Understanding Transmission Electron Microscopy 

Diffraction Patterns Obtained From Infrared 

Semiconductor Materials 

by Wendy L. Sarney 

ARL-TR-3128 December 2003 

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ARL-TR-3128 December 2003 

Understanding Transmission Electron Microscopy 

Diffraction Patterns Obtained From Infrared 

Semiconductor Materials 

Wendy L. Sarney 

Sensors and Electron Devices Directorate, ARL 

Approved for public release; distribution unlimited. 
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14. ABSTRACT 

Materials analysis is enhanced by transmission electron microscopy (TEM) images and their corresponding diffraction 

pattern data. While TEM images are widely reported and largely understood, the diffraction pattern data tends to be 

underused or completely neglected. Diffraction patterns complement TEM images by allowing accurate structural 

assessments, including lattice plane identification and defect characterization. This paper explains how to ‘read’ 

diffraction patterns by understanding how they relate to the crystal in real space. For ease of illustration we use 

examples from semiconductor materials grown for infrared detector research at ARL. 

15. SUBJECT TERMS

 Semiconductors, microanalysis, transmission electron microscopy 

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Contents 

1. Introduction 1

2. FCC materials: Crystallography and reciprocal space 1

3. The crystal structure factor and allowed diffraction spots 4

4. Relationship between sample preparation and the diffraction pattern 6

5. Examples from ARIL projects 7

5.1 II-VI Semiconductor Films .............................................................................................7 

5.2 III-V Semiconductor Films ...........................................................................................14 

6. Conclusion 15

7. Acknowledgment 16

8. References 16

iii
iv

List of Figures 

Figure 1. Schematic of the zinc blende crystal structure in real space. ...........................................2 

Figure 2. Schematic of the reciprocal lattice of the fee crystal structure. .......................................3 

Figure 3. Low-index diffraction patterns for fcc crystals examined along the (a) [111] , (b) 

[100], (c) [111] , and (d) [212] zone axes. .....................................................................................5 

Figure 4. Basic TEM sample preparation process. (a) Wafer with film grown onto the 

substrate. (b) Sample is cleaved, and (c) polished to electron transparency. (d) Final 

crystallographic orientation of he specimen in the TEM. (e) Diffraction pattern obtained 

from this sample, the dashed lines represent the objective lens aperture. .......................................6 

Figure 5. (a) TEM diffraction pattern of Si taken from a sample having a [111] growth 

direction. (b) A corresponding schematic of (a) showing the spot indices. (c) Resulting 

diffraction pattern when a [110] Si diffraction pattern (Fig. 5a) is tilted along the [002] axis. .....8 

Figure 6. Diffraction pattern taken at the interface of a ZnTe film grown on Si.............................9 

Figure 7. (a) Diffraction pattern of a Si substrate having a [113] growth direction. (b) 

Diffraction pattern of a ZnTe film having a [111] growth direction. (c) Diffraction pattern 

obtained at the ZnTe/Si interface.....................................................................................................9 

Figure 8. High resolution image of a ZnTe/Si interface. ...............................................................10 

Figure 9. (a) Diffraction pattern of a Si substrate having a [113] growth direction. (b) 

Diffraction pattern of the ZnTe film. .............................................................................................11 

Figure 10. Schematic of a crystal and its twin...............................................................................11

Figure 11. Schematic of the ZnTe diffraction pattern from (a) the parent crystal A, (b) the 

twin of the parent crystal B, and (c) regions A and B. ..................................................................12 

Figure 12. High resolution image of a ZnTe film grown on Si. Regions labeled with an A 

refer to the parent crystal and regions labeled with a B refer to the twin of the parent crystal.....13 

Figure 13. ZnTe film have twins across the (111) plane. ..............................................................14 

Figure 14. Diffraction pattern of a ZnTe film that has twins across the (111) plane (b) 

Diffraction pattern from parent crystal A and (c) region B, its twin across the (111) plane.........14 

Figure 15. Diffraction pattern from a superlattice consisting of InAs quantum dots and GaAs 

buffer layers. ..................................................................................................................................15 
1. Introduction 

One advantage of TEM over scanning electron microscopy (SEM) or visible light microscopy is 

the ability to obtain diffraction patterns from the specimen under observation. Diffraction 

patterns provide structural details related to the specimen’s orientation, polytype, phase, and 

defect morphology. Diffraction pattern analysis is an excellent complement to x-ray diffraction 

data. Unfortunately, many researchers do not know how to extract information from diffraction 

patterns. It is common practice for scientific journal publications to include numerous TEM 

images without any reference to their corresponding diffraction pattern data. TEM images look 

like visible light images, although they are formed very differently and cannot be interpreted in 

the same manner. Diffraction patterns and information, however, are more abstract since they 

involve thinking in reciprocal space. Most scientists understand and trust x-ray diffraction data. 

For this reason a microscopist will often accompany the TEM images with x-ray diffraction data, 

even when the same information could be obtained with TEM diffraction. 

In the Electro-optics and Photonics division at the Army Research Laboratory (ARL) we grow 

and analyze semiconductor materials for infrared device applications. These materials include 

III-V alloys based on GaAs, InAs, InP and the antimonides, and II-VI CdTe based alloys. This 

report discusses how TEM diffraction data can reveal important structural characteristics of 

materials grown by molecular beam epitaxy (MBE) at ARL. 

2. FCC materials: Crystallography and reciprocal space 

All crystals have both a real and reciprocal lattice. The real lattice consists of an array of points 

that corresponds to the position of atoms in the crystal’s unit cell. The reciprocal lattice also 

consists of an array of points, with each point corresponding to a set of planes within the crystal. 

Many semiconductor materials form in the zinc blende crystal structure, as shown in Figure 1. 

This structure consists of two interpenetrating face-centered cubic (fcc) lattices displaced by 1

/4 

of the length of the unit cell's diagonal. In a binary AB alloy (such as GaAs), all of the ‘A’ atoms 

will lie on one of the fcc lattices, while all of the ‘B’ atoms lie on the second fcc lattice. The zinc 

blende structure has ABAB stacking along the [111] direction. The structure is described in real 

space by its primitive translation vectors, which for an fcc lattice are: 

1 ( ) 1 ˆ ˆ 2 a ay z = + G

2 ( ) 1 ˆ ˆ , 2

a ax z = + G (1) 

3 ( ) 1 ˆ ˆ 2

a ax = + y G

where a is the lattice constant of the unit cell. 

1
The diffraction pattern contains all vectors normal to the reflecting planes in the specimen. These 

reciprocal lattice vectors, denoted as g

G , have a magnitude equal to the reciprocal of their corresponding reflecting plane. A plane lying in a cubic coordinate system is system in is described 

by three indices denoted as h, k, and l. The indices are found by identifying where the plane 

inter-cepts the three axes of the coordinate system. The intercepts are quantified in terms of the 

crystal’s lattice constants along these three directions. Next, take the reciprocal of these three 

numbers and reduce them to the smallest three integers having the same ratio. For cubic crystals, 

the relationship between the reciprocal lattice vector and the plane indices h, k, and l is 

2 22 1

hkl

hkl

g d a

+ + = = G (2) 

where dhkl is the lattice spacing. 

A crystal’s reciprocal lattice vectors are expressed as 

11 2 2 3 3 g vb v b vb =+ + G G G G

where v1, v2, and v3 are integers and 1 2 b b, , G G and 3b

G are the primitive vectors of the reciprocal 

lattice. These axis vectors b are related to the crystal’s real space primitive lattice vectors 

G a

G by 

the relationship: 

2 3

1

123

2 a xa b

a a xa = π ⋅

G G G

G G G

3 1

2

123

2 a xa b

a a xa = π ⋅ .

G G G

G G G (3) 

1 2

3

123

2 a xa b

a a xa = π ⋅

G G G

G G G

where x denotes the cross product. 

Figure 1. Schematic of the zinc blende crystal 

structure in real space. 

2
By applying the fcc primitive lattice vectors (Eq. 1) to Eq. 3, we find that the reciprocal lattice 

vectors of the fcc lattice are: 

 1 ( ) 2 b xy ˆ ˆ ˆ a

z

π = −+ + G

2 ( 2 b xy ˆ ˆ ˆ . a

z) π

= −+ G (4) 

The reciprocal lattice vectors of the fcc lattice (Eq. 4) are shown schematically in Figure 2. 

Figure 2. Schematic of the reciprocal lattice of the fee 

crystal structure. 

3
3. The crystal structure factor and allowed diffraction spots 

The structure factor of a crystal is defined by the relationship 

2 ( 1 ) , i i i hx ky lz

hkl j

j

F fe π + + =∑ (5) 

which is the sum of the atomic scattering amplitudes from each of the i atoms in the unit cell (fi) 

multiplied by a phase factor that accounts for the phase difference between waves scattered from 

atoms on different (hkl) planes [1]. The structure factor is the Fourier transform of the electron 

density of a crystal’s unit cell. For a binary alloy AB with a zinc blende crystal structure, the 

basis consists of the A atoms located on the fcc lattice and the B atoms are displaced by 1⁄4 of a 

unit cell diagonal from the A atoms. Substitution of the coordinates (xi, yi, and zi) of the A and B 

atoms into Eq. 5 leads to 

( ) ( ) ( 3 3 ) (3 3 ) ( ) () () 1 . 22 2

ii i hkl h k l hk l ih k ik l ih l Ff e e e fe e e A Bππ π

π ππ ++ + + ++ + ++

⎛ ⎞

=+ + + + + + ⎜ ⎟

⎝ ⎠

 (6) 

Further simplification of Eq. 6 results in Eq. 7. 

( ) ( ) () () 2 { } {1

i hkl ih k ih l ik l F f fe e e e A Bπ

π ππ

+ + + ++ = + ⋅+ + + }. (7) 

We then determine F for all hkl indices: 

F = 0 if h, k, and l are a mix of even and odd integers.

F = 4(fA ± ifB) if h, k, and l are all odd integers. (8) 

F = 4(fA - fB) if h, k, and l are all even integers and h+k+1=2N where N is odd. 

F=4(fA+fB) if h, k, and l are all even integers and h+k+1=2N where N is even. 

The relationship between the scattering intensity I and the structure factor F is I = / F /2. Therefore, F must be nonzero in order for diffraction spots to appear. Using Eq. 8, we find that the 

lowest index diffraction spots for a zinc blende crystal include 002, 111, and 220. 

The distance between a diffraction spot and the transmitted beam spot (the large spot in the 

middle of the pattern) is defined by the relationship 

,

hkl

L R

d

λ = (9) 

4
where λ. is the wavelength of the electron beam, and L is the camera length (specific to the 

TEM). The geometric arrangement of the spots in the pattern relative to one another is easily 

determined with the definition of a dot product. 

Figure 3 shows the four lowest index diffraction patterns that are observable for zinc blende 

materials. Each pattern is referred to by its ‘one axis’which is defined as the direction perpendicular to all of the crystal planes that satisfy the Bragg condition. These planes are represented 

by the spots in the diffraction pattern. It therefore follows that the zone axis also specifies the 

direction of the incident electron beam with respect to the crystal. For illustrative purposes, 

examine Figure 3a, which shows a diffraction pattern having a zone axis (sometimes it is simply 

called a diffraction pattern). Notice that [11 0] is perpendicular to the normal of all of the (hkl) 

planes represented in the pattern (such as (002), (111), (220), etc.). 

Figure 3. Low-index diffraction patterns for fcc crystals examined along the (a) [1 11] , (b) [100], (c) [111] , 

and (d) [212] zone axes. 

5
4. Relationship between sample preparation and the diffraction pattern 

Samples are normally prepared so that the lowest index planes are observed. Most zinc blende 

films are prepared to allow the observation of the [11 0] zone axis. Figure 4 shows a very basic 

set of schematics demonstrating the sample preparation process. The wafer illustrated in Figure 

4a has a (001) growth direction (this is typical for both the antimonide and InAs/GaAs quantum 

dot detector and laser structures). The sample is cleaved into a small rectangle having edges 

along the <110>-type directions (Figure 4b). We then polish and ion mill the sample until we 

obtain electron transparency along the (11 0) direction. The sample is placed into the TEM so 

that its (11 0) direction lies parallel to the electron beam. A sample oriented and prepared as 

shown in Fig 4a-d would have the diffraction pattern shown in Figure 4e. 

As expressed in Eq. 9, the distance between a diffracted and transmitted spot is inversely proportional to the corresponding lattice spacing. Therefore, spots that are closer to the transmitted 

Figure 4. Basic TEM sample preparation process. (a) Wafer with film grown onto the substrate. (b) 

Sample is cleaved, and (c) polished to electron transparency. (d) Final crystallographic orientation of 

he specimen in the TEM. (e) Diffraction pattern obtained from this sample, the dashed lines represent 

the objective lens aperture. 

6
beam correspond to larger lattice spacings, which are most likely to fall within the resolution 

limits of the TEM. High resolution images are obtained by placing an objective lens aperture 

around the first order diffraction spots. High resolution images obtained for an [11 0] incident 

electron beam would show lattice fringes corresponding to the (002), (111), and (111) planes. 

For GaAs, these planes correspond to lattice spacings of 2.8264 Å, 3.2639 Å, and 3.2639 Å 

respec-tively, which are within the resolution limits of a 200 kV TEM. By comparison, when the 

sample is oriented so that the electron beam is along the (111) direction we obtain the diffraction 

pattern shown in Figure 4e. The nearest diffraction spots would correspond to the {202} crystal 

planes. This would require us to image planes having lattice spacings of 1.9987 Å. A well 

aligned 200 kV TEM would be able to image the (202) planes (but the image quality would 

likely be inferior to that obtained for the sample imaged along the [11 0] direction). 

5. Examples from ARIL projects 

5.1 II-VI Semiconductor Films 

Many films are grown onto substrates with which they have a significant lattice mismatch. 

Sometimes the film and substrate have a crystal stacking mismatch (the substrate is then known 

as a nonisomorphic substrate). Growing films onto these types of substrates often leads to films 

with crystallographic defects that are apparent in TEM images and diffraction patterns. Common 

examples include III-V wide bandgap semiconductors such as GaN [1] and II-VI HgCdTe [2] 

semiconductors. An ongoing experiment at ARL involves growing CdTe layers on top of ZnTe 

buffer layers grown on Si substrates. 

Si has the diamond crystal structure, which is identical to the zinc blende structure with the 

exception that each atomic site is populated by the same atom. Using Eq. 5, we find that the 

structure factor for Si is nearly the same as that for GaAs, the only major exception is that F = 0 

for h + k + 1 = 2N, where N is odd. This means that the 002 reflection is now “forbidden.” 

Figure 5 shows a [1 1 0] diffraction pattern taken from a Si substrate having a [111] growth direction. Notice that this diffraction pattern is the same as that shown in Figure 3a (except that it is 

rotated by 54° since the growth direction is [111] rather than [002]). Figure 5 shows that the 

(002) spot is clearly visible in spite of it not meeting structure factor rules. 

Forbidden spots often occur due to multiple diffraction of the beam as it passes through the 

sample. Each diffracted beam can act as a pseudo-incident electron beam and be re-diffracted by 

7
other planes. The (002) spot results when the incident 1 1 0 1 T 0 beam is diffracted by the (111) 

plane and then re-diffracted by the (1 11) ) plane, as shown by vector addition 

111 1 11 002. + = (10) 

Some semiconductor films, such as SiC, have several polytypes. The appearance of forbidden 

spots in a diffraction pattern can cause polytype misidentification. In order to determine whether 

a spot is ‘real’ or the result of multiple-diffraction, the specimen must be tilted along the axis of 

the suspicious spot. In the case of the Si specimen (Figure 5a), if we tilt along the [002] axis, the 

111 and 111 spots lose intensity, and the 002 spot will disappear (Figure 5c). If the 002 spot was 

a ‘real’ allowed spot, it would remain visible despite our tilting the specimen. 

Si and ZnTe have a lattice mismatch of 11%. By placing the selected area aperture (which 

isolates the specific area of the sample that will contribute to the diffraction pattern) over the 

Si/ZnTe interface, we obtain an overlay of the Si and ZnTe patterns (schematic shown in Figure 

6). The ZnTe spots (denoted by the light gray circles) are located closer to the transmitted beam 

than the Si spots (denoted by the black circles), since ZnTe has a larger lattice constant 

(6.103 Å) than Si (5.431 Å). 

Figure 5. (a) TEM diffraction pattern of Si taken from a sample having a [111] growth direction. (b) A 

corresponding schematic of (a) showing the spot indices. (c) Resulting diffraction pattern when a 

[1 10] Si diffraction pattern (Fig. 5a) is tilted along the [002] axis. 

8
The pattern shown in Figure 6 occurs when the Si substrate and film have the same orientation. 

When we grow ZnTe onto Si substrates having a [113] growth direction, we obtain films with a 

[111] growth direction. Figure 7(a) shows a schematic of the diffraction pattern obtained for a Si 

substrate having a [113] growth direction. Figure 7(b) is a schematic of the pattern obtained for a 

ZnTe film having a [111] growth direction. If we center our selected area aperture over the 

ZnTe/ Si interface, we obtain the diffraction pattern shown in Figure 7(c). We can see that Figure 

8c is an overlay of the patterns in Figures 7(a) and 7(b).When an objective lens aperture is placed 

around the first order spots (shown by the dashed line in Figure 7c), and the TEM is placed in 

image mode, we obtain the image shown in Figure 8. We can identify the lattice planes in Figure 

8 by comparing the image with the diffraction patterns in Figure 7, since the orientation of the 

pattern directly corresponds to that of the image. For instance, a straight line drawn between the 

transmitted beam spot and the 111 spot in the ZnTe diffraction pattern corresponds to the [111] 

Figure 6. Diffraction pattern taken at the 

interface of a ZnTe film grown on Si. 

Figure 7. (a) Diffraction pattern of a Si substrate having a [113] growth direction. (b) Diffraction pattern of a ZnTe 

film having a [111] growth direction. (c) Diffraction pattern obtained at the ZnTe/Si interface. 

9
direction in the image. The {111} planes lie perpendicular to this line. The {111}, {111}, and 

{002} planes are labeled in Figure 8. The lattice spacings can be directly measured from the 

image or from the diffraction pattern (with the help of Eq. 9). We find that the {111}

ZnTe d value 

measured from both the image and diffraction pattern directly agrees with {111}

ZnTe d calculated 

with Eq. 4 using the known value for the ZnTe lattice constant. For some semiconductor 

film/substrate systems we occasionally find that the measured value does not agree with that 

calculated from Eq. 4. The most common reason is due to the film being tetragonally distorted to 

accommodate strain. Another likely reason is because something other than the expected binary 

alloy has been deposited (usually because of an error in an MBE recipe resulting in the 

unexpected growth of a ternary). We can calculate strain by comparing the measured d for a film 

with the known d for bulk, unstrained material. 

Figure 8. High resolution image of a ZnTe/Si interface. 

10
In a recent experiment ZnTe was grown on a Si substrate having a [113] growth direction. The 

diffraction patterns of the substrate and the film are shown in Figures 9(a) and (b), respectively. 

The film was expected to have a [111] growth direction. When this sample was examined with xray, the grower was surprised to find that the {111} peaks were weaker than anticipated. At first 

glance the ZnTe film diffraction pattern (Figure 9b) does not look like any of the conventional 

fcc patterns shown in Figure 3. Whenever an unconventional diffraction pattern is obtained from 

a film that is expected to be crystalline, a microscopist must determine whether the irregularity is 

arising from either defects or the growth of an unintended crystal structure. In general, 

diffraction patterns containing rings of distinct spots result from film polycrystallinity. 

Diffraction patterns consisting of streaky rings usually indicate that a film has amorphous 

regions. A film may be-come amorphous due to growth problems, electron beam damage from 

the TEM, or damage from the sample preparation process. 

Figure 9(b) shows a pattern of distinct spots with what may be a symmetry axis located 29.5° 

from the horizontal. These types of patterns often originate when a film contains twins, which 

are shown schematically in Figure 10. 

Diffraction patterns are very useful for identifying twins in a film. Twinning is difficult to detect 

with x-ray; in fact, symmetric x-ray measurements can not detect twinning across some crystal 

planes. ZnTe films grown on Si having a <111> or <113> growth direction often contain high 

densities of twinned regions. The grower may be unaware of these twins, and become confused 

by the weakness of certain x-ray peaks or the presence of unexpected peaks. 

Twinning is due to applied stresses within a crystal, which are often related to the lattice mismatch between a film and a substrate. The twinned portion of the crystal is a mirror image of the 

parent crystal. The twinned and untwinned regions have identical crystal structures, but the 

twinned region is misoriented across the twinning plane with respect to the parent crystal (Figure 

10). 

Figure 9. (a) Diffraction pattern of a Si substrate having a Figure 10. Schematic of a crystal and its twin. 

[113] growth direction. (b) Diffraction pattern of the ZnTe 

film. 

11
It is a relatively simple process to identify the unknown diffraction pattern in Figure 9b. We 

begin by drawing a schematic of the diffraction pattern obtained from a single crystal of ZnTe 

having a [111] growth direction (Figure 11 a). We will refer to the crystal that would generate 

this pattern as the parent crystal, or crystal ‘A’. This is the diffraction pattern that we would 

expect if the entire film was single crystalline and had a [111] growth direction. We draw a 

dotted line with the same orientation as that of the suspected symmetry axis (Figure 9b). The line 

passes through the 111 spot, indicating that the crystal may have twinning across the (111)

plane. If we rotate the parent crystal's diffraction pattern 180° about the (111) plane, we obtain 

the pattern seen in Figure l I b. Finally, if we superimpose the patterns in Figures 11 (a) and (b), 

we obtain the pattern shown in Fig 11 c. Notice that the schematic of Figure 11 c matches the 

diffraction pattern shown in Figure 9(b). Therefore, we conclude that the pattern shown in Figure 

9B is obtained from a ZnTe film that has twinned regions across the (111) plane. 

Figure 11. Schematic of the ZnTe diffraction pattern from (a) the parent crystal A, (b) the twin of the parent 

crystal B, and (c) regions A and B. 

If we isolate the first order diffraction spots (Figure 9) with an objective lens aperture, we obtain 

the image shown in Figure 12. The regions labeled B, which are the mirror image of the parent 

crystal (A) across the (1 11) plane, give rise to the diffraction spots shown in Figure l lb. The 

{111} planes in B are rotated 39.1 ° counter-clockwise with respect to the (111) planes in A. 

Since a significant fraction of the sample contains twinned regions it follows that much of the 

film does not have the expected [111] growth direction. This would lead to a weaker [111] x-ray 

diffraction peak than expected. It would also lead to the presence of several peaks that 

correspond to planes in the twinned regions. For in-stance, if a film contains a sufficient density 

of ‘B’ regions (as shown in Figure 12), then the x-ray will detect a (111) peak located 39.1° from 

the (111) peak corresponding to the parent crystal. 

12
Figure 12. High resolution image of a ZnTe film grown on Si. Regions labeled with an A refer to the 

parent crystal and regions labeled with a B refer to the twin of the parent crystal. 

Some types of twins may be completely undetected by symmetric x-ray scans. Figure 13 shows a 

TEM image of a ZnTe film that has twinning across the (111) plane. It is clear from this image 

that region B is the mirror image of the parent crystal A. Figure 14(a) is a schematic of the 

diffraction pattern obtained from the sample shown in Figure 13. The diffraction pattern of the 

parent crystal A is shown in Figure 14b. The pattern in Figure 14c is the mirror image (180° 

rotation about the (111) plane) of that shown in 14b. This type of twinning defect would not 

cause a distortion in the lattice spacing along the [111] growth direction. Also, the (111) planes 

in both regions A and B have the same orientation. Therefore, a simple symmetric x-ray study of 

the (111) planes would not detect any irregularities due to twinning across the (111) plane. It is 

very common for these types of x-ray scans to be done as first-level quality assessments of 

semicon-ductor wafers; however, that they are ‘blind’ to this type of twinning defect. Since 

twinning is a common problem in films having a (111) growth direction, it is critical that indepth diagnostic assessments beyond basic x-ray are used when analyzing these types of 

structures. 

13
Figure 13. ZnTe film have twins across the 

(111) plane. 

Figure 14. Diffraction pattern of a ZnTe film that has twins across the (111) 

plane (b) Diffraction pattern from parent crystal A and (c) region B, its twin 

across the (111) plane. 

5.2 III-V Semiconductor Films 

Many ARL projects involve depositing III-V semiconductor structures on GaAs, GaSb, InAs, or 

InP substrates. The substrates usually have a [001 ] growth direction, although occasionally 

substrates with a small miscut are used to minimize the film/substrate lattice mismatch. When 

viewed along the [1 10] zone axis, the diffraction pattern of single-crystalline III-V 

semiconductor materials with a [001] growth direction looks as shown in Figure 3a. 

Figure 15 shows a diffraction pattern obtained from a superlattice consisting of InAs quantum 

dots and GaAs spacer layers grown onto a GaAs substrate. Notice that, unlike the diffraction 

pattern obtained from the ZnTe/Si system, there is only one set of spots for the InAs/GaAs system. The lattice mismatch between InAs and GaAs is 6.9% (compared with 11 % for ZnTe/Si). 

Therefore, the distances between the InAs and GaAs spots corresponding to the same hkl plane 

are visually indistinguishable. The superposition of the InAs and GaAs diffraction patterns 

appear as one diffraction pattern. 

14
Figure 15. Diffraction pattern from a superlattice 

consisting of InAs quantum dots and GaAs buffer 

layers. 

Commercial software exists that takes digitally collected diffraction patterns from the TEM and 

compares them with the expected diffraction patterns from a database. It can decipher precise 

shifts in spot position (that we can't measure with our eyes and a ruler on the TEM negative) and 

use this information to calculate the strain in the film. The software can also be used to identify 

the structure, polytype, and composition (such as the percentage of Al in an AlGaAs film) of a 

specimen. 

We can generate TEM images of specific hkl planes by placing an objective lens aperture around 

an individual diffraction spot. This mode of operation is known as diffraction contrast imaging 

and is very useful for identifying defects and enhancing image contrast. Diffraction contrast 

imaging will be discussed in a future technical report. 

6. Conclusion 

Diffraction pattern analysis provides detailed structural information. This paper used several 

examples from both II-VI and III-V semiconductor films to demonstrate typical materials 

charac-terization that is accomplished with TEM diffraction patterns. 

15
7. Acknowledgment 

The author thanks Greg Brill for the MBE growth of the ZnTe/Si films and John Little for the 

MBE growth of the InAs quantum dot/GaAs films. 

8. References 

[1] Williams, David B. and Carter, C. Barry, Transmission Electron Microscopy II, Plenum 

Press, New York, p. 43, 1996. 

[2] Lee, C. D., V Ramachandran, Ashutosh Sagar, R. M. Feenstra, D. W. Greve, W. L. Sarney, 

L. Salamanca-Riba, D. C. Look, Song Bai, W. J. Choyke, and R. P. Devaty “Properties of GaN 

epitaxial layers grown on 6H-SiC(0001) by plasma-assisted molecular beam epitaxy,” J 

Electronic Materials, vol. 30, pp. 162-169, March, 2001. 

[3] Brill, G., S. Velicu, P. Boieriu, Y Chen, N. K. Dhar, T. S. Lee, Y Selamet, and S. 

Sivananthan, “MBE growth and device processing of MWIR HgCdTe on large area Si 

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