The interferogram of a high index phase mask of 200 nm period under normal incidence of a collimated beam at 244 nm wavelength with substantially suppressed zeroth order produces a 100 nm period grating in a resist film under immersion. The paper describes the phase mask design, its fabrication, the effect of electron-beam lithographic stitching errors and optical assessment of the fabricated sub-cutoff grating.
© 2010 OSA
Gratings with periods in the 100 nm range represent a growing interest in a number of applications. They have been used in X-ray spectroscopy [1,2], and they are currently used as test structures in the monitoring of microelectronic processes . In the optical domain they are at the edge of the region where first diffraction orders reach their cut-off and, very importantly, where the variety of available high-index transparent materials drastically shrinks. Most applications are therefore based on zeroth order effects for polarization processing: wave plates for the UV, where use is made of the possibly large difference of effective index between the TE and TM fundamental grating modes, as shown in ref  in the IR range. Such effects also occur in grating polarizers that use photonic crystal effects in conformally undulating multilayers  and in grating polarizers that use zeroth order resonant reflection mediated by +/− first order coupling to a waveguide mode, as shown in ref  in the near IR range. The most interesting optical function in terms of industrial impact is the low loss metal wire grid polarizer used in liquid-crystal displays (LCDs), where the filtered TE polarization is reflected and then rotated, instead of being absorbed, and is therefore given a second opportunity to be transmitted . This last application, as well as applications for light trapping in semi-conductor solar cells  and wide band omnidirectional, antireflection surfaces , requires an efficient, reliable and large area printing process, in addition to high spatial-frequency microstructuring.
There are only a few technologies available for the writing of 100 nm period gratings. Step-and-repeat cameras equipped with a 193 nm ArF excimer laser for the 45 nm node provide one possible approach . However, they give restricted flexibility in terms of substrate dimensions, weight and material. A feature size of 50 nm is within reach for direct electron-beam lithographic (EBL) patterning - but the pattern generation process is inherently slow - and the versatility remains limited. A substantially more flexible approach is that of the Nanoruler  which permits the writing of short pitch gratings on almost unlimited substrate sizes by the scanning of an elementary interferogram. This approach has notably succeeded in printing large-area 50 nm period gratings . Yet another approach is demonstrated in the present paper, which also relies upon the scanning of an interferogram. The interferogram is here produced by a phase mask flying over a resist-coated substrate . Our view is that a phase-mask writing strategy has great potential when very large area and high coherence gratings are required. The mechanical control is significantly simplified and the effects of environmental parameters are considerably reduced. The challenge along this road, at the 100 nm period milestone, is the realization of the phase mask structure for the cancellation of the zeroth transmitted order while preventing the cutoff of the +/− transmitted first orders. This encompasses the search for the prescribed depth and duty cycle of a binary corrugation in an appropriate high index thin film material transparent at the shortest possible wavelength. This challenge is at the edge of what is practically feasible at both the electromagnetic and materials levels.
2. Description of the phase mask
Printing a 100 nm period grating by means of a phase mask as illustrated in Fig. 1 first sets the question of what structure can produce a 100 nm period interferogram with sufficient uniformity and spatial frequency purity. Uniformity is an essential characteristic of the interferogram, since it guarantees the invariance of the printed grating whatever the distance between the phase-mask and the resist-coated substrate.
2.1 Geometrical requirements
The conditions for producing a uniform phase mask under normal exposure are the cut-off of all transmitted diffraction orders larger than 1, and the extinction of the 0th transmitted order. The condition for the existence of a single spatial frequency interference pattern of period p under the phase mask produced by the + and – 1st order is:
2.2 Exposure wavelength selection
Expression (1) sets a condition on the exposure wavelength: the 1st order cut-off wavelength of a 200 nm period phase mask required to print a 100 nm period grating is 200 nm, which implies that the only available exposure wavelengths that can be considered in situations with air between the phase-mask and the substrate is the 193 nm line of an ArF excimer laser or the 157 nm line of an F2 laser. The extreme UV wavelength of 13.2 nm cannot be considered in a transmission phase since the index contrast at such wavelength is too close to 1:1. An attractive wavelength range would be the 244-266 nm wavelength window, which is well covered by different laser technologies: the KrF laser at 248 nm, the fourth harmonic of a Nd:YAG laser (λ = 266 nm) and the doubled Ar ion laser, the latter being currently used extensively for the writing of fiber Bragg gratings. In the 244-266 nm wavelength range, however, the +/− 1st orders of a 200 nm period phase mask in air are cut-off. A +/−1st order transmission interferogram can therefore only be produced if the exposure is performed under immersion.
2.3 Zeroth order extinction
As shown in Ref , the extinction of the 0th transmitted order in a phase mask used in the single order regime (where the period is only slightly larger than the exposure wavelength) is not possible with a standard corrugated fused silica substrate, therefore one has to resort to a high-index layer deposited on the quartz substrate in which the corrugation is realized. The only existing high-index material that is transparent at 193 nm and that could possibly be used is LuAG , which has been developed as a high refractive-index lens material to achieve the 34 nm half-pitch node by using immersion lithography . The LuAG material is however not yet available in thin-film form and therefore the phase mask route for use of the 193 nm wavelength is not currently open. The only phase-mask solution is therefore to turn to the 244-266 nm wavelength window. In this wavelength range, there are a number of transparent high-index materials available in thin-film form: HfO2, diamond, Si3N4 for instance.
2.4 Phase mask material selection
Having opted for the 244 – 266 nm window, the conditions or efficient diffraction under immersion must still be fulfilled. A standard quartz phase mask with a 200 nm period would produce almost negligible diffraction under immersion in water, but it is a fortunate coincidence that resorting to a high index corrugation for cancelling the 0th transmitted order also provides the condition for efficient diffraction of the +/−1st orders. Considering water as an immersion liquid (n = 1.38 at 244 nm wavelength ), and LPCVD (Low Pressure Chemical Vapor Deposition) silicon nitride as the index corrugation (n = 2.31 + 0.002i at 244 nm ) gives an index contrast of 2.31/1.38 = 1.67, which is even larger than 1.51/1 = 1.51 - where 1.51 is the refractive index of fused quartz at 244 nm wavelength. Si3N4 is the preferred high index material, in spite of its non-negligible absorption loss, because it is widely used as a passivation layer in microelectronics and can be etched with precision, resulting in quasi-vertical walls.
As shown in Fig. 2 , the high-index phase mask consists of a fused quartz substrate of refractive index ns, a binary corrugation of thickness d, period Λ, line width L of index nl, and groove width S of index ng. The medium underneath the grating, which has a refractive index of ng, is typically air, but it is here pure distilled water.
3. Fabrication of the high index phase mask
Modelling of the phase mask is based on a grating-mode approach  which has been used since then to render the operation of high index contrast binary gratings more intelligible . In the phase mask of the present paper, the operating conditions (no transmitted orders higher than 1, and normal incidence) imply that only two even grating modes can propagate and be excited. As the interference contrast of the TM polarization is never 100% and can even fade completely when the +/−1st diffracted orders are directed at 45° relative to the normal, only the TE polarization is considered. There are two conditions for the 0th order extinction: on one hand the TE0 and TE2 grating modes must be excited equally by an incident plane wave through the phase-mask substrate. (The odd TE1 mode is not excited, since its field overlap with a normally incident plane wave is zero). On the other hand, the phase difference between these two modes, upon propagation through the grating layer, is close to π. It was shown in  that it is only in a very large index contrast corrugation involving a semiconductor layer that the reflection and mode coupling at the grating layer boundaries must be considered. In the present structure the TE0-TE2 interference scheme can simply be understood as a balanced Mach-Zehnder interferometer giving zero field in one output branch (the branch corresponding to the 0th order). The modal representation of the present structure is further analyzed in another paper . It is sufficient here simply to use an existing code based on the modal method  to determine the quartz-Si3N4-water structure that best suppresses the 0th transmitted order. The transmission of the structure is represented in Fig. 3 at λ = 244 nm and Λ = 200 nm with water as immersion liquid. Figure 3 top-left gives the power diffracted along the 0th and +/−1st orders versus the corrugated Si3N4 layer thickness at a fixed line/space ratio of 0.32. Figure 3 top-right shows the transmission versus the Si3N4 line width at a fixed layer thickness of 151 nm.
The modeling takes into account the absorption loss of silicon nitride. One checks that the phase difference between the TE0 and TE2 modes that is accumulated during propagation through the layer is close to π, i.e. for the selected thickness of silicon nitride:Figures 3 show that it is not possible to fully cancel the 0th transmitted order. The residual 4% in the 0th transmitted order results in a non-negligible over-modulation of the interferogram by a spatial frequency equal to twice the desired frequency as shown in Fig. 3 (bottom) versus the abscissa along the k-vector of the phase-mask grating. This 20% amplitude modulation can readily be smoothed out by using a high contrast resist. Complete suppression of the 0th order could be obtained by using a higher index layer such as HfO2; however, a binary grating with vertical walls is difficult to fabricate because the etching of HfO2 requires the ionic kinetic energy component of a RIBE process (Reactive Ion Beam Etching) to remove the non-volatile etching products from the grooves, this erosion giving rise to slanted walls (a RIE process using BCl3, O2 and/or Cl2 chemistries produces some residues which obstruct the grooves being etched). Table 1 gives the characteristics of the phase mask grating after using the optimization option of the modal code .
3.2 Phase mask fabrication and characterization
The structures were fabricated on 4” diameter UV-grade fused silica wafers. The first process was the LPCVD deposition of a 150 nm thick Si3N4 layer. The samples have been processed by the different partners for E-beam writing and Si3N4 etching. The three partners (Laboratoire de Photonique et des Nanostructures, Marcoussis, France, Joensuu University, Finland, and Glasgow University, United Kingdom) used electron-beam lithography for the phase-mask pattern definition according to the specifications on the period and line/space ratio, and RIE for the etching of the Si3N4 layer (Table 1). The fabrication conditions used are given in Ref .
The optical characterization of the phase mask grating must be carried out under immersion conditions in order to permit the 1st orders to propagate. The + 1st and −1st orders were measured by using a trapezoid UV-grade fused-silica prism. The gap between the phase mask and the prism was filled with water. The transmitted diffraction orders at 244 nm wavelength were measured by means of a silicon photodiode (Thorlabs S120 UV). The best samples exhibit less than 4% 0th order and more than 20% in each of the 1st orders. It is however an intriguing feature that the 1st order efficiency is relatively small (20% instead of the theoretically expected 30%). The measurements made on the whole set of phase-mask samples fabricated by the partners reveal that there is clearly an overall deficit of transmitted diffracted power which could possibly be explained by the silicon nitride layer being more absorptive than the values given in the literature ; it was however checked experimentally by absorption measurements that the complex index at 244 nm wavelength of the Si3N4 used is very close to that given in the literature (2.31 + 0.027i). The reason for this efficiency discrepancy is to be found in the geometry of the grooves as revealed from the analysis of the AFM and SEM scans of Fig. 5 and 6 .
The measurement of the diffraction efficiencies led to the observation of a striking feature of e-beam writing: the stitching errors. Figure 4 is the image of a beam cross-section on a fluorescent screen intercepting one of the 1st orders diffracted by a first series of phase masks. The extraction and transformation of the diffracted order at 244 nm wavelength trapped in the fused quartz substrate was made by means of a high purity semi-spherical drop of water placed at the diffracted beam impact. The far-field diffracted beam is distorted by the aberration of the water drop; however the traces of the e-beam writing fields and sub-fields are clearly recognizable. The contrast in the diffracted beam cross-section is high, which means that the stitching errors in this first series of phase masks are so large that there is substantial destructive interference along the field stitching lines on the beam cross-section. This qualitatively illustrates how severe the impact of the stitching errors can be on the diffracted wave front and on the homogeneity of the power density over the cross-section. To quantitatively retrieve the stitching errors from the far field picture of Fig. 4, one would have to solve the 2D inverse diffraction problem which is a difficult task beyond the scope of the present work. It can also be said that such analysis has become less relevant as the new generation of e-beams have practically reduced the stitching errors to the few nanometer range. A second series of phase masks was fabricated following another writing strategy : field stitchings can be reduced to their lowest value (below 20nm in the case of the VISTEC 5000 + e-beam machine of partner LPN) by a proper beam deflection calibration performed after measurement of the height of the sample surface. No such cross-section structure as seen in Fig. 4 was observed any more.
The groove profile of the phase masks was first measured by means of an AFM. Figure 5 is a typical AFM scan using a very fine tip (Veeco TESP-HAR with 5:1 aspect ratio). No precise information on the groove and line widths can be retrieved because of the convolution between the tip and the actual line profile, which is especially critical with a 200 nm period and an aspect ratio as high as 3. One important information can however be gained as the AFM was calibrated just before the measurement: the depth of the grooves is 130 nm and not the desired 150 nm.
The access to the line and groove widths was obtained by making a slice across the Si3N4 phase mask grating by focused ion beam (FIB) followed by a SEM scan whose picture is given in Fig. 6. The black layer on the corrugation is a carbon layer deposited to render the sample conductive. Subtracting the black layer thickness to the width of the Si3N4 line gives a line width of 56 nm. The walls of the grooves are remarkably vertical and there is some rounding at the groove bottom. This means that the e-beam lithography and the reactive etching achieved lateral dimensions according to the specifications within a few nanometers.
The depth of the grooves cannot be measured with high accuracy from the SEM of Fig. 6 because of the tilt of the sample in the electron beam. However, knowing the tilt angle and dividing the observed groove depth by the cosinus of this angle gives a depth estimate of 130 nm which confirms the AFM results. Whether there still is a few nanometer thick non-etched Si3N4 sole at the groove bottom is difficult to ascertain.
The characterization of the phase mask performed by AFM and FIB/SEM gives complementary information on the phase mask corrugation profile which permits to explain the difference between the expected diffraction efficiencies and the measured ones. Exact modeling was performed with these experimental data inclusive of the rounding of the groove bottom. With the corrugation duty cycle close to the specifications (56 instead of 50 nm), the insufficient groove depth (130 instead of 150 nm) appears to be the main factor responsible for the deficit of first order efficiency: whatever the thickness admitted for the residual non-etched Si3N4 sole between 0 and 20 nm, the + −1st order efficiency found by the modeling of the fabricated corrugation is between 20 and 25% instead of the targeted 30%. This is quite understandable as the groove depth is responsible for the constructive interference of the two involved grating modes leading to maximum first order diffraction efficiency.
4. The 100 nm period grating writing
A thin layer of deep UV negative photoresist (Sumimoto chemical NEB 22A) is deposited by spin coating on fused silica substrates. A drop of ultra pure water is placed between the nanostructured Si3N4 layer and the photoresist layer. The high index phase mask is exposed under normal TE incidence by a UV collimated laser beam (frequency doubled Ar-ion laser, λ = 244 nm) and produces a 100 nm period interferogram in the water-filled gap and in the resist film. The phase mask is illuminated for 90 seconds under an incident beam with a power density of 10 mW/cm2, which corresponds to a dose of 904 mJ/cm2. After a post-exposure bake (90°C for 60 seconds), the substrate is dipped into the appropriate photoresist developer.
Whereas the presence of the second space harmonic in the printed grating corresponding to the interferences between the first and zero orders of the phase mask is easy to detect with an air cover under oblique incidence, it is more difficult to ascertain the presence of the desired 100 nm grating without resorting to a SEM scan. An optical test was nevertheless designed that makes it possible to assess the presence of the first and the second harmonics corresponding to 100 and 200 nm period respectively, prior to proceeding to lengthy SEM and AFM searches for the 100 nm period component. Under 244 nm wavelength incidence in air on a 100 nm period grating, no 1st order propagates - whatever the angle of incidence. However, if the grating is on a fused silica substrate, the –1st transmitted order may have a propagating character in the substrate if the following phase matching condition is fulfilled: sinθi > λ/Λ – nsilica where θi is the angle of incidence in air, nsilica is 1.509 at λ = 244 nm and Λ is the 100 nm period. This means practically that, with an incidence angle larger than about 69 degrees in air, there is a –1st order propagating contra-directionally in the substrate at an angle relative to the normal given by sin−1((λ/Λ- sinθi)/nsilica). This beam is of course trapped in the substrate, but it can easily be observed at the substrate edge, and be used as a criterion for the existence of a 100 nm grating in the resist film. Figure 7 illustrates the grating test experiment. The modeling of a 100 nm period grating in a 70 nm photoresist layer on a fused silica substrate shows that the power in the –1st diffracted order at a 244 nm wavelength is 2% of the power of a TM-polarized beam at 75 degree incidence.
The presence of a 100 nm period corrugation was assessed by means of a Scanning Electron Microscope with a Field Emission Gun (FEG-SEM) which can operate with high resolution in a low vacuum mode without surface metallization. The SEM picture shows a 100 nm surface modulation and no presence of a 200 nm overmodulation. The AFM scan of the exposed sample is shown in Fig. 8 . It confirms the presence of only the fundamental spatial harmonic in the phase mask interferogram corresponding to the period of 100 nm. The corrugation is however not well revealed: 10 nm modulation amplitude only in a 70 nm thick resist layer. Considering that the aspect ratio is smaller than 0.15 and that the AFM tip is very sharp (aspect ratio of 5), the scan of Fig. 8 is likely to be close to the actual corrugation profile. We attribute so shallow a surface undulation to the modal instability of the frequency-doubled argon ion laser used to produce the grating, and to the unprotected beam path in air. Modal instabilities with a few second time dependence and air turbulence may slightly perturb the local orientation of the wave front incident on the phase mask and impose a slight but variable degree of obliqueness on the interferogram fringes. This effect would not hamper the printing of the circa 500 nm period grating in the fiber core of a FBG may blur the latent image of a 100 nm period grating in a UV resist layer. The fact that the resist used was negative may further explain why the developed resist layer is formed of a thick uniformly polymerized continuous base together with a small amplitude surface undulation.
We have shown that there is a viable route for the printing of 50 nm characteristic dimension periodic structures by means of a phase-mask with the carefully chosen combination of a high index material, an exposure wavelength where the latter is reasonably transparent and where at least three different laser technologies are available, and exposure under immersion to enable the +/−1st transmitted orders to propagate and form a 100 nm period exposure interferogram. This is close to the ultimate characteristic dimension that can be achieved by a phase mask under exposure in the 244 – 266 nm wavelength range before using a double or multiple printing strategy. The writing of a single spatial frequency grating of 100 nm period was demonstrated despite the slightly off-optimum ratio between 0th and + −1st orders. We have designed and demonstrated an optical set-up that permits the straightforward assessment of the presence of a 100 nm period corrugation. Further development can be pursued in three directions. The first one is a generalization issue: so far the grating printing conditions have been set up only for the case of a fused silica substrate. For other dielectric substrates the results will not be significantly different. However, the very interesting case of a metal-coated substrate must still be investigated from the beginning. Secondly, the technology has to be made scalable to large sizes via the “write on the fly” scheme . The third R&D direction is certainly the most promising one as it permit to skip exposure under immersion: as soon as the LuAG material  becomes available in thin-film form it will be possible to print 100 nm period gratings at 193 nm wavelength with an acceptable residual 0th order transmission, and to expand more easily the phase-mask approach to an interferogram scanning scheme for the printing, e.g., of large area polarizers for LCDs and to apply a double-printing technique.
The authors wish to acknowledge the contribution of the partners of the Networks of Excellence NEMO and ePIXnet for the phase mask fabrication. We are grateful to the planar technology service of the H. Curien Laboratory for SEM characterizations. The contribution of J. Van Erps was supported by the FWO (Fund for Scientific Research-Flanders) under a post-doctoral research fellowship.
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