Submicron Resolution X-Ray Strain Measurements On Patterned Films: Some Hows And Whys

1996 ◽  
Vol 428 ◽  
Author(s):  
M. A. Marcus ◽  
A. A. Macdowell ◽  
E. D. Isaacs ◽  
K. Evans-Lutterodt ◽  
G. E. Ice
Keyword(s):  
Mechanical Behavior ◽  
Strain Tensor ◽  
Energy Measurement ◽  
X Ray Diffraction ◽  
Strain Measurements ◽  
X Ray ◽  
Crystal Perfection ◽  
Patterned Films ◽  
Individual Grains ◽  
Interconnect Technology

AbstractAs interconnect technology moves deeper into the submicron realm, the physics governing the mechanical behavior, hence the reliability of metal lines changes. Events at the level of individual grains become more important. One would like to be able to measure the strain and orientation of single grains, and the distribution of strain across a grain. Such data may help us understand such effects as sunken grains, the erratic occurrence of stress voiding and Blechlength effects in electromigration. To get this information, techniques involving X-ray diffraction with submicron beams are being developed. These experiments involve detecting Laue spots from selected areas and energy-analyzing them to find the strain tensor. Motivations for such measurements, the specifications for a useful instrument, some designs now being developed and the intrinsic limitations of these approaches will be discussed. Design issues in the choice of focussing optics and energy measurement will be highlighted with calculations of how the Laue spots would look for different conditions of crystal perfection.

A common theory of line broadening and rocking curves

2015 ◽  
Vol 48 (2) ◽  
pp. 418-430 ◽  
Author(s):  
Gyula Zilahi ◽  
Tamás Ungár ◽  
Géza Tichy
Keyword(s):  
Rigid Body ◽  
Electron Backscatter Diffraction ◽  
Strain Tensor ◽  
Theoretical Description ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Peak Broadening ◽  
Individual Grains

X-ray diffraction peak broadening is discussed in terms of line broadening and rocking-curve broadening in a novel theoretical description. The nonlocal strain tensor is factorized by using the method of polar decomposition instead of the more conventional separation into symmetrical and antisymmetrical components. A number of X-ray line-broadening and rocking-curve experiments on the same single crystals or individual grains in bulk polycrystals prove that plastic deformation produces strained subgrains mutually rotated by rigid-body rotations. The novel theoretical description appropriately accounts for the rigid-body rotation and strain at the same time and provides straightforward separation of the two effects of line and rocking-curve broadening in the radial and normal directions of the diffraction vector. The mathematical results are discussed in terms of experiments of X-ray diffraction, Laue asterism and electron backscatter diffraction. From the experimental results it is shown that the simultaneous evaluation of line and rocking-curve broadening provides qualitative information about the redundant and geometrically necessary character of dislocations, not available if only one or the other is accessible.

Formalism for the determination of intermediate stress gradients using X-ray diffraction

2009 ◽  
Vol 42 (2) ◽  
pp. 192-197 ◽  
Author(s):  
Thomas Gnäupel-Herold
Keyword(s):  
Lattice Strain ◽  
Narrow Line ◽  
X Ray Diffraction ◽  
Beam Spot ◽  
Strain Measurements ◽  
One Dimensional ◽  
X Ray ◽  
Stress Gradients ◽  
Shaped Beam

A method is outlined that allows the determination of one-dimensional stress gradients at length scales greater than 0.2 mm. By using standard four-circle X-ray diffractometer equipment and simple aperture components, length resolutions down to 0.05 mm in one direction can be achieved through constant orientation of a narrow, line-shaped beam spot. Angle calculations are given for the adjustment of goniometer angles, and for the effective azimuth and tilt of the scattering vector for general angle settings in a four-circle goniometer. The latter is necessary for the computation of stresses from lattice strain measurements.

Strain Measurement by X-ray Diffraction Methods

1949 ◽  
Vol 1 (3) ◽  
pp. 211-224
Author(s):  
G. B. Greenough
Keyword(s):  
Strain Measurement ◽  
Plastic Anisotropy ◽  
Stress And Strain ◽  
Routine Method ◽  
X Ray Diffraction ◽  
Strain Measurements ◽  
X Ray ◽  
The Past ◽  
Polycrystalline Metals ◽  
The Individual

SummaryMany papers have been written on the measurement of strain by X-ray diffraction methods and on the interpretation of these strains in terms of stresses. Whereas, during the past few years, the experimental methods of determining the strains have. remained largely unchanged, research has shown that the older techniques for calculating stresses from strains are not always valid.In this paper an attempt is made to describe some of the principles of strain measurement by X-ray diffraction methods to those who are unfamiliar with the methods. The types of stress and strain systems which may exist in polycrystalline metals are then considered, particular attention being paid to the effect of the elastic and plastic anisotropy of the individual crystals. Some indication is given as to how the earlier methods of interpreting X-ray strain measurements should be modified, but no rigid routine method is proposed for use in a general case.

On the calibration of high-energy X-ray diffraction setups. I. Assessing tilt and spatial distortion of the area detector

2014 ◽  
Vol 47 (3) ◽  
pp. 1042-1053 ◽  
Author(s):  
Andras Borbely ◽  
Loic Renversade ◽  
Peter Kenesei ◽  
Jonathan Wright
Keyword(s):  
Rotation Axis ◽  
Strain Tensor ◽  
Calibration Procedure ◽  
High Energy ◽  
European Synchrotron Radiation Facility ◽  
Data Sets ◽  
X Ray Diffraction ◽  
Spatial Distortion ◽  
X Ray ◽  
Area Detector

The geometry of high-energy X-ray diffraction setups using an area detector and a rotation axis is analysed. The present paper (part 1) describes the methodology for determining continuously varying spatial distortions and tilt of the area detector based on the reference diffraction rings of a certified powder. Analytical expressions describing the degeneration of Debye rings into ellipses are presented and a robust calibration procedure is introduced. It is emphasized that accurate detector calibration requires the introduction of spatial distortion into the equation describing the tilt. The method is applied to data sets measured at the Advanced Photon Source and at the European Synchrotron Radiation Facility using detectors with different physical characteristics, the GE 41RT flat-panel and the FReLoN4M detector, respectively. The spatial distortion of the detectors is compared with regard to their use in structural and strain tensor analysis, a subject treated in part 2 of the calibration work [Borbély, Renversade & Kenesei (2014).J. Appl. Cryst.Submitted].

scholarly journals Evaluation of Internal Stress in Individual Grains of Cold-Rolled Stainless Steel by Energy Dispersive X-ray Diffraction

2013 ◽  
Vol 53 (1) ◽  
pp. 165-169 ◽  
Author(s):  
Kentaro Kajiwara ◽  
Masugu Sato ◽  
Tamotsu Hashimoto ◽  
Takuyo Yamada ◽  
Takumi Terachi ◽  
...  
Keyword(s):  
Stainless Steel ◽  
Internal Stress ◽  
Energy Dispersive ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cold Rolled ◽  
Individual Grains
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