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Estimation of Dislocation Density by X-ray Rocking Curve Analysis and Etch Pit
Method
Conference Paper · December 2009
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Abstract—X-ray rocking curve measurement is a
nondestructive method for assessment of crystalline perfection.
However, The FWHM values can give only qualitative
information about the dislocation density. In this work
dislocation density has been estimated by measuring the rocking
curve widths (FWHM) on several symmetric and asymmetric
crystal planes. The dislocation density has been estimated using
Ayer’s model developed earlier for highly deformed metallic
crystals. This paper reports the dislocation density estimation on
the LEC grown GaAs single crystal wafer. The estimated
dislocation density results are compared with Etch pit density
measurements. It is shown that if a constant value of the
instrument broadening is taken the estimated dislocation density
values show discrepancy with the measured EPD values. By
taking the different value for the instrument broadening for each
reflection plane gives a consistent value of the dislocation density
and compares well with the EPD values determined on the same
sample.
Index Terms—Dislocation, GaAs, HRXRD, SEM
I. INTRODUCTION
aAs wafer grown by Liquid Encapsulated Czochralski
(LEC) method are used as substrates for epitaxial growth
of several III-V material. These substrates are qualified prior
to the epitaxial growth for gross defect density. Dislocation
and point defects are the two most important defects types,
which often affect the material properties adversely. It is well
known that the defects in the substrates propagate through the
overgrowing epitaxial layer thereby deteriorating its quality
and suitability for any device fabrication. Also, the presence
of dislocations is usually associated with an enhanced rate of
impurity diffusion leading to the formation of diffusion pipes.
This effect translates into the introduction of trapping states in
the band gap, altering the etching properties of the wafer and
most importantly, altering the electrical properties of
thedevices. High dislocation densities have resulted in
lowering the breakdown voltage and raising the leakage
current in p-n junctions. It also changes the threshold voltage,
resistivity and drain source current in GaAs field effect
Manuscript received July 22, 2009. Akhilesh Pandey, Anshu Goyal, Ashok
Kumar Kapoor and R. Muralidharan, are with the Solid state Physics
laboratory, Lucknow Road, Delhi 110054, India, (corresponding auther
phone: [phone]; fax: [phone]; e-mail:
[email protected]
transistors.
TEM and EPD are the two techniques to determine the
dislocation density but these two techniques are destructive in
nature. TEM provides the accurate measurement of
dislocation density in highly defected crystals because it
examines small crystal volume. Etch pits density (EPD)
Measurements are normally used to estimate the dislocation
density using etching solution suitable for a particular plane of
a given material. The method is destructive in nature and is
highly selective. X-ray topography is also used to determine
dislocation density for low (<103 cm-2) dislocation contents
[10]. Unambiguous non-destructive estimation of dislocation
density is therefore desirable.
In this paper we discuss the application of a model
developed by Horden and Averbach [2] and later modified by
Ayers [3] for the estimation of dislocation density using X-
ray rocking curve broadening (FWHM) and estimate the
dislocation density of a LEC grown GaAs single crystal. EPD
measurements were also carried out and results are compared
with the dislocation density estimated by X- rocking curve
broadening. It is shown that for small FWHM values if one
assumes a constant value for the instrument broadening for all
the reflections, the estimated dislocation density values does
not correlate to the experimental values. We show that for
unambiguous estimation of dislocation density one should
take into account the variation in the instrument broadening
corresponding to each reflection.
II. EXPERIMENTAL PROCEDURE
GaAs bulk single crystal wafers were studied by X-Ray
rocking curve and EPD measurement. The material studied in
this work was grown by Liquid Encapsulated Czochralski
(LEC) method. A (001) oriented GaAs wafer was taken for
the dislocation analysis.
The X-ray rocking curve measurements were carried out
using the Phillips X-Pert Pro MRD HRXRD system. In this
system incident X-ray beam falls on the 4 bounce 4-crystal Ge
(220) Bertels monochro-collimeter, which limits the angular
divergence of the monochromater is 12arc-s. All measured
reflections were optimized for maximum intensity and
symmetric shape by ψ (rotation), φ (azimuth) and ω (rocking
angle). X-Rocking curve measurements symmetric and
asymmetric (by grazing exit geometry) planes of GaAs wafer
were recorded.
The chemical defect etching of the GaAs wafer was
Estimation of Dislocation Density by X-ray
Rocking Curve Analysis and Etch Pit Method
Akhilesh Pandey, Anshu Goyal, Ashok Kumar Kapoor and R. Muralidharan
G

Estimation of Dislocation Density by X-ray Rocking Curve Analysis and Etch Pit Method ♦ 359
done using the standard procedure [6] and is described below.
First the GaAs wafer was free etched for 10 minutes in a
solution of H2SO4, H2O2, DI (diIonized) water with ratio of
3:1:1 for cleaning the surface. The cleaned wafer was then
immersed in molten KOH maintained at ~ 3750 C in a
zirconium crucible. The sample was kept in the molten KOH
for 5 minutes with continuous stirring of the crucible and then
allowed to cool to room temperature. The sample was taken
out slowly from KOH by continuous dilution with DI water
[6]. The etched wafer was examined in SEM for the shape
and density of the etch pits. Hexagonal etch pits were
developed as shown in figure 3. The Etch Pits were counted
after taking SEM images at different points on the wafer and a
average value of the EPD was obtained.
III. DISCUSSION (THEORY)
Dislocations are known to broaden the x-ray rocking
curves by one or all of the following mechanisms viz. (a) by
introducing a rotation in the crystal lattice (b) dislocation
strain field can introduce non uniformity in the Bragg angle
(c) dislocations can be arranged to form boundaries between
the grains giving rise to crystal size effects in highly deformed
crystals (d) curvature [2, 3].
Assuming the x-ray rocking profile to be Gaussian (which
is a good approximation as shown in figure 1) the measured
X-ray rocking curve FWHM (βm(hkl)) can be expressed as
[2,3]
βm
2 =βi 2+ βo 2+ βα 2+ βε 2+βL 2+βr 2 (1)
where βα ,βε ,βL and βr are the line width due to lattice
tilting / twisting (lattice deformation), local strain, crystallite
size and curvature respectively. βo is the intrinsic half width
for the perfect crystal for different planes and βi is the
instrumental broadening which is the broadening of the
monochromater [2,10] .
Since the thickness of bulk single crystal GaAs sample was
greater than 500 μm, the contribution to βm due to crystallite
size and crystal curvature broadening effects can be neglected.
Subtracting the effect of all the broadening factors from the βm
(measured FWHM for a particular plane) one can get the
adjusted broadening value of βadj as,
βad
2 = βm 2 – (βi 2+ βo 2) = βα 2+ βε 2
Following the treatment developed by Ayers and the
dynamical diffraction theory for the calculation of β0, the
equations for the βα
2 and βε 2 and the associated dislocation
densities for the two factors can be written as
βα
2 = (2π ln2) b2 Dα = Kα
(2)
Dα= βα
2 / (2π ln2) b2
Where b is length of the burger vector, Dα is the dislocation
density. The strain broadening due to dislocation
βε2
= 0.09b2Dε (ln(1/(2.10-7 √ Dε))tan2 θ = K ε tan2 θ (3)
Dε is the dislocation density and b is the burger vector.
By combining equation (2) and (3)
βad
2=Kεtan2θ + Kα (4)
This is a straight line equation and the slope and the
intercept of the plot of βad
2 with tan2θ will give the values of
Kε and Kα respectively. The dislocation density can be
estimated using the equation 2 and 3. The orientation of all the
symmetric and asymmetric planes and the broadening terms
are given in Table I. Fig 1 is showing the X- ray Rocking
curve of (004) symmetric plane with Gaussion fitting.
Asymmetric (117) plane is too much far from other selected
planes, but this plane is responsible for strain broadening of
dislocation [2].
IV. RESULTS AND DISCUSSION
A plot of βad
2 vs tan2 θ is shown in figure 2. The straight
line fitting to the plot gives the values of Kα and Kε as 67 and
217 (arc-s)2 and the associated dislocation values were
estimated to be 2.2x105 and 4.6X106/cm2 respectively taking a
constant value of 12 arc-s for the instrument broadening.
The dislocation density was also estimated from the EPD
done on the same sample. The SEM micrograph of the EPD is
shown in Figure 3. The dislocation density obtained from the
EPD measurement was 1.5X105/cm2. It can be seen that there
is a discrepancy between the values of Dα and Dε and also the
two values differ greatly from the measured EPD values.
33.219 33.228 33.237
0
60000
120000
Intensity (A.U.)
ω(degree)
GaAs Recorded
GaAs Gaussian fit
Fig.1. X- ray rocking curve profile for GaAs wafer for (004) plane
h k l theta
(deg)
βm
(arc-s)
β0
(arc-s)
β ins
(variable
)
βadj-c
2
(arc-s)2
(constant
instrument
broadening)
tan2θ
βadj-v
2
(arc-s)2
(variable
instrument
broadening)
004 33.27 16.56 8.7 13.6 98.54 0.42 11.54
006 55.08 26.28 0.3 20.2 590.54 2.05 284.54
224 41.85 19.8 2.4 14 286.28 0.80 186.28
026 59.75 28.44 5.4 25 679.67 2.93 154.67
044 50.65 22.32 2.0 18 394.18 1.48 170.18
113 27.13 13.32 1.5 13 75.17 0.26 6.17
115 45.07 20.16 3.5 15.8 294.17 1.00 144.17
117 76.89 64.8 7.7 58.5 4039.75 18.32 717.00
Table 1. Different planes and the broadenings

360 ♦ XV International Workshop on the Physics of Semiconductor Devices 2009
Ayers and others have shown that a good agreement of the
two independent calculations indicating an internal
consistency of the technique. They also mentioned that a
slight difference in the values obtained from the two
calculations could be attributed to other external sources of
broadening such as point defects contribution to strain
broadening and curvature contributes mostly rotational
broadening.
-2 0 2 4 6 8 10 12 14 16 18 20
0
1000
2000
3000
4000
Y=217.14X+67.45
Constant instrumental Broadening
βadj2
tan2θ
In the present case the difference of almost an order of
magnitude between the values obtained from the two
calculations could not be accounted for any of the above cited
reasons.
We provide the following reason for this discrepancy and
suggest an improvement in the method to calculate the
dislocation density especially for the relatively low dislocation
density cases.
We found that the calculations are very sensitive to the
value of instrumental broadening βi particularly for low
FWHM values. Taking a constant value for this term, as done
by Ayers and others, will introduce large error in the final
calculations. It has been shown that the instrument
broadening depends on the scattering angle and increases as
the scattering angle increases [10]. The variation in the
instrument broadening with respect to scattering angle is
shown in Fig 4. For large FWHM values, as is the case for
heavily deformed materials, this may not affect the ultimate
results much because of the square term but for low FWHM
values the variation in the βi cannot be ignored.
The βad
2 vs tan2 θ were plotted again and the graph is shown
in figure 5. The slope and the intercept were obtained from the
straight line fit to the graph. The calculations were therefore
repeated and the dislocation density estimated from the two
equations now is given as:
D
α =3.0x105/cm2
D
ε =5.6x105/cm2
It can be seen that the two values are in agreement now and
also matches well with the values obtained from the EPD
measurements.
-2 0 2 4 6 8 10 12 14 16 18 20
0
100
200
300
400
500
600
700
800
Y=34.7X+91
βadj2
tan2θ
V. CONCLUSION
Dislocation Density was calculated by two different
methods for GaAs material by rocking curve broadening using
Ayer’s model and Etch pit method. Strain and rotation (Lattice
tilt or distortion) at dislocation are responsible for dislocation
in single crystal. Using variable instrumental factor results are
encouraging because dislocation density order from both the
methods are came out be same order. So using this Model
with variable instrumental factor dislocation density was
calculated nondestructively by X- ray rocking curve
broadening and with the Etch pit method. Using these two
methods results are comparable.
Fig 4. Variable FWHM of Ge(220) crystal with scattering angle 2θ
Fig 2. βad2(θ) vs tan2θ for constant instrument broadening
of 12(arc-s)
Fig 3. SEM images of chemically eatched GaAs wafer (a)
showing the GaAs wafer with small 20 magnification (b) By
focusing at a particular point at 500 magnifications
Fi
g
5:
β
a
dj
-
v
2
(
θ
)
vs tan2
θ
for variable instrument broadenin
g

Estimation of Dislocation Density by X-ray Rocking Curve Analysis and Etch Pit Method ♦ 361
ACKNOWLEDGMENT
Author acknowledges to Dr. E. Vardhrajan for his valuable
discussion and Chemical etching related studies and thanks to
director SSPL who gave the permission to publish this work
on IWPSD-2009.
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319
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245
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(1956) pp.1285-1291
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Taylor & Francis , London and New Yark 1998
[10] X’Pert HRXRD PANalytical system manual.
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