See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/331590057 Estimation of Dislocation Density by X-ray Rocking Curve Analysis and Etch Pit Method Conference Paper · December 2009 CITATIONS READS 0 94 Some of the authors of this publication are also working on these related projects: Smart Materials, Structures and Devices View project Surface Phonon Polariton in GaN layers View project All content following this page was uploaded by Akhilesh Pandey on 08 March 2019. The user has requested enhancement of the downloaded file. Estimation of Dislocation Density by X-ray Rocking Curve Analysis and Etch Pit Method Akhilesh Pandey, Anshu Goyal, Ashok Kumar Kapoor and R. Muralidharan 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 G 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: 91-11-23903761; fax: 91-11-23903761; 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 . 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  and later modified by Ayers  for the estimation of dislocation density using Xray 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 ♦ 359 done using the standard procedure  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 . 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. βad2=Kεtan2θ + Kα (4) This is a straight line equation and the slope and the intercept of the plot of βad2 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 . GaAs Recorded GaAs Gaussian fit III. DISCUSSION (THEORY) 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, βad2 = βm2 – (βi2+ βo2) = βα2+ βε2 Following the treatment developed by Ayers and the dynamical diffraction theory for the calculation of β0, the equations for the βα2 and βε2 and the associated dislocation densities for the two factors can be written as βα2 = (2π ln2) b2 Dα = Kα (2) Dα= βα2 / (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) 120000 Intensity (A.U.) 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] βm2 =βi2+ βo2+ βα2+ βε2+βL2+βr2 (1) 60000 0 33.219 33.228 33.237 ω(degree) Fig.1. X- ray rocking curve profile for GaAs wafer for (004) plane IV. RESULTS AND DISCUSSION A plot of βad2 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. hkl theta (deg) β0 βm (arc-s) (arc-s) β ins (variable ) βadj-c2 (arc-s)2 (constant instrument tan2θ broadening) βadj-v2 (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 7.7 58.5 4039.75 18.32 717.00 64.8 Table Different planes and thewas broadenings The 1. dislocation density 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. 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. 4000 Constant instrumental Broadening βadj 2 3000 2000 Y=217.14X + 67.45 1000 0 -2 0 2 4 6 8 10 12 14 16 18 20 2 tan θ Fig 2. βad2(θ) vs tan2θ for constant instrument broadening of 12(arc-s) 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 . 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 βad2 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: Dα =3.0x105/cm2 Dε =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. 800 700 600 βadj 2 500 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 400 300 Y=34.7X+91 200 100 0 -2 0 2 4 6 8 10 12 14 16 18 20 2 tan θ Fig 5: βadj-v2(θ) vs tan2θ for variable instrument broadening V. CONCLUSION Fig 4. Variable FWHM of Ge(220) crystal with scattering angle 2θ 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. 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. 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. REFERENCES   P.Gay, P.B.Hirsch, A.Kelly, Acta Metallurgica Vol. 1 ( 1953) pp. 315319 M.J.Horden, B.L.Averbach, Acta Metellurigica Vol. 9, (1961) pp. 237245 View publication stats   J.E.Ayers, Journal of Crystal Growth,135 (1994) pp. 71-77 A.D.Krutz,S.A.Kulin ,B.L.Averbach, Physical Review Vol.101 No.4 (1956) pp.1285-1291  Gunther Bauer, Wolfgang Richter, Optical Characterization of Epitaxial Semiconductor Layers, Springer, 1996, ch 6  J.M. 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