Restructuring the
Physics 234 Course to Include Nanoscale
Investigations
Stephanie Barker and Kurt Vandervoort
Funding for this project was provided by the National Science Foundation
Nanotechnology Undergraduate Education Program Award #0406533.
Purpose of the Project
• To develop modules to introduce atomic force microscope (AFM)
applications into the Physics 234 course.
• To investigate surfaces at the microscopic level to reveal properties
which account for macroscopic-scale phenomena in light.
• To introduce and familiarize students with research-grade
equipment at an introductory level as important career preparation.
• To explore interesting engineering applications of nanotechnology.
Existing Course Lab
Structure
Proposed Revisions to
Lab Structure
Experiments:
1. Data Analysis
2. A.C. Circuits
3. Microwave Optics
4. Geometric Optics
5. Physical Optics
6. Spectroscopy
7. Speed of Light
8. Michelson Interferometer
Experiements:
1. Data Analysis
2. A.C. Circuits
3. Geometric Optics*
4. Physical Optics*
5. Spectroscopy*
6. Microwave Optics*
7. Speed of Light
8. Michelson Interferometer
Appendix A**
Proposed revisions reflect the need to present physics concepts in an order that
introduce AFM applications in the proper context.
* Modifed Lab Modules
** An Appendix was added as a basic reference for the standard operation of the AFM
Geometric Optics Module
• Existing Objectives
– To observe the interaction of light with prisms, mirrors and lenses
– To measure refraction, reflection, critical and Brewster’s angles
– To verify the laws of reflection/refraction and the lens maker’s equation
• Additional AFM Module Objectives
– To visually examine rough and smooth gold plated slides to verify specular
or diffuse reflection
– To observe the microscopic surface topography of these slides
• Learning Enhancements
– Students will be able to directly confirm criteria that define the limit for
geometric optics by distinguishing the microscopic origin of specular and
diffuse reflection.
Gold Plated Slides Exhibiting Specular
and Diffuse Reflection
Microscopic Image of Speculary
Reflective Slide
Cross-Section of Specularly Reflective
surface
• Surface feature widths and lengths ~ 0.5 μm or 500 nm
• Surface feature heights ~ 10 nm
• Surface feature heights are significantly less than the wavelengths of visible
light (400-700 nm)
Microscopic Image of Diffuse Reflective
Slide
Cross-Section of Diffuse
Reflective Surface
• Surface feature widths and lengths ~ 20 μm or 20000 nm
• Surface feature heights ~ 2000 nm
• Surface feature dimensions much larger than the wavelengths of visible light (400700 nm)
Physical Optics Module
• Existing Objectives
– To observe the basis for the wave theory of light
– To study the diffraction and interference of light
– To calculate the wavelength of light
• Additional AFM Module Objectives
– To visually examine the surface of an iridescent butterfly wing
– To observe the microscopic surface topography of the wing
– To observe the microscopic surface topography of a compact disc
• Learning Enhancements
– Students will be able to see direct applications of physical optics in both
natural and industrial materials.
AFM Image of Morpho Butterfly Wing
Cross-section of Butterfly Wing
Effects of Thin-Layer Interference
• The bright, shifting colors of a butterfly wing are due to
interference which occurs in a series of thin layers on the
surface of the wing.
• These structures can cause constructive interference for
certain wavelengths of visible light, so that some colors
seem more brilliant than usual.
• The colors may change as you (or the butterfly) change
position, and the interference becomes visible at different
angles of view.
Interference in Thin Layers
• The film layer has thickness t and index
of refraction n > nair
• The wavelength λn of light in the film
layer is
λn = λ/n
• Ray B travels a distance 2t further than
Ray A before the waves recombine in
the air above the film and interfere
• Ray A has an additional 180 degree
phase shift following reflection
Condition for Constructive Interference
in Thin Films
•
If 2t = λn /2, then rays A and B recombine in
phase, and constructive interference occurs, so:
4nt = λ
where n is the index of refraction of the film, m is
the order of interference, and λ is the
wavelength of light in air.
CD Exhibiting the Effects of a Reflective
Diffraction Grating
AFM Image of a Compact Disc
Cross-section of Compact Disc
• Size of surface features are on the order of the wavelength of
visible light. Height of surface bumps is between 120 and 130 nm.
Physics of a Compact Disc
• The bumps that were imaged by the AFM are variations
in a thin polycarbonate layer. As the CD is “read” a laser
is focused onto the region of these bumps.
• When the laser spot encounters a bump, half of the area of
the spot covers the bump, and half covers the flat area
surrounding the bump. The waves that are reflected from
these two different heights destructively interfere.
• The condition for destructive interference depends on the
wavelength of the laser light in the polycarbonate layer.
Using Destructive Interference to Read a
Compact Disc
reflection from bump
Laser spot
reflection from flat area
Bump
Top View
Side View
• The condition for destructive interference between two waves is such that the total
pathlength differs by a distance that is ½ the wavelength.
• In this case, the laser light is emitted from the same location, and the bump is the only
change in pathlength that the waves encounter. The waves that encounter the flat areas
travel a distance further than those encountering the bumps. This extra distance is equal
to twice the height of the bump (2h).
• This difference in pathlength must be equal to ½ wavelength for destructive
interference, so:
 2h = ½ λ, or h = λ/4
Expected Height of Bumps in
Polycarbonate Layer
• λ0 ≡ wavelength of laser (in air) = 780 nm
• λ ≡ wavelength in polycarbonate layer
• n ≡ index of refraction for polycarbonate layer
= 1.56
λ = λ0/n = 500 nm
λ/4 = 125 nm
• The cross-section of the CD scan does show surface
feature heights that are near this value.
Spectroscopy Module
• Existing Objectives
– To observe the effects of a multiple-slit diffraction grating on the
polychromatic light emitted from gas spectra tube
– To understand how spectroscopy can be used to find the characteristic
spectrum of a gas, and furthermore identify each element present.
• Additional AFM Module Objectives
– To view a microscopic image of the diffraction grating used and compare its
actual features with any original assumptions about the construction of the
grating
• Learning Enhancements
– Students will be able to closer observe the results of intricate machining
involved in the application of nanoscale technology.
– Students will be introduced to the microscopic topography of a “blazed”
diffraction grating.
Image of a Multiple-Slit
Diffraction Grating
• The “grating” is not actually a series of slits, but a series of angled
grooves. Th size of these features is on the order of the
wavelength of light.
Microwave Optics Module
• Existing Objectives
– To gain some familiarity with microwave techniques and equipment.
– (Optional) To show that microwaves, like light, are transversely polarized
electromagnetic waves.
• Additional AFM Module Objectives
– To determine the blaze angle for a standard diffraction grating by analyzing
the cross-section of an AFM image.
– To observe the double-slit interference pattern for microwaves.
– To observe the effects of a macroscopic blazed diffraction grating on the
diffraction envelope.
• Learning Enhancements
– Students will experience the advantages of a blazed diffraction on the
macroscopic scale.
Blazed Diffraction Grating Cross-section
• The height and width of the grooves can be used to determine the shallower
angle, which is the blaze angle.
• Average groove spacing as measured by AFM is 1600 nm.
• This result is within 5% of the nominal spacing, considering 600 lines/mm.
• The blaze angle is measured to be 23o, which is within 10 % of the
manufacturer’s specification.
Blazed Diffraction Gratings
sin-1(nsinqB)
qB
m=2
• By blazing the grating the
diffraction envelope can be
shifted so that the maximum
intensity occurs for higherorder maximum (m>1) of the
interference pattern.
m=1
m=0
m = -1
m = -2
qB
Blaze condition:
sin-1(n sin θB) – θB = θm
+
q
-
T
Grating
Plates
Setup for the Microwave Experiment
R
The Macroscopic Diffraction Grating
Results for the Microwave Experiment
(Slit width = 4 cm; Slit separation = 6 cm)
Relative Intensity
White data points: No
diffraction grating
used
Black data points:
Macroscopic
diffraction grating
used
-50 -40 -30 -20 -10 0 10 20
Angle (Degrees)
30
40
50
• The intensity maximum of the diffraction envelope is
shifted to the m = -1 position.
Overview of Appendix A:
Basic Operation
Instructions for the AFM
• Includes background theory of atomic force microscopy
• Gives a detailed explanation of the functions of the software
used to perform a scan with the AFM, including an index of
the icons.
• Includes the step-by-step procedure for configuring the
scanning parameters and operating the instrument
• Explains several methods of analysis for an image, including
the 3D Image, Histogram, and Dimensional Analysis
functions.