X-ray Reflectivity

Introduction
X-ray reflectometry is a technique for investigating the near-surface structure of many materials. It probes the electron density with a depth resolution of less than one nm for depths of up to several hundred nm. The method involves measuring the reflected X-ray intensity as a function of X-ray incidence angle (typically small angles are used). The method is used for studies of thin films and multilayers of metals, semiconductors and polymers. It can accurately determine films thickness, density, average roughness, and the roughness correlation function.

A typical reflectivity setup is shown below (Fig. 1). There are two basic types of measurements - specular and diffuse reflectivity. In specular reflectivity (Fig. 1a), the incident X-rays impinge on the sample at a small angle Θ and the intensity of the specularly reflected X-rays is detected at an angle Θ from the surface; the scattering angle is 2Θ and the scattering vector is normal to the surface. Data are collected as function of Θ or equivalently Q = (4π/λ) sinΘ. Specular reflectivity data are analyzed to determine the depth dependence of the electron density of the material of interest (see below for details). In diffuse or off-specular reflectivity (Fig. 1b), the incidence angle is Θ-ω, while the reflected X-rays are detected at an exit angle of Θ+ω from the surface. In this situation, the scattering vector has a component parallel to the surface (Qx= (4π/λ) sinΘ sinω.). Measurements of the intensity as a function of Qx allow a determination of the lateral correlation function of roughness or the lateral length scale (characteristic wavelengths) of surface or interface roughness.

Instrumentation
Beamlines 7-2 and 2-1 are easily used for specular and diffuse reflectivity measurements, while 11-2 can be used for specular reflectivity. Most commonly, fixed slits are used to analyze the scattered beam, but for high resolution a crystal analyzer can be used. Please note that the sample must have a smooth, flat surface, preferably with an area of about one cm².


Analysis
Specular reflectivity - Specular reflectivity data are analyzed with a multilayer model analogous to that employed in standard optics (Fresnel formulae). The model incorporates several variable parameters (e.g., film thickness, density and roughness), which are fit to the data. Contact Mike Toney or Sean Brennan for more details on analysis programs.
Diffuse reflectivity - For a single rough surface, the diffuse reflectivity is related to the Fourier transform of the height-height correlation function which describes the characteristic in-plane length scales of the roughness and the 'jaggedness' of the roughness. For multilayered films, the diffuse reflectivity is more complicated and depends not only on the height-height correlation function of the various interfaces, but how the roughness is correlated perpendicular to the surface. See below for more details.

Applications of X-ray reflectivity
Specular and diffuse X-ray (and neutron) reflectivity are frequently used for studies of thin films and multilayers. The figure below (Fig. 2) shows an example of specular reflectivity measurements on thin lubricant films, which permit an accurate determination of the film thickness and roughness. This is crucially important in tribology of magnetic disk drives [1-3].

Multilayer materials are commonplace in many technological applications, but the characterization of the morphology of these materials is difficult. Specular X-ray reflectivity and, to a lesser extent, diffuse reflectivity are frequently used to investigate multilayers. Used together these methods can provide valuable insight into physical thickness and the interface roughness. For example, these methods have been used to study W/Si [4] and Si/Mo [5] multilayers, which have potential use in XUV optics, and Co/Cu multilayers, which exhibit giant magnetoresistence [6]. In the latter case, the use of anomalous reflectivity is beneficial in separating Co from Cu. Polymer multilayers can also be studied with specular and diffuse X-ray reflectivity [7], which have been used to distinguish between interdiffusion and physical roughness.

References

1. "Roughness of Thin Perfluoropolyether Lubricant Films: Influence on Disk Drive Technology", C. Mathew Mate, Michael F. Toney, and K. Amanda Leach, IEEE Trans. Magn. 37, 1821 (2001).


2. "Roughness of Molecularly Thin Perfluoropolyether Polymer Films" M.F. Toney, C.M. Mate, K.A. Leach, Appl. Phys. Lett. 77, 3296 (2000).


3. "Calibrating ESCA and Ellipsometry Measurement of Perfluoropolyether Lubricant Thickness", M.F. Toney, C.M. Mate, and D. Pocker, IEEE Trans Magn. 34, 1774 (1998).


4. "Interface Evolution in a W/Si Multilayer after Rapid Thermal Annealing Studied by X-ray Reflectivity and Diffuse Scattering", M. Jergel, V. Holý, M. Majková, S. Luby, R. Senderák, J. Appl. Cryst. 30, 642 (1997).


5. "Nonspecular X-ray Reflectivity Study of Roughness Scaling in Si/Mo Multilayers", J.M. Freitag & B.M. Clemens, J. Appl. Phys. 89, 1101 (2001).


6. "Study of the Interfaces in Co/Cu Multilayers by Low-Angle Anomalous X-ray Diffraction", A. de Bernabé, M.J. Capitán, H.E. Fiswcher, C. Priero, J. Appl. Phys. 84, 1881 (1998).


7. "Diffuse X-ray Scattering Study of Interfacial Structure os Self-Assembled Conjugated Polymers", Phys. Rev. B 66, 161201(R) (2002).

Further General Reading:

• "Elements of Modern X-ray Physics" by J. Als-Nielsen and D. McMorrow, (Wiley, New York, 2001).
• "X-ray Scattering from Soft-Mater Thin Films: Materials Science and Basic Research", by M. Tolan, (Springer, New York, 1998).
• "X-ray and Neutron Reflectivity", J. Daillant and A. Gibaud, eds. (Springer, Berlin, 1999).