Surface Roughness - Standards and Uncertainty

R. Krüger-Sehm and L. Koenders

Physikalisch-Technische Bundesanstalt, Braunschweig, Germany

Generation

- Grinding

- Honing

- Lapping

Function

- Gloss

- Paintability

- Wear

Characterisation

- Measurement

- Visualisation

- Quantification

Surfaces

Diamond turned Al surface different scales

Nomarski picture

3D picture of the AFM data obtained near the centre

Picture showing the grooves and some contamination

Diagram Wavelength vs. Amplitude - Instruments

100 nm

10 nm

1 nm

100 pm10 nm 100 nm

1 µm

1 µm 1 mm 10 mm

100 µm

10 µm

10 µm 100 µm

SEM

Light scattering (vis)

SPM

Confocal

microscope

Interference

microscope

Stylus

instrument

Wavelength

Ampl

itude

Instruments, Specimens and Procedures

Guidelines

SpecificationCalibrationEvaluationVerification

SurfaceMeasurement

Standards

SurfaceMeasurementInstruments

Standards

ISO 14 638 Geometrical product specifications(GPS) matrix model

ISO 5436-1 Standard specimen

ISO 5436-2 Software standards

ISO 4287 Definition of surface-parameters

ISO 4288 Surface properties – stylus instruments – rules and conditions

ISO 11562 Characteristics of Gauß filter

ISO 4291 Characteristics of 2RC filter

ISO 3274 Stylus instruments definitions

ISO 12179 Calibration of stylus instruments

ISO 13565-1 Filter-definition for Rk parameters

ISO 13565-2 Definition of Rk parameters

EN 10049 Measurement of Ra and RPc on metallic flat products with stochastic surface texture (skidded stylus)

EAL-G-20 Calibration of stylus instruments for measuring surface roughness

Standards for Roughness Measurement

Diagram Wavelength vs Amplitude - Standards

Dissemination of Units by Calibration Standards

Pt, D

Ra, Rz, Rsm,... Ra, Rz, Rq, ... Traceable Interference Microscope PTB

Stylus Instrument PTB

Interference Microscope

Stylus Instrument

Guidelines to support

traceability

MeasurementstandardsISO type

A

C D1, D2

established e.g. EAL G20, ISO12179

draft in VDI-committee PTB

Industry

Contact Stylus Instrument (ISO 3274), Specifications

Feature usual typical usual Lateral measuring range 20 mm 50 ...120 mm 300 mmVertical measuring range 0.3 µm 60 µm 1mm Vertical resolution 16 bit Straightness deviation @ 50 mm (Wt0) 20 nm 50 nm 100 nmNoise amplitude @ λc = 0,8 mm (Rz0) 1 nm 20 nm 30 nm Tip radius 0.1 µm 2 ... 5 µm 25 µm

x

zy

ze(x) traced profile

z0(x)instrument reference profile

feed unit

transducer

ampli-fier

A/D-conv.

para-meter

stylus tipsettingsparametersprofiletopography

zg(x) zc(x)zs(x)

l s-Filter

l c-Filter

Alternative setup

ISO 4288:

The waviness cutoff-wavelength depends on the surface specifications. In roundness and straightness measurement the separation wavelength is fixed to 0,8mm(rsp equivalent wave numbers). This must be observed in case of calculating the influence of the measured roughness in form measurement.

ISO 3274:

The primary profile contains the influence from the stylus. Further calculations do not describe the real surface, but a morphological changed one.

ISO 3274:

Applicable for stylus instruments with datum (plane). ISO 12179 allows secondary measuring systems. Practical result: standardisation of metal sheet measurement with skidded stylus systems in SEP 1940, rsp. prEN 10049.

Special Remarks

Periodic profiles

RSm in mm

Stochastic profiles

Ra in µm

Stochastic profiles

Rz in µm

Sampling length

l r in mm

evaluation length

l n in mm

Cutoff

λ c in mm

short wave-length

λ s in µm

Bandwidth

B

max. tip radius r tip

in μm

max. sampl interval

in µm

>0.013 ..0.04 >(0.006) .0.02 >(0.025) ..0.1 0.08 0.4 0.08 2.5 30 2 0.5

>0.04 ..0.13 >0.02 ..0.1 >0.1 ..0.5 0.25 1.25 0.25 2.5 100 2 0.5

>0.13 ..0.4 >0.1 ..2 >0.5 ..10 0.8 4 0.8 2.5 300 2 (5) 0.5

>0.4 ..1.3 >2 ..10 >10 ..50 2.5 12.5 2.5 8 300 5 1.5

>1.3 ..4 >10 ..80 >50 ..200 8 40 8 25 300 10 5

Excerpt of Standards:

•ISO 3274 (1996)

•ISO 4287 (1997)

•ISO 4288 (1996)

•ISO 11562 (1996)

Measurement Conditions

Calibration of Devices

Quality management: Calibration have to be done periodically

and have to be documented!

Aim, result Sample/Standard To do Noise of instrument Flat glass Determination of Rz0, Ra0, ... Straightness deviation of the datum

Flat glass Determination of Wt0

Control/correction of vertical axis/amplification

Certified depth setting standard

Determination of Ptn, Dn for position „c“; comparison with certified value

Repeatability of probing Certified depth setting standard

n repetitions of Pt at the same position

• Depth measurement standards „Type A“ according to ISO 5436 -1

• Nominal values of grooves from 20 nm to 10 µm

• Lateral width from 2 µm to 100 µm • Roughness on measurement areas

down to 1 nm • Uncertainty (k=2) between 3 nm and

25 nm

Depth Setting Standards (1)

dept

h of

pro

file

groo

ve d

epth

roug

hnes

s

width

1 2

3 4

5 6

DPt

roug

hnes

s dept

h

Depth Setting Standards (2)

Substrate: Ø ~ 50 mm, 10 mm thick

Ni-P on Ni , Hardness ~ 580 HV

Grooves ~ 0.24 µm to 75 µm

Width at groove ground 100 µm to 200 µm

• Depth measurement standards „Type A1“ according to ISO 5436 -1

• Nominal values of grooves between 1 µm and 5 mm

• Lateral sizes between 100 µm and 1mm

• Roughness on measurement areas about Rz = 20 nm

• Traceability to length unit by stylus instrument traced back by gauge block, traced back by interferometric calibration

• Uncertainty (k=2) between 25 nm and 60 nm

Depth Setting Standards (3)

Lateral calibration standard

For λc/mm 8 2,5 0,8 0,25 0,08

50 µ

m50

µm

4x

4x

4x

start on reference plane

20 µm (2x)

Feature Typical value Geom etric (type C) Depth(Rz1m ax ) 1, ..., 10 µm Period lateral (RSm ) 80, ..., 250 µm λc 250 µm ; 0.8 m m ; 2.5 m m Lateral standard (type C) Depth 5 µm Period lateral (RSm ) 25, 100, 250, 1000,

2500 µm for λc 80, 250, 800, 2500,

8000 µm

Design

Image:

Dark field

Measurement scheme

Roughness Standard Specimen

Geometrical Calibration Standard (Type C)

Feature Typical value

Geom etric (type C) Depth(Rz1m ax ) 1, ...,10 µm

Period lateral (RSm ) 80, ..., 250 µm λc 250 µm ; 0,8 m m ; 2.5 m m

Profil of geometrical standard

Roughness Calibration Standards, Specifications

Feature typical

Rz 1 ... 20 µm Ra 0.16 ... 3 µm λc 0.8 mm; 2.5 mm

Profile repetition 4 mm

starting points of the evaluation lengths in mm from the starting line

Meßstellenplan für PTB-Rauhnormale (gg), λc= 2,5 mm

Startpunkte der Meßstrecken in mm von Startlinie

richtung

Startlinie

starting line

PTB

Maßstab 5:1

Mess-

scale 5:1

Mittellinie

symmetry line

(1,2

5 m

m)

0,50 mm (11x)

0,20 mm (11x)

Roughness - Standards, Measurement Schemes

starting points of the evaluation lengths in mm from the starting line

Meßstellenplan für PTB-Rauhnormale (g, m, f), λc = 0,8 mm

0.55 4.6 8.65 12.7

Startpunkte der Meßstrecken in mm von Startlinie

richtung

Startlinie

starting line

PT

B

Maßstab 5:1

0.3

0

Mess-4.35

4.1

scale 5:1

8.4

8.15

12.5

12.2

Mittellinie

symmetry line

3 m

m3

mm

Same scale

0.0 1.0 2.0 3.0 4.0 5.0-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

Rauhnormal

μm

mm

• Roughness measurement standard „Type D2“ according to ISO 5436-1

• Nominal values of Rz = {150, 300, 450} nm, expressed in Ra between Ra = 25 nm and 80 nm

• Manufacturing by single diamond turning of digital generated profile amplitude and shape of profile predictable

• profile repetition length 1,25 mm,

• For λc = 0,25 mm

• Calibration with contact stylus instrument, traced back by depth measurement standard

• Uncertainty of calibration (k=2) ~ 6 % and 8 %,

• Approved in Round Robin of 11 DKD-laboratories

• Useable for calibration of interference microscopes, for calibration and verification

Super fine roughness standards

Nano-Roughness-Standards & Specifications

- 1-dim Profil

- Profile Repetition 5*40 µm

- Measuring length 40 µm for5 nm < Ra < 20 nm

- Scan range < 100 µm => λc

- x-y Scans => use of pictures

- Tip shape => λs

- data points < 4000 => λs

Roughness measurement

Aim, result Used standard To Do Noise of device Flat glass Determination of Rz0, Ra0, ... Control or correction of the vertical axis/amplification

Certified depth setting standard

Determination of Ptn, Dn for position „c“, Comparison with certified value

Selection of waviness filter

Roughness standard to be calibrated

Determination of Ra, Rz with λc=0,8 mm Using ISO 8288 (DIN 4768) to select λc

Determination of roughness

Roughness standard to be calibrated

Measurement plan; determination of roughness parameters and standard deviation

Estimation of measurement uncertainty

Calculation following the rules of GUM and related guides

Calibration Verification

Parameter calculation Puncertainty of roughness profil

λc-filter function Fcuncertainty of primary profil

λs-filter function Fsuncertainty of total profil

Model of Uncertainty of Roughness Parameter

Instrument function GSurface profile

uncertainty of parameter value u(K) K

=

P

{Fc

[Fs

(G

(ze (x)) ]}

x

zy

ze(x) traced profile

z0(x)instrument reference profile

feed unit

transducer

ampli-fier

A/D-conv.

para-meter

stylus tipsettingsparametersprofiletopography

zg(x) zc(x)zs(x)

l s-Filter

l c-Filter

Instrument-Function of Stylus Instrument

zg(x) = C ⋅ [ze(x) + zref(x) + z0(x) + zpl(x)+zsp(x)]

where

C Calibration factor z0 Noise of instrument

ze Contacted profile zpl Plastic deformation of surface

zg Total profile zsp Profile deviation by tip radius dev

zref Profile of reference plane

Uncertainty Budget (1)

zg(x) = C ⋅ [ze(x) + zref(x) + z0(x) + zpl(x)+zsp(x)] = C ⋅ zu(x)

where

C Calibration factor zu uncalibrated profile

Model for stylus instruments

Using the product rule

u2(zg) = u2(C) ⋅ z2u + C ⋅ u2(zu)

with with

C = Ptm/Ptn C = Dm/Dn

where where

Ptm value measured Dm value measured

Ptn value certified Dn value certified

Evaluation of Depth Setting Standardsde

pth

of p

rofile

groo

ve d

epth

roug

hnes

s

width

1 2

3 4

5 6DPt

roug

hnes

s dept

h

paraboladept

h of

pro

file

groo

ve d

epth

roug

hnes

s

width

1 2 5 6

3 4

dept

h

Pt D

roug

hnes

s

fitting

Evaluation of type A1 and type A2 depth setting standard, influence of roughness

A

A1: Reference line @ levelling 1A2: Reference line @ levelling 2A:Levelling deviationPt1: @ levelling 1Pt2: @ levelling 2

PtPt

Influence of levelling

Uncertainty Budget (2)Using the product rule u2(zg) = u2(C) ⋅ z2

u(x) + C ⋅ u2(zu) with C = Ptm/Ptn where Ptm value measured Ptn value certified

Each value is uncertain u2(Ptm), u2(Ptn) u2(C) = 1/Pt4m ⋅ [Ptn2 ⋅ u2(Ptm) + Ptm2 ⋅ u2(Ptn)]

With a calibrated instruments Ptn ≈ Ptm (C ~ 1) u2(C) = 1/Pt2m ⋅ [u2(Ptm) + u2(Ptn)]

u2(C) ⋅ zu2 = 1/Pt2m ⋅ [u2(Ptm) + u2(Ptn)]

If the depth of the standard is close to the value of the sample to be measured zu

2/Pt2m ~ 1 u2(C) ⋅ zu

2 = u2(Ptm) + u2(Ptn) u2(zg) = u2(Ptm) + u2(Ptn) + u2(zu)

Model for this valueCalibration certificate

Uncertainty Budget (3)

Model for Pt Ptm is not measured at the same position as the groove is calibrated.

Ptm = Ptn + ∆Pt + b

Track n

Track m- value of the standard at right track

- gradient of the standard ∆Pt/∆y

- repeatability of the instrument b

u2(Ptm ) = u2(Ptn ) + u2(∆Pt) + u2(b )

)(2nPts( )2

31 Gay ⋅⋅2

41

nU⋅

Uncertainty Budget (4)

Effect of λs

Measured profile has uncorrelated points. Due to filtering the points are correlated! The effect of filtering can be expressed by a factor fs [Krystek] u(zf) = fs ⋅ u(zunf) f2s = Δx/(α⋅ λs ⋅√2) where α = √log(2)/π

Krystek Measurement uncertainty propagation in the case of filtering in roughness measurement 2001 Meas. Sci. Technol. 12 63

Table for factor fs

λs in µm Δx in µm fs 2.5 0.5 0.55 8 1.5 0.53 8 0.5 0.31

Uncertainty Budget (5)Effect of λc

Similar to λs. The effect of filtering can be expressed by a factor fs [Krystek] u(w) = fc ⋅ u(zs) f2c = Δx/(α⋅ λc ⋅√2) Where α = √log(2)/π However, λc is much more larger than Δx since the uncertainty of the filtered is nearly similar to those of the unfiltered.

zc = zs – w

u2(zc) = u2(zs) + u2(w) u2(zc) = u2(zs) + f c u(zs)

Krystek Measurement uncertainty propagation in the case of filtering in roughness measurement 2001 Meas. Sci. Technol. 12 63

Table for factor fc

λc in µm Δx in µm fc 250 0.5 0.055 800 0.5 0.031 2500 1.5 0.017

Uncertainty Budget (6)

Effect of parameter function K The uncertainty of the parameter K depends on the algorithm. By the algorithm for K the uncertainty may be different to those of the single point. It is described as a “smoothing factor” S since the uncertainty is reduced in most cases. Example: usys(Rz) = S(Rz) * u(zg) Here S(Rz) is the smoothing factor!

using

Uncertainty Budget (7)

zu(x) = ze(x) + zref(x) + z0(x) + zpl(x)+zsp(x)

u2(zu) = u2(ze) + u2(zref) + u2(z0) + u2(zpl) + u2(zsp) where u2(ze) uncertainty of probed profile

⋅⋅

nRzs

S)(1 2

2

u2(zref) uncertainty of reference profile 12

20Wt

u2(z0) uncertainty due to noise of instrument ( )2

02 1211 Rz

S⋅⋅

u2(zpl) uncertainty due to plastic deformation 3

2pla

u2(zsp) uncertainty due to unknown tip shape

2

2 )(20131

⎟⎠

⎞⎜⎝

⎛⋅⋅⋅ spru

mnm

S μ

S is smoothing factor of parameter

Uncertainty of Points of Profile (1)

Ch.

Input quantity keyword

Determined by

Typical value

Sensitivity-coeff.

Method, distribution

Variance /nm2

3.1 Reference standard

2

41

nU⋅ Un = 15 nm (Cal.

certificate)

1 B Gauss

56

3.2 Deviation in localisation ( )2

31 Gay ⋅⋅ ay = 100 µm

G = 20 nm/mm

G B Rect.

1,3

3.3 Repeatability )(2nPts s = 3 nm 1 B

Gauss 9

3.4 Topography ⋅

⋅nRzs

S)(1 2

2 s(Rz) = 50

nm 1 A

Gauss 521

Chapters are given in relationship to DKD 4-2

Example for a roughness standard of type D with Rz ≈3 µm

Uncertainty of Points of Profile (2)

Ch. Input quantity keyword

Determined by Typical value

Sensitivity-coeff.

Method, distribution

Variance /nm2

3.5 Straightness datum 12

20Wt

Wt0 = 50 nm 1 B

Rect. 0

3.6 Residual noise ( )2

02 1211 Rz

S⋅⋅ nm200 =Rz 1 A

Rect. 83

3.7 Plastic deform. 3

2pla

apl = 5 nm 1 B

Rect. 8,3

3.8 Stylus tip 2

2 )(20131

⎟⎠

⎞⎜⎝

⎛⋅⋅⋅ spru

mnm

S μ

u(rsp ) = 0,5 µm

-20 nm/mm B Rect.

83

Point variance

Sum of variances )(2gzu 761,6

Point )( gzu 28 nm

Chapters are given in relationship to DKD 4-2

Uncertainty of Points of Profile (3)

Ch.

Input quantity keyword

Determined by

Typical value

Sensitivity-coeff.

Method, distribution

Variance /nm2

3.1 Reference standard

2

41

nU⋅ Un = 15 nm (Cal.

certificate)

1 B Gauss

56

3.2 Deviation in localisation ( )2

31 Gay ⋅⋅ ay = 100 µm

G = 20 nm/mm

G B Rect.

1,3

3.3 Repeatability )(2nPts s = 3 nm 1 B

Gauss 9

3.4 Topography 22

2)(1 fs

nRzs

S ⋅⋅

s(Rz) = 50 nm

1 A Gauss

130

Chapters are given in relationship to DKD 4-2

Example for a roughness standard of type D with Rz ≈3 µm

Using ls filtering!

Uncertainty of Points of Profile (4)

Ch. Input quantity

Determined by Typical value

Sensitivity-coeff.

Method, distribution

Variance /nm2

3.5 Straight-ness datum

220

12 sfWt Wt0 = 50

nm 1 B

Rect. 0

3.6 Residual noise ( ) 22

02 1211

sfRzS

⋅⋅⋅ nm200 =Rz 1 A Rect.

25

3.7 Plastic deform. 2

2

3 spl f

a⋅

apl = 5 nm 1 B Rect.

2.5

3.8 Stylus tip 22

2 )(20131

ssp frumnm

S⋅⎟

⎠

⎞⎜⎝

⎛ ⋅⋅⋅μ

u(rsp ) = 0,5 µm

-20 nm/mm B Rect.

2.5

Point variance

Sum of variances )(2szu 226,3

Point uncert.

)( szu 15 nm

Chapters are given in relationship to DKD 4-2

Using ls filtering!

u2sys(Rz) = S2 ⋅u2(zs) = (10/25)* u2(zs)

usys(Rz) = 0.6* u (zs) ~ 9 nm

Since S is smaller than 1 U(Rz) can be approximated with the coverage factor of k = 2 by

[2)( ⋅≈RzU 2

41

nU⋅ + nRzs )(2

+ 12

20Rz

+ 212 )](Rzuv

Abbreviation Uncertainty Source Determined by 2

41

nU⋅ calibration factor from calibration certificate

nRzs )(2

statistic on surface standard deviation of Rz,

n preferred 12

12

20Rz

noise flat glass roughness measurement, 12

by rectangular probability distribution

212 )](Rzuv unknown systematic

errors comparison

Comment: Approximation of starting model of uncertainty, containing the most important sources or those, which are subject to change

Uncertainty of Parameter

lamba-ctype in mm Ra Rz1max Rz Ra Rz1max RzGeometrical coarse 2,5 0,2 0,3 0,2 0,5 0,3 0,3standard coarse 0,8 0,2 0,3 0,4 0,4 0,3 0,3Type C3 medium 0,8 0,3 0,4 0,4 0,2 0,2 0,2

fine 0,8 0,4 0,3 0,4 0,5 0,3 0,5fine 0,25 0,6 0,6 0,5 0,5 0,5 0,5

number of labsRoughness very coarse 2,5 0,5 0,6 0,7 0,4 0,5 0,3standard coarse 0,8 0,5 0,6 0,5 0,5 0,5 0,4type D1 medium 0,8 0,4 0,3 0,5 0,5 0,5 0,1

fine 0,8 0,3 0,7 0,7 1,1 0,3 0,9number of labs 7 5Roughness coarse 0,25 0,3 1,3 0,5 0,6 1,5 0,6standard medium 0,25 0,3 1,2 0,8 0,4 0,8 0,7type D2 fine 0,25 0,9 2,1 1,9 1 2,4 1,9number of labs 6 4

Parameters with lamba-s Parameters without lamba-s

9 4

Comment:• Noticed are the standard deviations of the average values of parameters (excerpt)• Average over laboratories, numbers are mentioned• Labs far from average are excluded (En-criterion of EAL G7)• With λs no significant improvement of uncertainty component, even deterioration• better value in comparison with and without ls

Comparison of Roughness Parameters in DKD - Round Robin

Contribution to Uncertainty

0,5%

2,0%

0,5%

0,5%traceability

surface

noisecomparison

Expanded uncertainty of roughness parameters, e.g. Rz: ~ 3.5% of measurement value.

Contribution of Sources: