profilometer [Fig. 10(b,d)].

Fig. 9. SIMS sample reconstructed wavefronts (a,c) amplitude and (b,d) phase images for λ 1. The SiO2 layer thicknesses are assumed to be respectively (a,b) 100 nm and (c,d) 35 nm. The dashed rectangles delineate the ROI used for the spatial averaging for the phase normalization and the plain line rectangles define the ROI for bottom crater average values.
Fig. 10. (a,c) Topographic images of SIMS crater sputtered in two layers of (a) 100 nnm and (c) 35 nm SiO2 and Si; (b,d) profiles comparison between DHM [8 pixels average profile along red line] and Tencor Alphastep 200 profilometer.

7. Results discussion

Measured and theoretical RIs (Table 1) are in very good agreement. The error on Si RI is smaller than 10-3 and for the deposit SiO2 smaller than 2 × 10-2. The larger difference for SiO2 RI can be explained by two reasons. The SiO2 RI depends on the deposition procedure [20

20. C. Cobianu, C. Pavelescu, and A. Paunescu, “The effect of deposition conditions on the refractive index of LTCVD SiO2 films,” Journal of Materials Science Letters 4, 1419–1420 (1985). [CrossRef]

] and on thickness for thin layer (0–10 nm) [24

24. A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, “Measurements and modeling of thin silicon dioxide films on silicon,” J. Electrochem. Soc. 1, 234–238 (1990). [CrossRef]

, 25

25. Y. Wang and E. A. Irene, “Consistent refractive index parameters for ultrathin SiO2 films,” J. Vac. Sci. Technol. B 18, 279–282 (2000). [CrossRef]

].

The stylus profilometer and DHM reflectometry measurements are also in very good agreement as shown in Figs. 6, 8 and 10. In Table 1, only the first LR step height uncertainties do not overlap for 3.5 nm. That can be explained if profiles are not taken exactly in the same position, in addition with some other error sources. First, the noise on the complex wavefront measurement (residual parasitic interferences, shot noise, and so on) has influence on height measurement, and especially on thiner layer as shown in the HR target of Table 1, where the incertitude for the smallest step is about 2.5 times larger than the higher ones of HR target. One can also note the same behavior in Figs. 10(c,d), where small depths that correspond to thin SiO2 layer are noisier; especially the concentric pattern on reconstructed amplitude [Fig. 9(c)], coming from a parasitic interference, gives an important contribution in the reconstructed depth field [Fig. 10(c)]. This problem is inherent to the DHM setup configuration. Reduced coherence length, small misalignment of optics or numerical spatial filtering could permit to avoid most of these parasitic interferences. Nevertheless, it is very difficult to avoid all of them, especially for a DHM microscope configured with a turret of several magnification MO.

Secondly, an error on the RI determination for the reasons previously given, contributes also to a mismatch between real and measured heights. This effect could also explain the abrupt and noisier transition near layer interfaces in graphs (c,d) of Figs. 8 and 10. Finally, the non dispersion assumption and normal incident wave contributes to increase the uncertainty. An advantage of DHM can be seen in Fig. 6(d), where step edges are sharper for DHM reflectometry than for profilometer. Indeed the stylus tip size induces rounded edges transition. Furthermore, DHM has the advantage to avoid mechanical calibration to convert detected signal in height, on contrary of profilometer or AFM instruments; DHM calibration depends only on the wavelength sources.

Finally, the measured layer thicknesses of SiO2 from the SIMS sample (Fig. 10) coincide very well with the certified values (33.7 nm and 103 nm for 35 nm and 100 nm certification). The difference can be explained by the same arguments as before: complex data noise, mismatch between real and used RI.

One notes that the DHM reflectometry principle is demonstrated for a small magnification MO (10×). For higher magnification, the basic principle is still valid if the illumination wave could still be assumed collinear. If this assumption could not be satisfied, the incident angles should be in the theoretical equation. Furthermore, for high NA, the depth-of-focus (DOF) limits the precision for layer thickness larger or near the DOF. Indeed, the waves reflected from interfaces out of DEF gives an out-of-focus contribution that can be eventually shifted compared to the first interface if the sample is not perpendicular to the optical axis.

8. Conclusion

These results show that DHM reflectometry allows full field topographic thickness of semi-transparent layers micro-structures, with a resolution better than 2 nm for layer larger than 20–30 nm. Furthermore, we demonstrate that DHM reflectometry allows RIs determination with a precision better than 2×10-2 for the deposited material RI and 1×10-3 for the wafer RI. With this new DHM measurement modality, surface topography of both homogeneous and non-homogeneous material samples are measured precisely. This opens new application fields for DHM, like thin films and multiple material specimen investigation.

Acknowledgments

The research leading to these results has received funding from the European Community’s Seventh Framework Programme FP7/2007–2013 under grant agreement no 216105. The authors thank Bamdad Afra from the Advanced Photonics Laboratory in EPFL (Ecole Polytechnique Fédérale de Lausanne) for the delivery of the stylus profilometer measurements. Ahmet Ata Akatay is supported by the CCMX NMMC grant: “Study of complex interfacial properties with nanoscale resolution optical microscopy”.

References and links

1.

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-34-6994. [CrossRef]

2.

S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, “Surface topography of microstructures in lithium niobate by digital holographic microscopy,” Meas. Sci. Technol. 15, 961–968 (2004). [CrossRef]

3.

J. Kühn, F. Charriére, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, “Axial sub-nanometer accuracy in digital holographic microscopy,” Meas. Sci. Technol. 19, 074,007–74,008 (2008). [CrossRef]

4.

T. Ikeda, G. Popescu, R. Dasari, and M. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005). [CrossRef] [PubMed]

5.

P. Marquet, B. Rappaz, P. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). URL http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-30-5-468. [CrossRef] [PubMed]

6.

B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, “Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer,” Cytometry Part A 73a, 895–903 (2008). [CrossRef]

7.

B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, “Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye-enhanced dispersion of perfusion medium,” Opt. Lett. 33, 744–746 (2008). URL http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-7-744. [CrossRef] [PubMed]

8.

H. Wahba and T. Kreis, “Characterization of graded index optical fibers by digital holographic interferometry,” Appl. Opt. 48, 1573–1582 (2009). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-8-1573. [CrossRef] [PubMed]

9.

C. Yelleswarapu, S.-R. Kothapalli, and D. Rao, “Optical Fourier techniques for medical image processing and phase contrast imaging,” Opt. Commun. 281, 1876–1888 (2008). [CrossRef] [PubMed]

10.

C. Moore, “Optical reflectometry elucidates layer thicknesses,” III-Vs Review 12, 34–37 (1999). [CrossRef]

11.

P. Hlubina, J. Lunacek, D. Ciprian, and R. Chlebus, “Spectral interferometry and reflectometry used to measure thin films,” Applied Physics B: Lasers and Optics 92, 203–207 (2008). [CrossRef]

12.

S. Debnath, M. Kothiyal, J. Schmit, and P. Hariharan, “Spectrally resolved white-light phase-shifting interference microscopy for thickness-profile measurements of transparent thin film layers on patterned substrates,” Opt. Express 14, 4662 (2006). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-11-4662. [CrossRef] [PubMed]

13.

S. K. Debnath, J. Kothiyal, P. Mahendra, Schmit, and P. Hariharan, “Spectrally resolved phase-shifting inter-ferometry of transparent thin films: sensitivity of thickness measurements,” Appl. Opt. 45, 8636–8640 (2006). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-34-8636. [CrossRef] [PubMed]

14.

J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15, 7231–7242 (2007). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7231. [CrossRef] [PubMed]

15.

C. Mann, L. Yu, C.-M. Lo, and M. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-22-8693. [CrossRef] [PubMed]

16.

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography.” Appl. Opt. 39, 4070–4075 (2000). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-23-4070. [CrossRef]

17.

T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14, 4300–4306 (2006). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4300. [CrossRef] [PubMed]

18.

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification and complete aberration compensation in digital holographic microscopy,” JOSA A 23, 3177–3190 (2006). URL http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-12-3177. [CrossRef] [PubMed]

19.

P. Pereyra and A. Robledo-Martinez, “On the equivalence of the summation and transfer-matrix methods in wave propagation through multilayers of lossless and lossy media,” Eur. J. Phys. 30, 393–401 (2009). [CrossRef]

20.

C. Cobianu, C. Pavelescu, and A. Paunescu, “The effect of deposition conditions on the refractive index of LTCVD SiO2 films,” Journal of Materials Science Letters 4, 1419–1420 (1985). [CrossRef]

21.

URL http://refractiveindex.info/.

22.

D. S. McPhail, “Applications of Secondary Ion Mass Spectrometry (SIMS) in Materials Science,” Journal of Materials Science 41, 873–903 (2006). [CrossRef]

23.

Y. Yamamura and M. Ishida, “Simulation of oxide sputtering and SIMS depth profiling of delta-doped layer,” Applied Surface Science 203–204, 6268 (2003). [CrossRef]

24.

A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, “Measurements and modeling of thin silicon dioxide films on silicon,” J. Electrochem. Soc. 1, 234–238 (1990). [CrossRef]

25.

Y. Wang and E. A. Irene, “Consistent refractive index parameters for ultrathin SiO2 films,” J. Vac. Sci. Technol. B 18, 279–282 (2000). [CrossRef]

OCIS Codes
(120.1840) Instrumentation, measurement, and metrology : Densitometers, reflectometers
(120.5700) Instrumentation, measurement, and metrology : Reflection
(230.4170) Optical devices : Multilayers
(310.0310) Thin films : Thin films
(090.1995) Holography : Digital holography

ToC Category:
Holography

History
Original Manuscript: December 8, 2009
Revised Manuscript: February 2, 2010
Manuscript Accepted: February 3, 2010
Published: February 5, 2010

Citation
Tristan Colomb, Stefan Krivec, Herbert Hutter, Ahmet Ata Akatay, Nicolas Pavillon, Frédéric Montfort, Etienne Cuche, Jonas Kühn, Christian Depeursinge, and Yves Emery, "Digital holographic reflectometry," Opt. Express 18, 3719-3731 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-4-3719


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References

  1. E. Cuche, P. Marquet, and C. Depeursinge, "Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms," Appl. Opt. 38, 6994-7001 (1999). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-34-6994. [CrossRef]
  2. S. de Nicola, P. Ferraro, A. Finizio, S. Grilli, G. Coppola, M. Iodice, P. De Natale, and M. Chiarini, "Surface topography of microstructures in lithium niobate by digital holographic microscopy," Meas. Sci. Technol. 15, 961-968 (2004). [CrossRef]
  3. J. Kühn, F. Charrière, T. Colomb, E. Cuche, F. Montfort, Y. Emery, P. Marquet, and C. Depeursinge, "Axial sub-nanometer accuracy in digital holographic microscopy," Meas. Sci. Technol. 19, 074007 (2008). [CrossRef]
  4. T. Ikeda, G. Popescu, R. Dasari, and M. Feld, "Hilbert phase microscopy for investigating fast dynamics in transparent systems," Opt. Lett. 30, 1165-1167 (2005). [CrossRef] [PubMed]
  5. P. Marquet, B. Rappaz, P. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, "Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy," Opt. Lett. 30, 468-470 (2005). URL http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-30-5-468. [CrossRef] [PubMed]
  6. B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. Magistretti, and P. Marquet, "Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer," Cytometry Part A 73a, 895-903 (2008). [CrossRef]
  7. B. Rappaz, F. Charrière, C. Depeursinge, P. Magistretti, and P. Marquet, "Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye-enhanced dispersion of perfusion medium," Opt. Lett. 33, 744-746 (2008). URL http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-7-744. [CrossRef] [PubMed]
  8. H. Wahba and T. Kreis, "Characterization of graded index optical fibers by digital holographic interferometry," Appl. Opt. 48, 1573-1582 (2009). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-8-1573. [CrossRef] [PubMed]
  9. C. Yelleswarapu, S.-R. Kothapalli, and D. Rao, "Optical Fourier techniques for medical image processing and phase contrast imaging," Opt. Commun. 281, 1876-1888 (2008). [CrossRef] [PubMed]
  10. C. Moore, "Optical reflectometry elucidates layer thicknesses," III-Vs Review 12, 34-37 (1999). [CrossRef]
  11. P. Hlubina, J. Lunacek, D. Ciprian, and R. Chlebus, "Spectral interferometry and reflectometry used to measure thin films," Applied Physics B: Lasers and Optics 92, 203-207 (2008). [CrossRef]
  12. S. Debnath, M. Kothiyal, J. Schmit, and P. Hariharan, "Spectrally resolved white-light phase-shifting interference microscopy for thickness-profile measurements of transparent thin film layers on patterned substrates," Opt. Express 14, 4662 (2006). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-11-4662. [CrossRef] [PubMed]
  13. S. K. Debnath, J. Kothiyal, Mahendra P. Schmit, and P. Hariharan, "Spectrally resolved phase-shifting interferometry of transparent thin films: sensitivity of thickness measurements," Appl. Opt. 45, 8636-8640 (2006). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-34-8636. [CrossRef] [PubMed]
  14. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, "Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition," Opt. Express 15, 7231-7242 (2007). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7231. [CrossRef] [PubMed]
  15. C. Mann, L. Yu, C.-M. Lo, and M. Kim, "High-resolution quantitative phase contrast microscopy by digital holography," Opt. Express 13, 8693-8698 (2005). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-22-8693. [CrossRef] [PubMed]
  16. E. Cuche, P. Marquet, and C. Depeursinge, "Spatial filtering for zero-order and twin image elimination in digital off-axis holography," Appl. Opt. 39, 4070-4075 (2000). URL http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-23-4070. [CrossRef]
  17. T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, "Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram," Opt. Express 14, 4300-4306 (2006). URL http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4300. [CrossRef] [PubMed]
  18. T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, "Numerical parametric lens for shifting, magnification and complete aberration compensation in digital holographic microscopy," J. Opt. Soc. Am. A 23, 3177-3190 (2006). URL http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-12-3177. [CrossRef] [PubMed]
  19. P. Pereyra and A. Robledo-Martinez, "On the equivalence of the summation and transfer-matrix methods in wave propagation through multilayers of lossless and lossy media," Eur. J. Phys. 30, 393-401 (2009). [CrossRef]
  20. C. Cobianu, C. Pavelescu, and A. Paunescu, "The effect of deposition conditions on the refractive index of LTCVD SiO2 films," Journal of Materials Science Letters 4, 1419-1420 (1985). [CrossRef]
  21. URL http://refractiveindex.info/.
  22. D. S. McPhail, "Applications of Secondary Ion Mass Spectrometry (SIMS) in Materials Science," J. Mater. Sci. 41, 873-903 (2006). [CrossRef]
  23. Y. Yamamura and M. Ishida, "Simulation of oxide sputtering and SIMS depth profiling of delta-doped layer," Applied Surface Science 203-204, 62-68 (2003). [CrossRef]
  24. A. Kalnitsky, S. P. Tay, J. P. Ellul, S. Chongsawangvirod, J. W. Andrews, and E. A. Irene, "Measurements and modeling of thin silicon dioxide films on silicon," J. Electrochem. Soc. 1, 234-238 (1990). [CrossRef]
  25. Y. Wang and E. A. Irene, "Consistent refractive index parameters for ultrathin SiO2 films," J. Vac. Sci. Technol. B 18, 279-282 (2000). [CrossRef]

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