Discipline: Physics Subject: Characterization Techniques

Discipline: Physics

Subject: Characterization Techniques for Materials II

Unit 3: Surface Morphology

Lesson/ Module: Atomic Force Microscopy-I

Author (CW): Dr. Ajit K. Mahapatro

Department/ University: Department of Physics and Astrophysics,

University of Delhi, New Delhi-110007

Characterization

Techniques for Materials II [e-PG Pathshala]

Department of Physics and Astrophysics, University of Delhi, Delhi 1

Contents

Learning Objectives…………………………………...…………………………………..……….2

1. Introduction ………………………………..……………………………………...........…............3

2. Basic working principle of AFM……..…………….…….………………………………...…………3

2.1. Surface Sensing………….…….……………………………..…………………….………4

2.2. Detection of Cantilever Deflection………….…….……………………………..…………4

2.3. Image Processing………….…….……………………………..…………………………4

2.4 Feedback Mode Operation………………………..……………………………………4

3. Components of AFM……….……………………………………….…………….….……………6

3.1 Piezo ceramic scanner …………………………………………………………..………6

3.1.1 Raster scanning …………………………………………………………..……….…7

3.1.2 Hysteresis …………………………………………………………..……….…7

3.1.3 Creep…………………………………………………………..……….…8

3.2 Probes ……………………………………………………………………………...8

4. Force Measurement ……………………………………………………………………………9

5. Beam Deflection Detection………………………………………………………………………11

6. Scanning of the Sample Surface ……………………………………..………………………….11

7. Comparison between AFM and Electronic Microscopes ……………………………………12

Summary……………………………………………………………………………………..13

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Learning Objectives:

From this module students may get to know about the following:

i. Basic concepts and necessary components of AFM

ii. Components of the AFM

iii. Force Measurements and Beam Deflection Detection Leading to Scanning

Sample Surfaces

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1. Introduction

Imaging the surface features at nano/micro-meter scale provide realization of systems at the atomic and

molecular level, and helps gaining in-depth knowledge that could lead to new research discoveries and

technological developments in the areas of materials science, polymer science, electrochemistry, life

science, biophysics, biotechnology and nanotechnology. Atomic force microscopy (AFM) was invented

by Binning in 1986. Currently, AFM is used to map and study the three-dimensional surface topography

at micro/nano-meter scale for various types of materials including metals, semiconductors, soft biological

samples, and conductive and non-conductive materials, in different environments of air, liquid, and

vacuum. AFM can generate images at atomic resolution with height resolution at angstrom scale

precession. Recently, AFM is used as a technique for performing manipulations of nano-objects and in

nano-imprint technology for writing features at molecular dimension using molecular ink.

2. Basic Working Principle of AFM

The basic principle is based on capturing the interaction force between an interacting probe (supported on

a flexible cantilever) of tip dimensions at molecular level and surface of the sample. Depending on the

process of interaction, different operation modes could be defined. There are three important stages in

AFM (as schematized in Figure 1) combined to generate the three dimensional topography of the

sample’s surface at atomic resolution, including (1) surface sensing, (2) detection of cantilever deflection,

and (3) image processing.

Figure 1. Schematics of Atomic force microscopy (AFM)

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2.1 Surface Sensing

A cantilever with molecular sized tip is used to scan over surface of the sample (as shown in Figure 2),

and measured the forces between the cantilever of dimension < 10 nm and surface at very short distances

(~ 0.2-10 nm). As the tip approaches the surface, attractive force between the surface and tip causes the

cantilever to attract towards the surface. With the cantilever approaching more closer to the surface, the

tip is almost in contact and develops repulsive force, resulting deflection of the cantilever away from the

surface. This process of deflection of cantilever due to surface sensing is performed at every point of the

cantilever-surface positioning during scanning.

Figure 2. Interaction of the cantilever with surface causes bending of cantilever in AFM

2.2 Detection of Cantilever Deflection

A laser beam is used to detect the position of the cantilever throughout the process during approaching

with attractive force of the tip towards the sample surface and deflecting away from the surface due to

repulsive force on reaching more close to the sample.

An incident beam is reflected from the top of the cantilever and monitored the change in the direction of

the reflected beam with respect to the cantilever position. A position sensitive photo diode (PSPD)

capable of detecting changes in Amstrung precision is used to track any slight changes in the cantilever.

During measurement of the surface curvature, the cantilever deflects when the AFM tip passes over the

top of a surface feature, and the subsequent change in position of reflected beam in the scanning direction

is recorded through the PSPD.

2.3 Image Processing

An AFM images the topography of a sample surface by scanning the cantilever over a region of interest.

The raised and lowered features on the sample surface influence the deflection of the cantilever, which is

monitored by the PSPD. By using a feedback loop to control the height of the tip above the surface is

maintained at constant laser position.

2.4 Feedback Mode Operation

Feedback control is used in AFM for maintaining a consistent interaction or force between the

probe and surface. The schematic of a typical feedback system for AFM is given in Figure 3.

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Figure 3. Schematic description of AFM feedback loop

The feedback control measures the force between the surface and probe, activates the piezoelectric

ceramic to establish a relative position of the probe and surface to maintain a consistent force between

them at a user-specified set point level. Foe example, in contact mode, when the control signal (the

cantilever deflection) is above the setpoint, the feedback loop tries to reduce the force between the

cantilever and the sample by contracting the piezo in z-axis, and moves the tip a little further away from

the surface. When the deflection is less than the specified setpoint, the feedback loop expands the piezo in

z-direction to move the tip closer to the surface of the sample. Although signal processing varies

according to the image mode used (contact mode, tapping mode, etc), the feedback loop always performs

essentially the same function. The feedback system used to control the tip-sample interactions and the

resulting images are optimized for each new sample. This optimization is accomplished by adjusting

various gains in the feedback circuit of the scanning probe microscopy.

In the AFM, the feedback control electronics take an input from the force sensor and compares the signal

to a setpoint value. An error signal (Zerr) is then sent through a feedback controller. The output of the

feedback controller (Zout) then drives the z-piezo through a high voltage amplifier. The most common

form of feedback control for AFM is the PID controller consisting of proportional (P), integral (I) and

derivative (D) controller, takes the error signal and processes it as:

where P, I, and D are the gain settings appropriately selected for tracking the surface by the probe as it is

scanned. The ‘I’ term facilitates the probe to move over large surface features, and P and D terms allow

the probe to follow the smaller, high-frequency features on a surface. When the PID parameters are

optimized, the error signal image is minimized (Figure 3). The higher the feedback gains, the faster the

feedback loop reacts to changes in topography while scanning. However, since the AFM is not infinitely

fast in responding to the output of the PID controller, the increase of the feedback gains to a certain point

is limited, beyond this the feedback loop becomes unstable. This is the limiting factor for the maximum

achievable scan speed.

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3. Components of the AFM

Figure 4. Components of AFM

3.1. Piezo ceramic scanner

Scanning probe microscopy (SPM) scanners are composed of piezoelectric materials. The scanner is

constructed by the independent combination of piezo-electrodes for x, y, and z position coordinates into a

single tube or flexure scanner. The scanner formed can manipulate samples and probes in the three

dimensions with highly accurate precision. These are ceramic materials extend or contract with respect to

the polarity of the applied voltage gradient and conversely develop electrical potential in response to

mechanical pressure. In this way, movements in x, y and z direction are possible.

Figure 5. Schematics showing piezoelectric effect depending on the applied bias.

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3.1.1 Raster scanning

A series of voltage ramps are created by the x-y signal generators to drive the x and y piezoelectric

ceramics in the pizotube scanner of AFM (as shown in Figure 6). The scan range is set by adjusting the

minimum and maximum values for the applied voltage. The scanning position is set by offsetting the

voltages to the ceramic. Finally, the scan orientation is rotated by changing the phase between the signals.

Figure 6. Construction of piezotube scanner

3.1.2 Hysteresis

Differences in the properties of material and dimensions of piezoelectric element, develops signals with

scanner responding in a different way to the applied bias. This response is conveniently recorded in terms

of sensitivity, which is the ratio of piezo movement to piezo voltage, i.e. how far the piezo expands or

contracts with the applied voltage. Sensitivity is not a linear relationship with respect to scan size. Piezo

materials have inherent nonlinearities and shows hysteresis. The effect of nonlinearity and hysteresis can

be seen from the curves presented in Figure 7. As the piezo expands and retracts throughout its full range,

its movement with applied bias is reduced in the beginning of the extension but larger at the end. The

same process is repeated when the piezo is retracted from it’s position. This produces forward and reverse

scan directions to show hysteresis behavior between two scan directions. Nonlinearity and hysteresis can

cause feature distortion in SPM images and has to be properly corrected.

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Figure 7. Schematics showing piezoelectric effect depending on the applied bias.

3.1.3 Creep

The drift of the piezo displacement after a DC offset voltage is applied to the piezo ceramic is known as

creep (Figure ) and occurs either by changes in x and y offsets, or while the usage of “frame up” and

“frame down” commands such that piezo rapidly travels over a large area to restart the scan. When a large

offset is applied, the scanner stops scanning and a DC voltage is applied to the scanner for the movement

of offset distance. The majority of the offset distance is moved rapidly by the scanner and slows down for

the remaining distance. Resuming the scan, after a large offset distance moves with the scanner moving

slowly in the direction of the offset. Creep is the result of this slow movement of the piezo over the

remaining offset distance once scanning is resumed. Creep appears in the image as an elongation and

stretching of features in the direction of the offset for a short duration of time after the offset.

3.2. Probe

The probe represents a micro machined cantilever with a sharp tip at one end, which is brought into

interaction with the sample surface. Each probe has different specifications and shape. The two most

common geometries for AFM cantilevers are rectangular ("diving-board") and triangular. Generally, V-

shaped cantilevers are used due to low mechanical resistance to vertical deflection and high resistance to

lateral torsion. The dimension of the cantilevers ranges from 100 to 200 µm in length (l), 10 to 40 µm in

width (w), and 0.3 to 2 µm in thickness (t).

Integrated cantilevers are usually made from silicon (Si) or silicon nitride (Si3N4). They are characterized

by their force constant and resonant frequency, which have to be chosen according to the sample to be

studied. Additionally an optical detection system and electronics for the management of scanning

procedures and data acquisition are necessary.

AFM cantilevers are typically made either of silicon or silicon nitride, where silicon nitride is reserved for

softer cantilevers with lower spring constants. The dimensions of the AFM cantilever are very important

as they dictate its spring constant or stiffness; this stiffness is fundamental to governing the

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interaction between the tip and the sample and can result in poor image quality if not chosen carefully.

The relationship between the cantilever’s dimensions and spring constant (k) is defined by the equation:

k = Ewt3/4L3

where, w is the cantilever width, t is the cantilever thickness, L is the cantilever length, and E is the

Young’s modulus of the cantilever material.

4. Force Measurement

The cantilever is designed with a very low spring constant (easy to bend), making it highly sensitive to

force. The probe is attached on the end of a cantilever. The amount of force between the probe and

sample depends on the spring constant (stiffness of the cantilever), and distance between the probe and

sample surface. This force is described using Hooke’s Law:

F = - (k. x)

where, k is the spring constant and x is the cantilever deflection

If the spring constant of cantilever (typically ~ 0.1 - 1 N/m) is less than that for surface, the cantilever

bends and the deflection is monitored. The interaction of the probe with the force field associated with the

surface of the sample provides the dependence of the force upon the distance between the tip and the

sample (Fig. 8). The force measured by AFM can be classified into long-range forces and short-range

forces. The long-range forces dominate when scanned at large distances from the surface and can be Van-

der Waals force, capillary forces (due to the water layer often present in an ambient environment). When

the scanning is in contact with the surface the short range forces are very important, in particular the

quantum mechanical forces (Pauli Exclusion Principle forces).

Figure 8. Potential energy curve of a probe and sample.

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In the contact mode, the cantilever is less than a few angstroms away from the surface of the sample and

the interatomic force acting between the probe and the sample is repulsive (the purple region shown in

Fig. 8). The magnitude of this repulsive force increases as the probe begins to contact the surface and at a

later time it causes the cantilever to bend up.

In the non-contact mode, the cantilever is held on the order of 10-100 Å away from the sample’s surface.

Thus as result of long range Van der Waals interaction, the interatomic force between the probe and the

sample is attractive (the blue area in the Fig. 8). Attractive force near the surface is caused by a nanometer

sized layer of contamination present over the surfaces at ambient conditions. The amount of

contamination depends on the environment in which the microscope is being operated.

One complete cycle of the probe approaching towards the surface of the material, getting into contact, and

bending away from the sample is demonstrated in Fig. 9. At the right side of the curve (position A) the

scanner is fully retracted and the cantilever remains undeflected, since the tip is not in contact with the

sample. As the scanner experiences the attractive Van der Waals force, the cantilever comes close enough

to the sample surface. In the position B, the cantilever suddenly bends slightly towards the surface. As

the scanner continues to extend, the probe experiences a repulsive force (position D) and the cantilever

deflects away from the surface, approximately linearly (blue color). After full extension, at the extreme

left of the plot (position C, black color), the scanner begins to retract. The cantilever deflection retraces

the same curve. In the position E, the scanner retracts enough to make the tip spring-free.

Figure 9. Force dependence on the tip-sample distance

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5. Beam Deflection Detection

The laser is focused to reflect from the cantilever and onto the sensor. The position of the beam in the

sensor measures the deflection of the cantilever, and hence the force between the tip and sample. The

probe of the AFM scans the sample and the readings for the displacement of the cantilever is collected by

the photodiode through a laser beam reflected from the back of the cantilever. The photo diode is divided

into four parts as shown in the Fig 10. When the laser is displaced vertically along the positions top (1, 2)

and bottom (3, 4), a bending due to topography is developed, while if the displacement is horizontally

along the left (1, 4) and right (2, 3), a lateral force is produced i.e. torsion due to friction.

Finally, the topographic information = Photodiode signals [(1)+(2)]-[(3)+(4)]

Figure 10. Beam deflection detection

6. Scanning of the Sample Surface

The tip passes back and forth in a straight line across the sample. In a typical imaging mode, the tip

sample force is held constant by adjusting the vertical position of the tip (feedback). Tip is brought within

nanometer range of the sample.

A topographic image is built up recording the vertical position when the tip is rastered across the sample,

using a computer (Figure 11). During contact with the sample, the probe predominately experiences

repulsive Van der Waals forces (contact mode). This leads to the tip deflection as described below. As the

tip moves further away from the surface, attractive Van der Waals forces are dominant (non-contact

mode).

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Figure 11. Raster motion during Scanning in AFM

Stiffer cantilevers protect against sample damage because they deflect less in response to a small force.

This means a more sensitive detection scheme is needed. Radius of the tip of cantilever limits accuracy

for the image analysis and resolution, as shown in Fig. 12 below.

Figure 12. Tip radius dependence on image resolution.

7. Comparison between AFM and Electronic Microscopes

Optical and electron microscopes can easily generate two dimensional images of a sample surface. The

magnification is as large as 1000 for an optical microscope, and a few hundreds thousands ~100,000

for an electron microscope. However, these microscopes can’t measure the vertical dimension (z-

direction) of the sample, the height (e.g. particles) or depth (e.g. holes, pits) of the surface features. AFM,

which uses a sharp tip to probe the surface features by raster scanning, can image the surface topography

with extremely high magnifications, up to 1,000,000 , comparable or even better than electronic

microscopes. In AFM, the measurement is performed in three dimensions, the horizontal X-Y plane and

the vertical Z dimension. Resolution (magnification) at Z-direction is normally higher than X-Y.

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Summary

The AFM can generate an accurate topographic map of the surface features.

The interaction of the probe with the force field associated with the surface of the

sample provides the dependence of the force upon the distance between the tip

and the sample.

A topographic image is built up on the computer by recording the vertical

position as the tip is rastered across the sample.

Force Measurements and Beam Deflection Detection Leading to Scanning

Sample Surfaces.

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Discipline: Physics Subject: Characterization Techniques