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How Accurate Is X-ray Characterization? (Special Feature Characterization)

Virtually all manufacturers of compound semiconductor materials invest large sums in X-ray diffraction equipment to develop their processes and to control their quality. Questions that they typically ask equipment vendors are, "How reproducible is this tool? How do I know that the results are reliable? How does it compare with other tools?" Manufacturers normally insist on stringent "tool matching" requirements so that a sequence of tools, in different locations and ordered at different times, will perform in the same way. However, I believe that equipment vendors should strive for a specified accuracy, as well as repeatability, of the information extracted, since in the long run the only stable measurement systems are those that are traceable to absolute intrinsic or international standards. This is a realistic possibility for X-ray characterization, since it depends upon simple parameters that can be made traceable. This article discusses these issues. A fuller discussion will be found in a recent paper [1]. Basics of X-ray Characterization shows the general method of X-ray characterization. An incident beam, collimated and conditioned in wavelength by suitable crystal or multilayer optics, falls on the specimen at a known angle. The intensity of scattering of X-rays is measured at another known angle, but the incident angle, rather than the scattered angle, is usually the important one for the interpretation. The intensity of scattering is measured as a function of this angle over a short range, usually no more than a few degrees and sometimes as small as a tenth of a degree. There are two important regimes: diffraction from crystal planes, often the 004 "symmetric reflection" (so-called because the diffracting planes are parallel to the typical 001 surface) for which the incident angle lies in the range 3035 for almost all compound semiconductors external reflection from the crystal surface and surface layers, for which the incident angle lies between 0 and about 4 Diffraction gives information about strain in the crystal lattice, from which material compositions may be inferred. Reflectivity gives information about electron density normal to the surface, from which densities, hence compositions and interface roughnesses may be inferred. Both regimes contain information about interferences between layer interfaces, from which layer thicknesses may be deduced. As a rule, diffraction is more sensitive to compositions and reflectivity to thicknesses and roughnesses, but there are exceptions. Fuller details of the theory and interpretation of diffraction [2] and reflectivity [3] may be found in the books cited. Traceable Measurements It is important to understand the concept of a traceable measurement. While tool matching can and does satisfy the requirements of ISO 9000 quality control, it does not provide a metrologically stable system of measurement, nor one that can be used to compare results from tools and software made by different vendors. In contrast, "accuracy" entails coupling of the measurement in question to an invariant primary standard, or at least to a highly reproducible secondary standard that is well-connected to a primary invariant. For example, characteristic X-ray emission lines embody all of the needed features for the wavelength parameter. These lines are highly reproducible (within 1 part in 106), and have been linked to the base unit of length in the International System of Units (the SI) by an unbroken measurement chain that does not degrade the indicated reproducibility. Apart from wavelength, X-ray diffraction or reflectivity data depend only upon the measurement of angle and intensity. Angle is macroscopically self-calibrating if a full 360 encoder or gear train is used. We don t need a standard to tell us that 1 exact revolution is 360. However, there are normally cyclic harmonic errors in linearity, especially in gear trains. The linearity of interpolation must therefore be determined separately. A rotary table can be calibrated for linearity at a national standards laboratory to a small fraction of an arc second, but this is inconvenient and laborious. The regularity of X-ray fringes from a sample such as a superlattice is a good test. In practice the best encoders that are currently used on diffractometers, taken together with their mounting and reading systems, give harmonic errors below 1 arc second over 360, while 10 arc second accuracy over tens of degrees is relatively straightforward. This will typically contribute less than about 0.05% to the error in (for example) composition or thickness. Dr Keith Bowen is Group Director of Technology for Bede plc. He chairs the Atomic Physics sub-panel of the NAS-NRC Evaluation Panel for the NIST Physics Laboratory and, together with other industrial representatives, is advising the NIST Materials Laboratory on the production of X-ray SRMs for the semiconductor industry. Intensity is less important for composition analysis but is important for analysis of graded layers such as are found in metamorphic buffer layers or in HBT structures. However, X-ray counters are inherently linear below the pulse pileup regime, and even then the non-linearity is easily calibrated. This is rarely a significant source of error. Analytical software is very much in the accuracy loop when the data are interpreted. Automatic optimization (parameter fitting) programs that avoid being trapped in local minima [4] remove the subjectivity from the process. Grundmann and Krost [5] have made a detailed comparison of software interpretation programs demonstrating that there are substantial differences between vendors programs. Given accurate structural models and materials parameters the best programs are capable of calculating the X-ray scattering to a precision and accuracy that is significantly better than the measurement, and hence are not themselves a source of error. However, the poorest programs could give substantial error. For example, a common approximation in some programs is sinu = u at small angles, which gives significant error for larger-range scans such as for HEMTs or superlattices. Hence it is necessary for software to be tested and certified. Materials Parameters The largest error in the analysis is, without doubt, the accuracy of the materials parameters used. These are, lattice parameter and Poisson ratio, used to determine the strain in the epitaxial layer (Poisson ratio is needed because a coherent layer is strained in the plane of the interface and therefore expands or contracts normal to the interface). Lattice parameters can be measured to better than 1 in 107 but unfortunately only silicon and germanium, amongst commonly available semiconductors, are available in this homogeneity. In GaAs, for example, variations at the level of parts in 105 in a single boule are common. Poisson ratios are also somewhat uncertain for some materials, but fortunately the variations in this ratio between materials, and as a function of alloying, are not large. In summary, with lattice parameter and Poisson ratio data from the literature, we can expect an absolute accuracy of 25% in composition and 0.51% (1s) in thickness, for a single layer or a simple set of uniform layers. With better knowledge of material data, such as exists only for the Si-Ge system at present, we can usually improve the composition accuracy to 0.5% also. Reproducibilities can be significantly better than 0.5%. Graded layers are less accurately determined, because there is not an abrupt change in composition or electron density at the interface, and the absolute errors in these cases are about 5%, though the reproducibilites are still about 0.5%. These are the typical acceptance criteria for an X-ray tool in the semiconductor industry. It is interesting to note that the widespread use of HRXRD came about exclusively within the compound semiconductor industry. It is now finding extensive application in the silicon industry, but the more rigorous demands of standardization, reproducibility and accuracy in that industry are in turn feeding back improvements to compound semiconductor characterization. Choosing the Correct Type of Measurement A couple of examples will show how important it is to do the right type of measurement. In general, diffraction is the choice if strained layers and large mismatches are expected. shows a GaAs-based PHEMT structure in which the 104 active In0.209Ga0.791As layer is determined to 1 in thickness and 0.1% in composition. On the other hand, a thin AlGaAs/GaAs layer (say about 500 of each), is not at all well determined by diffraction because the peak from the thin, closely-matched layer cannot be distinguished from the intense substrate reflection. As shown in , this material gives good fringe contrast in reflectivity, from which the thicknesses of these layers can be determined to better than 1%. Reflectivity is the choice if thin, closely-matched layers that show significant change in electron density are expected. It is also insensitive to dislocation content, and good reflectivity data can often be obtained with material that is too defective to give good diffraction data. Standard Reference Materials At present, the verification of calibration, linearity and correct set-up of an X-ray tool are up to the manufacturers and customers. This process, leading to the traceability of the tool, would be greatly aided by the provision of Standard Reference Materials and a program to establish SRMs for high performance X-ray systems has recently begun at NIST [6]. The first standards will be made of epitaxial silicon-germanium on silicon since this is the only material available in sufficient quality at present. However, since SiGe epilayers can be made so that they cover the diffraction range that is appropriate for most III-V materials, they are perfectly suitable for calibrating and verifying tools used for compound semiconductors. shows how good these standards can potentially be. The agreement between the X-ray data and the simulation, and between the X-ray interpretation and the SIMS profile is excellent. They differ only in the interface regions in which the well-known beam-mixing phenomenon gives artifacts in the SIMS profile. While the SRMs will first be issued simply with certified diffraction patterns, the plan is that later generations of SRMs (including compound semiconductors) will be issued with certified compositions and thicknesses. The equivalent performance of different tools will then be certifiable by tracing all measurements to the same set of national standards. References [1] D. K. Bowen and R. Deslattes, X-ray Metrology by Diffraction and Reflectivity, 2000, NIST Conference on ULSI Metrology, AIP (2001) [2] D.K. Bowen and B.K. Tanner, High Resolution X-ray Diffraction and Topography (Taylor & Francis, London, 1998) [3] V. Holy, U. Pietsch and T. Baumbach, High resolution X-ray scattering from thin films and multilayers, (Springer-Verlag, New York, 1999) [4] M. Wormington, C. Panaccione, K.M. Matney and D.K. Bowen, Phil. Trans. R. Soc. Lond. A 357, 2827 (1999). [5] M. Grundmann and A. Krost, Physica Status Solidi, B218 417 (2000) [6] James Cline, Materials Laboratory; Richard Matyi and Richard Deslattes, Physics Laboratory
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