Physics 366 Lab Report 3

Michael Dobbs, Sonoma State University

December 1, 2014

Abstract

Atomic Force Microscopy was used to analyze multiple samples to

identify their surface composition and determine their top structure.

Compiled data was used to calculate the roughness of the sample.

1 Introduction

Atomic Force Microscopy is a powerful tool used to identify the surface struc-ture of a solid by contouring the top layer with a sharp tipped probe andamplifying the hills and troughs via laser reflection and detection. Piezoelec-tric materials are used to finely tune the x and y distance parameters, and aharmonic oscillator is utilized in close contact mode to move the cantileverin the z direction. A Scanning Probe Microscopy program processes the dataand calculates the roughness of the sample.

2 Background

Gustav Schmalz designed the first Optical Profiler in 1929 in Germany. Heran a probe attached to a cantilever across the surface, shined white light to amirror attached to the probe, and amplified the signal to photographic film.The film was exposed to the reflected light of various wavelengths, causingmultiple colors to show up on the film, corresponding to varying heights onthe surface. This older design was subject to possible bending or crashing ofthe probe, causing a much lower resolution of the surface on the film. Referto Figure 1.

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2.1 Probe Mechanics

Modern atomic force microscopes utilize lasers of a single wavelength and adetector that monitors the position that the light hits it as a function of xand y distance. Refer to Figure 2.

When the surface of a sample is very small, one must be able to finely tunethe position of the probe to obtain the most accurate results. To control themovement of the cantilever at such fine distances, piezoelectric materials areused. Piezoelectric materials (such as Quartz or Lead Zirconate Titanate)undergo a change of geometry when placed in an electric field. The motionand direction depend on the type and shape of the material, and the fieldstrength which is controlled by applying a current through the material. Thebattery voltage is applied and the distance change follows the equation:

d2 � d1 = KV (1)

where d1 and d2 are the initial and final lengths respectively, V is the appliedvoltage, and K is the piezo constant. [1] K must have a smaller value thatallows for the change in voltage to induce a very small change in distance.Each dimension (x, y, and z) are controlled by a di↵erent piezoelectric. Referto Figures 3 and 4.

Cantilevers are attached to the electronics and hold the probe in place.They can be triangular or rectangular in shape and are primarily made ofsilicon or silicon nitride. [1] The attached probe can be pyramidal or conicalin shape and a sharp tip is desired for the most accurate results. To obtain thedesired radius of curvature around 2 nanometers, the material is chemicallyetched, or ion milled, usually leaving the tip only a couple of molecules thick.Refer to Figure 5.

To keep the tip close to the sample, a force sensor is used to monitor thepotential energy as a function of distance between the tip and the sample.This follows the potential energy diagram in Figure 6.

2.2 Contact Mode

In contact mode, the tip is slid across the surface of the sample and a feedbackloop maintains a constant distance between the cantilever and the sample byvertically moving the scanner to keep the force the same. Refer to Figure 7.The computer calculates this force following:

F = kz (2)

2

where k is the spring constant and z is the cantilever deflection. [1] So as tonot break the sensitive tip, the force is on the magnitude of .01 N/m.

This mode is advantageous because the tip can scan rough samples, showcontrast on flat samples, display atomic resolution, and work in air or liquid.Drawbacks include the damaging of soft samples by the dragging of the probeand the distortion of features due to the lateral force between the probe andthe grooves of a dip in the sample, which causes a square well to be seen asa triangular well.

2.3 Close Contact Mode

In close contact mode, a harmonic oscillator attached to the cantilever oscil-lates the probe at an amplitude of 20 to 100 nanometers. The tip of the probetaps the surface at the bottom of the wave and a feedback loop maintains aconstant amplitude. [1] Refer to Figure 8.

This mode is advantageous because the tip gets closer to the sample,resulting in higher lateral resolution. The tip is harder to break becausethe force is smaller and does less damage to soft samples. Lateral forces areeliminated due to the oscillation of the probe. The only drawback is thateach scan takes longer than contact mode.

3 Operation

To obtain accurate results, one must follow operating instructions carefullyso as not to damage the probe tip or obtain questionable results.

3.1 Probe Exchange

To replace or substitute probes, one can release the scanner and slide it outfor easier access. A magnet connects the cantilever to the scanner and keepsthe probe in place. Using tweezers, carefully take out the cantilever andmonitor which side contains the probe as it cannot be seen with human eyes.Put the new tip in and check that the magnet has captured the cantilever.Replace the scanner and begin loading the sample.

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3.2 Computer Operation

Load the sample and turn on the computer. The electronics in the AFM arecontrolled by the computer, which operates the following components: [1]

• Coarse Z Motion Translator: used for moving the probe in the z direc-tion for long distances

• Coarse X-Y Translation Stage: used for moving the sample in the x-ydirection for long distances

• X and Y Piezoelectric Transducer: used for moving the probe in thex-y direction for small distances (on the scale of nanometers)

• Force Sensor: detects the potential force between the tip and the surface

• Z Piezoelectric Ceramic: used for moving the probe in the z directionover small distances

• Feedback Control Unit: connects the force sensor to the computer andsignals the piezoelectric materials to change so as to keep a constantdistance between the probe and the surface so as to not break the tip

• X-Y Signal Generator: generates the voltage to be applied to the piezo-electric materials

After the data is obtained and the signal is processed, the computer displaysthe surface height as a function of x-y position using the contrast of color.Refer to Figure 3.

One must align the tip and load the correct software for the current tip.Approach the tip to the surface of the sample using the coarse and piezo-electric z motion transducers. Set the frequency, amplitude, and position ifusing close contact mode. Begin scanning by setting an area to scan anda time interval for each x and y component. After scanning, the computercompiles the data and displays a square spectra representing the surface ofthe sample, which can be converted to a 3D image.

4 Data Analysis

Three samples were scanned via Atomic Force Microscopy using contact modeand close contact mode. Various characteristics of the sample were calculated

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including the mean of the height, the root mean square of the height, andthe roughness of the sample.

The mean height is defined as the sum of all the measured heights dividedby the total number of measurements (N), and can be written in summationor integral form following:

h̄ =1

N

NX

i=1

h

i

=1

(b� a)(d� c)

Zb

a

Zd

c

h(x, y) dy dx (3)

where h

i

is a characteristic height on the spectra, a and b are the scanninglimits in the x direction, and c and d are the scanning limits in the y direction.Since x and y are independent, the mean height of each variable may also bewritten as:

h̄

x

=1

(b� a)

Zb

a

h(x) dx (4)

and,

h̄

y

=1

(d� c)

Zd

c

h(y) dy (5)

The roughness is an account of the deviations of a surface from the meanof that surface. If the deviations are large, the surface is rough, and viceversa. Roughness is defined as the standard deviation of the height and canbe written as a sum or an integral following:

�

h

=1

N

vuutNX

i=1

(hi

� h̄)2 =1

(b� a)(d� c)

sZb

a

Zd

c

(h(x, y)� h̄)2dy dx (6)

and written independently:

�

h,x

=1

(b� a)

sZb

a

(h(x)� h̄

x

)2dx (7)

and,

�

h,y

=1

(d� c)

sZd

c

(h(y)� h̄

y

)2dy (8)

These calculations are displayed in the data tables in the Figures of eachspectra.

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A Silicon coated glass sample was scanned using contact and close contacttips. Refer to Figures 9 and 10. The dots seen on the sample are the Siliconbits on the glass. The same area of 55.55 µm

2 was scanned, using the samescanning speed. Contact mode calculated a roughness of 38.19 mv whileclose contact mode calculated 6.59 nm, showing the higher precision of closecontact mode in comparison to contact mode. The bits of Silicon caused thissample to have a high standard deviation of height due to the probe beingraised over the lumps. The horizontal dark lines visible across the spectra onFigure 10 were due to students bumping the table on which the AFM wasplaced, causing the probe to jump and miscalculate the height.

A Silicon wafer was scanned using contact and close contact tips. Referto Figures 11, 12, and 13. This sample is a lot smoother than the siliconcoated glass sample, as the roughness calculated using contact mode and closecontact mode were 13.66 mv and 71.47 mv respectively. As seen from thespectrum of Figure 11, the sample is very smooth with only a few aberrations.In Figure 12, a smaller portion of the total area was selected (47.72 µm

2 ofthe total 888.79 µm

2), and the roughness increased to 128.09 mv due tothe smaller area having greater variations in height comparably, whereas thelarger area contained a great portion of it that was relatively flat. The flatarea can be seen on the left hand side of the 3D spectra of Figure 13, whereon the right side it dips and creates a larger roughness.

A thermally evaporated Aluminum sample was scanned using a closecontact tip and the height of the sample was analyzed using the line analysistool of the program. Refer to Figures 14 and 15. An area of 2.22 µm

2 wasscanned and found to have a roughness of 20.67 nanometers. This very highroughness is due to the very tall lump in the top right corner of the spectrum,causing the standard deviation to increase greatly. Using line analysis, onemay compare a roughness that doesnt include the bump to one that does.Figure 15 shows Line 1 having a roughness of 10.80 nm (not including thebump) and Line 2 having a roughness of 60.11 nm (including the bump).Thebump on Line 2 is shown on the right side of the 2D height graph in Figure 15.The data from Line 1 and Line 2 were fit to a summation of functions usingMathematica and the resulting equations for height were used to calculatethe mean height and roughness of the samples using equations 4,5 and 7,8displayed on the last page of the report. The program calculated a roughnessaverage of 10.80 nm for Line 1, and using Mathematica, a value of 14.789 nmwas calculated, corresponding to the red highlighted result on the page afterthe figures. This approximation is higher than the actual due to the fitted

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line not hitting every point on the spectra, leading the area under the curveto be greater. The program calculated a roughness average of 60.11 nm forLine 2, and using Mathematica, a value of 49.366 nanometers was calculated.This result is smaller than the actual due to my fitting equation not beingable to model the quick bump around y = 1.25µm, leading to a smaller areaunder the curve, and thus a lower roughness.

5 Conclusion

Atomic Force Microscopy is a practical tool for analyzing the surface of asample. As long as one is careful to not break the probe, accurate analysis ofthe top layers contours may be conducted. By utilizing close contact mode,one may obtain a more precise image of the surface than by using contactmode. The computer program can calculate the surface roughness, which ischaracteristic of the smoothness of the sample. The AFM is conclusive whenthe sample is relatively flat so that the calculations give reasonable results,otherwise the data is inconclusive due to a wide range of heights.

References

[1] Shi, Hongtao. PHYS 366: Intermediate Experimental Physics,Atomic Force Microscopy 2014. url: http://www.phys-astro.sonoma.edu/people/faculty/shi/p366/lectures/afm.pdf

6 Figures and Data

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Figure 1: Gustav Schmalz Optical Profiler (1929)

Figure 2: Schematic of Modern AFM System

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Figure 3: Electronic Schematic of AFM System

Figure 4: Piezoelectric Mechanics

Figure 5: Typical Cantilever and Probe

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Figure 6: Potential Energy Diagram Between Probe and Surface

Figure 7: Contact Mode Mechanics

Figure 8: Close Contact Mode Mechanics

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Figure 9: Silicon Coated Glass Sample, Contact Mode

Figure 10: Silicon Coated Glass Sample, Close Contact Mode

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Figure 11: Silicon Wafer, Contact Mode

Figure 12: Silicon Wafer, Close Contact Mode

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Figure 13: Silicon Wafer, Close Contact Mode, 3D Representation

Figure 14: Thermal Evaporation Coated Aluminum Sample, Close ContactMode

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Figure 15: Thermal Evaporation Coated Aluminum Sample, Close ContactMode, Line Analysis

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