Determining the Presence of Ordering in Ternary 

Semiconductor Alloys Grown by Molecular Beam Epitaxy

by Wendy L. Sarney and Stefan P. Svensson

ARL-TN-0520 January 2013

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Army Research Laboratory

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ARL-TN-0520 January 2013

Determining the Presence of Ordering in Ternary 

Semiconductor Alloys Grown by Molecular Beam Epitaxy

Wendy L. Sarney and Stefan P. Svensson

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
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Determining the Presence of Ordering in Ternary Semiconductor Alloys Grown by 

Molecular Beam Epitaxy

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Wendy L. Sarney and Stefan P. Svensson

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14. ABSTRACT

Some ternary semiconductor alloys spontaneously order during growth. We observe this phenomenon in some alloys grown for 

infrared (IR) applications by molecular beam epitaxy (MBE). Ordering can affect not only the crystal structure, but also 

important optical and electronic properties that ultimately affect a material’s suitability for IR device applications. It is

important to be aware of the presence of ordering, which is not usually detectable by the standard (004) x-ray diffraction (XRD) 

measurements typically used as a simple measurement of film quality.

15. SUBJECT TERMS

Transmission electron microscopy, molecular beam epitaxy, diffraction, semiconductors

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iii

Contents

List of Figures iv

1. Introduction 1

2. Motivation and Army Interest 1

3. Identification of CuPt Ordering 3

4. Identification of Rotation-induced Compositional Ordering 7

5. Conclusion 9

6. References 10

List of Symbols, Abbreviations, and Acronyms 11

Distribution List 12
iv

List of Figures

Figure 1. Lattice constant vs. bandgap diagram of common III-V semiconductors.......................2

Figure 2. Simulated diffraction pattern of zinc-blende ternary crystal..........................................4

Figure 3. Partial unit cell of a ternary alloy with CuPt ordering.....................................................5

Figure 4. Simulated diffraction pattern of zinc-blende ternary crystal with CuPt ordering. ........6

Figure 5. Diffraction pattern of InAsSb with rotation-induced ordering......................................8

Figure 6. InAsSb/InAs SL with rotation-induced ordering within the InAsSb layers....................9
1

1. Introduction

Under certain conditions, some ternary semiconductor alloys spontaneously order during growth. 

At the U.S. Army Research Laboratory (ARL), we observe this phenomenon in some alloys 

grown for infrared (IR) applications by molecular beam epitaxy (MBE). Ordering can affect not 

only the crystal structure, but also important optical and electronic properties that ultimately 

affect a material’s suitability for IR device applications. It is important to be aware of the 

presence of ordering, which is not usually detectable by the standard (004) x-ray diffraction 

(XRD) measurements typically used as a simple measurement of film quality.

2. Motivation and Army Interest

One common example of ordering seen in many semiconductor alloys is copper platinum (CuPt)

type ordering. In the case of an ABxC1-x ternary, where A is a group III and B and C are groupVs, the two group V atoms are ordered on the 

111

sublattice planes. Other groups, for 

example, conducted extensive studies of the effect of CuPt ordering on the reduction of bandgap 

of gallium indium phosphide (GaInP) (1). The difficulty in detecting and controlling ordering led 

to a large discrepancy in measured values reported from different authors (2). 

Over the last several years, ARL’s III-V program has investigated quantum well infrared 

photodetector (QWIP) structures type II strained layer superlattices (Type II-SLS), and type II 

quantum dot infrared photodetector (QDIP) superlattices (SL). The Type II-SLS is the focus of 

most recent research activity and funding within the IR community. This is because it has been 

presumed that no direct bandgap III-V material could reach longwave infrared (LWIR)

wavelengths.

Indium arsenide antimonide (InAsSb) has the smallest direct bandgap among the III-V 

compound semiconductors (3), as shown in figure 1. Recent work at ARL, in collaboration with 

Stony Brook University, shows a larger bowing parameter for InAsSb than previously believed 

and therefore the random alloy InAsSb l can reach LWIR bandgaps without resorting to SLs (4). 

Upon further development, this will provide a III-V analog to direct bandgap mercury cadmium 

telluride (HgCdTe), with the benefits of higher quantum efficiencies (QEs) and higher absorption 

relative to the SL approach. In addition, the bulk InAsSb did not suffer from the growth 

challenges associated with a multi-interface approach, nor did it contain gallium (Ga), which is

the source of the low minority carrier lifetimes that plague Ga-based type-II SLs (5). A bulk 
2

approach likely would have numerous advantages over a SLS approach, with less inefficiency 

and transport burdens, and stronger absorption. 

Figure 1. Lattice constant vs. bandgap diagram of common III-V semiconductors.

To develop InAsSb alloys for LWIR, we needed to be certain that the low bandgaps were 

inherent to the unstrained alloy and were not reliant on a hard-to-control property such as 

ordering. Prior work by other labs indicated that ordering was common in InAsSb and could 

reduce the bandgap. For instance, Wei and Zunger predicted that this effect could theoretically 

lower the bandgap in perfectly ordered InAsSb even to the semi-metallic regime (6). Kurtz et al. 

observed bandgap narrowing experimentally (7). 

The ARL approach is unique in that, with Stony Brook University, we developed graded buffer 

layers that allow the growth of unstrained, unrelaxed InAsSb alloys having native lattice 

constants over a range of compositions on both indium antimonide (InSb) and gallium 

antimonide (GaSb) substrates (8). Transmission electron microscopy (TEM) results indicate that 

this unstrained material does not have ordering. Therefore, disordered InAsSb with its native 

lattice constant is a viable candidate material for low-temperature, LWIR detector applications.
3

3. Identification of CuPt Ordering

We use InAsSb as an illustrative example, but the following treatment is valid for any zincblende cubic ternary alloy exhibiting CuPt ordering. 

The intensity of the diffraction spots is typically reduced to the square of the structure factor

2

hkl Fhkl I 

(1)

First, we consider the disordered case, which has a zinc-blende structure with the space group 

T d F43m

2

 . The space group of a crystal refers to the three-dimensional symmetry of the 

smallest repeatable unit of the crystal. The atoms are in the positions listed below:

In: 













4

1

4

1

4

1













4

1

4

3

4

3













4

3

4

1

4

3













4

3

4

3

4

1

As or Sb: (000)













0

2

1

2

1













2

1

0

2

1













2

1

2

1

0 

The general equation for the structure factor is

2 ( )

i i i

i hx ky lz

i

hkl i F f e

 

 



(2)

where x, y, and z are the positions of the atoms in the unit cell and h, k, and l are integer Miller 

Indices.

Therefore, for the completely disordered case:

 

( ) ( ) ( )

(0.5 0.5 )]1

( )

2

i h k i k l i h i

hkl In As S b F f e f f e e e

h k l

i

  

     

 

  



(3)

Substituting in the atomic positions gives:

Fhkl  0 for hkl mixed

4[0.5( 5 ) ]for odd

4[0.5( 5 ) ]for 2(2 1); n : integer, even

4[0.5( 5 ) ]for 4 ; n : integer, even

F f f if hkl

F f f f h k l n hkl

F f f f h k l n hkl

hkl As S b In

hkl As S b In

hkl As S b In

  

      

     

A crystal with a disordered, zinc-blende structure and the structure factor given in equation 3 has 

a diffraction pattern shown in figure 2 for the [110] zone axis.
4

4,-4,4

4,-4,2

4,-4,0

4,-4,-2

4,-4,-4

3,-3,3

3,-3,1

3,-3,-1

3,-3,-3

2,-2,4

2,-2,2

2,-2,0

2,-2,-2

2,-2,-4

1,-1,3

1,-1,1

1,-1,-1

1,-1,-3

0,0,4

0,0,2

0,0,-2

0,0,-4

-1,1,3

-1,1,1

-1,1,-1

-1,1,-3

-2,2,4

-2,2,2

-2,2,0

-2,2,-2

-2,2,-4

-3,3,3

-3,3,1

-3,3,-1

-3,3,-3

-4,4,4

-4,4,2

-4,4,0

-4,4,-2

-4,4,-4

Zone axis : [1,1,0]

Figure 2. Simulated diffraction pattern 

of zinc-blende ternary crystal.

If CuPt ordering is present, then the As and Sb atoms are arranged on the 

111

group-V 

sublattice planes. This size of the unit cell needed to describe the ordered material is double that 

needed for the disordered case. The atoms are arranged as shown in figure 3. The In atoms are 

represented by the red spheres, the As by the black spheres, and the Sb by the blue spheres. The 

positions for a unit cell of size 2a are listed below:

In:













8

1

8

1

8

1













8

1

8

5

8

1













8

1

8

7

8

1













8

3

8

3

8

1













8

3

8

7

8

1













8

5

8

1

8

1













8

5

8

7

8

1













8

5

8

5

8

1













8

7

8

3

8

1













8

7

8

7

8

1













8

3

8

1

8

3













8

7

8

1

8

3













8

1

8

3

8

3













8

5

8

3

8

3













8

3

8

5

8

3













8

7

8

5

8

3













8

1

8

1

8

5













8

5

8

1

8

5













8

3

8

3

8

5













8

7

8

3

8

5













8

1

8

5

8

5













8

5

8

5

8

5













8

3

8

7

8

5













8

7

8

7

8

5













8

1

8

1

8

7













8

3

8

1

8

7













8

5

8

1

8

7













8

1

8

7

8

7













8

7

8

1

8

7













8

3

8

5

8

7













8

7

8

5

8

7













8

5

8

7

8

7

As: (000)













0

4

1

4

1













4

1

4

1

0 











0

2

1

2

1













2

1

0

2

1













2

1

2

1

0 











4

1

0

4

3













4

3

0

4

1













4

1

2

1

4

1













4

3

4

3

0 











0

4

3

4

3













2

1

4

1

4

3













4

3

2

1

4

3













2

1

4

3

4

1













4

3

4

1

2

1













4

1

4

3

2

1
5

Sb:













00

2

1













0

2

1

0 











2

1

00 











4

1

0

4

1













4

3

4

1

0 











4

1

4

3

0 











0

4

3

4

1













2

1

4

1

4

1













4

1

4

1

2

1













2

1

2

1

2

1













4

3

0

4

3













0

4

1

4

3













4

3

2

1

4

1













4

1

2

1

4

3













2

1

4

3

4

3













4

3

4

3

2

1

Figure 3. Partial unit cell of a ternary alloy with CuPt ordering.

For simplicity, we neglect the contribution from In, since the positions of the In atoms are the 

same in the disordered lattice as they are in the ordered lattice.

Therefore, using the atomic positions for the group V elements in equation 2 gives

(3 3 )

2

( 2 )

2

( 3 )

2

(3 )

( ) ( ) ( ) 2

( )

2

( )

2 1

k l

i

h k l

i

h l

i

h l

i

i h k i h l i k l

k l

i

h k

i

hkl As F f e e e e e e e e e

    

  

 

   





      

   

  

 







     

         (2 3  )

2

(2 3 )

2

( 3 2 )

2

(3 2 3 )

2

(3 2 )

2

(3 3 )

2

h k l

i

h k l

i

h k l

i

h k l

i

h k l

i

h k

i

e e e e e e

     

+

          

   

  

( 3 )

2

(3 )

2

( 3 )

2

( )

( ) ( ) ( ) ( ) ( ) ( ) 2

h k

i

k l

i

k l

i

h l

i

i h i k i l i h k i h l i k l

S b f e e e e e e e e e e

   

     







       

         

 

    (2 3 3 )

2

(3 3 2 )

2

(3 2 )

2

( 2 3 )

2

(3 )

2

(3 3 )

( ) 2

(2 )

2

( 2 )

2

h k l

i

h k l

i

h k l

i

h k l

i

h k

i

h l

i

i h k l

h k l

i

h k l

i

e e e e e e e e e

     



 

(5)
6

This expression becomes

(3 3 )

2

( 2 )

2

( 3 )

2

(3 )

( ) ( ) ( ) 2

( )

2

( )

2

( )

2 1

k l

i

h k l

i

h l

i

h l

i

i h k i h l i k l

k l

i

h k

i

h l

i

hkl As S b F f f e e e e e e e e e e

    

  

  

   





      











 

   

  

  







     

         (2 3  )

2

(2 3 )

2

( 3 2 )

2

(3 2 3 )

2

(3 2 )

2

(3 3 )

2

h k l

i

h k l

i

h k l

i

h k l

i

h k l

i

h k

i

e e e e e e

     

(6)

In terms of a unit cell of side a, the superstructure spots of type 













2

1

2

1

2

1

have a structure factor

16( ) As Sb F  f  f

(7)

for the perfectly ordered case. If we take into account the ordering parameter, S, where S=0 

defines a completely disordered alloy and S=1 defines complete ordering, equation 7 is modified 

as

16 ( ) As Sb F  S f  f

(8)

A zinc-blende ternary alloy with CuPt ordering has a diffraction pattern, shown in figure 4 for 

the [110] zone axis.

Figure 4. Simulated diffraction pattern of 

zinc-blende ternary crystal with 

CuPt ordering.
7

4. Identification of Rotation-induced Compositional Ordering

Compositional ordering along the growth direction can also be induced during MBE growth of 

any compound semiconductor composed of more than two elements on the different lattice sites. 

This originates from the source-substrate geometry and the substrate rotation used to even out 

thickness variations across the wafer. Unlike the parameter thickness, composition cannot be 

averaged at a given location in the film. Instead, as we have published in prior studies, at any

arbitrary point at a finite radial distance from the rotation center, a compositional SL may form 

with a band-edge amplitude that increases towards the edge of the sample (9, 10).

For instance, again using the example of InAsSb, this rotation-induced effect results in a SL of 

InAs1-xSbx/ InAs1-ySby with a period, W, equal to G/R*60, where G is the growth rate in Å/sec 

and R is the rotation speed in revolutions per minute. The difference between x and y will 

increase from zero at the rotation center of the sample to larger values towards the edge. 

Rotation-induced ordering must be considered since it changes the bandgap of the alloy. To 

minimize this effect, all samples processed for devices should be prepared from material taken

near the rotation center, where the SL effect disappears.

Rotation-induced ordering lengthens the unit cell along the growth direction, leading to the 

presence of additional diffraction spots in normally forbidden locations along the [001] direction. 

An example is shown in figure 5. 

When samples are imaged using a chemically sensitive reflection, the SL becomes visible. One 

example of a chemically sensitive reflection is the (002) spot, which is not normally chosen since 

its structure factor is weaker than that of the standard (004) spot. For this same reason, most 

standard x-ray rocking curves are collected for the (004) reflection. The (002) reflection is 

chemically sensitive because its structure factor is largely dependent on the difference between 

the group V atomic scattering factors, i.e.,

4 ( ) 002 S bF x f f  As  . (9)
8

Figure 5. Diffraction pattern 

of InAsSb with 

rotation-induced ordering.

This is opposed to the (004) reflection, which is dependent on the sum of the group III and group 

V elements.

4[ (1 ) ]

004 220 As S b In F  F  xf   x f  f

(10)

where x is the As mole fraction.
9

An example is shown in figure 6, which is an InAs0.72Sb0.28/InAs SL. Rotation-induced ordering 

in the InAs0.72Sb0.28 layers leads to the fine period SL within the ternary layers. This, in turn,

creates a “superlattice within a superlattice” effect.

It is very easy to miss the presence of rotation-induced ordering, since a nonconventional 

diffraction spot must be used to make it visible. 

Figure 6. InAsSb/InAs SL with rotation-induced ordering within the InAsSb layers.

5. Conclusion

In this report, we discuss two common cases of ordering in semiconductor alloys grown by ARL 

for IR applications. The treatment in the report serves as an illustrative example, as well as a 

reference for calculating structural factors of other alloys. Since ordering can affect the electronic 

and optical properties of alloys, it is important to fully characterize a material to determine the 

presence and extent of ordering.
10

6. References

1. Gomyo, A.; Iobgayashi, K.; Kawata, S.; Hino, I.; Suzuki, T.; Yuasa, T. J Crystal Growth

1987, 77, 367.

2. Stringfellow, G. B.; Lindquist, P. F.; Burmeister, R. A. J. Electron. Mater. 1972, 1, 437.

3. Thompson, A. G.; Wolley, J. C. Can. J. Phys. 1967, 45, 225.

4. Wang, D.; Lin, Y.; Donetsky, D.; Shterengas, L.; Kipshidze, G.; Belenky, G.; Sarney, W. L.;

Hier, H.; Svensson, S. P. Proc. SPIE 2012, 8353–38.

5. Svensson, S. P.; Donetsky, D.; Wang, D.; Hier, H.; Crowne, F. J.; Belenky, G. J. Crystal 

Growth 2011, 334, 103.

6. Wei, S.-H.; Zunger, A. Appl. Phys. Lett. 1991, 58, 2684.

7. Kurtz, S. R.; Dawson, L. R.; Biefeld, R. M.; Follstaedt, D. M.; Doyle, B. L. Phys. Rev 1992, 

B46, 1909.

8. Sarney, W. L.; Svensson, S. P.; Hier, H.; Kipshidze, G.; Donetsky, D.; Wang, D.;

Shterengas, L.; Belenky, G. Structural and Luminescent Properties of Bulk InAsSb. J. Vac. 

Sci. Technol. 2012, B30 (2).

9. Svensson, S. P.; Uppal, P. N.; Gill, D. M. J. Vac. Sci. Technol. 1994, B14, 2192.

10. Sarney, W. L.; Svensson, S. P. Materials Characterization 2007, 58, 284.
11

List of Symbols, Abbreviations, and Acronyms

ARL U.S. Army Research Laboratory 

CuPt copper platinum

Ga gallium 

GaInP gallium indium phosphide 

GaSb gallium antimonide 

HgCdTe mercury cadmium telluride

InAsSb indium arsenide antimonide

InSb indium antimonide 

IR infrared 

LWIR longwave infrared 

MBE molecular beam epitaxy

QDIP quantum dot infrared photodetector

QEs quantum efficiencies 

QWIP quantum well infrared photodetector

SL superlattice

TEM transmission electron microscopy

Type II-SLS type-II strained layer superlattice

XRD x-ray diffraction
12

NO. OF

COPIES ORGANIZATION

1 ADMNSTR

ELEC DEFNS TECHL INFO CTR

ATTN DTIC OCP 

8725 JOHN J KINGMAN RD STE 0944

FT BELVOIR VA 22060-6218

1 US ARMY RSRCH DEV AND ENGRG 

CMND

ARMAMENT RSRCH DEV & ENGRG 

CTR

ARMAMENT ENGRG & TECHNLGY 

CTR

ATTN AMSRD AAR AEF T J MATTS

BLDG 305

ABERDEEN PROVING GROUND MD 

21005-5001

1 US ARMY INFO SYS ENGRG CMND

ATTN AMSEL IE TD A RIVERA

FT HUACHUCA AZ 85613-5300

1 US GOVERNMENT PRINT OFF

DEPOSITORY RECEIVING SECTION

ATTN MAIL STOP IDAD J TATE

732 NORTH CAPITOL ST NW

WASHINGTON DC 20402

3 US ARMY RSRCH LAB

ATTN IMNE ALC HRR 

MAIL & RECORDS MGMT

ATTN RDRL CIO LL TECHL LIB 

ATTN RDRL SEE I W SARNEY

ADELPHI MD 20783-1197

TOTAL: 7 (1 ELEC, 6 HCS)