Determination Of Temperature Dependent Unstressed Lattice Spacings In Crystalline Thin Films On Substrates

1997 ◽  
Vol 505 ◽  
Author(s):  
G. Cornella ◽  
S. Lee ◽  
O. Kraft ◽  
W. D. Nix ◽  
J. C. Bravman
Keyword(s):  
Thin Films ◽  
Thermal Expansion ◽  
Coefficient Of Thermal Expansion ◽  
Strain Analysis ◽  
Lattice Parameter ◽  
Gold Films ◽  
Sample Material ◽  
Temperature Dependent ◽  
X Ray

ABSTRACTX-ray strain analysis via Generalized Focusing Diffractometry (GFD) [1], and the concurrent need for accurate values of the unstrained lattice parameter, are discussed. A new method for determining the unstrained lattice parameter without knowledge of the elastic constants of the sample material is described. Stress measurements at varying temperatures, and extraction of the coefficient of thermal expansion from these measurements, are demonstrated for aluminum and gold films.

Extraction of the Coefficient of Thermal Expansion of Thin Films from Buckled Membranes

1998 ◽  
Vol 546 ◽  
Author(s):  
V. Ziebartl ◽  
O. Paul ◽  
H. Baltes
Keyword(s):  
Thin Films ◽  
Finite Element ◽  
Thermal Expansion ◽  
Silicon Nitride ◽  
Excellent Agreement ◽  
Energy Minimization ◽  
Coefficient Of Thermal Expansion ◽  
Temperature Dependent ◽  
Minimization Method ◽  
Energy Minimization Method

AbstractWe report a new method to measure the temperature-dependent coefficient of thermal expansion α(T) of thin films. The method exploits the temperature dependent buckling of clamped square plates. This buckling was investigated numerically using an energy minimization method and finite element simulations. Both approaches show excellent agreement even far away from simple critical buckling. The numerical results were used to extract Cα(T) = α0+α1(T−T0 ) of PECVD silicon nitride between 20° and 140°C with α0 = (1.803±0.006)×10−6°C−1, α1 = (7.5±0.5)×10−9 °C−2, and T0 = 25°C.

Studies of the Coefficient of Thermal Expansion of Low-k ILD Materials by X-Ray Reflectivity

2006 ◽  
Vol 914 ◽  
Author(s):  
George Andrew Antonelli ◽  
Tran M. Phung ◽  
Clay D. Mortensen ◽  
David Johnson ◽  
Michael D. Goodner ◽  
...  
Keyword(s):  
Thin Films ◽  
Thermal Expansion ◽  
Coefficient Of Thermal Expansion ◽  
Chemical Vapor ◽  
Dielectric Materials ◽  
Free Standing ◽  
Dielectric Thin Films ◽  
X Ray ◽  
Chemical Vapor Deposited ◽  
Low K

AbstractThe electrical and mechanical properties of low-k dielectric materials have received a great deal of attention in recent years; however, measurements of thermal properties such as the coefficient of thermal expansion remain minimal. This absence of data is due in part to the limited number of experimental techniques capable of measuring this parameter. Even when data does exist, it has generally not been collected on samples of a thickness relevant to current and future integrated processes. We present a procedure for using x-ray reflectivity to measure the coefficient of thermal expansion of sub-micron dielectric thin films. In particular, we elucidate the thin film mechanics required to extract this parameter for a supported film as opposed to a free-standing film. Results of measurements for a series of plasma-enhanced chemical vapor deposited and spin-on low-k dielectric thin films will be provided and compared.

Determination of the Mechanical Response of Thin Films with X-Rays

1993 ◽  
Vol 308 ◽  
Author(s):  
I. C. Noyan ◽  
G. Sheikh
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Mechanical Response ◽  
Strain Analysis ◽  
Local Strain ◽  
X Rays ◽  
Stress Strain ◽  
X Ray ◽  
The Individual

ABSTRACTThe mechanical response of a specimen incorporating thin films is dictated by a combination of fundamental mechanical parameters such as Young's moduli of the individual layers, and by configurational parameters such as adhesion strength at the interface(s), residual stress distribution and other process dependent factors. In most systems, the overall response will be dominated by the properties of the (much thicker) substrate. Failure within the individual layers, on the other hand, is dependent on the local strain distributions and can not be predicted from the substrate values alone. To better understand the mechanical response of these systems, the strain within the individual layers of the thin film system must be measured and correlated with applied stresses. Phase selectivity of X-ray stress/strain analysis techniques is well suited for this purpose. In this paper, we will review the use of the traditional x-ray stress/strain analysis methods for the determination of the mechanical properties of thin film systems.

X-ray determination of lattice parameter and thermal expansion of the compound CdIn2Se4

1982 ◽  
Vol 71 (2) ◽  
pp. K225-K229 ◽  
Author(s):  
P. Kistaiah ◽  
K. Satyanarayana Murthy ◽  
K. V. Krishna Rao
Keyword(s):  
Thermal Expansion ◽  
Lattice Parameter ◽  
X Ray

Calibration of a heating/cooling chamber for X-ray diffraction measurements of mechanical stress and crystallographic texture

2006 ◽  
Vol 39 (2) ◽  
pp. 194-201 ◽  
Author(s):  
M. Wohlschlögel ◽  
U. Welzel ◽  
G. Maier ◽  
E. J. Mittemeijer
Keyword(s):  
Thermal Expansion ◽  
The Other ◽  
X Ray Diffraction ◽  
Temperature Dependent ◽  
X Ray ◽  
Specimen Holder ◽  
Lattice Strains ◽  
Cooling Chamber ◽  
Line Positions

Methods have been developed for the calibration of specimen temperature and of specimen displacement caused by the thermal expansion of the specimen holder in a heating/cooling chamber equipped with a strip or plate heater mounted on an X-ray diffractometer. For the temperature calibration two methods were proposed. One method relies on X-ray diffraction measurements of thermal lattice strains, whereas the other method is based on resistance thermometry. The method proposed for the determination of the temperature-dependent specimen displacement is based on the measurement of diffraction-line positions of the specimen employing two diffraction geometries, one being sensitive to the specimen displacement and the other being insensitive to the specimen displacement. The thermal displacement of the specimen due to thermal expansion of the specimen holder is significant and was determined as about 38 µm per 100 K.

Determination of Thermal Expansion by High-Temperature X-Ray Diffraction

1961 ◽  
Vol 5 ◽  
pp. 238-243 ◽  
Author(s):  
Dale A. Vaughan ◽  
Charles M. Schwartz
Keyword(s):  
Thermal Expansion ◽  
High Temperature ◽  
Ceramic Materials ◽  
Lattice Parameter ◽  
Specimen Preparation ◽  
X Ray Diffraction ◽  
X Ray ◽  
And Control ◽  
Measurement And Control

AbstractTwo high-temperature X-ray diffraction cameras are described which have been employed at Battelle to determine thermal expansion of metals and ceramic materials. Specimen preparation and temperature measurement and control are described. Lattice-parameter data vs. temperature are presented for uranium, uranium dioxide, and magnesium oxide.

scholarly journals X-ray strain analysis of {111} fiber-textured thin films independent of grain-interaction models

2011 ◽  
Vol 44 (2) ◽  
pp. 409-413 ◽  
Author(s):  
D. Faurie ◽  
P.-O. Renault ◽  
E. Le Bourhis ◽  
T. Chauveau ◽  
O. Castelnau ◽  
...  
Keyword(s):  
Thin Films ◽  
Single Crystal ◽  
Strain Analysis ◽  
Direct Determination ◽  
Fiber Texture ◽  
Elastic Response ◽  
Diffraction Measurement ◽  
X Ray ◽  
Anisotropic Elastic

The anisotropic elastic response of supported thin films with a {111} fiber texture has been studied using anin-situmicro-tensile tester and X-ray diffractometry. It is shown which specific X-ray diffraction measurement geometries can be used to analyze the elastic strains in thin films without requiring any assumptions regarding elastic interactions between grains. It is evidenced (theoretically and experimentally) that the combination of two specific geometries leads to a simple linear relationship between the measured strains and the geometrical variable sin2ψ, avoiding the transition scale models. The linear fit of the experimental data allows a direct determination of the relationship between the three single-crystal elastic compliances or a direct determination of theS44single-crystal elastic compliance and the combination ofS11+ 2S12if the macroscopic stress is known. This methodology has been applied to a model system,i.e.gold film for which no size effect is expected, deposited on polyimide substrate, and it was found thatS44= 23.2 TPa−1andS11+ 2S12= 1.9 TPa−1, in good accordance with values for large crystals of gold.

scholarly journals Non-ambient X-ray and neutron diffraction of novel relaxor ferroelectric xBi2(Zn2/3,Nb1/3)O3–(1 – x)BaTiO3

2021 ◽  
Vol 54 (5) ◽  
Author(s):  
Jessica Marshall ◽  
David Walker ◽  
Pamela Thomas
Keyword(s):  
Neutron Diffraction ◽  
Lattice Parameter ◽  
The Novel ◽  
Temperature Dependent ◽  
Low Loss ◽  
Neutron Data ◽  
Ferroelectric Relaxor ◽  
X Ray ◽  
Unit Cells

The first determination of the phase diagram of the novel ferroelectric relaxor xBi(Zn2/3Nb1/3)O3–(1 − x)BaTiO3 (BZN-BT) has been achieved with a combination of high-resolution X-ray and neutron diffraction up to the miscibility limit near x(BZN) = 20.0% over a temperature range 20 < T < 400 K. The combined X-ray and neutron data show that the instability within the xBZN-(1−x)BT system reaches a maximum at x = 3.9% and is driven by B-site displacement and distortion of the oxygen octahedra in the polar phases. Composition-dependent effects include a narrow Amm2-dominated region focused at x = 3.9%, significant convergence of the lattice parameters in both P4mm and Amm2 phases, and sharp maxima in piezoelectric coefficient d 33 and maximum polarization P max. Lattice parameter dilation at x ≥ 4.0% was observed for both P4mm and Amm2 unit cells, alongside the first appearance of Pm 3 m at 295 K and the onset of significant dielectric relaxation. Low-temperature neutron diffraction indicated a weak or non-existent temperature dependence on the transition from ferroelectric at x = 3.9% to ferroelectric relaxor at x = 4.0%. Temperature-dependent phase transitions were eliminated near x = 3.0%, with the ferroelectric limit observed at x = 5.0% and a transition to a low-loss relaxor dielectric near x = 8.0%.

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