ECE350 Semiconductor Electronic Devices
LAB 2
ECE350 Semiconductor Electronic Devices
Lab 2 (Part B)– Optical Analogue of X-Ray
Crystal Diffraction
Edward S. Rogers Sr. Department of Electrical and Computer Engineering
University of Toronto
Last Revised Aug. 2022
1 Introduction
In this part, you will analyze the structure of periodic 1D and 2D arrays by their optical diffraction
patterns. This is analogous to using X-rays to study the structure of crystals.
2 Background and Key Concepts
Diffraction of a wave by a periodic array is due to phase differences that result in constructive and
destructive interference. The diffraction pattern of a crystal is a picture of the reciprocal lattice and
therefore yields the structural information of the crystal. Diffraction can be observed when a wave
passes through a periodic array if the period spacing is similar to the wavelength of the incident
wave. As the lattice constant of a crystal is on the order of 10s of Angstroms (Å), X-rays are
required to produce the diffraction patterns. In this experiment, you will make a change of lengthscale. By using the periodic arrays with spacing 10-4 m-10-5 m, visible light from a laser can be
used instead of X-rays to produce diffraction patterns.
Reference: Kittel. Introduction to Solid State Physics. Ch.2
3 Equipment
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JDS Uniphase He-Ne Gas Laser (wavelength: 632.8 nm)
PASCO Educational diffraction grating slide with three vertical line arrays labelled A, B,
and C
PASCO Diffraction pattern slide: array of square apertures shown in Figure 3; array of
equilateral triangular apertures shown in Figure 4
Optical rail (2 m in length), optical rail carriers, posts, slide holder, screen, ruler
4 Cautionary Notes

NEVER LOOK DIRECTLY INTO A LASER BEAM OR SHINE A LASER TOWARD
OTHER PERSON.
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ECE350 Semiconductor Electronic Devices
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LAB 2
AVOID SCRATCHING THE EXPENSIVE SLIDES. HOLD THE SLIDES ONLY BY
ITS EDGES.
5 Procedure
The experimental setup is shown in Figure 1. A Helium-Neon (He-Ne) laser (632.8 nm) is used as the
light source. The laser, slide, and screen are placed on an optical rail with the beam aligned along it.
When laser light is incident on a slide containing periodic arrays, the Fraunhofer diffraction pattern of
the arrays appears on the projection screen.
Figure 1 Optical diffraction experiment setup
Mathematically, the Fraunhofer diffraction equation and the Bragg diffraction equation are similar,
both of which are dependant on the array spacing (d), wavelength (λ), and diffraction angle (θ) as
follows:
(a)
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(b)
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ECE350 Semiconductor Electronic Devices
LAB 2
Figure 2 A comparison of (a) Fraunhofer diffraction with (b) Bragg diffraction
As can be seen in Figure 2, the path difference of the top and bottom rays is 𝑑 ∙ 𝑠𝑖𝑛𝜃 for the
Fraunhofer diffraction case and 2𝑑 ∙ 𝑠𝑖𝑛𝜃 for the Bragg diffraction. This leads to the conditions:
𝑑 ∙ 𝑠𝑖𝑛𝜃 = 𝑛𝜆 (Fraunhofer) and 2𝑑 ∙ 𝑠𝑖𝑛𝜃 = 𝑛𝜆 (Bragg), where 𝑛 is integer number representing
the diffraction order.
In the experiment, you will first observe how the size and direction of the diffraction pattern are
related to the periodic arrays. Then you will measure the diffraction pattern spacing 𝑍, the distance
between the slide and the screen, 𝐿, and then calculate the diffraction angle 𝜃 . For a given
wavelength 𝜆, you can then calculate the array spacing 𝑑.
(1)
Turn on the He-Ne laser. Move the screen back and forth on the optical rail and observe the
laser beam on the screen.
(2)
Insert a PASCO Educational Diffraction Grating on the slide holder which should be placed
between laser and the screen. Each grating slide has three vertical line gratings A, B, and C,
each with different line densities (lines/mm).
(3)
Adjust the grating slide to let the laser light to be incident on grating A. Move the screen
closer and away from slide, observe and record the diffraction pattern. Does the pattern
change as change L?
(4)
Adjust the grating laterally. Observe the diffraction pattern. Does the diffraction pattern
move as you move the gratings laterally? Why/Why not?
(5)
Measure the diffraction pattern spacing and the distance L as shown in Figure 1, then
calculate the grating density (lines/mm) of grating A by using the Fraunhofer diffraction
equation.
(6)
Repeat Procedure (3)-(5) for slide gratings B, and C.
(7)
Remove the grating slide and insert the Diffraction Pattern slide.
(8)
Adjust the slide to let laser light be incident on the array of square apertures shown in Figure
3. Observe and record the diffraction pattern. Measure the diffraction pattern spacings and
the distance between the slide and the screen. Does the diffraction pattern move as you move
the gratings laterally? Why/Why not? From your measurements, determine the lattice
constant of the square array.
(9)
Adjust the slide to let the laser light be incident on the array of the triangular apertures shown
in Figure 4. Observe and record the diffraction pattern. Measure the diffraction pattern
spacings and the distance between the slide and screen. Does the diffraction pattern move as
you move the gratings laterally? Why/Why not? From your measurements, determine the
lattice constants of the triangular apertures.
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ECE350 Semiconductor Electronic Devices
LAB 2
(10) Turn the laser off, then hold the PASCO Educational Diffraction Grating by its edges and
look at a fluorescent light tube through the grating. What do you see?
(11) After finishing the experiment, put the slides back into the box and ensure the laser is turned
off.
6 Hypothesis
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Draw the diffraction patterns of a vertical array of lines and a horizontal array of lines.
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Draw the diffraction pattern of an array of square apertures (X=0.025 mm, Y=0.075 mm)
as shown in Figure 3. Assume a=X+Y is the pattern period/lattice constant.

Draw the diffraction pattern of an array of triangle apertures (X=0.025 mm, Y=0.075 mm)
as shown in Figure 4. Assume a=X+Y is the pattern period/lattice constant.
Figure 3 Array of square apertures
(Lattice constant a = X+Y = 0.100 mm)
Figure 4 array of triangle apertures
(Lattice constant a = X+Y = 0.100 mm)
7 Pre-Lab Questions
1. How does a periodic array of scatterers produce a diffraction pattern?
2. How can you use Fraunhofer diffraction to measure the lattice constant a 1D or 2D periodic
array?
8 Results
Include the following data in your post-lab report:
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ECE350 Semiconductor Electronic Devices
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Diffraction patterns for the three 1D and two 2D arrays.
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Data needed to calculate the lattice constants.
LAB 2
9 Post-Lab Questions
(1) What are the geometries of the lattices and the lattice constant of gratings A, B, and C?
(2) Calculate the lattice constant of the square apertures array. How do your results compare to
the specifications in Figure 3? How does the diffraction pattern vary as you move the arrays
along x, y, z?
(3) What is the lattice constant of the array of the triangle apertures? How do your results compare
to the specifications in Figure 4? How do the results compare with your hypothesis? How does
the diffraction pattern vary as you move the arrays along x, y, z?
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