Design of a Metrological Atomic Force Microscope Head

Design of a Metrological Atomic Force Microscope Head
Design of a Metrological Atomic
Force Microscope Head
I. de Rijk
DCT 2008.141
Master’s thesis
Coaches:
dr. ir. P.C.J.N. Rosielle
ir. C. Werner
Supervisor:
prof. dr. ir. M. Steinbuch
Technische Universiteit Eindhoven
Department of Mechanical Engineering
Control Systems Technology Group
Eindhoven, December, 2008
Summary
Atomic Force Microscopy (AFM) uses the interaction forces between an atomically
sharp tip and a sample surface to measure surface properties. The tip is part of a
cantilever and is scanned over the surface while maintaining a constant deflection
of the cantilever. The deflection is kept constant by adjustment of the distance between the tip and sample. The constant deflection of the cantilever gives a constant
interaction force between the tip and sample. The measured adjustment of the distance between the tip and sample gives a constant interaction force image, which
closely resembles the topography of the surface.
To calibrate commercial AFM’s, calibrated samples are needed. A metrological
AFM is being developed for the Dutch standards laboratory (NMi- Van Swinden
Laboratory) for the calibration of these samples. This AFM consists of a sample
stage and a stationary AFM head. The sample stage manipulates the sample in
the scan directions and adjusts the distance between the tip and sample. The AFM
head is kinematically mounted on the stationary part of the sample stage. The AFM
head contains the cantilever and measures its deflection. The design of the AFM
head is described in this report.
The most important requirements of the design are:
• A vertical measurement resolution at the cantilever tip of 0.1 nm.
• The thermal center should be at the cantilever tip.
• The implementation of observation of the cantilever backside and tip is required.
The deflection measurement of the cantilever is performed by Optical Beam Deflection (OBD). In OBD a laser hits the cantilever backside at an angle, is reflected and
hits a detector at some distance from the cantilever. At deflection of the cantilever,
the bending of the cantilever causes displacement of the laser spot on the detector,
this spot displacement is measured. The OBD system contains three separate and
replaceable modules:
• The laser diode module, consists of a laser diode and beam shaping optics
and is designed for optimal thermal stability.
• The cantilever module consists of holder on which the cantilever is mounted
externally. The holder is kinematically mounted on the base of the AFM head.
• The photo diode module is equipped with a four segmented photo diode
with a lateral resolution of < 0.1 µm to measure spot displacement. With
ii
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a cantilever to detector distance of 40 mm the requirement of the vertical
resolution at the cantilever tip (0.1 nm) is met.
The observation is performed by a commercial lens and CCD camera. The measurement and observation system are integrated into a compact design with its
thermal center at the cantilever tip.
Samenvatting
Atomic Force Microscopie (AFM) gebruikt de inter-atomaire krachten tussen een
scherpe tip en een oppervlak om oppervlakte-eigenschappen te bepalen. De tip
maakt deel uit van een cantilever, die over het oppervlak bewogen wordt. De buiging van de cantilever wordt hierbij constant gehouden door de afstand tussen de
tip en het oppervlak te manipuleren. De constante buiging van de cantilever resulteert in een constante inter-atomaire kracht tussen de tip en het oppervlak. Door de
verplaatsingen van de manipulatie te meten, wordt een constante kracht afbeelding
van het oppervlak verkregen. Deze afbeelding komt sterk overeen met de topografie
van het oppervlak.
Om commerciële AFM’s te kalibreren zijn gekalibreerde samples nodig. Voor de
kalibratie van deze samples wordt een metrologische AFM ontwikkeld voor het
Nederlands meetinstituut (NMi- Van Swinden Laboratorium). Deze AFM bestaat
uit een sample manipulator en een stationaire AFM kop. De sample manipulator
beweegt het sample in de scan richtingen en past de afstand tussen tip en sample
aan. De AFM kop is kinematisch bevestigd op het statische deel van de sample manipulator. Verder bevat de AFM kop de cantilever en meet de buiging. Het ontwerp
van de AFM kop is beschreven in dit verslag.
De belangrijkste eisen van het ontwerp zijn:
• De benodigde verticale meetresolutie aan de tip van de cantilever is 0.1 nm.
• Het thermisch centrum zit op de cantilever tip.
• Observatie van de achterkant van de cantilever en de tip moet mogelijk zijn.
De meting van de buiging van de cantilever wordt gedaan door Optische Reflectie
(OR). Bij optische reflectie wordt een laser onder een hoek op de achterkant van de
cantilever geschenen, deze wordt gereflecteerd en eindigt op een detector op enige
afstand van de cantilever. Bij buiging van de cantilever verplaatst de spot op de detector, deze verplaatsing wordt gemeten. Het OR systeem bevat drie afzonderlijke
en vervangbare modules:
• De laser diode module, bestaande uit een laser diode en optiek om de laser
straal te vormen. De module is ontworpen met optimale thermische stabiliteit.
• De cantilever module bestaat uit een houder waarop de cantilever extern
wordt gepositioneerd. De houder is kinematisch verbonden met de basis
van de AFM kop.
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• De foto diode module is voorzien van een photo diode met vier segmenten.
Deze diode heeft een laterale resolutie van < 0.1 µm om de laser spot verplaatsing te meten. Met de detector op een afstand van 40 mm van de cantilever wordt aan de eis van de verticale resolutie van 0.1 nm voldaan.
De observatie wordt uitgevoerd met een commerciële lens en CCD camera. Het
meet- en observatiesysteem zijn geïntegreerd in een compact ontwerp waarvan het
thermische centrum op de tip van de cantilever zit. Hiermee wordt aan alle gestelde
eisen voldaan en is de metrologische AFM kop ontworpen.
Glossary
Symbol
Unit
Measurement system
a
m
acol
m
d
m
E
Pa
f
m
ID
A
Ijn
A
Ip
A
Isn
A
Itn
A√
N EP
W Hz
Popt
W
RSH
Ω
s
m
w
m
η
A/W
◦
θ
∆a
m
∆f
Hz
∆z
m
∆i
A
Discription
Spot size on detector
Collimated beam waist
Collimating to focussing lens distance
Modulus of elasticity
Focal length
Photo diode dark current
Johnson noise
Photo generated current
Shot Noise
Total noise
Noise equivalent power
Optical power
Shunt resistance
Cantilever to detector distance
Beam waist at focus
Photo sensitivity
Beam divergence angle
Spot displacement on cantilever
Noise measurement bandwidth
Vertical cantilever deflection
Current difference in photo diode
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Symbol
Cantilever
hCL
kCL
lCL
tCL
wCL
αT OP
αCL
βCL
RT OP
Unit
Discription
m
N/m
m
m
m
Tip height
Stiffness
Length
Thickness
Width
Tip full angle
Angle of incidence on cantilever
Cantilever to sample angle
Tip radius
◦
◦
◦
m
Observation
A
m×m
DOF
m
FOV
m×m
M
Xcam
m
Xdif f
m
Xsys
m
λ
m
NA
-
CCD sensing area
Depth Of Field
Field Of View
Magnification
Camera resolution
Diffraction limit
System resolution
Wavelength
Numerical Aperture
Thermal
RT
αT
αcv
αr
αct
λT
Thermal resistance
Thermal expansion coefficient
Convection heat transfer coefficient
Radiation heat transfer coefficient
Thermal contact resistance
Heat conduction coefficient
K/W
m/m/K
W/(m2 K)
W/(m2 K)
m2 K/W
W/m/K
Contents
1
Introduction
2
2 Metrological Atomic Force Microscope
2.1 Requirements of the AFM . . . . . . . . . . . . . . . . . . . . . . .
2.2 Sample stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Measurement principle . . . . . . . . . . . . . . . . . . . . . . . .
3
Measurement system
3.0.1 Optical Beam Deflection . . .
3.1 Cantilever Module . . . . . . . . . . .
3.1.1 Cantilever . . . . . . . . . . .
3.1.2 Mechanical design of the CLM
3.2 Photo Diode Module . . . . . . . . . .
3.2.1 Detector . . . . . . . . . . . .
3.2.2 Mechanical design PDM . . .
3.3 Laser Diode Module . . . . . . . . . .
3.3.1 Laser source . . . . . . . . . .
3.3.2 LDM arrangement . . . . . . .
3.3.3 Mechanical design of the LDM
3.3.4 Thermal design of the LDM . .
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5
5
5
7
8
9
14
14
16
19
19
24
26
26
29
31
40
4 Observation system
44
5
48
AFM Head
6 Conclusions & Recommendations
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
53
54
A Position requirements of the OBD system
A.1 Analytic analysis of the beam profile . .
A.1.1 Component A - Laser diode . . .
A.1.2 Component B - Collimating lens
A.1.3 Component C - Focussing lens .
A.2 Stroke requirements of the modules . .
A.2.1 Laser diode module . . . . . . .
A.2.2 Photo diode module . . . . . . .
56
56
57
57
58
58
58
59
B Alignment procedure of the LDM
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60
viii
CONTENTS
C Component specifications
1
63
Chapter 1
Introduction
Scanning Probe Microscopy (SPM) was born in 1982 with the invention of a scanning tunneling microscope by Binnig et al. [1]. This microscope uses an atomically
sharp tip, which is placed sufficiently close to a conducting sample surface such
that tunneling of electrons between the two occurs. The tunneling current as a
function of the position of the tip across the sample provides information about
the topography of the surface.
SPM enables the measurement of physical properties of materials on scales down
to the size of atoms. In general, the interaction between a small tip (probe) and a
sample is used to create images of chracteristics like topography, magnetic properties and thermal properties. One of the techniques within SPM is Atomic Force
Microscopy (AFM), which uses the interaction forces between atoms to determine
the topography of a sample. The main interaction forces between atoms are [2]:
• Chemical bonds. Exist between two or more molecules when electrons are
shared between them.
• Van der Waals. Caused by correlations in the fluctuating polarizations of
nearby atoms (always attractive).
The summation of the forces as a function of the distance between two atoms is approximated by the Lennard-Jones potential. Figure 1.1(a) shows a typical LennardJones potential. At close proximity the force between the atoms is repulsive, at
some distance the force becomes attractive and the force decreases to zero as the
distance increases further.
In AFM the short or large range interaction forces can be uses in either static or
dynamic mode. Using the short range interaction forces (repulsive) in a static way
is called the contact mode. In contact mode AFM, the topography of a sample is
determined by making a constant interaction force image of the sample. The typical area of operation of this force is shown in the Lennard-Jones potential in Figure
1.1(a). The constant force image equals the constant distance image, thus the topography, with the assumption that the interaction forces between atoms are constant,
schematically shown in Figure 1.1(b).
The tip is part of a beam, which is connected to a chip on one side and is equipped
with the tip on the other side of the beam. The beam and tip combination is called
2
3
Interaction force
Typical area of operation
Repulsive force
Tip
0
Attractive force
Distance between two atoms
Sample
(a)
(b)
Figure 1.1: a) Lennard-Jones Potential; b) Schematic tip-sample interaction on
atomic scale.
a cantilever, the cantilever with chip is shown in Figure 1.2. By constant deflection
of the cantilever a constant force is applied between the tip and the sample. The
figure shows the case in which the sample is moved in z direction to change the tip
to sample distance and in x and y to scan the surface. A constant deflection of the
cantilever is maintained by feeding back the measured deflection to the z actuator,
which manipulates the sample and adjusts the tip to sample distance.
l
w
Cantilever
t
z
Cantilever chip
Sample
y
x
Figure 1.2: Schematic cantilever-sample interaction. Typical dimensions of the
cantilever are l × w × t = 200 × 30 × 2 µm.
A metrological AFM is developed for the Dutch standards laboratory (NMi - Van
4
CHAPTER 1. INTRODUCTION
Swinden Laboratory). This AFM is used to calibrate other AFMs. To calibrate, the
measurement needs to be traceable to the definition of length.
Definition
of length
Metrological
AFM
NMi
Calibrated
grating
Commercial
AFM
Customer
Figure 1.3: Calibration chain of length for commercial AFM’s
Figure 1.3 shows the calibration chain from the definition of length to a commercial
AFM. The definition of length is the definition of the meter, which is the distance
that light travels in vacuum in 1/299,792,458 second. The metrological AFM is
used to calibrate a grating sample (which shape is explained in Section 2.2). This
calibrated grating sample is used to calibrate commercial AFM’s.
The metrological AFM has a schematic setup as shown in Figure 1.2. The sample is translated to perform height adjustment and the scan movement, while the
cantilever remains stationary. The scanning range is 1 × 1 × 1 mm, with subnanometer position resolution, the specified measurement uncertainty is in the
nanometer range [4].
The AFM is divided into two parts:
• The sample stage, which performs the spatial translation and measurement
of this translation,
• The AFM head, which is the part holding the cantilever and is equipped with
the deflection measurement system of the cantilever.
The design of the sample stage is not discussed in this report. The objective of the
project described in this master’s thesis is:
Design a Metrological Atomic Force Microscope Head.
Chapter 2 explains the working principle of the metrological AFM in more detail
and discusses the measurement principle. Chapter 3 focuses on the design of the
measurement system for the cantilever deflection in the AFM head. The measurement system is split up in modules, in each section a module is designed, starting
with the requirements and resulting in a design. Chapter 4 is dedicated to the
observation system. Chapter 5 brings the measurement and observation system
together in one design and analyzes the measurement- and thermal loop. Chapter
6 draws the conclusions and gives recommendations on the project.
Chapter 2
Metrological Atomic Force
Microscope
In this chapter the requirements for the metrological AFM head are discussed in
more detail. Furthermore, the working principle of the sample stage is shown and
the measurement principle is explained.
2.1
Requirements of the AFM
The most important aspects for the metrological AFM head design are:
• Vertical measurement resolution ≤ 0.1 nm (1 × 10−10 m)
• Thermal center at the cantilever tip
• Minimal Abbe offset
• Dynamic: first eigenmode > 2 kHz
• Observation of the backside and tip of the cantilever
To minimize the influence of thermal expansion due to homogeneous temperature
changes, the thermal center of the AFM head needs to be designed at the cantilever
tip. To minimize errors due to an Abbe offset [3], the cantilever tip needs to be located as close as possible to the measurement point of the sample stage. Observation of the cantilever backside is needed for alignment of the measurement system.
The initial approach of the cantilever to the sample is performed by observing the
tip and sample while manipulating the sample position.
2.2
Sample stage
The spatial movement of the sample is performed by the sample stage. The sample is placed on the sample table, as shown in Figure 2.1. The sample stage is
constructed from three identical orthogonal axes which are aligned symmetrically
around the vertical. Each axis contains an elastic straight guide. These straight
5
6
CHAPTER 2. METROLOGICAL ATOMIC FORCE MICROSCOPE
guides, each consisting of two struts and one parallelogram, allow the sample table to translate, but suppress its rotation. The three parallelograms are actuated
by Lorentz actuators. Figure 2.1 also shows the three half balls, as part of the kinematic mount to place the AFM head. The half balls are on a pitch circle of ∅80mm.
Three differential interferometers (not in the figure) are used to measure the translation of the stage. The optical axes of these orthogonally oriented interferometers
are aligned with the AFM head probe for minimal Abbe offset.
Figure 2.1: Sample stage (simplified)
The majority of the sample stage parts are made from aluminum (7075) barstock.
This material is suitable because:
• it has good thermal properties (heat conduction coefficient, λT = 130W/m/K)
and mechanical properties,
• all aluminum parts are made from the same certified barstock,
• the barstock offers rotation symmetric internal stresses, thus rotation symmetric expansion coefficient.
The use of the same aluminum in the AFM head also prevents thermal expansion
coefficient differences, thus the majority of the components in the AFM head is
made from aluminum 7075.
2.3. MEASUREMENT PRINCIPLE
7
Calibration sample
The calibration samples are gratings with a typical pattern and dimensions as
shown in Figure 2.2. The gratings are used to calibrate the step height. Measurement data from only the grey areas shown is used, to prevent the cantilever tip
shape to have influence on the measurement.
2 - 10 µm
20 - 200 nm
Grating-sample
Figure 2.2: Schematic cross section of a grating sample. Grey= measurement
area
2.3
Measurement principle
In regular contact AFM’s the deflection of the cantilever is kept at a constant value
by adjusting the tip to sample distance. In the new AFM the sample is moved up
and down periodically as the surface is scanned. The resulting cantilever deflection
is shown in Figure 2.3, the tip stays within the range of the atomic interaction
forces. Only the points at which the deflection of the cantilever is zero are used
as a trigger for the readout of the interferometers. The measurement data from
the interferometers determines the samples topography. The reasons to use this
measurement principle, called zero-cross-system, are the following:
• Nonlinear effects, for example the nonlinearity of the cantilevers stiffness are
avoided. Calibration of these effects is not needed.
• Moving the sample up and down instead of keeping the sample at its position
within 1 nm results in reduced control requirements.
Cantilever deflection
In practice the sample is moved at several hundred hertz with an amplitude of ±10
nm.
= zero-cross-point
0
Time
Figure 2.3: Cantilever deflection with zero-cross-system
Important aspects for the design of a metrological AFM have been identified. The
working principle of the sample stage was explained and the measurement principle was discussed. The measurement system of the AFM head is addressed in the
next chapter.
Chapter 3
Measurement system
Several measurement systems are considered to measure the deflection of the cantilever. In this chapter a measurement system is selected, after which a more
detailed explanation of the systems working principle is given. The mechanical
design of the components will follow from the requirements and evaluations of
different designs.
System selection
The three common deflection detection systems and their major advantages and
disadvantages are:
1. Capacitance detection: The cantilever is one side of a capacitor, deflection is
measured as change in capacitance.
Advantages
Relatively simple and compact
Disadvantages
Electrostatic gradient can cause
snap-in of cantilever to capacitor
plate
Drift in tip-sample capacitance
Stray capacitance
Low noise
2. Optical Beam Deflection (OBD): A laser is pointed on the backside of the
cantilever under an angle and is reflected on a spot displacement detector, at
some distance. Deflection and thus bending of the cantilever is measured as
laser spot displacement on the detector. Because of the optical path length
required, the system is sensitive to angle deviations of the laser source [2],[5].
Advantages
High resolution easily achievable
Easy to operate
Torsion and deflection of cantilever
can be measured
No influence optical path elongation
Disadvantages
Medium laser power needed
Tuning of optics required
Length optical path
8
9
3. Interferometry: A laser beam is split into a reference and measurement
beam. The measurement beam is pointed perpendicular on the backside
of the cantilever, the reference beam travels an equal path length. At cantilever deflection the path length of the measurement and reference beam
differs, the difference can be measured as a phase shift of the optical waves
in the laser. Differences in the speed of light between the reference and
measurement path, due to temperature gradients, are also measured as displacements.
Advantages
Traceability wavelength
Large bandwidth
Not influenced by cantilever shape or
size
Disadvantages
Complicated system
High laser power needed
Sensitive to temperature gradients
The OBD system is chosen as measurement system because of the low complexity.
Furthermore, the system has a potential compact design without the listed general
disadvantage if the mechanical design is correct.
3.0.1
Optical Beam Deflection
In this section the working principle of the OBD is analyzed. Properties of the laser
beam are evaluated and its effect on the focal spot is shown. Furthermore, the layout of the system is determined.
The components of the OBD measurement system are listed below in the order in
which they are discussed in the next sections.
• Cantilever Module (CLM) holds the cantilever.
• Photo Diode Module (PDM) contains the spot displacement detector.
• Laser Diode Module (LDM) contains the laser source with beam-shaping optics.
The lay-out of the OBD is shown in Figure 3.1. The figure shows the optical axis of
the laser beam with and without cantilever deflection. The laser beam is focused on
the cantilever by the LDM and hits the detector at distance s. The relation between
the vertical cantilever deflection ∆z and spot displacement ∆a on the detector is
given by:
s
∆a = 3 ∆z
l
(3.1)
In which l[m] is the cantilever length and s[m] is the cantilever to detector distance.
The vertical resolution of the OBD can be increased by:
• Selecting a cantilever with a smaller length lCL ,
• Increasing the cantilever to detector distance s,
• Selecting a detector with a small minimal detectable spot displacement ∆a.
10
CHAPTER 3. MEASUREMENT SYSTEM
A realistic value for the minimal detectable ∆a is ≤ 0.1 µm (from commercial
detectors), a typical cantilever is 200 µm and the desired minimal measurable ∆z
is 0.1 nm. This leads to s ≤ 40 mm and s = 40 mm is used for the mechanical
design.
Laser source
Spot displacement
detector
∆a
αCL
Optical axis
Cantilever
lCL
βCL
s
∆z
Figure 3.1: Basic lay-out of OBD
The laser hits the cantilever at an angle of incidence, αCL . This angle is needed to
place the laser source and detector in this setup. It is possible to have a setup in
which αCL = 0 with the use of extra optics, but the extra reflections influences the
performance of the OBD.
Angle βCL is needed to avoid contact between the cantilever and sample (except for
the tip) and to have space to fix the cantilever to its holder.
In Figure 3.1 the OBD-plane is parallel to the length of the cantilever, a close-up of
the focal spot is shown at the left of Figure 3.2. The focal spot is elliptical due to the
angle of incidence, αCL . In this configuration the detector measures bending of
the cantilever as displacement of the spot in the plane and torsion of the cantilever
as displacement perpendicular to the OBD-plane.
To make placement of the laser source and cantilever holder easier, as a next step
the OBD-plane is positioned perpendicular to the length of the cantilever and the
spot is oriented on the cantilever as shown in the right image of Figure 3.2. This
has one disadvantage: The long axis of the elliptical spot on the cantilever, due to
angle αCL is oriented along the restricted width of the cantilever, instead of along
the length.
Manipulation lay-out
Three modules are identified within the OBD system (CLM, LDM and PDM). Manipulation of these modules is required for:
• Initial positioning of the focal spot on the cantilever in the CLM.
• Positioning of the detector spot in the middle of the detector in the PDM.
11
Cantilever
Focal spot
Laser beam
OBD-plane
Figure 3.2: Focal spot on cantilever
Three manipulation lay-outs of the modules along the optical axis are shown in
Figure 3.3. The cantilever to detector distance s, was already determined to be 40
mm. The focal distance from the LDM to the cantilever is expected to be in a range
of 20 − 30 mm. The lay-outs with their main advantages and disadvantages are:
1. Coupled rotation and translation of the LDM. With the point of rotation on
the cantilever, a rotation of the LDM results in translation on the PDM. Translation of the LDM allows positioning of the focal spot on the cantilever.
Advantages
No manipulation of
the PDM needed
Disadvantages
Large ratio needed for rotation to translation
resolution at 40 mm
Combination of mechanism with rotation and
translation manipulation affects thermal stability
Rotation and translation are not entirely decoupled
2. Decoupled rotation of the LDM and translation of the PDM. Rotation of the
LDM to position the spot on the cantilever and translation of the PDM to
position the spot on the detector decouples the manipulation of both spots.
Advantages
Positioning of spots
decoupled
Disadvantages
Considerable ratio needed for rotation to
translation resolution at 40 mm
Large lateral stroke needed at PDM, caused
by rotation
3. Decoupled translation of the LDM and PDM. The LDM is translated to position the focal spot on the cantilever and the PDM is translated to position the
spot on the detector.
Lateral (perpendicular to optical axis) translation of the LDM and PDM is chosen
as the manipulation lay-out.
12
CHAPTER 3. MEASUREMENT SYSTEM
Advantages
Positioning of spots
decoupled
Manipulation resolution requirements
easiest
Disadvantages
Manipulation of two modules needed
LDM
CLM
PDM
“Coupled
rot- & trans-lation”
“Decoupled
rot- & trans-lation”
“Decoupled
translations”
20-30 mm
s= 40 mm
= Point of rotation
Figure 3.3: Module manipulation lay-outs, 2D along optical axis. The arrows
represent orientation of manipulation.
Spot size
In the OBD-system a laser needs to be focused on the backside of the cantilever.
The width of a cantilever varies between 13 and 65 µm, a spot size of 10 µm on the
cantilever is typically required. Aspects which determine the spot size, w are:
• Intensity distribution of the laser beam, wG ,
• Astigmatism, wA ,
• Position inaccuracies of the laser source and optics, wP ,
• Angle of incidence on the cantilever, wI .
The intensity distribution of a laser source is approximately Gaussian. A typical
Gaussian distribution is shown in Figure 3.4 on the left side. A common way to
describe the width of a laser beam is 1/e2 , which is the width at 13.5% of the peak
intensity. The Full Width Half Maximum (FWHM) is the width at half the peak
intensity. The right figure shows the beam emitted from a commercial laser diode,
for which the intensity distribution depends on the radial orientation (parallel or
perpendicular to the emitting junction).
Wavefronts of the laser beam are essentially spherical surfaces, which can be described by a Gaussian distribution. As a consequence of this distribution, the focal
13
Relative intensity
I0 = 1
FWHM
0.5
1/e2 13.5 %
0
0
Angle ( o )
Figure 3.4: Laser beam intensity profile of diverging beam, FWHM = Full
Width Half Maximum. Typical Gaussian profile (left); profile of laser diode,
Hitachi 6340 (right)
spot size is restricted, shown in Figure 3.5. With the assumption that the beam
profile is distributed Gaussian, the spot size can be approximated by [6]:
fλ
wG ∼
=
πa
(3.2)
Where λ[m] is the wavelength of the light.
1/e2 irradiance profile lines
Spherical wavefront
w
acol
f
Figure 3.5: Gaussian beam focused by a converging lens; a= collimated beam
waist; w=beam waist at focus; f = focal distance
In case that rays, propagating in two perpendicular planes of the laser beam, have
different foci, astigmatism is present. In case of a ideal circular laser beam, the
foci will result in focal lines (Figure 3.6). In the middle between the focal spots is
a circular spot, the circle of least confusion; this spot is used as focal spot. Astigmatism, AS [m] is a property of the laser source and is expressed as the distance
between the foci. The influence of astigmatism on the spot size, w in the setup
shown in Figure 3.6, is given by Equation (3.3). In Subsection 3.3.2 the influence
of astigmatism in case of a lens system is analyzed, together with the influence of
position inaccuracies of the LDM components on the spot size.
f
AS /2
=
a
wA
(3.3)
14
CHAPTER 3. MEASUREMENT SYSTEM
Focus 2
Focus 1
Circle of least
confusion
Figure 3.6: Astigmatism
The angle of incidence on the cantilever, αCL , results in an elliptic shape of the
spot. The elongation of one of the axes, wI , is given by:
w = cos(αCL )(w + wI )
3.1
(3.4)
Cantilever Module
The Cantilever module (CLM) contains the cantilever. In this section a cantilever is
selected and the holder for the cantilever is designed.
3.1.1
Cantilever
A cantilever is a one side clamped beam with a tip on its end. Two common types
of cantilevers are commercially available:
• A cantilever with a rectangular shaped beam
• A cantilever with a triangular shaped beam, shown in Figure 3.7
The cantilevers are made by lithographical means and are commercially available
with a great variety of properties. The available properties of rectangular and triangular shaped cantilevers for contact mode AFM are listed in Table 3.1.
Table
Property
Shape
Materiala
Length
Stiffness
Tip
Height
Top angle
Radius
a In
general
3.1: Properties of contact
Symbol
Rectangular
Silicon (Si)
lCL
75 − 495 µm
kCL
0.1 − 10 N/m
hCL
αT OP
RT OP
5 − 20 µm
24 − 70◦
10 − 30 nm
mode cantilevers
Triangular
Silicon Nitride (Si3 N4 )
85 − 325 µm
0.01 − 0.58 N/m
2.5 − 3.5 µm
66 − 70◦
10 − 90 nm
3.1. CANTILEVER MODULE
15
lCL
1.6
3.4
wCL
Backside
hCL
0.4
tCL
α
TOP
Figure 3.7: Typical triangular shaped cantilever
In general the triangular shaped cantilevers are made from Silicon Nitride and
the rectangular ones from Silicon. The triangular shaped cantilevers offer a lower
vertical stiffness. Lower vertical stiffness results in higher sensitivity to atomic interaction force and decreases the chance of damaging the cantilever tip or sample
while scanning.
An extra layer (typically 30 nm) of a different material can be deposited on the
backside of the cantilever. The main purpose of such a layer is to increase the reflectivity. Silicon cantilevers reflect about 25% of the light, where an aluminum
coating increases the reflectivity to about 65% [10].
Analysis of the OBD in Subsection 3.0.1 showed that the vertical resolution at the
cantilever tip increases with a smaller cantilever length. However, the stiffness increases with decreasing length together with the risk of breaking the cantilever.
The tip radius determines how many atoms influence the total interaction force between the tip and the sample. A bigger radius means more atoms influencing the
interaction force. The deflection of the cantilever tip is averaged by the number of
atoms interacting with the tip. More averaging of the measured height decreases
the lateral resolution. However, the lateral resolution is less critical, since step
height is measured.
A smaller cantilever length results in a higher vertical resolution at the cantilever
tip, see Subsection 3.0.1. A relatively short cantilever, with a length of (lCL = 200
µm), is chosen. In this case the desired vertical resolution (0.1 nm) is achieved
when the detector is placed at s = 40 mm distance from the cantilever. The desired
low stiffness led to the choice of a triangular Si3 N4 cantilever with the required
length and stiffness, kCL = 0.02 N/m (namely Veeco OTR4B). Details about the
cantilever can be found in Appendix C.
16
CHAPTER 3. MEASUREMENT SYSTEM
3.1.2
Mechanical design of the CLM
The manipulation of the cantilever to position the cantilever tip in the required
position can be performed on board, in the AFM head, or externally, by an external manipulator. In case of external manipulation the cantilever is externally
positioned on a holder, which is mounted on the AFM head, without the need for
on-line alignment. External manipulation is chosen because:
• An on board mechanism influences the thermal stability
• Quick replacement of cantilevers is possible, since preparation of several cantilevers can be performed off-line.
Points of attention for the mechanical design of the CLM are the following:
• Cantilever tip should be in the thermal center and Abbe point of the AFM
• Replacement of the cantilever should be easy
• The cantilever and the mechanisms needed to mount the cantilever to the
AFM head need to leave space for the measurement and observation system
• A simple and disposable holder, or a more complex and reusable holder
• Material should fit the design
In Table 3.2 selected possible materials for the cantilever holder are listed. The thermal properties are the thermal expansion coefficient αT and thermal conductivity
λT .
The difference in αT between the material of the cantilever, which is silicon or silicon nitride and the material of the holder quantifies the potential stresses between
the materials at temperature changes.
Table 3.2: Properties possible materials for cantilever holder
αT
λT
E
Material
[µm/m/K] [W/m/K] [GPa]
Silicon
2.5
124
112
Silicon Nitride
2.8
30
290
Silicon Carbide
4.0
120
410
Pyrex 7740
3.3
1.1
63
Molybdenum
5.4
138
330
Nilo, Alloy 36
1.5
10
N/Aa
Nilo, Alloy 42
5.3
11
N/A
Aluminum 7075
23.6
130
72
a Not
specified for Nilo, properties close to Invar (E=150 GPa)
Three designs for the cantilever holder are discussed. The first design (block) is
shown in Figure 3.8. The laser volume shown in this figure represents the volume
that is kept clear around the laser beam. The mounting surface of the cantilever
is under a 10◦ angle to introduce that angle between the cantilever and the sample
(dotted line in figure). Three half balls, as part of the kinematic mount, are glued
3.1. CANTILEVER MODULE
17
to the block. The main advantage of the block design is the space available to implement a preload mechanism, to preload the block on the V-grooves of the AFM
head base (not shown in the figure).
The second design (plate) is shown in Figure 3.9. In this design a simple plate
of material can be used as holder, a broken piece of silicon wafer is applicable.
Matching thermal expansion coefficients and wafer flatness at the area where the
cantilever and half balls are mounted are the main advantages. The shape and edge
quality of the plate are less important, since the thermal center of the holder is determined by the half balls (glued) and V-grooves in the AFM head (not shown in
the figure). Furthermore, this design leaves enough space for observation.
The third design (tangential) is shown in Figure 3.10, in which the, under 120◦
radially oriented, half balls are part of the kinematic mount. The area milled free in
the middle of the plate leaves enough space for the observation and the cantilever
is mounted on a surface at a 10◦ angle.
Mounting the cantilever on the holder can be performed in several ways, the following methods are considered:
• Glue
• Anodic bonding
• Clamp
The main difficulty when gluing the cantilever to its holder after it is manipulated
is keeping it in position until the glue has hardened. The shrinkage of the glue can
cause the cantilever to move laterally. In case the shrinkage is oriented perpendicular to the mounting surface this problem is prevented. The hardening takes time,
is not reversible (the glue must be broken to detach the cantilever from the holder),
but is relatively cheap and does not require much space in the design.
With anodic bonding covalent bonds are made between silicon atoms and alkali
ions in a substrate. These bonds are made at an elevated temperature (several
hundred degrees Celsius) while applying a DC voltage across the substrate and the
silicon chip. Pyrex 7740 contains alkali ions and its expansion coefficient is close
to that of silicon. This bonding method does not require any extra space and in
principle the entire chip surface is bonded to the substrate. However, the elevated
temperature can cause the cantilever to laterally move during bonding, internal
stresses are introduced, the imperfect flatness can cause the bonding to be localized and the bonding is not reversible.
Clamping the cantilever to the holder allows mounting with a defined force (about 1
mN needed), can be introduced by a separate clamp and allows reuse of the holder.
Clamping has the potential for the best design, but is difficult to integrate since
space it limited. Furthermore, a clamp design on this small scale that transfers
only force in one defined direction, not position, is difficult. The final design of the
clamp to mount the cantilever on the holder and the preload mechanism to preload
the CLM on the AFM head base, is not shown in this report. The choice for one of
the three holder depends on the lay-out of the observation system and is made in
Chapter 5.
18
CHAPTER 3. MEASUREMENT SYSTEM
Figure 3.8: Cantilever holder block design
Figure 3.9: Cantilever holder plate design, plate is 12 × 6 mm
Figure 3.10: Cantilever holder tangential design, outer dimensions plate: ∅14
mm
3.2. PHOTO DIODE MODULE
19
External manipulator
To manipulate the cantilever on its holder before fixation an external manipulator
is needed. The kinematic mount of the CLM between the module and the AFM
head base is used to locate the module in an external setup. The module is placed
on its back, so with the cantilever tip facing upwards. This way an optical microscope can be used to monitor the location of the cantilever tip while manipulating
the cantilever. Using a crosshair microscope in combination with an appropriate
manipulator should enable manipulation in the diffraction limit range, manipulation within ±0.5 µm is assumed. The detailed design of the external manipulator
for the CLM is not within the scope of this project.
3.2
Photo Diode Module
The Photo Diode Module (PDM) contains the spot displacement detector of the
measurement system. In this section the detector is selected after which the mechanical design of the PDM will follow from the detector properties and the manipulation requirements.
3.2.1
Detector
To detect the spot displacement two types of detectors are considered: segmented
and lateral Position Sensing Detectors (PSD). The requirements are listed in Table
3.3.
Table 3.3: Requirements of PSD
Resolution
≤ 0.1 µm
Stroke
±0.6 mm
Linear range
±6 µm
The maximum stroke is expected to be required at the cantilever tip to sample
approach procedure. With an estimated cantilever deflection of 1 µm, the stroke
on the detector is 0.6 mm.
Linearity within the range of the zero-cross-system supplies the AFM controller
with extra information: a linear line of the measurement points instead of a single
zero-cross point in case on non-linearity. The ±10 nm vertical stroke of the zerocross-system at the cantilever tip equals ±6 µm linear range at the detector.
Lateral and segmented PSD’s both use silicon photo diodes. Photo diodes operate by absorption of photons and generate a flow of current in an external circuit,
proportional to the incident optical power [7].
Segmented PSD
The left image of Figure 3.11 shows a schematic drawing of a segmented PSD.
Segmented PSD’s are substrate photodiodes divided into segments, separated by
a gap. A symmetrical spot generates equal photocurrents in all segments, when it
is positioned at the center. The difference in currents from the diodes is used to
20
CHAPTER 3. MEASUREMENT SYSTEM
describe the x and y displacement of the spot, as shown in Equation (3.5) and (3.6).
The signal is normalized by the total signal, thereby the detector is not sensitive for
uniform changes in optical power. Segmented PSD’s can offer the required ≤ 0.1
µm resolution due to the match in photosensitivity between the segments.
x=
(iB + iD ) − (iA + iC )
iA + iB + iC + iD
(3.5)
y=
(iA + iB ) − (iC + iD )
iA + iB + iC + iD
(3.6)
L
iA
iY2
iB
A
B
iX1
C
D
iC
Gap
iX2
L
y
iD
x
z
iY1
Figure 3.11: Schematic drawing of a segmented PSD (left) and duo-lateral PSD
(right). Grey area= laser spot
Lateral PSD
The right image of Figure 3.11 shows a duo-lateral PSD. Lateral PSD’s are single
element photodiodes with no gaps. The spot produces a current in two opposite
electrodes. The output at the electrodes is proportional to the distance from the
spot to the electrode, through the resistive layer of the photodiode. In a duo-lateral
PSD’s two resistive layers and four electrodes are present. The relation to determine the spots location is given by Equation (3.7) and 3.8.
iX2 − iX1
2x
=
L
iX1 + iX2
(3.7)
iY 2 − iY 1
2y
=
L
iY 1 + iY 2
(3.8)
Segmented or lateral PSD
The main advantages and disadvantages of segmented and lateral PSD’s are listed
in Table 3.4.
[7], [8]
3.2. PHOTO DIODE MODULE
21
Table 3.4: Advantages and disadvantages of segmented and lateral PSD’s
PSD-type
Advantages
Disadvantages
Segmented Superior resolution
Linearity restricted
High accuracy around neutral Intensity distribution effects
position
linearity
Minimal spot size restricted
by gap
Lateral
Linearity on entire detector
area
Independent of intensity distribution
In segmented PSD’s the change of optical power on the diodes is not linearly related to the displacement of the spot, due to the circular spot with an approximately
Gaussian intensity distribution. A linear relation can only be assumed in a spot
displacement range within 10% of the spot diameter [9].
A segmented PSD is chosen to be applied in the OBD, since the zero-cross-system
only requires linearity around the neutral position and the segmented PSD offers
a higher lateral resolution.
Detector sensitivity
The ratio between the output current of the segmented PSD and the vertical cantilever tip movement is the detector sensitivity. The sensitivity is analyzed to optimize the detection system. Equation (3.9) shows the basic OBD system equation
from Subsection 3.0.1.
s
∆a = 3 ∆z
l
(3.9)
In which ∆a and ∆z are the displacements at the detector and cantilever tip respectively, s, is the distance between cantilever and detector and lCL is the length of the
cantilever. The displacement of the spot produces a difference in photo-induced
currents, ∆i, approximated by Equation (3.10) [10]. The assumptions made to derive the equation are:
• A linear relation between ∆a and ∆i
• Power loss at the gap between the segments is neglected
2
∆i = ηPopt ∆a
a
(3.10)
In which η[A/W] is the photo sensitivity of the diode and Popt [W] is the total optical
power of the laser spot. Combining Equation (3.9) and (3.10) leads to equation
(3.11), the sensitivity of the detector to tip displacement.
∆i
s
= 6ηP
∆z
al
The detector sensitivity can be increased by:
(3.11)
22
CHAPTER 3. MEASUREMENT SYSTEM
• Choosing a smaller cantilever length, l
• Using a bigger cantilever to detector distance, s
• Selecting a detector with a higher photo sensitivity, η
• Increasing spot diameter a, since the optical power P , increases with a2
Noise
The resolution of a segmented PSD depends on the noise of the diode and the signal processing electronics. The two noise sources of the diode are shot noise and
thermal noise (or Johnson noise).
Shot noise is related to the statistical fluctuation in both the photocurrent and the
dark current. The dark current is a small current which flows when a reverse voltage is applied to a photodiode even in dark state. The magnitude of the shot noise
is expressed as the root mean square noise current, defined by Equation (3.12) [11].
p
Isn = 2q(IP + ID )∆f
(3.12)
Where q = 1.6 × 10−19 C, is the electron charge, IP is the photo generated current
and ID is the photo detector dark current and ∆f is the noise measurement bandwidth.
Thermal noise is the noise generated due to the thermal generation of charge carriers in the diode. The magnitude of this noise current is defined by Equation (3.13)
[11].
r
4kB T ∆f
Ijn =
(3.13)
RSH
Where kB = 1.38 × 10− 23 J/K, is the Boltzmann constant, T , is the temperature
in [K] and RSH is the shunt resistance of the photo diode. The shunt resistance is
the voltage-to-current ratio in the vicinity of 0 V.
The total noise current is the combination of the shot and thermal noise, defined
by Equation (3.14). A common specification
√ of the noise generated by a photo diode
is the Noise Equivalent Power (NEP) [W/ Hz] , which is given by equation (3.15)
[11]. Where η is the photo sensitivity [A/W]. A PSD with a low amount of noise,
thus a low NEP-value is required.
q
2 + I2
Itn = Isn
(3.14)
jn
N EP =
Itn
η
(3.15)
The analog signal processing electronics sum, subtract, divide and amplify the signals from the photo diode. In general the output of the electronics consists of three
signals: a x, y and total photo generated current IP signal. General specification
show that the resolution achievable for a diode and electronics combination is well
below 0.1 µm. However, since the specifications of the desired electronics are not
available, the noise level of the processing electronics is not quantified.
3.2. PHOTO DIODE MODULE
23
Detector selection
Table 3.5 shows a comparison of two segmented PSD’s. The PSD from Hamamatsu offers the lowest noise, thus the highest potential resolution. This detector
is chosen, more details can be found in Appendix C.
Table 3.5: Properties of segmented PSD’s
Properties
Four segmented PSD’s
Supplier
Osi optoelectronics Hamamatsu
Name
Spot-4D
s4349
Dimensions [mm]
1.3 × 1.3
3.0 × 3.0
Gap [µm]
127
100
a
Photo sensitivity
[A/W]
0.42
0.42
√
NEP [W/ Hz]
8.7 × 10−15
4.0 × 10−15
aλ
= 635 nm
From the detector sensitivity analysis it follows that a bigger spot,a, with more total
power increases the sensitivity. However there are restrictions to the spot size and
its movement:
• The spot surface and its stroke are restricted by the surface of the diode, since
power loss at the edge will influence the measurement (left image of Figure
3.12).
• The spot has to overlap a part of all segments of the PSD at all times (middle
and right image of Figure 3.12).
• The laser beam is circular with an approximate Gaussian intensity distribution, the photocurrents are not linear related to the spot displacements. A
linear range of 10% of the spot diameter was already assumed.
A
B
A
B
A
B
C
D
C
D
C
D
Gap
Figure 3.12: Restrictions to spot displacement. Grey= laser spot
Figure 3.13 shows the restrictions, depending on spot size, a and spot displacement,
∆a. From the requirements stated in Subsection 3.2.1 a maximum spot displacement of 0.6 mm should be possible. This leads to a desired spot size of 1.8 mm
and leaves a linear range of 180 µm (6 µm required for the zero-cross-system). The
maximum recommended optical power density on the detector is 100 W/m2 [7].
For the ∅1.8 mm spot this leaves a maximum optical power of 0.25 mW.
24
CHAPTER 3. MEASUREMENT SYSTEM
Restrictions spot movement
a, Spotsize on detector [mm]
3
Overlap restriction
Detector size restriction
Linear
2.5
2
1.5
1
0.5
0
0
100
200
300
400
500
600
700
800
∆ a, Spot displacement [um]
Figure 3.13: Restrictions to spot displacement. Grey= area within boundaries,
dark grey= linear area
3.2.2
Mechanical design PDM
The required lateral stroke to align the PSD is ±500 µm (Appendix A.2.2). If the
starting position of the spot is well within the approximated linear range (±180
µm), this position can be identified as the zero-crossing position. Thus the manipulation resolution does not need to equal the detector resolution (0.1 µm). To use
the zero-crossing system (±6 µm) well within the linear range the required resolution of the PDM manipulation is set to ±5 µm.
Figure 3.14 shows an exploded view of the PDM. The active area of the PSD is
packaged by a metal casing, which provides protection together with a glass window
in front of the active area. The pins-side of the PSD is glued to the inner face of the
support ring. The ring is placed on the AFM head base (not in figure) with three
contact surfaces, which guide the lateral movement. To preload the support ring,
a wave spring (schematically in figure) is pressed against the support ring by the
fixation plate. This plate is fixed to the AFM head base by three bolts.
Manipulation and fixation PDM
To manipulate the PDM laterally, two eccenters are placed radially around the support ring under 120◦ . The eccenters are separated from the support ring by a beam
as part of the eccenter frame. The two beams prevent the tangential component of
the eccenter to cause the support ring to rotate. The frame provides the stop of the
beams and contains a third beam to preload the support ring on the eccenters. The
preload is applied by rotating the rectangular shaped knob by 90◦ and the frame is
bolted to the AMF head base.
The sequence to position the PDM is as follows:
1. The PSD is glued to the support ring in the alignment procedure (Appendix
B).
3.2. PHOTO DIODE MODULE
25
y
x
z
Figure 3.14: Exploded view of PDM
2. The support ring in placed on the AFM head base with the wave spring and
fixation plate, without fastening the bolts. This way the rings and plate can
be laterally moved as a package, the bolts in the AFM head base will move
within the area of the holes in the fixation plate.
3. The eccenter frame is preloaded on the support ring. The bolts of the eccenter frame are also loose, allowing the frame and support ring to be roughly
positioned by the eccenters while monitoring the output signal of the PSD.
4. After rough positioning within ±0.1 mm the bolts of the eccenters frame are
tightened (the bolts of the fixation plate are still loose).
5. Lateral fine positioning can now be performed with the eccenters.
6. The bolts of the fixation plate are tightened
The angle of the eccenters used for the rough and fine positioning of the PDM determines it’s ratio. The ∅3 mm eccenter has a 0.5 mm eccentricity. Assuming that
a 10◦ angular adjustment is possible, together with the biggest ratio in the eccenter
rotation, shows that an adjustment within ±1 µm is possible. This is better than
the required ±5 µm and allows the same eccenters and frame to be used for manipulation of the LDM, which does need the ±1 µm manipulation.
The intensity distribution of the laser beam in the OBD system depends on the
radial orientation, parallel or perpendicular to the emitting junction of the laser
diode. The specified intensity distribution can be found in Appendix C. To get a
linear relation between the spot displacement en the photo generated current of
the photo diode, the intensity distribution of the spot has to be symmetric around
the axes of the photo diode. To align the axes of the photo diode with the axis of the
laser beam manipulation of the PDM around θ is needed. On the connector-side
of the support ring are two ∅0.8 holes under 180◦ . These holes allow a wrench to
be placed to manipulate θ.
The support ring, fixation plate and AFM head base are made from aluminum.
As a consequence, the thermal expansion coefficients will match, but the friction
26
CHAPTER 3. MEASUREMENT SYSTEM
coefficient between the AFM head base and the PDM is µ = 1.35 (maximum). For
the approximated mass of the module of 3 gr on a horizontal plane, this means
0.04 N friction force. The preload beam is designed to deliver at least that force
over its stroke.
3.3
Laser Diode Module
In the measurement system the Laser Diode Module (LDM) is the laser source.
The LDM will focus the laser on the backside of the cantilever in the CLM. After
selection of the laser source, the mechanical design will follow from the position
and manipulation requirements of the source and the focus arrangement.
3.3.1
Laser source
To select the best laser source for the measurement system, the required specifications are compared with available sources. The requirements are:
• The optical power of the laser beam, after the reflections and refractions of
the laser beam, should be the maximum amount of allowable optical power
on the detector (0.25 mW). Section 3.1.1 showed that the reflection of the
cantilever can vary between 25 and 65%. Thus variable optical power of 0 − 2
mW is required.
• Wavelength: in general the photo sensitivity of the detector increases with the
wavelength. Visibility of the light is required to observe the laser spot on the
cantilever, thus a wavelength of around λ = 650 nm (red laser) is required.
• Intensity distribution: around the neutral position of the spot, the relation
between power difference on the detector and position is approximately linear (Subsection 3.2.1). The intensity distribution of the spot directly influences the linearity between power difference and spot movement. Thus the
intensity distribution of the laser spot should be symmetric around the perpendicular axes of the laser beam.
• Pointing stability: the influence of the pointing stability on the vertical resolution of the cantilever is required to be ≤ 10%. From there, assuming an
air temperature stability of ≤ 20 mK, inside the enclosure of the AFM [12],
requires a pointing stability of ≤ 4.6 µrad/K.
The requirements for the laser source are listed in Table 3.6.
Table 3.6: Laser source requirements
Properties
Requirements
Optical power
0 − 2 mW
Wavelength
650 ± 50 nm
Intensity distribution Symmetric around the ⊥ axes of the laser beam
Pointing stability
≤ 4.6 µrad/K
Heat dissipation
Minimal to minimize thermal deviations
Size
Minimal
3.3. LASER DIODE MODULE
27
The laser source can be on board, in the AFM head, or placed external and connected to the head by an optical fibre. Advantages and disadvantages of the laser
source placement are listed in Table 3.7. In both cases the beam exiting the fibre
or laser source needs to be collimated and focused on the cantilever. The beam
shaping optics needed are comparable in size for both cases.
Table 3.7: Advantages and disadvantages of on board and external placement
of the laser source
Advantages
Disadvantages
External
External heat generation
Long optical route
On board OBD-components together
Heat source in AFM head
Simple laser diode applicable
The stability of the laser source determines the performance of the measurement
system. In case the laser source in placed external the stability can be influenced
by the long optical route, the stability of the fibre and the connectors influence the
intensity distribution of the spot. The on board placement is chosen and extra attention is needed for the thermal stability of the laser source.
The LDM consists of a laser diode and beam-shaping optics. Such modules are
commercially available or can be home built. The commercial modules, with beamshaping optics, still need extra optics to get the required focus on the cantilever. In
Table 3.8 two commercial modules and two laser diodes are compared with the requirements of the laser source. It can be seen that the commercial modules can
not deliver the required pointing stability. One module approaches the required
stability, but the size of this module without the extra optics is too large.
The Hitachi HL6340 is chosen as source for the LDM, since it meets the requirements and uses the least electric power, thus the least heat dissipation in the AFM
head. (more details can be found in Appendix C).
Table 3.8: Laser source properties (optical and electrical properties at maximum
optical power)
Properties
Required Commercial modules
Laser diodes
Name
Minilase
Premier
HL6340
VPSL
Optical power
0−2
0-5
0-5
0-5
0-3
[mW]
Wavelength [nm]
650 ± 50
670
655 ±5
635 ±5
635 ±5
Beam output a
k ∅1 mm k ∅2 mm > 17◦ × 20◦ > 8◦ × 8◦
Pointing stability
≤ 4.6
≤ 50
≤5
[µrad/K]
Electric power
198 ± 20
N/A
60
81
[mW]
Size (∅ × length) < 15 × 50 9.5 × 20
15 × 44
5.6 × 3.5
5.6 × 3.5
[mm]
a ’k’=
Collimated beam, ’>’= Diverging beam
28
CHAPTER 3. MEASUREMENT SYSTEM
Sheet metal cap
Emit point
Glass
Figure 3.15 shows an image of the selected laser diode. The light emits from the
junction of a semiconductor, this emitter is protected by the sheet metal cap and
the glass window. The emitter is connected to the brass of the baseplate, which has
high thermal conduction. The laser diode has an internal photo diode, which can
be used to control the optical power output of the laser diode. The three pins on
the baseplate provide the electrical connection to the power source and the output
signal of the internal photo diode [13].
Brass baseplate
Figure 3.15: Typical laser diode in ∅5.6 mm package
Laser diode driver
The laser diode driver supplies the power for the laser diode. Two driver modes are
possible:
• Automatic Power control (APC), supplies the laser diode with a constant
power by using the feedback of the internal photo diode of the laser diode
• Automatic Current Control (ACC), supplies the laser diode with a constant
current without the use of feedback from the laser diode
The main advantages and disadvantages of the driver modes are listed in Table 3.9.
APC
ACC
Table 3.9: Advantages and disadvantages of APC and ACC
Advantages
Disadvantages
Less need for temperature con- Internal photo diode can suffer
trol
from drift and noise
Faster control loop
Optical power output temperature dependant
Recommended by laser diode
supplier
APC is chosen. In practice most drivers are equipped with both driver methods,
thus switching between the methods is possible. The driver with the best power
3.3. LASER DIODE MODULE
29
stability and matching internal photo diode current range is selected (Wavelength
LDD200-3P). Power stability: < 0.02% in 24 hours.
3.3.2
LDM arrangement
The beam emitting from the junction of the laser diode needs to be focused. In the
LDM the diverging bundle from the laser diode is first collimated (made parallel)
before focusing on the cantilever backside. With this method commercially available lenses can be used, which are developed to collimate and focus a diverging
laser bundle from a laser source.
The divergence of the beam depends on the orientation relative to the junction.
The divergence properties of the laser diode are listed in Table 3.10. The divergence
angle is defined as the full angle at half peak intensity (explained at the beginning
of this chapter).
Table 3.10: Laser beam divergence properties
Property
Symbol Min. Typical Max. Test conditions
Beam divergence parallel
θk
13
17
25
Poptical = 5 mW
to junction [◦ ]
Beam divergence perθ⊥
16
20
25
Poptical = 5 mW
pendicular to junction [◦ ]
Figure 3.16 shows the optical path of the laser beam from the laser diode to the
cantilever. One lens (B) collimates the diverging beam from the laser diode and
one lens (C) focusses the beam on the cantilever. To determine the required focal
distances f1 and f2 , already determined dimensions are needed:
• Cantilever to detector distance, s = 40 mm
• Spot size on detector, d = ∅1.8 mm
Furthermore the beam convergence angle to the cantilever equals the beam divergence angle from the cantilever (Equation (3.16)).
f2
s
=
acol
d
(3.16)
Choosing f1 = 2.75 mm and f2 = 30 mm allows the use of lenses with practical sizes, leaves enough space between laser diode and the focusing lens and will
allow enough space for the observation system between the LDM and the cantilever.
Using Equation (3.16) the required collimated beam waist is determined at acol =
∅1.35 mm. From the intension distribution of the laser diode (Shown in Appendix
C)the divergence of the laser beam is ≈ 40◦ × 50◦ at ≈ 99% of the optical power,
which results in an elliptical spot acol = 1.9 × 2.3 mm (with the collimating lens,
f1 = 2.75 mm). To get the required acol = 1.35 mm a beam resizer(disc with hole
∅1.35 mm) is applied between the collimating and focusing lens. consequences
are:
• ≈ 13.5% (typically 0.15mW ) of the optical power is dissipated at the beam
resizer
30
CHAPTER 3. MEASUREMENT SYSTEM
• Besides the focal spot ellipticity due to the angle of incidence, no extra ellipticity of the spot on the cantilever.
• No elliptical spot on the detector, thus no need to align the axes of the detector
with the axes of the ellipse
• The required spot size of ∅1.8 mm on the detector
Position inaccuracies
With the dimensions of the OBD and focal distances of the lenses determined, the
size op the focal spot and the required position accuracies of the LDM components
can be determined.
From spot size analysis in Subsection 3.0.1:
• The Gaussian beam waist is ∅4.7 µm
• The effect of the 0.7 µm astigmatism on the focal spot size is +∅1 µm, with
the use of thin lens theory (optical effects due to the thickness of lenses are
ignored).
• With the required spot size of 10 µm on the cantilever, this leaves 4.3 µm for
the influences of the position inaccuracies of the LDM components on the
spot size
A
Laser
diode
B
Collimating lens
C
Focusing lens
D
Cantilever
E
Detector
x
acol
z
y
d
f1
∆f
f2
s
Figure 3.16: Optical path from laser diode to cantilever (not on scale).
The analytical relation between translation and rotation of the LDM components
can be found in Appendix A.1. Analysis of the analytical relations led to the position
requirements for the components and the resulting inaccuracies listed in Table
3.11. The analysis is performed using thin lens theory and the combination of the
inaccuracies does not equal the summation of the individual inaccuracies, since all
inaccuracies are simultaneously analyzed.
From the table it can be seen that the influence of the position inaccuracies on
cantilever spot is an extra ∅1.2 µm. Taking into account the elliptical shape due to
3.3. LASER DIODE MODULE
31
Table 3.11: Position inaccuracies LDM components and consequences for cantilever and detector
Individual
Cantilever module
Photo diode module
Translation
[µm]
±x/y[µm] +∅-spot[µm] ±x/y[µm] ±∅-spot[µm]
±x/y
Laser diode
2
22
∼0
46
∼0
Lens B
5
45
∼0
110
∼0
Lens C
10
10
∼0
23
∼0
±z
Laser diode
1
∼0
0.8a
8.4
5.3
Lens B
1
3.6
0.8
8.4
5.3
Lens C
10
∼0
0.3
∼0
0.4
Rotation
[mrad]
±φ/ψ
Laser diode
10
∼0
∼0
∼0
28
Lens B
50
1
∼0
2
∼0
Lens C
50
0.1
∼0
0.3
∼0
Combination
87
1.2
176
35
a Axial
focal spot displacement= 120 µm
the angle of incidence (approximated at αCL = 20◦ ) on the cantilever, the long axis
of the spot equals 7.3µm. This is within the required ∅10 µm spot size.
3.3.3
Mechanical design of the LDM
The components of the LDM were selected and the position requirements have
been determined. Several mechanical designs are explained and compared after
which a design is chosen.
Ball in three leaf springs design
Figure 3.17 and 3.18 show respectively an exploded and assembled view of the ball
in three leaf springs design. Starting at the laser diode, the flat surface of the solid
brass baseplate on the emit side is placed on the support ring. The baseplate can
be laterally manipulated by radial placement of an external lever.
The support ring is made from the same material (brass) as the baseplate, thus no
thermal expansion differences and good conduction properties (λ = 122 W/m/K).
Since the support ring is used to transport the heat away from the laser diode it is
expanded around the emitting point of the laser diode to receive as much radiated
heat as possible from the laser diode.
The mount between the support ring and frame is a kinematic one with three half
balls with radial V-grooves under 120◦ . The V-grooves and half sapphire balls offer good thermal isolation (six point contacts) between the brass support ring and
aluminum frame, enable easy replacement of the laser diode and define a thermal
center, which is close to the axis of the support ring. In case the emitting point of
the laser diode is shifted to the thermal center, the emitting point is insensitive to
32
CHAPTER 3. MEASUREMENT SYSTEM
y
z
x
Figure 3.17: Exploded view of LDM ball in three leaf springs design
Figure 3.18: Assembled view of LDM ball in leaf three springs design
homogenous expansion of the components.
3.3. LASER DIODE MODULE
33
The frame is made of aluminum to avoid thermal expansion differences between
the frame and the AFM head base. The balls are made from sapphire. The contact tension between the ball and frame are the result of the force from the preload
(maximum= 2.22 N) on the three balls in total, this leaves 0.52 N for each contact
point. The Hertz contact tension is 850 MPa [14], this exceeds the ultimate tensile strength of the aluminum (572 MPa), thus plastic deformation will occur. To
prevent permanent deformation the aluminum is anodized.
The preload between the base plate of the laser diode, support ring and frame is
introduced by a wave spring between the baseplate and the preload plate, which
is bolted to the frame. In the emit direction of the laser diode, there are three
tangential leaf springs, as part of the frame, under 120◦ holding a ball that contains
the two lenses. The ball with three leaf springs combination offers:
• Good thermal isolation between the lenses and the frame (three contact points)
• The possibility to translate the lenses in z direction and rotate around φ, ψ
and θ
• A thermal center on the midpoint of the ball
The slightly bigger ball radius(+50 µm) than the inner circle described by the three
contact points on the leaf springs enables a static situation between manipulating
the ball and gluing it to the three leaf springs. The glue around the contact points
is spread around by capillary forces. The ball is equipped with two parallel flat
surfaces on which the optical quality surfaces of the lenses can be manipulated laterally.
The relatively big mass of the ball with lenses connected to the three leaf springs
could give a dynamic problem. The expected first eigenmode is shown in Figure
3.19. Analytically the first eigenmode is found at 8.9 kHz. Computation with Finite
Elements Method (FEM) led to the same eigenmode, with a frequency of 11 kHz.
It is clear that the first eigenmode is well within the required > 2 kHz of the AFM
head.
y
x
z
Figure 3.19: First eigenmode of the ball in three leaf springs design. Ball mass:
m = 0.9 gr, leaf springs dimensions: h × b × l = 0.25 × 2.5 × 3.5 mm
From the position requirements of the LDM components:
• Manipulation of ball in z direction within ±1 µm
34
CHAPTER 3. MEASUREMENT SYSTEM
• Manipulation of φ and ψ within ±0.1 rad
To manipulate the ball, a manipulator is needed. To connect or imbed a manipulator, which performs the z, φ and ψ manipulation and keeps the required position,
until the glue has fixed the ball is difficult. The thermal isolation advantage of the
ball in three leaf springs is of less importance, since the laser diode is already well
isolated from the frame by the six point contacts with the frame. Taking into account that the angle deviation of the lens surfaces are well within the ±0.1 rad leads
to an other design for the lens manipulation.
Parallelogram design
y
z
x
Figure 3.20: Exploded view of LDM parallelogram design
Figure 3.20 and 3.21 respectively show the exploded and assembled view of the parallelogram design. Only the frame with the lenses are discussed here, since the
laser diode side of the frame is largely similar to the ball in leaf spring design. It
can be seen that a single parallelogram is integrated in the frame. The parallelogram only holds the collimating lens, which is guided by the parallelogram for
z displacement between the emitting point and the lens. As a consequence the
distance between the fixed focusing lens and the collimating lens will change, but
since the beam is collimated between the lenses, there is no effect on the beam
exiting the LDM. The z stroke needed from the parallelogram is ±50 µm, which is
mainly needed for the inaccuracy of the collimating lens’ focal length (±1% of 2.75
mm) together with estimated errors in z direction.
The parallelogram needs to be manipulated within ±1 µm with a stroke of ±50
µm. To deliver the resolution a ratio of 1:7 is introduced. With this ratio manipulation within ±7 µm with a ±350 µm stroke is required at the input side, which is a
achievable resolution of a setscrew.
Two designs are discussed to embed the 1:7 ratio. The first design (one-step manipulator) is shown in Figure 3.22. The ratio of 1:7 is delivered in a monolithic and
compact design. In this design stresses are left in both arms of the manipulator,
this can cause stability problems.
3.3. LASER DIODE MODULE
35
y
z
x
Figure 3.21: Assembled view of LDM parallelogram design
The second design (lever) is shown in Figure 3.23. This design is slightly bigger in
z direction, is also monolithic and delivers the same ratio, but it has better stability
properties. Furthermore the actuation of the lever is less difficult than actuation of
the one-step-manipulator, since the rotation of surface A is less in case of the lever
design. Hence, the lever design is chosen.
The input side of the lever needs to be manipulated. The minimal stroke and resolution required at the input side of the lever are ±350 µm and ±7 µm respectively.
Three manipulator designs are discussed.
First the on-board manipulator design shown in Figure 3.24 is discussed. The
manipulation strut is connected to the lever by gluing the lever-plug to the lever
and strut. The other side of the strut is glued to the stud bolt. The stud bolt is
translated by rotating the M1 nut and blocking the rotation of the stud bolt with the
36
CHAPTER 3. MEASUREMENT SYSTEM
x
y
z
Figure 3.22: One step manipulator design
x
y
z
Figure 3.23: Lever design
rotation block pin. The pin translates in a key-way, which is axially machined in the
fixed plug by wire EDM. Rotating the M1 nut within 10◦ allows manipulation within
7 µm. The preload between the fixed part of the frame and the lever is applied by a
compression spring. All components of the manipulator can be assembled off-line,
after which the manipulator is glued to the frame.
The on board manipulator remains in the AFM head when the AFM is in use, thus
spot size adjustment can be made when the AFM head is assembled. As a consequence, extra space in the head is required. Furthermore, the on-board manipulator raises stability questions, since the manipulator will act as a thermal actuator
when the temperature changes.
The second design uses an external manipulator. Figure 3.25 shows the clamp
3.3. LASER DIODE MODULE
x
37
y
z
Figure 3.24: On board frame manipulation design
design. In this design the strut is translated by a differential. By rotating the differential nut, the push stud bolt can only move the strut in negative y direction (the
lever and parallelogram deliver the preload on the strut). In case the strut has to
be moved in positive y direction an external preload is required. To do so a ∅0.4
mm strut with a ball attached to its end is positioned against the lever with its ball
in a center hole. By bending the preload strut the preload is applied coaxial to the
manipulation strut. To prevent the push stud bolt from rotating, a leaf spring is
bolted to it. The other side of the leaf spring is connected to a ring of the alignment
setup.
To fix the manipulation strut a clamp with an axial wire cut is fixed to the frame.
When rotating the M1.6 nut against the frame, the axial force between the nut
and frame together with the threads angle will cause the clamp to compress. At
compression the clamp will slightly move in y direction and will cause the strut to
translate from the moment that the friction between clamp and strut is big enough
until the moment the clamping is complete. Furthermore, the strut will slightly expand in axial direction because of the compression. The lever has to be positioned
by trial and error.
To make the production of the frame and the assembly of the frame manipulation
easier, the wire EDM of the frame is performed in two steps.
• At the first wire EDM step some material is left to fix the lever (a bridge), to
prevent the lever from moving around uncontrolled. The strut is glued to the
lever, the clamp is installed and compressed to fix the strut.
• The second wire EDM step will remove the bridge and the external manipulator can be installed
The differential manipulator of M1.6 (pitch= 0.35 mm) and M3 (pitch= 0.50 mm)
offers manipulation within 4.2 µm, assuming a rotational manipulation on the differential nut within 10◦ .
38
CHAPTER 3. MEASUREMENT SYSTEM
x
y
z
Figure 3.25: External frame manipulation clamp design
The clamp design offers a less complex, more stable and more compact design
than the on-board design. However, the clamp as method to fix the strut could give
some problems.
• Stress is present between threads around the clamp and in the clamp, which
can cause stability problems
• Some iteration will have to be performed to get the required position after
the clamp is applied
• Plastic deformation can occur at the location where the strut is clamped, thus
the strut will have preferred positions. This makes the iteration process difficult
The third manipulation design is shown in Figure 3.26, the glued design. In this
design the strut is glued to the lever and the glue plug. The glue plug is manipulated by differential means. In this case the fixed nut is bolted to the alignment
setup to prevent rotation and the differential bolt rotates. To prevent the glue plug
from rotating a rotation block is placed through the glue plug in a slot in the fixed
nut. After manipulation the glue plug is fixed by applying glue in the glue groove
through a glue hole.
3.3. LASER DIODE MODULE
39
x
y
z
Figure 3.26: External frame manipulation glue design assembly
The differential manipulator of M1.6 (pitch= 0.35 mm) and M4 metric fine thread
(pitch= 0.50 mm) offers manipulation within 4.2 µm assuming a rotational manipulation on the differential nut within 10◦ .
All designs shown are equipped with a steel manipulation strut to manipulate the
lever in y direction without coupling the rotation of the lever to the manipulator
translation. Since the space in y direction is restricted, a short strut is required.
Using a steel strut of ∅0.15 mm the minimum length of the strut is 1.5 mm to stay
below a tension of 1500 MPa.
As a conclusion the glue design offers the most compact design, most reliable fixation method and least complex design, thus this design is preferred.
FEM analysis of the parallelogram design, with lever and lever manipulation shows
that the first eigenmode is at 18.5 kHz, followed by the second at 20.5 kHz, thus
considerably better than the required 2 kHz.
40
CHAPTER 3. MEASUREMENT SYSTEM
Manipulation and fixation LDM
The LDM has to be aligned initially to position the laser spot on the point of interest
on the cantilever. The lateral manipulation of the LDM is performed with the use
of two eccenters, similar to the manipulation of the PDM (Subsection 3.2.2). The
stroke needed follows from the position requirements in Appendix A.2 and equals
±150 µm. To be able to position the laser spot of ∅10 µm on a cantilever with a
minimum width of 15 µm a resolution of ±1 µ m is required for the LDM manipulation. Subsection 3.2.2 already showed that the eccenter design of the PDM can
manipulate the module with the required stroke and resolution.
The support ring, fixation plate and AFM head base are made from aluminum. As
a consequence, the thermal expansion coefficients will match, but the friction coefficient between the AFM head base and the LDM is µ = 1.35 (maximum). For the
approximated mass of the module of 5 gr on a horizontal plane, this means 0.07
N friction force. The preload beam is designed to deliver at least that force over its
stroke.
After manipulation, the support ring of the module is fixed to the AFM head base
with a wave spring, also similar to the fixation of the PDM.
3.3.4
Thermal design of the LDM
The laser diode typically produces 50 mW of heat at its optical output level of 2 mW.
The heat is transported by convection, radiation and conduction. The most heat is
transported by the method with the least thermal resistance. An environmental
temperature of 20◦ C and a laser diode base plate temperature of 22◦ C is assumed.
The thermal resistances for the different transport methods are:
• Convection. With a heat transfer coefficient of αcv = 3.7 W/(m2 K), the natural convection on the 50 mm2 flat sides of the laser diode will have a thermal
resistance of RT = 3.2 × 104 K/W.
• Radiation. The heat transfer coefficient is, αr = 0.3 W/(m2 K). With the same
surface as for the convection, this leads to a thermal resistance of RT =
6.8 × 104 K/W.
• Conduction. A conducting surface of 10 mm2 between the base plate and
the support ring is present. The thermal resistance of the contact is approximated at αct = 5 × 10−5 m2 K/W, this is the thermal resistance of mediumrough aluminum on aluminum with silicone oil as interface fluid [15]. The
resulting thermal resistance is RT = 5 K/W.
From this rough analysis it is concluded that convection and radiation can be neglected in case the temperature difference between the base plate and environment
is around 2◦ C.
To transport the heat from the laser diode through the support ring to the environment several methods are available:
The convection by air with v = 0, natural convection, is preferred because of its
simplicity.
3.3. LASER DIODE MODULE
Method
Convection - Air
v 6= 0
v=0
Fluid
Thermoelectric
41
Complexity
Size
Remarks
Very low
Low
Very high
High
Big
Medium
Big
Small
Potential disturbance cantilever
Circulation system needed
Controller needed
A commercial pin heatsink with relatively small dimensions is selected, shown in
Figure 3.27.
Figure 3.27: Pin heatsink, ∅28.5 mm, pin-height=4.5 mm
To thermally connect the laser diodes support ring to the heatsink, but decouple
them mechanically, thermal strap are applied. These thermal straps are thin metal
wires with a high thermal conduction. Copper wires are selected, because of the
good heat conduction (λ = 390 W/m/K) and availability of a large range of wire
thicknesses.
Figure 3.28 shows the schematic thermal route from the laser diode to the environment and Table 3.12 shows the resulting thermal resistances of the route. This
analysis neglects transport by convection and radiation along the thermal route.
The total thermal resistance results in ∆T = 1.3 K.
A
Laser diode
qin= 50 mW
R1
B
Support ring
R2
C Thermal straps
R3
D
Heatsink
R4
E Environment
T= 20 oC
Figure 3.28: Schematic thermal route from the laser diode to the environment.
RT 1−4 =contact resistance
42
CHAPTER 3. MEASUREMENT SYSTEM
Table 3.12: Thermal resistance of thermal route
Surface Length Thermal resistance Remarks
[mm2 ]
[mm]
[K/W]
RT 1
13
3.8a
B. Support ring
7
1.5
1.8
Brass
RT 2
20
2.5
C. Thermal straps 6
15
6.4
Copper
RT 3
20
2.5
D. Heatsink+RT 4
10
From specification
Summation
27
a Thermal
resistance of the contact approximated at αct = 5 × 10−5 m2 K/W [15]
The stiffness of the thermal straps can be decreased (better mechanical decoupling)
by choosing an appropriate shape, increasing the length and decreasing the thickness of the copper wires. The thermal resistance increases with length and inversely with the conducting surface.
Mechanical design of the thermal route
Figure 3.29 and 3.30 show the mechanical design of the thermal route. The thermal straps consist of three bundles with 1000 ∅0.05 mm copper wires to get the
required 6 mm2 conducting surface in total. Using thin wires and introducing the
bend in the straps reduces the stiffness, thus decreases the mechanical coupling.
The straps are clamped to the support ring and the heatsink base (not in figure).
Using a conducting fluid between the clamps decreases thermal resistance. The
heatsink base is placed on the AFM head base with spacers mainly consisting of
the thermal isolating polyamide 6,6 (λ = 0.2 W/m/K). The heatsink is mounted
on its base with thermal conductive adhesive.
Figure 3.29: Exploded view of thermal components of the LDM
3.3. LASER DIODE MODULE
Heatsink base
43
Strap
Figure 3.30: Detail of thermal components of the LDM
To further improve the thermal performance of the AFM head conducting paste
should be applied radially between laser diode and support ring.
Chapter 4
Observation system
Observation is needed in the AFM head to view the:
• Focal spot. To align the LDM, the focal spot on the cantilever needs to be
observed.
• Approach. The approach of the cantilever tip to the sample surface.
The required resolution and Field Of View (FOV) for the two observations are:
Resolution
FOV
Focal spot
≤ 2 µm
≥ 100 µm
Approach
≤ 2 µm
≥ 50 µm
To observe the alignment of the focal spot (≥ ∅10 µm) on the cantilever (width
≥ 13 µm), ≤ 2 µm resolution is needed. The minimal FOV of the focal spot view
is based on a good view of the entire cantilever width, which is 65 µm maximum.
For the approach, the resolution is needed to see the tip (height>2.5 µm) and the
FOV to see the biggest tip available (20 µm).
A CCD camera in combination with a lens(system) offers a compact design and enables remote observation on a display in contrast to observation through an ocular.
Thus a CCD camera and lens(system) is selected.
The choice for hardware capable to image with the required resolution and FOV
are mainly governed by equations 4.1, 4.2, 4.3 and 4.4.
F OV × M = A
(4.1)
Where M = Magnification and A= CCD sensing area.
Xsys × M = Xcam
(4.2)
Where Xsys is the system resolution and Xcam the camera resolution, which equals
2× the pixel size of the CCD.
Xdif f =
λ
2N A
(4.3)
44
45
In which Equation (4.3) [16] is the diffraction limit of the focal spot in contrast to
the cantilever backside, where λ[m] is the wavelength of the light and N A[−] is the
Numerical Aperture.
DOF =
λ
Xcam
2 + M × NA
NA
(4.4)
Equation (4.4) [16] defines the Depth Of Field, which is the distance along the optical axis at which the image in within focus. In case a surface, like the cantilever
backside, is observed under an angle the DOF determines what part of the cantilever that is in focus and which part is blurred. Other points of attention while
selecting the hardware are:
• Compact design of lens and CCD
• Maximum Working Distance (W.D., distance from lens to focal point)
• Use of commercial components, no home built lens system
The properties of the selected lens and CCD and their resulting optical performance are listed in Table 4, more specifications of the CCD can be found in Appendix C.
Table 4.1: Properties of the selected objective
Property
Objective lens
M
50X
20X
NA
0.35
0.25
W.D.
18 mm
25 mm
Size
∅26×27 mm ∅26×20 mm
FOV
132 × 106 µm 330 × 265 µm
Xsys
0.21 µm
0.52 µm
Xdif f a
0.9 µm
1.3 µm
DOF
5.5 µm
10.6 µm
aλ
lens and CCD for observation
CCD
# pixels
1280 × 1024
Pixel size 5.2 × 5.2 µm
Area size 6.6 × 5.3 mm
Size
32 × 34 × 27.4 mm
= 635 nm (laser diode light)
The resolution is determined by the largest distance, thus the diffraction limit,
Xdif f in this case. The 20X objective lens offers enough resolution and makes
placement of the observation system easier, because of the bigger working distance
and smaller N A, thus this objective lens is chosen.
Observation lay-out
To determine the lay-out of the observation system in the AFM head, four designs
are discussed. The size of the chosen 20X objective lens (∅26 × 20 mm) disables
designs in which the lens is placed vertical or horizontal, since this causes conflicts
with the measurement system or the sample stage. The four designs and their major advantages and disadvantages are listed below.
The first design (Top-direct) is shown in Figure 4.1a. The figure shows the outlines
and centerline of the camera bundles, determined by the NA and working distance.
46
CHAPTER 4. OBSERVATION SYSTEM
The grey area represents the laser volume of the measurement system. The top
camera bundle is directly aimed at the cantilever at an angle of incidence of 40◦ ,
which allows 16.5 µm of the cantilevers length to be in focus. The approach bundle
is introduced with the use of a mirror.
• The first design (Top-direct) is shown in Figure 4.1a. The figure shows the
outlines and centerline of the camera bundles, determined by the NA and
working distance. The grey area represents the laser volume of the measurement system. The top camera bundle is directly aimed at the cantilever at an
angle of incidence of 40◦ , which allows 16.5 µm of the cantilevers length to
be in focus. The approach bundle is introduced with the use of a mirror.
Advantages
One simple mirror needed
Disadvantages
Space for cantilever mounting surface restricted
Simple
• The second design (Top-mirror) is shown in Figure 4.1b. The top and approach camera bundles are introduced with use of a mirror.
Advantages
More space available to mount the
cantilever
Disadvantages
Placement of mirrors difficult
Measurement lay-out needs adjustments to place lens of top bundle
• The third design (Split) splits the camera bundle into an approach and top
bundle.
Advantages
One camera in one position for two
views
Angles of view close to ideal
Space to mount cantilever
Disadvantages
Placement of special split mirror is
difficult
Complex
• The fourth design (Front-back) closely resembles the first design, with the
difference that the top camera approaches from the front of the cantilever.
Advantages
Space to mount cantilever
Disadvantages
Switching views needs second camera or big manipulation
Simple
The fourth design (Front-back) is chosen, mainly because of the space it leaves
for the measurement system, the lens is not partly between the LDM and PDM,
thus the angle of incidence can be smaller. Furthermore the other design left a
very restricted amount of space between the lens and sample stage, which makes
47
Top camera
bundle
Top camera
bundle
Laser
volume
Mirror
Approach camera
bundle
Cantilever
Approach camera
bundle
Cantilever
(a)
(b)
Top camera
bundle
Mirror
Mirrors
Top camera
bundle
Approach camera
bundle
Split
mirror
Approach
camera
bundle
Cantilever
Mirror
(c)
Cantilever
Mirror
(d)
Figure 4.1: a) Top-direct design; b) Top-mirror design; c) Split design; d) Frontback design
it difficult to construct a stiff AFM head base, the Front-back design leaves enough
space.
The camera for the observation system is not connected to the AFM head base. To
minimize the thermal and prevent mechanical influences the camera is placed on
a different base. The mechanical and stability requirements for this base are low
compared to the AFM head base. The design of this observation base is not discussed in this report.
To observe the cantilever, illumination is needed. For this purpose fiber optic illuminators are available. Fibers down to ∅0.205 mm are available with lengths up to
48 mm. The AFM head design allows a fiber-end to be placed close to the cantilever
vertically between the LDM and PDM. A second fiber for the approach illumination
can be placed horizontally.
Chapter 5
AFM Head
In this chapter the measurement- system and observation system are combined
in the AFM head. Furthermore, the measurement and thermal loop are analyzed.
Figure 5.1 shows side views of the measurement system plane.
z
z
y
x
x
y
Figure 5.1: Side views of measurement system plane
The choice of the observation lay-out in Chapter 4 leaves a restricted amount of
space for the cantilever holder. From the three discussed cantilever holder designs
in Subsection 3.1.2, the plate design can be placed in the AFM head without interfering the the camera bundles. Figure 5.2 shows the lay-out of the observation
system with the measurement system including the cantilever holder. It should
be noted that the figure shows two CCD camera’s with a lens, in practice only the
approach camera is placed at standard operation. The top camera is only needed
for initial alignment of the LDM.
48
49
z
x
y
Figure 5.2: Side view of measurement and observation system
Figure 5.3 shows the AFM head without a base, placed on a simplified version of
the sample stage.
Measurement loop
Figure 5.4 shows a cross-section of the AFM head on the sample stage through the
measurement plane. An impression of the shape of the AFM base is used in the
figure. This impression enables an analysis of the measurement- and thermal loop
and gives insight in the space available for the AFM head base. In the final base
design (is not in this report) the use of material is optimized to get the highest stiffness with the least amount of material.
A schematic representation of the measurement loop, of the sample position, is
shown in Figure 5.5. The optical axis of the measurement laser beam points at the
measurement point, measuring in Abbe. The reference beam of the interferometer
hits the reference mirror. The half balls of the kinematic mount, to mount the AFM
head, are placed on the reference mirror to minimize the length of the measurement loop. The path of the measurement continues through the AFM head base,
the kinematic mount of the CLM and to the cantilever tip. From the measurement
mirror of the sample stage the path of the measurement loop goes through several
components in the sample stage (simplified in Figure 5.5) and the sample itself.
Thermal loop
A schematic representation of the thermal loop is shown in Figure 5.6. The sample
stage is designed in such a way that the thermal center is located on the measurement point. Furthermore, the thermal expansion in z direction is approximately
50
CHAPTER 5. AFM HEAD
Figure 5.3: AFM head without a base on simplified sample stage
zero at the top face of the reference mirror.
To prevent errors due to temperature changes in x and y direction the AFM head
is mounted on three half balls (on the zero z expansion plane) in V-grooves radially
under 120◦ . Mounting is this way results in a thermal center in the measurement
point. The mount between the cantilever holder and the AFM head base is also
kinematic with its thermal center on the central axis through the cantilever tip.
In z direction the expansion of the materials over the length ∆zT by path A has
to equal the expansion of the materials by path B. In that case the net effect of
homogeneous thermal expansion at the cantilever tip is zero. The design of the
(grey) volume T in Figure 5.6 is not finished. The materials and their lengths in
this volume are used for thermal compensation. This means that the total thermal
expansion length of path A and B are equal.
This chapter has shown the lay-out of the measurement system together with the
observation in the AFM head. Furthermore the measurement en thermal loop have
been discussed.
51
Figure 5.4: AFM head with an impression of the base
AFM head
base
Reference
mirror
Path measurement
loop
Measurement
point
Reference
laser beam
Measurement
mirror
Measurement
laser beam
Figure 5.5: Measurement loop
52
CHAPTER 5. AFM HEAD
z
x
y
A
∆zT
B
AFM head
base
T
Reference
mirror
Zero z-expansionplane
Figure 5.6: Thermal loop
Chapter 6
Conclusions &
Recommendations
6.1
Conclusions
As part of a metrological Atomic Force Microscope (AFM) an AFM head is designed. The sample stage performs the spatial manipulation of the sample and the
AFM head holds the cantilever, measures its deflection and is equipped with an observation system. Based on the required vertical resolution at the cantilever tip (0.1
nm) the best deflection measurement system, for this application, is determined
to be the Optical Beam Deflection (OBD) system. Within the OBD system three
separate and replaceable modules have been designed:
• A Laser Diode module, consisting of a laser diode and beam shaping optics, is designed with optimal thermal stability. The module can be laterally
manipulated by eccenters within ±1 µm for focal spot alignment on the cantilever.
• The cantilever is part of the cantilever module. The module consists of a
holder, which is kinematically mounted to the AFM head base. The cantilever
is externally manipulated on its holder before fixation.
• The Photo Diode Module is equipped with a four segment photo diode with a
lateral resolution < 0.1 µm for spot displacement measurement. To align the
laser beam on the detector the module is laterally manipulated by eccentrics
within ±1 µm.
For initial alignment and for the tip to sample approach procedure an observation
system is designed to view the focal spot on the cantilever and the cantilever tip
respectively. The measurement system and facilities for the observation system are
integrated into a compact design with its thermal center at the cantilever tip.
53
54
CHAPTER 6. CONCLUSIONS & RECOMMENDATIONS
6.2
Recommendations
The following recommendations are made for future research:
• By experimental determination of the optical and electrical properties of the
laser diode a better approximation can be made about the linearity of the
measurement system and the heat dissipation of the laser diode.
• An external setup, with a crosshair optical microscope should be designed to:
– Align the cantilever on its holder
– Inspect the cantilever tip and the location of the tip with the cantilever
module mounted on the AFM head base
Bibliography
[1]
Binnig G., Rohrer H., Gerber Ch. and Weibel E., Physical Review Letters, 49(1),
57-61 (1982).
[2]
Sarid D., Scanning Force Microscopy, New York, Oxford University Press
(1994).
[3]
Rosielle P. C. J. N., Constructieprincipes 1 - Bedoeld voor het nauwkeurig bewegen en positioneren, Lecture notes 4007, Eindhoven University of Technology
(2004).
[4]
Werner C., Design of a long stroke translation stage for AFM, Internal report,
Eindhoven University of Technology (2005).
[5]
Meyer E., Progress in Surface Science, 41, p3-49 (1992).
[6]
Pedrotti S.J. and Pedrotti L.S., Introduction To Optics, New Yersey, PrenticeHall (1993).
[7]
Segmented Photodiodes, http://www.udt.com/application-notes visited: 2311-2008).
[8]
Photodiode Technical Information, http://sales.hamamatsu.com (visited: 2311-2008).
[9]
Fundamentals of Beam Position Measurement, http://www.mellesgriot.com,
(visited: 25-06-2008).
[10] Fukuma T., Kimura M., Kobayashi K., Matsushige K. and Yamada H., Review
of Scientific Instruments, 76, 053704 (2005).
[11] Photodiode Characteristics and Applications,
application-notes (visited: 23-11-2008).
http://www.udt.com/
[12] Seggelen J. van, NanoCMM, Eindhoven University of Technology, University
Press (2007).
[13] Operating Principles of Laser Diodes, http://www.opnext.com/products/diodes
(visited: 23-11-2008).
[14] Young W.C., Roark’s Formules for Stress & Strain, New York, McGraw-Hill
(1989).
[15] Janna W.S., Engineering Heat Transfer, New York, CRC Press (2000).
[16] Microscope Objectives, http://www.olympusmicro.com (visited: 24-11-2008).
55
Appendix A
Position requirements of the
OBD system
A.1
Analytic analysis of the beam profile
To determine the position requirements for the components of the measurement
system, the influences of the positioning inaccuracies on the laser beam will be
analyzed. A schematic drawing of the optical axis with the components of the
measurement system is shown in figure A.1 (not on scale).
A
Laser
diode
B
Collimating lens
wB
C
Focusing lens
D
Cantilever
E
Detector
x
wC
z
y
f1
d
f2
s
Figure A.1: Schematic drawing of the optical axis of the measurement system
It should be noted that the analytical analysis uses thin lens theory as an approximation of the beam and lens behavior. Thin lens theory can be used in case
the lens thickness (along optical axis) is small compared to the focal length. The
thicknesses and focal lengths of the two lenses used are:
The collimating lens is relatively thick. However, the selected lens is a high performance dedicated lens to collimate a diverging laser beam of the specific wavelength. The erros caused by the thickness is expected to be within 27 %, which is
56
A.1. ANALYTIC ANALYSIS OF THE BEAM PROFILE
Lens
Collimating lens
Focusing lens
Thickness [mm]
2.75
30
57
Focal length [mm]
1.9
3.2
the percentage left as margin on the cantilever spot size.
A.1.1
Component A - Laser diode
A lateral displacement of the emitting point of the laser diode, ∆xA , leads to:
• An angle from lens B, the beam is still parallel, but has an angle, βB =
this has two consequences to:
∆x
f1 ,
– A translation on lens C, dβB , leading to:
∗ An angle from lens C, βC =
βB d
f2
=
∆xd
f1 f2
– An angle from lens B, βB , leading to:
∗ Divergence from lens C, αC =
wC /2(1−cos(βB ))
f2
An axial displacement of the emitting point, ∆zA , leads to:
• A diverging beam after lens B, with angle αB =
wB /2∆zA
f1 (f1 +∆zA )
,this leads to:
– A diverging angle from lens C, αC , leading to:
∗ An axial translation of the focal point, ∆zD =
wB /2∆zA (f2 )2
wC /2f1 (f1 +∆zA )−f2
An angle of the emitting point, ∆φA , leads to:
• Translation on lens B, ∆xB = ∆φA f1 , this has two consequences:
– An angle from lens B, βB = ∆φA , leading to:
∗ An angle from lens C, βC =
∆φA d
f2
– A diverging angle from lens B, αB =
cos(∆φA ) ≈ 0 for small angles
A.1.2
wB /2(1−cos(∆φA ))
f1
Component B - Collimating lens
A lateral displacement of lens B, ∆xB , leads to:
• An angle from lens B, βB =
∆xB
f1 ,
this has two consequences:
– A translation on lens C, βB d, leading to:
∗ An angle from lens C, βC =
βB d
f2
=
∆xd
f1 f2
– An angle from lens B, βB , leading to:
∗ A diverging angle from lens C, αC =
An axial displacement of lens B, ∆zB , leads to:
wC /2(1−cos(βB ))
f2
≈ 0, since
58
APPENDIX A. POSITION REQUIREMENTS OF THE OBD SYSTEM
• A diverging beam after lens B, with angle αB =
wB /2∆zB
f1 (f1 +∆zB )
,this leads to:
– A diverging angle from lens C, αC , leading to:
∗ An axial translation of the focal point, ∆zD =
wB /2∆zA (f2 )2
wC /2f1 (f1 +∆zA )−f2
An angle of lens B, ∆φB , leads to:
• A diverging angle from lens B, αB =
0 for small angles
A.1.3
wB /2(1−cos(∆φB ))
f1
≈ 0, since cos(∆φB ) ≈
Component C - Focussing lens
A lateral displacement of lens C, ∆xC , leads to:
• An angle from lens C, βC =
∆xC
f2
An axial displacement of lens C does not give any first order errors, since the beam
is parallel when it approaches lens C.
An angle of lens C, ∆φC , leads to:
• A diverging angle from lens C, αC =
0 for small angles
A.2
wC /2(1−cos(∆φC ))
f2
≈ 0, since cos(∆φC ) ≈
Stroke requirements of the modules
To determine the required lateral strokes of the LDM and PDM a summation of the
estimated position inaccuracies will be made for these modules.
A.2.1
Laser diode module
The required lateral stroke of the LDM is a combination of the following items:
• Position inaccuracies of the LDM-components. As listed in table 3.11, the
inaccuracies of the laser diode and the two lenses cause a translation of the
spot on the cantilever, with a maximum of ±87 µm
• The position inaccuracy of the cantilever’s point of interest as a summation
of the reproductivity of the kinematic mount and the positioning of the cantilever on the holder is estimated to be within ±10 µm
• To be able to move the spot over the width of the cantilever an extra (±25 µm)
is needed
The total required stroke of the LDM is estimated to be within ±150 µm.
A.2. STROKE REQUIREMENTS OF THE MODULES
A.2.2
59
Photo diode module
The required lateral stroke of the PDM is a combination of the following items:
• The detector is glued under an optical microscope to the supporting ring of
the PDM within ±10 µm
• Position inaccuracies of the LDM-components. As listed in table 3.11, the
inaccuracies of the laser diode and the two lenses cause a translation of the
spot on the photo diode (±176 µm). This translation is largely compensated
by the LDM’s lateral translation leaving ±89 µm at the PDM
• The angle offset of the laser diode’s emitting point causes a translation of the
spot on the cantilever, which is compensated by translating the LDM. It also
causes a translation of the spot at the PDM of ±115 µm
• The required stroke on the cantilever of ±50 µm is also needed at the PDM
• An other possible major contribution to the spot’s lateral displacement on the
detector is an angle of the cantilever. This angle is a summation of the cantilever’s geometrical quality, its mount on the holder, the geometrical properties of the holder and the properties of the kinematic mount. These errors
are difficult to quantify. In case the cantilever has an angle of 1 mrad, this
leads to 40 µm translation at the PDM.
The total required stroke is estimated to be within ±500 µm.
Appendix B
Alignment procedure of the
LDM
Figure B.1 shows the steps to be taken in the alignment procedure of the LDM
components. The alignment procedure uses the PSD and support ring from the
PDM and requires an external collimated laser beam. An external manipulator is
needed for the lateral manipulation. The following actions need to be performed at
the alignment steps:
1. Center PSD
• The Beam resizer determines the centricity of the beam in the final
LDM setup, thus is used to center the PSD.
• The PSD is not fixed to the support ring and can be translated in x and
y by the external manipulator while monitoring the PSD output.
• When the PSD is aligned with the collimated laser beam, it is glued to
the support ring to center and fixate the PSD on the correct position.
2. Center ring
• The Beam resizer is removed and the center plug and ring are installed
on the LDM-frame.
• The center ring can be translated in x and y , while monitoring the PSD
output.
• When centered the center ring is glued to the plug.
3. Align collimating lens
• The center plug and ring are removed to place the collimating lens.
• Translating the lens in x and y and monitoring the PSD output allows
alignment of the collimating lens.
4. Align laser diode
• The center ring and plug are replaced by the laser diode and its support
ring.
60
61
• By lateral translation of the laser diode the emit point can be centered.
5. Align focussing lens
• The beam resizer and collimating lens are installed.
• The lens is rotated over its optical surface (R = 18.72 mm). The spot
displacement is monitored at a larger distance, ∆zalign (not on scale in
de figure).
• The rotation allows centering of the beam bundel, but the divergence of
the bundel is also influenced
6. Focal distance manipulation (not in figure)
• By monitoring the spot size at ∆zalign = 70 mm, the spot size in the
final setup on the PSD can be estimated.
• The laser diode to collimating lens distance needs to be adjusted in this
step. The lever manipulation is installed and used to adjust the focal
distance of the LDM.
62
APPENDIX B. ALIGNMENT PROCEDURE OF THE LDM
Step 1
PSD support ring
PSD
y
LDM - frame
Collimated laser
z
x
Ball in V-groove
Spacer 1
Beam resizer
Step 2
g
Center ring
Center plug
Step 3
Collimating
lens
LD
support ring
Step 4
Laser Diode
∆zalign
Step 5
Focussing lens
Spacer 2
Figure B.1: Alignment procedure steps. Grey= laser beam
Appendix C
Component specifications
Cantilever
Table C.1: Properties
Property
Supplier
Name
Shape
Material
Length
Width
Thickness
Stiffness
Tip
Height
Top angle
Radius
of the selected cantilever
Veeco
OTR4B
Triangular
Silicon Nitride
180 ± 20 µm
30 ± 2 µm
0.4 ± 0.1 µm
0.02 N/m
3 ± 0.5 µm
72 ± 4◦
15 − 20 nm
PSD
Table C.2: Properties
Property
Supplier
Name
Dimensions
Gap
Max. reverse voltage
Photo sensitivity a
Terminal capacitanceb
Dark current
NEP
aλ
= 635 nm
voltage= 5 V; frequency= 1 MHz
b Reverse
63
of the selected PSD
Hamamatsu
s4349
3.0 × 3.0 mm
100 µm
20 V
0.42 A/W
25 pF
0.01 nA
√
4.0 × 10−15 W/ Hz
64
APPENDIX C. COMPONENT SPECIFICATIONS
Laser diode
Table C.3: Properties of the selected Laser diode
Propertya
Supplier
Opnext/Hitachi
Name
HL6340MG
Optical power, Popt
0 − 5 mW
Wavelength
635 ±5 nm
Astigmatism
0.1 µm
Astigmatism at Popt = 2 mW
0.7 µm
Beam divergence k to junction 17◦ (13 - 25)
Beam divergence ⊥ to junction 20◦ (16 - 25)
Monitor current
0.03 mA (0.01 - 0.06)
Operating current
25 mA (25-40)
Operating voltage
2.4 V (2.4 - 2.7)
Size
∅5.6 × 3.5 mm
a Optical
and electrical properties at Popt = 5 mW
Figure C.1: Intensity distribution of laser diode
65
CCD camera
Table C.4: Properties
Property
Supplier
Name
Sensor
Pixels (H × V )
Pixel size (H × V )
Sensing area (H × V )
Pixel depth
Frame rate
Video output
Lens mount
Size
Weight
of the selected CCD camera
Edmund optics
EO-1312 (monochrome)
1/2" Progressive scan CMOS
1280 × 1024
5.2 × 5.2 µm
6.6 × 5.3 mm
8-bit
25 fps
USB2.0
C-mount
32 × 34 × 27.4 mm
63 gr
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