Emerging Trends in Surface Metrology

Emerging Trends in Surface Metrology P.M. Lonardy’(l), D.A. Lucca2(1), L. De Chiffre3(1) University of Genoa, Italy 2 Oklahoma State University, USA 3 Technical University of Denmark, Denmark

Abstract

Recent advancements and some emerging trends in the methods and instruments used for surface and near surface characterisation are presented, considering the measurement of both topography and physical properties. In particular, surfaces that present difficulties in measurement or require new procedures are considered, with emphasis on measurements approaching the nanometre scale. Examples of new instruments and promising innovations for roughness measurement and surface integrity characterisation are presented. The new needs for tolerancing, traceability and calibration are also addressed. Keywords: surface, metrology, surface integrity

The authors thank the following contributors: J.L. Andreasen, Denmark K.D. Bouzakis, Greece C.A. Brown, USA A.A. Bruzzone, Italy H.E. Hintermann, Switzerland R.J. Hocken,USA T. Inamura, Japan L. Koenders, Germany R. Leach, UK H. Sato, Japan H. Trumpold, Germany E. Uhlmann, Germany E. Westkamper, Germany D.J. Whitehouse. UK

1 INTRODUCTION Since its founding fifty years ago, ClRP has maintained a major interest in the evaluation and measurement of surface microgeometry, as recalled by Peters et al. in a recent, comprehensive keynote paper [ I ] . In fact, it is fair to say that CIRP, as a scientific organisation, has been a major contributor to advancements in this field through its theoretical studies, experimental research and cooperative work. The evolution of manufacturing technology, with the introduction of new production techniques and new measurement instruments, has greatly enlarged the fields of interest related to surface metrology. During the early years metrology of the surface was mainly limited to mechanical production, whereas today it is of significant importance also for the electronics and optoelectronics industries and is starting to emerge in biomedical applications. The investigation of nanometre-scale features, initially motivated by the electronics industry, has opened new and wide horizons which interest many branches of engineering. As the overall dimensions of an object decrease, the importance of the surface relative to that of

the volume increases. In a nanocrystal, for example, a 1000 atom cluster has approximately 25% of its atoms at the surface [2]. As a result the properties of the solid are strongly influenced by the properties of its near surface. Consequently the investigation of surface integrity, including the physics and chemistry of nanosurfaces, is a relevant, multidisciplinary area of research. The ClRP keynote papers presented in recent years are significant examples of the subjects that have gained new or renewed attention, both in academia and in industry. For example, 3D analysis and characterisation of surface microtopograpy has been addressed by Lonardo et al. [3], including discussions of standardisation and traceability. Vorburger et al. [4] presented a review of STM and AFM, emphasising their industrial usage. Lucca et al. [5] addressed recent progress in the development of characterisation tools for the assessment of surface integrity. Structured and engineered surfaces were discussed by Evans and Bryan [6], with definitions, examples and indications of measurement needs. New characterisation methods of surface texture were reviewed by De Chiffre et al. [7]. This paper attempts to address some current measurement challenges, considering in particular surfaces of emerging interest that present difficulties in measurement, or require the definition of new, sound procedures. Some recent advances in the methods and instruments for surface and near surface measurements are presented. The needs for tolerancing, calibration and traceable measurements in order to ensure high metrological standards, an area of significant interest [8], are discussed in terms of recently presented proposals and solutions. 2 DEFINING THE SURFACE The classical definition of a surface, as the boundary between the bulk solid and an adjacent liquid or gaseous phase, is inadequate in the area of practical surface technology. How the surface is defined is dependent on both the function of the surface and the measurement

technique used to characterise it. For example, the functional properties of a surface may not be solely dependent on its outermost layer, but on regions deeper into the bulk. Whereas, for example, the uppermost layer is responsible for a surface's reflectivity and gloss, the magnetic properties of a computer hard disc are influenced by a surface region several nanometres thick. Characterising the surface in terms of depth regimes (Table 1) has been taken as a first step towards a new measurement strategy [9]. The proposed approach relies on a database containing all relevant functional and geometric parameters correlated to the measurement systems used and their depths of investigation.

Table 1: Surface regions [9, 101. The results of a particular measurement method strongly depend on the physical principle on which the method is based. It is widely known that different results can be obtained when measuring the same surface with different instruments [ I I ] . The stylus method is by far the most widely used method for surface evaluation, and the results obtained with it are generally assumed as a reference for assessing other methods [12]. Its main advantage is its fidelity, i.e., the ability to transfer the geometry being measured to the output of the system. However, due to the applied force, the stylus penetrates elastically (and possibly plastically) to a depth below the surface, depending on its size, the elastic modulus and the hardness of the surface. Moreover, because of the contact there is the possibility that the stylus will damage the surface [3]; this is detrimental not only to the surface, but also to the measurement results. In this case, the measurement acquired is not of the original surface, but of the modified one. To address this problem Whitehouse introduced a "potential damage index" calculated for flat, smooth surfaces, flat, random rough surfaces and flat, sinusoidal surfaces [13]. The index considers the static and dynamic forces of the stylus, as well the yield stress, or the hardness of the material. In order to reduce the damage, the static force can be made small. However, if it is too small the stylus is no longer kept on the surface while tracking and the measurement loses all fidelity [14]. The ability of the stylus system to follow the surface geometry without losing contact has been called "trackability" [ I 51. The most important alternatives to the stylus technique are the optical methods. These are non-contacting techniques and therefore the problem of damaging the surface is eliminated. However, some concerns about

their capability to accurately measure the surface do exist. These refer to the fact that the mechanical stylus is substituted by a light beam, which is reflected or scattered by the surface. The interaction between light and the surface can be very complex, depending on the wavelength of light, the roughness of the surface and the nature of the body. The depth of penetration of the light also affects the measurement. The light penetrates the surface to different depths according to the absorption coefficient of the material. The intensity €(z) at the depth z is [16]: (11

€(z) = €, exp(-az)

where €, is the intensity at z=O and a is the absorption coefficient, which depends on the incident wavelength. The intensity €, at the entrance to the surface is a fraction of the incident light, due to reflection. In metals both the absorption coefficient and reflectivity are generally high. For other materials, on the contrary, both reflectivity and absorption are low, such that a large fraction of the incident light penetrates into the material. Moreover, in the case of a layered surface, multiple reflections at different depths can occur. This variability of penetration affects the optical path length and hence the measurement. Another cause of uncertainty can result by the possible presence on the surface of small features, such as peaks with small radii of curvature or cracks and holes. These can generate diffraction effects that can alter the measurement. Moreover, the slopes of the surface texture are critical in the measurements since they affect reflectivity. Other measurement methods have similar problems in uniquely defining the surface. Consequently from an engineering point of view the surface should be defined as a region extending from the external layer to the subsurface. Some authors have proposed [I71 to introduce the definition of a "superficial layer" as a set of material points, which are contained between the external surface and an apparent surface, which is the limit of changes in properties of the subsurface layer. The measurement technique to be used for the surface metrology should be chosen according to the function of the surface, taking into account not only the functional and geometrical parameters, but also the depth regime involved (Figure 1).

u Depth regime

e Measurement technique

Figure 1: Methodology for choosing the measurement technique.

3

SURFACES OF EMERGING INTEREST

3.1 Surfaces in nanotechnology The surfaces that have been the principal object of interest in the past have been mainly the result of the classical machining processes such as turning, milling and grinding. A great number of papers have been devoted to studying the influence of the process parameters, tools, machine tools and workpiece materials. For these machined surfaces roughness values range from several micrometres to rarely below 0.1 pm. The assessment lengths defined by the standards range from 0.08 mm to 8 millimetres [18]. The progression towards higher levels of miniaturisation has dramatically reduced these length scales, such that it is increasingly common to be faced with the nanometre scale in dimensional metrology and roughness quantification. Nanotechnology is concerned with manipulation and measurement of matter at a length scale between 1 and 100 nm [2]. An example of attempts to perform metrology at the lower end of this scale has recently been reported. The sub-atomic measuring machine, jointly developed by the Centre for Precision Metrology at the University of North Carolina at Charlotte, and MIT accomplishes a positioning noise near to 0.1 nm [191. The impact of nanotechnology on manufacturing, as well as the introduction of emerging products and new processes have been extensively discussed by Hocken [20]. Computer hard disks are an important example of surfaces with stringent nanotechnological properties. Diamond turning was used for many years to produce mirror-like surfaces on aluminium substrates for particulate magnetic coatings. However, this preparation is not adequate for low flying recording heads. Today, rigid disks are produced using thin film technology [21, 221. In order to obtain a hard surface capable of being produced with minimal roughness, the aluminium is chemically plated with a nickel-phosphorus film of 10 pm thickness. This film is very hard (approximately HB = 550) and can be abrasively polished to Rq = 1.0 nm. The polishing operation is followed by a texturing process which produces circumferential grooves or, more recently, by laser texturing, which serves to minimise head stiction to the disk surface. The overall roughness of the structured surface is Rq = 3-5 nm. By vacuum deposition, or PVD techniques, chromium underlayers followed by the magnetic layers are applied. The chromium underlayer is used for the epitaxial match with the cobalt-based alloys of the magnetic film. The grain structure of the underlayer, which is replicated by the superimposed film, can be easily controlled. The typical thickness values of the underlayer and layer are 50 and 30 nm respectively. To protect the magnetic layer from the contact of the recording head, an overcoat of 10-15 nm is applied by PVD. Generally, diamond-like carbon (DLC) [23] or amorphous carbon doped with hydrogen or nitrogen are used. This overcoat has not only the function of protecting the magnetic layer, but also of supporting the lubricant, an organic polymer, that is the final layer (1-3 nm) of the disk structure. Presently, the information density which can be stored on the hard disks approaches 400 million bits per square centimetre, i.e., a single bit is contained in an area of 500 nm x 500 nm. The recording head sliders scan the disks at a distance of 5-10 nm [24]. Recently the possibility of texturing the slider rather than the disk has been reported. The sliders are generally made of ceramics such as A1203, TIC and ZrO2-Y2O3 [25]. By ion beam etching the surface an island-type texture is obtained, resulting from

the different etching rates of the different phases. The height of the islands can be controlled by varying the etching dose. Island heights from 3 to 20 nm have been obtained with an accuracy of f 1 nm. Optical interferometry, as well as AFM, are being developed to achieve online measurements of these surfaces [4]. Another application which requires surface metrology and feature characterisation at the nanometre scale is in the manufacture of semiconductor devices. The performance of these devices has doubled every 18-24 months over the last three decades, and the semiconductor industry association believes that this trend will be maintained for at least one additional decade. The increase in performance is achieved mainly by shrinking the size of the individual transistors [26]. Figure 2 shows the forecast for the minimum feature size as a function of the year of introduction. The surface roughness of these silicon wafer surfaces is found to be critical, as it can strongly affect the electronic performance and breakdown voltage [27].

I

I

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First shipment Process Development Exploratory Research

20 15

I

I

I

\ \ I

2000

2004 2008 2012 Year of Introduction

Figure 2: Forecast for the minimum feature size of transistors [26]. Other surfaces related to the emerging field of nanotechnology are those composed of thin layers deposited onto a substrate. The deposition of layers, having properties different from those of the substrate, is a common technique used to improve the functionality of a surface. The thickness of these layers can range from one nanometre to a few millimetres, according to the deposition method and the function required. The yield strength, hardness, and toughness of the thin films generally improve with decreasing grain size down to nanometresized grains. In addition to improved mechanical properties, nanocrystalline materials can exhibit higher thermal expansion, lower thermal conductivity and unique optical, magnetic and electronic properties [28]. Consequently, thin film materials are of great importance to several advancing technologies, such as microelectromechanical systems (MEMS). Many efforts are being devoted to the analysis of the mechanical and tribological properties of various thin films by using new instruments capable of measuring mechanical properties at the nanometre scale. Hardness and elastic modulus of these films are normally investigated through nanoindentation [29] which is further discussed in section 6. Recently, a technique based on nanohardness testing, supported by a FEM simulation, has been introduced [30, 311. Thin films are generally deposited on flat substrates, however many substrates present textured surfaces. In this case the thin coatings replicate the substrate topography, but can introduce some irregularities. When the structure of the layer is the object of interest it can be

difficult to separate the structure of the layer from that of the substrate. To overcome this problem a procedure based on the use of atomic force microscopy in a pulsed force mode has been proposed [32].

3.2

Engineered and structured surfaces

A number of manufacturing methods which have been recently developed allow for surfaces to be specifically designed to provide a particular function. The keynote paper by Evans and Bryan [6] suggests adopting the foll owi ng terminology for these surfaces:

3.3 Surfaces resulting from rapid prototyping Over the past fifteen years a number of technologies have emerged which are capable of producing three dimensional objects directly from a CAD model, through a repetitive deposition of material layers. These innovative technologies, known as rapid prototyping (RP) or additive freeform fabrication (AFF), offer higher ease and versatility in producing parts with complex geometries, in comparison to conventional fabrication methods. A list of the most established commercial methods is presented in Table 2.

"Structured surfaces": - surfaces with a deterministic pattern of usually high aspect ratio with geometric features designed to give a specific function; "Engineered surfaces": surfaces where the manufacturing process is optimized to generate variation in geometry and/or near surface material properties to give a specific function. Later, Stout and Blunt [33] developed a classification proposing a hierarchical structure, where the surfaces are divided into two main categories: engineered and nonengineered surfaces, with structured surfaces belonging to the class of engineered surfaces (Figure 3). Engineered surfaces were redefined: - surfaces produced in specific ways that deliberately alter surface and subsurface layers to give a specific functional performance. Each of the categories is then associated with a group of processes and with a group of properties.

Unstructured Random

Systematic Figure 3: Surface classification according to [33] Some differences emerge between the two classifications. For example, machining processes, such as turning, are considered in one case central to the production of structured surfaces, and in the other case pertinent to non-engineered, and hence, unstructured surfaces. Topographic characterisation of structured surfaces is poorly performed through conventional measurement methods, and the deterministic features of functional importance are not described by the conventional, statistically averaged parameters. An approach to the measurement of structured surfaces can be found within the techniques developed for computer vision. In this context a methodology based on non-linear image processing operators has been applied to analyse the texture of cylinder liners [34]. A technique based on image processing has also been applied on the atomic scale to characterise structured surfaces [35]. In the ClRP keynote paper by De Chiffre et al. [7] a methodology based on the use of tree data structures and volume elements (voxels) has been suggested.

Table 2: Commercial RP technologies (adapted from [36]). Dimensional accuracy and surface finish of the parts obtained by these techniques are quite important and a topic of current research. A common feature of almost all the methods is the periodicity of the surface texture, due to layer deposition. The texture of the horizontal surfaces is mainly influenced by the hatch spacing, whereas the texture of the vertical and oblique surfaces depends on the layer thickness. The oblique surfaces have the worst quality due to the effect of stair stepping (Figure 4).

Figure 4: Stair-stepping effect on a curved surface. Each RP technology provides different build styles, i.e., sets of predetermined parameters used to create the build files. The effects of build styles on dimensional accuracy, surface quality and build time applied to stereolitography have been investigated [37]. Theoretical models have been developed to calculate the roughness parameters of inclined layered surfaces. Referring to Figure 5, where d, is the horizontal space between layers and h, is the layer thickness, the following equation can be written for Ra [38]:

Conversely, h, can be expressed as a function of Ra and the slope of the surface p: hc = 4RaJ1+ tan'

p

(3)

In order to keep Ra constant, the layer height should be modified as a function of the slope.

Figure 5: Geometry of an inclined layer surface The powder-based RP methods, such as SLS, produce surfaces whose texture is dominated by the particle size. Coarse powders or granules are required to enable layering. An application of SLS is the fabrication of shell moulds by using pre-coated sands. Topography measurement of these surfaces presents some difficulties. The coarse structure and the abrasive properties hamper contact methods, while due to the high porosity the use of optical methods can be problematic. Lonardo and Bruzzone [39] measured roughness parameters of SLS specimens by an optical method, based on conoscopy, adopting a methodology that allows for discarding points where the measurement fails. The problem of identifying and positioning the edges of the sand components was also addressed, using a statistical approach. 3.4 Surfaces of biornaterials The importance of the surface properties of biomaterials used for medical implants is well known [40]. Certainly the mechanical and chemical characteristics of these materials affect cell response and implant durability, however the surface topography plays an important role as well. Hip joints, dental implants and bone fracture implants require appropriate and different roughness textures. In hip joints the ball surface should have minimum roughness, in order to prevent excessive wear and the risk of a replacement operation [41]. The production of this prosthesis is very expensive, due to the stringent requirements for shape [42] and surface quality. Very accurate measurements are performed in production to monitor the polishing process. Stout and Blunt [43] attempted to correlate the surface topography of two hip joint ball surfaces with service performance. Dental implants are screws (Figure 6) made of commercially pure titanium [44]. Their surfaces are treated, mechanically or chemically, in order to produce a controlled texture necessary for effective bone integration. The mechanical treatment consists of blasting with particles of alumina or TiOn, which results in a random texture with roughness values depending on the particle size [45].

Figure 7: SEM image of the implant surface The chemical treatment is an etching process that produces a preferential corrosion of the surface, according to the orientation of the crystalline grains. Studies on the characterisation of these surfaces have been reported [46, 471. The surface of the implant shown in Figure 7 has been etched in hydrofluoric acid and then oxidised in a solution of H2N03 + HCI. The quality of the surface is critical, as small modifications of the surface treatment can lead to poor results, even to the failure of osteointegration [48]. Bone fracture implants [49] consist of different shapes depending on the application. Typically they are subjected to fatigue stress, such that their resistance and life are influenced by surface topography. 3.5 Optical surfaces The optical performance of a surface is generally associated with the capability to form an image. For the components of an optical system the prevailing issue is the correctness of the geometric form with roughness kept at a minimum. Specular surfaces are typically required. There are other cases, however, where the optical performance of a surface is not based on specularity. These concern the function of an object, as well as its aesthetic aspect. A common property that is required of such surfaces is gloss. This property is defined by the amount of light entering a solid angle compared with the total light scattered from the surface. Gloss depends on the reflective properties of the material and can be controlled by the finishing level. For coatings and paints it is determined by the nature, shape and dimension of pigments. Facet-type pigments produce a brilliant appearance, whereas spherical pigments diffuse the light, giving a mat finish. Paper is a special example of a surface with optical properties which are both functional

and aesthetic. Papers with a gloss finish produce a better quality in printing images or photographs, whereas mat or diffusing papers, which minimise light reflection, are generally preferred for reading. The gloss level of a surface can be directly measured through optical instruments. In a ClRP keynote paper [50] a review of suitable methods has been presented. The relationship between gloss and surface texture has been extensively studied beginning with the work of Bennett and Porteus [51]. Whitehouse [52] presented a theory based on the "unit manufacturing event" to control the light distribution from a surface by choosing the manufacturing process parameters which give the appropriate angle distribution. Special optical properties can be achieved by texturing the surface with appropriate shapes. Important examples, among others, are retro-reflective surfaces used in road signs and Fresnel lenses [6]. In a study by Whitehouse [52] results obtained in modifying the reflection properties of silicon surfaces are presented. The surfaces, which were prepared by optical interference lithography, exhibit a structure with a constant period of 300 nm and different depths, varying between 35 nm and 190 nm. A decrease in reflectivity was observed with increasing the structure depth. The light wavelength ranged from 200 nm to 3000 nm. 3.6 Soft surfaces

There is a class of materials that is commonly defined as "soft". Most biological tissues, many polymers and some metallic alloys fall into this class. In the recent literature an increasing interest has been observed in the contact measurements of soft surfaces. The stylus method underestimates the topography of soft surfaces [54] and the AFM encounters problems when attempting to measure soft surfaces. The softness of a material, i.e., the ease of undergoing deformation, is a property which can involve both the elastic and the plastic behaviour, depending on the elastic constants and the yield stress of the material. According to Hertz's theory [55], in the elastic regime, when a sphere is loaded against a plane surface under a force F, the diameter d of the contact zone is given by:

d = (3FD F )

where

p

=

4F .

- IS the mean pressure on the indented area, c is a

d2 constant whose theoretical value is 2.66, and the exponent m is related to the strain hardening behaviour of the indented material. For a non-strainhardening material and for dccD, equation (7) gives:

F = coyxDh

(8)

Equations (6) and (8) make it possible to compute the elastic and plastic deformations produced on a flat surface by a stylus or a rounded cantilever tip of an AFM. While elastic deformation causes errors in the measurement of the heights, plastic deformation can alter the surface micro geometry. It was found [46] that titanium surfaces having a hardness of 153 HV are flattened after a roughness measurement by a stylus. The force applied to the stylus was 5 mN and the radius of the stylus was 5 pn. For these values and assuming oy = 300 N h m 2 equation (8) gives: h = 0.2 pn. AFM experiments conducted by Bhushan and Ruan [57] on polymeric magnetic tapes using silicon nitride cantilever tips with loads of 100 nN showed the occurrence of plastic deformation, with the soft material pushed in the sliding direction of the tip. Whitehouse [58] has discussed the effect of the variation of the depth h on fidelity, considering that h changes by varying the radius of curvature of the surface at the point of contact. Recently applied techniques, such as tapping mode, phase contact and pulsed phase mode have been shown to be highly effective in the scanning probe microscopy of soft materials [4, 321. Optical methods can also be successfully applied to soft materials. In Figure 8 an example of paper with two grooves left by a ballpoint pen is shown. The image has been obtained by using a scanning conoscopic probe (SCP).

(4)

where D is the diameter of the sphere and E* is the equivalent Young's modulus, which is a function of the Young's moduli and Poisson's ratios of the two materials:

For d-=D a relationship between the force F and the elastic indentation depth h can be written:

(6) When the force reaches a limiting value, dependent on the yield stress of the indented material, plastic deformation occurs. In the fully plastic regime the Meyer equation can be applied [56]: rn

P = c-.[;)

(7)

Figure 8: SCP image of paper with two crossed grooves left by a ballpoint pen (courtesy Pertel, Turin).

3.7 Surfaces with re-entrances Currently available surface metrology instruments produce a record of the surface which is single valued, i.e., they cannot evaluate re-entrances [59]. Many real surfaces, however, especially those manufactured by nonconventional methods, are not in fact single valued and possess cavities, porosity or undercuts. When a mechanical or optical probe explores such a surface it senses only the nearest feature missing the hidden features. The measured profile will have a shape which

depends on the shape of the probe. Figure 9(a) illustrates this for a conical stylus, while Figure 9(b), is for a parallel light beam. Over the re-entrant part the measured profile is defined by the flank of the probe.

A methodology to correctly compute roughness parameters of profiles with high slopes has been recently presented [61]. The errors resulting from the adoption of the conventional standardised procedures when subtracting the acquired profiles from the mean line are el imi nated. 4

Significant challenges arise as one attempts to decrease the characteristic length scale of the measurement from millimetres to nanometres. Several well-known issues are reviewed below. A measuring system can be represented by a chain of transducers in which the first element is the sensor and the last element is the actuator (Figure 12).

profiles

Figure 9: Surface with re-entrance and corresponding profiles recorded with conical (a) and cylindrical (b) probe. In general a feature is not detected when the angle a between the probe axis and the local normal to the surface is larger than a limiting angle, whose value ( 4 90") depends on the conicity of the probe. Figure 10 refers to the case of a measurement through optical triangulation where the ray obliquely incident on the surface can not detect the portion of the profile included between points A and B. probe axis \

MEASUREMENTS AT REDUCED LENGTH SCALES

a

ZM-k

Figure 12: Scheme of a measuring system The transfer function of the system depends on the physical principle on which the measurement is based. An issue of all measuring systems is their fidelity, namely, the ability of the system to relay, with a minimum of distortion, the input information generated by the sensor to the output

~

Figure 10: Probe axis obliquely incident on the surface: part of the profile is not detected. The lack of current methods suitable for examining reentrances is an important limitation when the true surface and not its envelope is relevant to its function. An approach for the determination of the presence of reentrances has been recently proposed [60]. The presence of re-entrant areas over peaks causes contact with the stylus flank and the measured profile will present slopes equal to one half the included angle of the stylus. If the geometry of the stylus is known, through the analysis of the local slope of the measured profile an indication of the presence of re-entrant features can be obtained. For a more certain determination of the presence of re-entrant areas it may be necessary to develop a methodology based on the observation of the surface under different angles (Figure 11). The procedure should require three steps: rotation of the surface, or the probe, measurement under the applied angle, subsequent reconstruction of the profile. probe

I

...+pqq

Chain of Transducers

1

.

In the tactile instruments the sensor is a probe that is traced across the surface and its movement is mechanically or electrically transferred to the transducers and displayed. In the non-contacting methods the sensor indirectly receives information about the surface being measured and transfers this information to the transducers. Alternatively, a servomechanism moves the sensor or the surface with the intention of keeping constant their reciprocal distance, hence the term "follower". This movement is then the input signal to the transducers. Unfortunately, in all these systems many sources of noise affect the results of the measurement, modifying the input signal, adding spurious information and altering the transfer function. This is, of course a general problem, but it becomes more important when the characteristic length scale of the measurement decreases, since the signal-tonoise ratio is seen to decrease. Another factor which must be considered as length scale is decreased is reduced stiffness. When an elementary solid is reduced in scale without modifying its shape, the stiffness K, or the ratio of force F to elastic deformation q, decreases linearly with the dimensions L. In addition, K', or the ratio of force F to stress 0,decreases with L2. This can be seen in Table 3 where the equations for K and K' for three simple cases are shown. The natural frequency of an elementary solid is:

where K is the stiffness, M is the mass and a is a coefficient depending on the geometry and the constraint conditions. Figure 11: Rotation of the profile.

K=-

Type of load

*

F

77

F

7IE -L 4h2

-L2

371E -L 64h2

71:L2

371E -L 4h2

-L2

71:

4h2

32h2

71:

8h2

L

h = - , L = length, d = diameter, E = Young's modulus d Table 3: Ratios of force to elastic deformation and force to stress, for three simple cases. As the mass decreases with L3 the natural frequency o,, increases with L-'. Passing from millimetre to nanometre dimensions, keeping h constant, the stiffness K decreases by a factor of lo6, the ratio K' decreases by a factor of 10" and the natural frequency increases by l o 6 (Figure 13). Decreased mass at the nanometre scale makes the solid very mobile and subjected to large accelerations and high frequency of vibration. Quoting Whitehouse "at the nanometre level everything is moving: nothing is really stable. Anything can cause nanometre movement" [52]. Equally important is the significant decrease of K which indicates that the allowable force to maintain the stress below the yield point in order to avoid permanent deformation, becomes extremely low. Apart from the mechanical aspects here discussed, there are thermal, electrical, magnetic and optical effects which must be taken into account at the nanometre scale, including, at smaller scales, quantum effects [62].

Surface topography concerns all the geometric features of the surface, including form and texture [ I l l , where "texture" has the standardised meaning of the combination of roughness, waviness and lay [33, 641. The distinction between form and texture is dependent on the length scale chosen. In the measurement of conventional surface topography this distinction is well established and the procedures used to make it are well defined. As the length scale for measurement decreases, however, what may be defined as texture at conventional scales may be considered to be form at the nanometre scale. As a result, it is necessary to specify the measurement regime, referring to macro-, micro- and nano-topography when the measurement involves millimetres, micrometres and nanometres, respectively. In the following section some current instruments and methods used for micro- and nano-topography characterisation are presented, considering stylus instruments, the atomic force microscope and optical instruments. 5.1 Stylus instruments The operating principle of the stylus instruments is quite simple: the vertical movement of a tip, which follows the profile of the surface, is acquired as a function of the horizontal displacement. The finite size of the stylus was not considered to be critical in the past when measuring traditional engineering surfaces. With the need for finer surface measurement, however, the issue of stylus tip size has been the subject of study in recent years. Since the stylus is unable to penetrate into all the valleys the true surface is never detected. Moreover, the locus of the probe trajectory as it tracks across the surface is distorted with respect to the true surface profile. This measured envelope introduces non-linear distortion [65]. Figure 14 shows the difference between the true contact point P and the apparent (or nominal) contact point V on the vertex of the stvlus.

Figure 14: Profile, true contact point P and trajectory of the apparent contact point V. Inm

1pm

Imm Dimension

Im

Figure 13: Variation of K, K'and o,,when changing the dimension. 5

If the true contact points lay in the vertical plane containing the trajectory of V, it is theoretically possible to recover the profile, provided the shape of the stylus is known. This case is met when the surface has a mono-directional texture and is measured transversally.

MEASUREMENT OF SURFACE TOPOGRAPHY

Starting from the early 1930s when the first instruments were developed, the science of surface topography has continuously evolved, enriched by the progress in measurement systems and methods. The advent of computers in the late 1960s favoured the introduction of digital techniques, which increased the performance of the instruments, allowing for 3D analysis and a higher level of flexibility in filtering and analysing the acquired data. The drawback was the well known proliferation of parameters [63], often stigmatised by the ClRP community.

7

xv

x

Figure 15: Relationship between apparent profile g(x) and true profile f(x).

Referring to Figure 15, let g(x) denote the apparent profile, i.e., the trajectory of the vertex V, and ~ ( x the ) profile of the stylus. The true profile f(x) is then given by: (9) where the variable x, = x-x is the abscissa of V and the origin of the axis The stylus is tangent to the profile at P, so that the slopes of ~ ( x and ) f(x) are equal at that point:

x.

Introducing the derivative of equation (9) with respect to x in equation (10) gives:

whose solution is a relationship between the variables x and x,, and allows for a calculation of f(x) from equation (9). By using analogous relationships it is possible to determine the form of the stylus by measuring the profile taken over a known reference surface [66]. A different approach to recover the true profile of the surface considers the application of neural networks to correct for the integrating effect of a finite stylus tip [67]. When the points of true contact with the surface lie outside the trajectory plane of the stylus, the problem becomes three-dimensional and more difficult to solve. In any case, knowledge of the stylus geometry is fundamental when high precision measurements are required. Recently, Leach and Hart [68] carried out an experimental study aimed at measuring the shape of commercial styli having different radii ranging from 0.1 pm to 10 pm. The measurement methods included the use of an SEM, a razor blade, a wear gauge and roughness standards. The study showed that it is not always possible to rely on the values supplied by a stylus manufacturer or distributor. During their long-standing history, stylus instruments were not subjected to basic changes in operating principle, but to continuous improvements. Development issues of present interest include the instrument's metrological characteristics, speed of response and the development of portable instruments. At the National Physical Laboratory a stylus instrument has been developed which can make traceable measurements of surface texture in both the vertical and horizontal directions with an uncertainty of 1 nm [69, 701. Laser interferometers are used to determine the coordinates of the stylus tip. A key element in the instrument's design is the loop stiffness from the tip of the stylus to the top of the specimen mounting plate. The x and y slideways, which constitute the reference datum, are of a dry bearing prismatic design. Three small polymeric pads support the weight of carriage and two additional pads constrain the slide allowing linear motion. The instrument has been developed as a method for providing a fully traceable surface texture measurement service. The time required for a stylus instrument to acquire data for 3D analysis can be considerably long, depending on the dimensions of the area to be measured and the acquisition speed. Consequently there is an increasing demand for instruments characterised by high-speed measurements. Typically the speed of translation is about 0.5 m d s , such that a time of about 100 min can be required for the measurement of 5 mm x 5 mm surface

area using a line spacing of 10 pm. Higher speeds cause dynamic problems which must be addressed. A prototype stylus instrument, suitable for rapid measurement of small surface areas has been recently developed [71]. The key features of the instrument are: a spring on the stylus arm which applies a static force of approximately 1 mN on the surface, and a lightweight hollow aluminium arm. As reported, the stylus tip remains in contact with the surface at speeds of 5 mm/s, which is an order of magnitude faster than the speed of most stylus instruments. Another emerging trend is the development of a generation of portable stylus profilers. In addition to the requirements of high accuracy and speed, there is the necessity of making measurements in industrial environments, or on large sized workpieces. Presently, there are a number of commercially available portable instruments which can be placed directly onto the surface being measured. These instruments are generally 2D and have a limited scan range [72]. A novel, portable three-dimensional stylus instrument capable of relatively large area scans has been described [73], with details on the mechanical design, as well as the procedures adopted for calibration. The main features of the instrument are a vertical resolution better than 30 nm and a scan range of 4.5 mm x 5.5 mm. 5.2 Atomic Force Microscope The era of scanning probe microscopy (SPM) started in 1972 with the invention of the Topografiner by Young et al. [74], who built an instrument capable of measuring the surface with a vertical resolution of 3 nanometres. Subsequent developments were introduced by Binnig et al. with the inventions of the scanning tunneling microscope (STM) in 1983 and the atomic force microscope (AFM) in 1986 [75]. The AFM has greatly expanded the applications of SPM, allowing for the measurement of the topography of both insulating and conducting surfaces at near atomic resolution. Attempts have also been made to use the AFM as a precision machine tool for micro-cutting [76]. The ClRP keynote paper of 1997 by Vorburger et al. [4] presented a comprehensive review of the industrial applications of STM and AFM, discussing also the metrological requirements. Although the resolution of SPMs can be very high, some concern exists about their accuracy. Drift, hysteresis, non-linearities and noise are the main causes of errors, which affect the vertical and lateral displacements. These errors are intrinsically due to properties of the piezoelectric actuators and can be only partly corrected by calibration of the scales. The most serious limitation of the piezoelectric ceramics is creep, their tendency to continue to expand after a voltage is applied. Electronic compensation networks used in series with the PZT drivers that equalise the response over time [77] have been employed to help correct for this Recently, significant efforts have been made to transition the SPMs from imaging devices to metrological instruments capable of providing accurate and traceable measurements. Metrological AFMs have been built using laser interferometers [78, 79, 801 or capacitance sensors [81, 821 for measuring the instrument displacements. The use of laser interferometers is more complicated and expensive, but can provide traceability to the wavelength of light. Capacitance sensors are simpler, but require calibration. A hybrid solution has been adopted at the IMGC [83] whereby the x and y displacements are monitored by two heterodyne interferometers and the z displacement is measured by three capacitive sensors. In addition to the ability to measure the instrument's displacements, the shape of the cantilever tip also affects the achievable accuracy of the AFM. The tip radius, the

apex angle and the overall size of the probe are the main factors influencing the resolution of the measurement. An experiment carried out at Nippon Steel Corporation [27] compared two cantilever tips with different radii (200 nm and 20 nm) in the roughness measurement of polished silicon wafers. The measured Rq values for the same surface were about 0.8 nm and less than 0.6 nm for the 20 nm and 200 nm tips respectively. Recent cantilevers have been produced with tips with radii smaller than 5 nm and high aspect ratios. For measurements on samples with very steep features, tips with near vertical sidewalls have been proposed [84]. The end of these tips have an aspect ratio of typically 7 : l with a half cone angle smaller than 5" (Figure 16).

optical system consisting of a uniaxial birefringent medium coupled with two circular polarisers (Figure 17). The first polariser decomposes the ray into two orthogonally polarised components, which propagate through the birefringent medium, as an ordinary and an extraordinary ray, at different velocities, acquiring a difference in phase. The second polariser (analyser) recombines the two components producing interference. The phase delay between the two components is dependent on the angle made by the ray with the optical axis of the birefringent medium. If a light cone is collected by the optical system, at the exit of the analyser a series of concentric cones will be generated, which are the loci of the rays having a phase delay given by:

A@, = 2ni

(i = 1, 2, 3, ...)

Correspondingly, on a plane C perpendicular to the optical axis a series of concentric fringes will appear. The mathematical treatment presented by Lonardo and Bruzzone [92] gives:

Figure 16: AFM tip with a high aspect ratio [84] For applications where a high resistance to wear is required, diamond coated tips are now commercially available. A promising innovation is the use of carbon nanotubes (CNT) as tips for scanning probe microscopes. The extraordinary electrical and mechanical properties of these nanostructures make their use very challenging [85]. The features for a CNT tip include a diameter as small as 0.7 nm, length extending to several micrometers, high elastic flexibility and high resistance to wear. The first attempt to attach a CNT to an ordinary probe tip was made by Dai et al. [86] in 1996. Since then, many techniques have been developed to produce CNT probes. Both single-walled nanotubes (SWNT) and multi-walled nanotubes (MWNT) can be used. Some recent experiments carried out by Nguyen et al. [87] have shown that SWNT probes can obtain a lateral resolution as small as 2 nm and the MWNT probes show no detectable degradation in lateral resolution after more than 15 hours of continuous scanning on a Si3N4 surface. 5.3 Optical instruments

The first successful attempts of using optical methods to obtain information about surface topography go back to Schmaltz [88] in 1934. Over the years a large number of methods have been developed, with the goal of offering the benefit of non-contacting measurements [89, 901. Among the techniques which have been industrially exploited and more extensively applied are [3]: triangulation, auto-focussing and interferometry. Examples of relatively new methods which have generated increasing interest are the scanning conoscopic probe (SCP) and the scanning near field optical microscope (SNOM, also known as NSOM). SCP is based on a classic interferometric technique, known as optical conoscopy which is associated with the use of a birefringent medium. The application of conoscopy to surface metrology was introduced by Sirat [91]. A light beam emitted by a point P passes through an

where h is the wavelength of the light, r, is the radius of the ifh fringe, d is the distance between point P and the plane C, L is the length of the birefringent medium and k is a constant depending on the principal refractive indices. By measuring the sequence of r, the distance d can be calculated. birefringent medium

n

C

Figure 17: Optical path for conoscopy. Instruments based on SCP use a laser beam focused at the measurement point, perpendicular to the scanning plane. The metrological characteristics vary according to the adopted optics. Typical values given by the manufacturer are reported in Table 4. The measuring range allows for the application of SCP to 3D measurements of surfaces at macro- and micro- scales. An advantage of the method is that the incident beam and the reflected cone are coaxial and very narrow, making it possible to measure cavities and edges. A limitation of the technique which is common to many optical methods, is the difficulty in measurement of glossy surfaces.

Table 4: Metrological characteristics of a SCP.

SNOM is a technique which was developed in 1984 by Pohl et al. [93] and which was aimed at overcoming the diffraction limit of conventional optical systems, as defined by the Rayleigh criterion. An optical probe with subwavelength dimensions is scanned across a surface, keeping the distance of the probe tip from the surface constant and at a nanometric level. In this way the spatial resolution of the optical image is not dependent on the wavelength of the incident light, but is solely dependent on the size of the aperture. Presently, apertures with dimensions of 50-100 nm have been manufactured by using focused ion beams [94]. Critical to the successful application of SNOM is the fabrication of the probe and the control of the distance from the probe tip to the surface. Efforts have been made to identify the procedure needed to obtain reproducible probes with good optical properties [95]. SNOM instruments which are commercially available today use tapered metal-coated glass fibres for the probe. To keep the distance from the surface constant during a scan, shear force methods are often used [96, 971 where a dither piezo induces vibrations on the fibre tip with amplitudes of a few nanometres and which decrease when the tip approaches the sample surface. Attempts to couple SNOM probes with other measuring systems have been recently proposed. The goal is the integration of topographic measurements with information on optical properties. Hybrid systems of SNOM with Scanning Tunnelling Microscopy (STM) have been described. One example [98] uses an optical fibre with the aperture covered with a thin transparent metal layer, so that the tip also acts as an STM probe. The coincidence of channels for both electron and photon transport allows for simultaneous SNOM/STM images to be obtained with lateral resolution down to a few nanometres. More common are the attempts to combine SNOM with AFM [99, 100, 941. In some applications the cantilever tip possesses a small hole where a light beam is focused. Alternatively, the cantilever is an optical waveguide that transmits the light to the aperture at the tip. In spite of the large amount of available literature and the variety of applications proposed over the last decade, near field optical microscopy has not yet reached the level of a standard measurement instrument, nor have the possibilities of this technique been fully explored. Large range topography characterisation and surface mapping Topographic characterisation of fine surfaces on mechanical workpieces with complex geometry and with relatively large dimensions presents significant challenges. For example, characterisation of mechanical surfaces such as injection moulding dies, medical implants, etc. often requires scanning of larger areas of the surface or areas located apart from each other. Scanning stylus instruments are characterised by a large range-to-resolution ratio. Interference microscopes have a high vertical resolution, but only cover a small area with modest lateral resolution. AFMs are characterised by high vertical as well as lateral resolution, but only over a relatively small scanning area. An attempt to overcome these limitations is made by the use of surface mapping, where adjacent areas of a surface are stitched together to cover larger regions. In particular, the development of free standing AFMs which could be arbitrarily positioned on the workpiece enabled the use of the AFM on larger workpieces. The integration of an AFM and a CMM can combine the high resolution of a AFM with the flexibility of a CMM. De

Chiffre et al. [101,102] describe the construction, testing and use of an integrated system for topographic characterisation of fine surfaces on parts having relatively large dimensions. An atomic force microscope (AFM) was mounted on a manual three-coordinate measuring machine (CMM) achieving free positioning of the AFM probe in space. This enabled the limited measuring range of the AFM (40 pm x 40 pm x 2.7 pm) to be extended by positioning the AFM using the movements of the CMM axes (400 mm x 100 mm x 75 mm). The integrated system can be used in three different ways: The CMM locates the AFM probe in any position within its working volume (X x Y x 2 max 400 mm x 100 mm x 75 mm) and a measurement covering max 40 pm x 40 pm is performed (corresponding to the maximum scan area of the AFM). The CMM positions the AFM probe at different places for spotwise investigation of larger areas within the C MM working volume. The CMM is used to reposition the AFM probe in between surface roughness measurements to stitch together different areas covering continuous regions larger than 40 pm x 40 pm. An application of the instrument was the surface mapping of an area larger than 40 pm x 40 pm of a dental plate. Four overlapping areas of 40 pm x 40 pm were scanned and tiled together to produce an area of 65 pm x 65 pm. Figure 18 shows the comparison of the four tiled areas with a reference single scan measurement of 40 pm x 40 pm. The Sa values are 0.15 pm and 0.16 pm respectively. Stitching together multiple measurements of adjacent areas using an interferometric microscope in connection with a precision stage has been described by Wyant et al. [103]. It was found that a 20 percent overlap of the regions give a good compromise between good repeatability and obtaining a large field of view with a minimum number of data sets. An attempt to solve the problem essentially through the use of software has been reported [104].

5.4

Figure 18: Surface mapping of a dental plate. Top: four overlapping tiled areas (65 pm x 65 pm). Bottom: reference single-scan measurement (40 pm x 40 pm) [IOI].

5.5 Truly 3D characterisation of surface topography

Investigations related to the description and characterisation of surfaces of emerging interest have typically involved techniques and methods developed for conventional surfaces. One of the difficulties posed by non-conventional surfaces is the measurement of the relevant features. Contact probing is often impossible due to the lack of accessibility and to the steep slopes, which may be well in excess of the 45 degrees that can be followed by the stylus of a conventional surface roughness instrument. Optical techniques have problems created by the reflectivity associated with free form geometries and steep slopes. Atomic force microscopy suffers from measuring range limitations. All in all, current techniques are not fully 3D but somewhat less than 2%D, i.e., only portions of the surface with respect to the third dimension can be accessed and characterised. There is a clear need to produce a new tool for truly 3D characterisation of surface topography suitable for quantitative characterisation of surfaces featuring steep slopes, abrupt contours, re-entrances, and high aspect ratios. The need is to develop a technique where the complete topography can be determined by a truly 3Dcharacterisation of the surface, developing metrologically correct techniques producing traceable measurement results. Among the methods that potentially can be cons ide red for co m pleme ntary a ppIicat ions a re: a) confocal microscopy in connection with sweeping techniques, see e.g., [105]; b) large atomic force microscopy, using a probe mounted on a coordinate measuring machine to cover the sub-micrometre range on large components [ l o l l ; c)

SEM used in conjunction with image processing from stereographs [106];

d)

optical profilometry using multiple wavelength diode laser interferometry [107]; e) contact profilometry used in conjunction with the development of special stylii, and a multitracing procedure and surface reconstruction software with deconvolution algorithms, as described in section 3.7, suitable for steep slopes and sharp edges in the micro metre range. Moreover, standardisation of 3D analysis should be pursued, defining the size of the measured area, since large variations of the measured parameters can be observed by varying this area, in comparison with 2D analysis [108]. 6

CHARACTERISATION OF THE NEAR SURFACE

Challenges in the characterisation of the near surface are being brought on by the increasing importance of ultrafinely finished surfaces. In addition to low values of surface roughness, the extent of the near surface region, altered by processing is also quite small (typically less than 1 pm). The difficulties in assessing the surface and subsurface integrity of finely finished surfaces have recently been addressed in a ClRP keynote paper [5]. In particular the need to assess very finely finished surfaces is often motivated by the processing of single crystal materials, in particular semiconductors for photonic applications. Very near surface gradients of crystallinity, stoichiometry, porosity, etc. and/or the presence of defects and residual stresses can have significant effects on the performance or life of the surface. For example, for a precision optical surface, the presence of residual stresses may alter the necessary geometric form, or for

coatings, gradients in material properties and the presence of defects and residual stresses may cause cracking or delamination. Examples of several emerging methods for the characterisation of mechanical properties, and the presence of defects and subsurface damage of finely finished surfaces are presented below. 6.1 Nanoindentation Although there has been much progress in the development of a variety of techniques for near surface mechanical analysis of bulk materials and thin films, there still remain significant challenges in the characterisation of surface regions of several hundred nanometres or less. For example, whereas conventional microindentation has long been employed to measure surface mechanical properties, there are significant limitations with this technique when attempting to characterise thin films or surface regions less than several micrometres. As a result of the substantial progress which has been made in the development of indenting instruments which measure load versus depth (depth sensing instruments), nanoindentation is emerging as a powerful tool for near surface mechanical analysis. Nanoindentation has been shown to be able to successfully characterise surface hardness and the elastic modulus of the very near surface of solids and thin films including studies on metals [log, 1101, ceramics [ I 11, 1121 and single crystal materials [113, 1141. Studies on the viscoelastic-plastic properties of glasses and polymers [115, 1161 have also been reported. Recently, nanoindentation has also been used to determine the near surface residual stress state [ I 171. Fundamental understanding of the measurements which result from nanoindentation, however is still being developed. For the measurement of elastic modulus and hardness with nanoindentation, continuous load versus indenter displacement-measuring instruments combined with methods to determine the contact area between the indenter and the sample surface are typically employed. The differences in values for elastic modulus and hardness obtained using the projected contact areas calculated from the Oliver and Pharr method [I181 and those from direct measurement of the contact area with an atomic force microscope [119, 1201, have been reported [121]. The relationship between the ratio of the projected contact area (or corner to corner area) obtained from the Oliver and Pharr method [ I 181 to the direct area measurement of the indenter image (which accounts for material pile-up) has been analyzed [122]. The effects of indenter tip rounding have also been considered [123].

Charactensation of Elastic Modulus, Hardness and the Onset of Plasticity The measured indentation load versus penetration depth curves can be used to determine the hardness and elastic modulus at a particular depth, and may also be used to investigate the response of the surface during the initial stages of loading. In a very recent study, Lucca et al. [I241 investigated the effects of surface preparation on the mechanical response of single crystal ZnO. Figure 19 shows a typical load-depth curve obtained for the (0001) etched surface (light circles) and the (0001) chemomechanically polished surface (dark circles).

nanoindentation. In a recent study, the increase of residual stress resultant from UV laser-induced cracks in fused silica has been measured using nanoindentation [129]. This relative residual stress measurement (relative to the existing residual stress of the bulk) was made with the aid of a simple theoretical model based on the change of penetration depth and the change in elastic modulus and hardness. In a study of the indentation of intergranular phases of silicate glasses in polycrystalline alumina, the change in the load-displacement curve from the strained silicate-glass films, which had a known value of residual stress, was used to make an estimate for the absolute residual stress [130]. Recently a new method for estimating residual stresses by instrumented sharp indentation, assuming the residual stresses and the residual plastic strains to be equi-biaxial and uniform over a depth which is at least several times larger than the indentation contact diameter, has been proposed [ I 311.

h

z, v

a d m C

.-0 .I-

m

. I -

S Q1

TI

S -

Penetration Depth, h (nm) Figure 19: Load-depth curves obtained for etched and c he momec ha nica IIy po Iis hed (000 1)Zn0 s u rfaces (after Lucca et al., [124]). The curves show: (a) elastic loading, (b) an abrupt increase in penetration depth at constant load, (c) elastoplastic loading, (d) creep at constant maximum load, and (e) unloading. The point at which the unloading curve (e) intersects the depth axis is the permanent depth of indentation. The data enables the evaluation of hardness and elastic modulus according to the method of Oliver and Pharr [ I 181, where the initial stage of unloading is fit to a power law. This allows for the determination of the stiffness during unloading, S = dP/dh, and the contact ., The hardness area, A at the maximum applied load, P and and elastic modulus are then obtained by H = P,,/A S = dP/dh = 2€rA'/2/711'2where 1/€r=(l-v2)/€+(1-v12)/€land € and v are the elastic modulus and Poisson's ratio for the specimen and €, and vI are the same values for the indenter. The abrupt increase in penetration seen at point (b) in Figure 19, referred to as "pop-in" [125], has been observed in a large variety of materials including metals [I261 and semiconductors [127]. It has been most commonly associated with the sudden nucleation of dislocations and the onset of plasticity [125, 1281, although in some cases it has been attributed to oxide layer breakthrough [126]. For the etched and chemomechanically polished surfaces in this study, pop-in was observed at a lower critical load for the etched surfaces as compared to the chemomechanically polished surfaces. The nature of the pop-in observed in ZnO can be examined by considering the initial portion of the loading curve (a). For indentations performed with a maximum load below the critical load at pop-in, the strain produced was found to be totally recoverable. The Hertzian solution for a non-rigid spherical indenter in contact with an elastic halfspace is shown in Figure 19 as the dotted line. This purely elastic behaviour suggests that the release of strain energy at pop-in corresponds to a dislocation nucleation event [125], and the initial yield point. Characterisation of residual stress state The influence of applied stress on the measurement of hardness and elastic modulus using nanoindentation has been investigated by Tsui et al. [I221 and Jarausch et al. [117]. These studies paved the way for new techniques for estimating near surface residual stress using

6.2 Backscattering Spectrometry Rutherford Backscattering Spectrometry (RBS) is a wellestablished technique for probing surface and near surface atomic composition. Using ion beams with MeV energies, it has been used to provide accurate information on stoichiometry, elemental area density and impurity distribution. When employed such that the incident beam is aligned with one of the principal planes of symmetry of a single crystal (channeling conditions), RBS can provide information about both atomic composition and crystal structure. Applications have included the study of the lattice position of impurities of crystalline solids and study of the nature of crystalline or amorphous thin films. Recently, it was demonstrated that channeling could be used to provide quantitative information about the subsurface damage of finely finished single crystals [132, 133-1351. The high energy, light particles used (e.g., H or He ions) can penetrate deeply into the crystal without significant surface damage. Techniques used to study the crystal structure of solids such as x-ray and neutron diffraction rely on radiation with wavelengths comparable to the lattice spacing m) such that the crystal is seen as a diffraction grating to the incident radiation. An incident beam of MeV He ions with wavelength on the order of 1014 m sees the crystal not as a diffraction grating but as columns and rows of atoms which direct its motion through the crystal. As the beam encounters the crystal, some ions make close impact with the atoms at the surface, and experience large angle scattering events. The majority, however, are able to penetrate the crystal. If the crystal contains a thin, disordered or amorphous layer, the scattering yield at the surface increases over that for an undamaged, aligned crystal. If the layer is thin enough, some ions can make their way through the disordered layer, and will encounter ordered structure below. In this case, the backscattered yield will decrease, and a measure of the thickness of the disordered layer based on energy loss can be made. If principally one type of defect is contained below the surface (i.e., stacking faults, dislocations, etc.), studies have shown that the rate of energy loss through the crystal, or dechanneling rate, may possibly be used to identify the type of defect [136, 1371. Channeling can be used for investigating near surface lattice disorder and defects present in bulk surfaces, and can yield information on the crystalline structure of the epitaxial film and of the substrate/film interface. Grazing incidence scattering geometry allows for enhanced depth resolution such that depths as shallow as 10 nm can be investigated. Previous work demonstrated the use of glancing angle detector positioning to obtain damage

depth profiles of the subsurface damage in ultraprecision machined CdS, and chemomechanically polished CdS and ZnSe [132, 1341. 6.3 Electrical properties scanning probe rnicroSCOPY The relationship between the presence of defects in a material and changes in the electrical properties of the surface has been studied for some time. Changes in the local atomic bonding resultant from defects have a direct influence on the surface electrical properties. For example, dangling bonds associated with dislocations can act as acceptor-like sites [138, 1391 which can influence electrical properties by trapping carriers so that the free carrier concentration is reduced. Also, a positive space charge is developed around trapped carriers, e.g., electrons, which changes the local carrier concentration and band structure. Alberts et al. [I381 measured the carrier concentration of various AI,Gal.,As layers on a (001) Si substrate prepared using organometallic vapor phase epitaxy. For a 4 pm thick film the presence of dislocations and microtwins near the AI,Gal.,As/Si interface was confirmed using cross-sectional TEM. In this region the hole concentration, obtained by electrochemical capacitance-voltage (C-V) measurement, was found to increase two orders of magnitude. Similar results have been obtained with ZnSe films on GaAs [140, 1411. The trapping of electrons in the n-type ZnSe lead to a decrease in the carrier concentration of about one order of magnitude near the ZnSe/GaAs interface. Girault et al. [I421 introduced dislocations in n-Hgo8CdonTe by uniaxial plastic deformation at room temperature, and found that at small deformations the carrier concentration decreases while at higher deformations the carrier concentration increases. A possible explanation given for the increase was the generation of donor-type point defects at higher deformations. Guergouri et al. [I391 studied the effects of dislocations introduced by indentation on p-Cdo 9dn004Te. From C-V curves measured before and after indentation, the carrier concentration was found to increase from 9.25 x 101’ cm-3to 2.4 x 1013 ~ m - ~ . Whereas the traditional materials analysis techniques, including secondary ion mass spectrometry (SIMS), spreading resistance profiling (SRP), and capacitancevoltage (C-V) measurements have long been used for the characterizations of the electrical properties of surfaces mentioned above, they are limited by one-dimensional capability and spatial resolution. The maturation of atomic force microscopy (AFM) has brought on the development of a variety of techniques, based on the AFM, which enable the measurement a variety of properties including work function, electric field strength, resistance and capacitance. The scanning probe microscope now enables these measurements to be performed with twodimensional spatial resolution down to 10 nm. The capability for high lateral spatial resolution allows for mapping local properties changes within the plane of the finished surface or can provide the possibility for crosssectioned samples (e.g., cleaved crystals) to be scanned across their thickness enabling damage-depth information to be obtained. Below, three techniques for electrical properties measurement are described. In all three techniques a probe is scanned in contact (or near contact) with the surface, and topography and electrical properties are acquired simultaneously, enabling a direct correlation of a feature’s location with its electrical properties. Scanning Capacitance Microscopy

In scanning capacitance microscopy (SCM), a conductive probe and the surface, typically a semiconductor or

insulator, form a capacitor for which the change in capacitance with voltage is measured when an AC voltage is applied. SCM uses an AC bias usually in the kHz frequency range because the typical measured capacitance is on the order of lo-” F. The capacitance is measured by a high frequency RCA-type detector [I431 which produces a voltage that corresponds to the change in capacitance for the applied AC bias. The method exploits the fact that the capacitance-voltage relationship is a function of the carrier concentration. In scanning capacitance spectroscopy (SCS) [144, 1451the applied DC bias between the probe and sample is cycled on successive scan lines. This gives dC/dV at several different applied voltages which can be numerically integrated to get the C-V curve of a small region. In a study relating to defect characterisation, Hansen et al. [I461 studied the change in capacitance at the surface termination of threading dislocations present in a GaN film grown by MOCVD on c-plane sapphire substrates. The dislocation density of the film was estimated to be -5 x 10’ ern-'. By comparing the topography and the dC/dV measurement, a low dC/dV signal was found to be correlated with the dislocations. A nearly 2 V increase in the flatband voltage near the dislocation indicative of the presence of negative charge was found. It was postulated that this observed effect could be due to deep acceptorlike trap states near the valence band, or the segregation of charged impurities or point defects because of the chargektrain field that surrounds the dislocation. The SCM has also seen recent use in the measurement of carrier concentration. Two-dimensional measurement of carrier con centrat ion profiles with resolutions approaching nanometer scales have been reported [147-1491, and several recent studies have reported improved techniques for the measurement carrier concentration in Si with SCM [ I 50,1511. Scanning Surface Potential (Kelvin Probe) Microscopy Scanning surface potential microscopy, also know as scanning Kelvin probe (SKPM) microscopy [ I 521 measures the contact potential difference (difference in work functions) between the probe and the sample. To measure the contact potential difference, an AC voltage with DC offset is applied to a metal-coated probe, and the sample, probe, and a well-controlled air gap between the probe and sample act as a capacitor. The associated electric field results in a force between the probe and sample, which at the frequency of the applied voltage, is proportional to the difference between the DC offset voltage and the contact potential difference between the sample and probe. A feedback loop is used to adjust the DC offset voltage to null the force at the frequency of the applied AC voltage. The offset voltage is equal to the contact potential difference between the sample and probe. A method for correcting for the possible distortions in measured potential which may occur because of topography has been recently reported [ I 531. In a study of a cleaved GaAs/AIAs multiple quantum well and a cleaved InAIAs/lnGaAs heterostructure, surface potential on layers as thin as 40 nm was able to be measured [154]. Lateral resolution as small as 10 nm have been reported [ I 551. Agreement between measurements of the location of a Si p-n junction made by scanning capacitance microscopy and scanning Kelvin probe microscopy has been reported [ I 561. Scanning Spreading Resistance Microscopy The recent development of scanning spreading resistance microscopy (SSRM) has been reported by DeWolf et al. [157-1601. SSRM uses a conducting probe and a contact

on the back of the sample to measure resistance. Mathematical models which include the current spreading effects are used to extract carrier profiles from the measured resistance profiles. A one-dimensional model has been reported [I571 and there are present efforts to extend the model to two dimensions. SSRM has been used to examine a series of 50 nm steps on Si doped with B in concentrations of lo1'- lozo cm-3 [158]. It was shown to be able to resolve the steps with a resolution of 10-20 nm for the various concentrations with the highest concentration yielding the best resolution. In another paper by the same research group [I591 multilayer InP structures were measured with SSRM and compared to SIMS. SSRM was able to measure features as small as 50 nm over a concentration range of IO1'-lO1' cm-3for both n- and p-type material. 6.4

Photoluminescence (PL) Spectroscopy

Photoluminescence (PL) spectroscopy is a sensitive, nondestructive technique that can provide information on the type and distribution of defects and/or impurities in a semiconductor [ 1611. In direct bandgap semiconductors, PL is the result of photo-excited electrons returning to their ground state and emitting photons characteristic of the material. PL has been used extensively to investigate optical properties and electronic band structure of semiconductors [162]. Because the band structure is sensitive to the presence of defects and impurities, the PL response is altered according to the type and density of defects or impurities. While defects or impurities in the crystal may result in new PL spectral peaks resultant from the recombination of electrons and holes at the defect [163], they may also introduce nonradiative mechanisms that do not result in photons (e.g., an Auger-type process). Such nonradiative mechanisms compete with the radiative luminescence and effectively lower the relative intensity of the spectral peaks. As a result, the spectral content of PL measurements combined with the overall PL intensity can provide important information regarding the crystalline quality [161]. The best resolution of PL spectra occurs at temperatures well below room temperature since lower temperatures reduce the thermal broadening of the photo-excited carriers. Cooling the semiconductor to 4 K (liquid He) reduces the thermal broadening from 25 meV at room temperature to c 1 meV [164]. A variety of studies assessing near surface damage on polished compound semiconductors have employed PL. Laczik et al. [165, 1661 investigated the subsurface damage present in polished (100) LEC S-doped InP wafers using total light, room temperature PL. To obtain damage vs. depth information, the wafers were chemically angle-polished with a taper angle of about 0.01 degree, using the method of Huber [167, 1681. The technique combining the PL and the angle-polish was capable of c 2 pm lateral and c 10 nm depth resolution. The study revealed damage extending to about 50 nm below the surface with a "good" region extending to 10 nm below the surface which appeared to be damage free. The damage was interpreted as consisting mainly of dislocations with the possibility of some cracks. The precise nature of the "good" region was not determined and whether it was indeed damage-free required further investigation. Whereas total light measurement can be an effective tool for imaging contrasts between damaged and undamaged regions, PL spectroscopy offers the advantage of measuring the spectrally resolved PL response of the material to photo-excitation. Swaminathan et al. [I631 used low temperature (10-70 K) PL spectroscopy to study GaAs with the surface conditions of: as-cut. mechanically

polished with a 600 grit SIC paper, scribed with a carbide tipped tool and chemically (Br3-CH30H) polished. For wafers subjected to surface damage from saw cutting, mechanical polishing and scribing, a new luminescence band at about 1.4 eV was observed at 10 K and thermally quenched above 30 K. For the chemically polished samples, no 1.4 eV band was observed. The band was attributed to point defects created by limited dislocation motion at or near the surface. The near band edge PL intensity of as-cut samples was approximately an order of magnitude less than the polished samples, suggesting more severe mechanical damage. In an early study, Akimova et al. [I691 combined PL spectroscopy at low temperature (T=77 K) with periodic chemical etching to perform depth profiling of the subsurface damage layer in CdS crystals subjected to mechanical and chemomechanical polishing. The depth of damage was found by measuring the variation of the chemical etch rate, as well as the band edge and deep level PL intensities, with the thickness of the layer removed by etching. The depth of the damage layer was less with chemomechanical polishing than with mechanical polishing and increased with diamond grit size for mechanical polishing.

7 TOLERANCING AND STANDARDISATION The field of texture was revised by I S 0 in 1996-2001 with the introduction of a number of new standards belonging to the Geometrical Product Specifications (GPS) collection, as reviewed in a recent keynote paper [7]. The new I S 0 standards distinguish among parameters referring to unfiltered parameters (P), roughness parameters (R) and waviness parameters (W) and allow for a more precise definition and verification of surface texture tolerances than before, through a detailed specification of the measuring conditions. Among other aspects, the emerging GPS philosophy underlines the importance of relating tolerances to functionality, this being approached by the use of a number of different surface texture parameters. As discussed in the above-mentioned keynote paper, work is still needed in order to achieve a clear and complete description of surface functionality. In conventional 2D surface texture measurement, wavelengths under 13 pm and amplitudes less than 25 nm (corresponding to Ra values of 6 nm) are not covered by existing I S 0 standards [ I 81, which therefore disregard typical ranges of interest to the usual AFM metrology (Table 5). Since the ranges of definition seem to be dictated by the physical possibilities of existing stylus instruments, it can be assumed that the definitions also can be extended to values below those, but this must be investigated.

Table 5: Definition ranges for surface texture measurement according to I S 0 [18]. Three dimensional surface texture measurement is not yet covered by international standards, but it is the object of on-going research projects in Europe and other countries. Standards concerning this area are currently being considered bv I S 0 TC 213 and are expected to amear in

the near future. These standards are basically a result of research carried out within the European Programme, from which several new 3D parameters have been proposed [170]. The new areal parameters in the proposal are divided into two groups: Field Parameters that use all the available data from the texture surface; and Feature Parameters that use only data from previously identified segments from the texture surface. Field Parameters are grouped in S-Parameters, Field Curves, and VParameters.

worthwhile to repeat here the recommendation by a ClRP Working Group in a recent keynote paper [7]: Feature separation is recognized to be more important than quantification. The latter can be performed using simple parameters like e.g., the standard deviation. Conventional tolerancing rules generally used for common manufacturing processes cannot be applied to components in the micrometre range, or to surfaces in the nanometre range, and new definitions are required. Weckenmann discusses the fact that the relevance of new tolerancing rules will increase when tolerancing small irregularities and microstructures of the workpiece surface in the micro and nano-techniques [171]. 8 TRACEABILITY AND CALIBRATION Due to increasing needs for quality assurance, efforts are currently being made to achieve traceability with lower uncertainties. This applies to conventional 2D surface texture measurements as well as to the emerging fields at the nanometre level and to 3D surface topography characterisation. Some of the most recent achievements in the field of calibration standards and instruments are mentioned below. The mass production and use of calibration standards for surface roughness down to the nanometre scale has been described by Trumpold et al. [172]. The design of these calibration standards is based on injection moulding of plastic negatives with different step height, sinusoidal, triangular and arcuate profiles, covering Pt-values from 0.05 pm up to 100 pm and PSm values from 0.8 pm up to 800 pm. Primary calibration standards have been produced by ion-beam and plasma etching (step height standards), by holographic generation of sinusoidal structures (Figure 20) with two-beam interference exposure and by ultra-precision diamond cutting. From primary standards compression and injection moulded plastic negatives and Ni-negatives have been made from which again Ni-positives were produced. The replication processes showed negligible deviations from the Pt and Pa values compared to the primary standards.

Table 6: S and V field parameters proposed in [I701 Table 6 shows the S and V Parameters proposed in [I701 for consideration by ISO. Many parameters in the proposal are derived from the corresponding 2D parameters, while some are uniquely devised for surface characterization. It is expected that the findings related to the areal description of surface texture will lead to a new revision of the conventional 2D parameters. It is

Figure 20: Master CD with sinusoidal profiles [172]. The production of nanometre scale transfer standards for calibration of the three orthogonal axes of a scanning probe microscope is described by [ I 731. The standards range from step heights of 8 nm to 2400 nm and horizontal

pitch from 30 nm to 10000 nm. The calibration standards are supplied with a computer program for the calculation of calibration parameters and their associated uncertainties. Comparison measurements on the reference standards by 13 partners are reported in [I741 (see also [175]). Actuators have been known for many years as complementary to artefacts in connection with calibration of surface roughness instruments. A novel low-cost active vertical calibrator has been developed at the University of Warwick, as reported in [172]. The prototype has worked well on stylus instruments and AFMs. It has a sensitivity making nanometre-level of approximately 3 nm d-', control quite easy. A range of 1 pm is readily obtained. Among the recent achievements that address the issue of traceability, NPL has developed NanoSurf IV, a surface texture measuring instrument that measures displacements in two orthogonal axes with traceable metrology inherent in its design [69, 701. The uncertainty analysis has been calculated according to the I S 0 Guide to the Expression of Uncertainty in Measurement (GUM) [176]. The combined standard uncertainty of measurements in the X and 2 axes at 95% confidence is f 1.3 nm. NanoSurf IV is linked to the realisation of the metre via the calibrated frequency of its laser source. Another instrument developed to achieve metrologically enhanced conditions is based on a new combination of a monolithic x-ray interferometer made from silicon and a scanning tunnelling microscope for use in calibrating grating structures with periodicities of 100 nm or less. This instrument has been described by [ I 771. The instrument movements are traceable to the definition of the metre and the nonlinearity associated with the optical interferometers used to measure displacements in more conventional metrological scanning probe microscopes removed. The development of appropriate calibration procedures is dynamically following instrument and artefacts development. The guidelines for calibration of stylus instruments have recently been revised by I S 0 [178]. Calibration procedures for standards as well as for calibrating instruments in X-, Y- and 2-direction have been developed and tested under the above-mentioned project [I721 and proposals for standardisation of calibration standards and calibration procedures were derived from the results of the project. Calibration of the computation algorithms in surface texture instruments is an important issue for achieving traceability of measurement results. Reference software for roughness analyses has been made available by the PTB [I791 following the concept in the new I S 0 5436-2 [180]. Optical techniques are receiving increasing interest, but are more difficult to deal with compared to stylus instruments with respect to traceability. A recent proposal for a guideline to calibrate interference microscopes is described in [181]. The guideline applies to the calibration of optical microscopes for the measurement of surface topography using standards described in I S 0 5436-1 for the calibration of stylus instruments. Uncertainty budgeting for surface roughness measurements is a very important aspect of traceability. The current uncertainty budgeting for calibration of stylus instruments is given by EAL [I821 but complete budgeting of measurements on different workpieces has not been made generally available. Basic works listing the uncertainty contributions in surface measurements have been published recently by Schwenke [183], KrugerSehm [I841 and Haitjema [185]. It is suggested that the measuring uncertainty can be reduced, to a certain

extent, by simulation, e.g., Monte Carlo simulation [ I 83, 1851. The uncertainty of AFM measurements is addressed in [175]. The uncertainty in 3D measurements is the object of the European project SURFSTAND [ I 701 but results have not yet been made publicly available. This is a field of significant interest, and a major amount of effort is expected to be made here in the coming years. 9

CONCLUSIONS

Following the evolution of technology, with the introduction of new production techniques and measuring instruments, the field of surface metrology has broadened its interest to include both traditional topography analysis and near surface characterisation. In this regard, a broader definition of the surface, which takes into account the depth regime of importance should be considered. A number of surfaces of emerging interest are associated with new products or innovative processes and require special attention with regard to their surface metrology. Of increasing importance is the characterisation of surfaces at the nanometre scale. Although the measurement of surface topography is a wellestablished engineering science, it continues to evolve. Stylus instruments, the AFM and optical instruments are continuing to undergo improvements and innovations to meet new demands. In addition, challenges in the characterisation of the near surface are being brought on by the increasing importance of ultra-finely finished surfaces and new techniques for near surface characterisation are emerging. Tolerancing and standardisation, as well traceability and calibration, are areas of significant importance, and are seen to require further study and the development of more specific standards to meet the emerging needs of surface metrology. 10 REFERENCES Peters, J. et al., 2001, Contribution of CIRP to the development of metrology and surface quality evaluation during the last fifty years, Annals of the CIRP, 50/2:471488. Moriarty, P., 2001, Nanostructured materials, Reports on Progress in Physics, 64:297-381. Lonardo, P.M., Trumpold, H., De Chiffre, L., 1996, 3D surface microtopography Progress in characterization, Annals of the CIRP, 45/2:589-598. Vorburger, T.V., Dagata, J.A., Wilkening, G., Lizuka, K., 1997, Industrial uses of STM and AFM, Annals of the CIRP, 46/2:587-620. Lucca, D.A., Brinksmeier, E., Goch, G., 1998, Progress in assessing surface and subsurface integrity, Annals of the CIRP, 47/2:669-693. Evans, C.J., Bryan, J.B., 1999, "Structured", "textured" or "engineered" surfaces, Annals of the CIRP, 48/2:541-556. De Chiffre, L., Lonardo, P.M., Trumpold, H., Lucca, D.A., Goch, G., Brown, C.A., Raja, J., Hansen, H.N., 2000, Quantitative characterisation of surface texture, Annals of the CIRP, 49/2:635852. Leach, R.K., 1999, Calibration, traceability and uncertainty issues in surface texture metrology, NPL Report CLM 7, 1-56. Kraus, M.R.H., Westkaemper, E., 2000, Functional and depth-oriented characterization of technical surfaces, Proc. Id euspen Topical Conference on Fabrication and Metrology in Nanotechnology, Copenhagen, 1:I 31-136.

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