Higher-order Laue Zone Lines Research Articles

Self-interference of split HOLZ line (SIS-HOLZ) for z-dependent atomic displacement measurement: Theoretical discussion

A characteristic of the majority of semiconductors is the presence of lattice strain varying with the nanometer scale. Strain originates from the lattice mismatch between layers of different composition deposited during epitaxial growth. Strain can increase the mobility of the charge carriers by the band gap reduction. So, measuring atomic displacement inside crystals is an important field of interest in semiconductor industry. Among all available transmission electron microscopy techniques offering nano-scale resolution measurements, convergent beam electron diffraction (CBED) patterns show the highest sensitivity to the atomic displacement. Higher Order Laue Zone (HOLZ) lines split by small non-uniform variations of lattice constant allowing to measure the atomic displacement through the crystal. However, it could only reveal the atomic displacement in two dimensions, i.e., within the x–y plane of the thin film of TEM specimen. The z-axis atomic displacement which is along the path of the electron beam has been missing. This information can be obtained by recovering the phase information across the split HOLZ line using the self-interference of the split HOLZ line (SIS-HOLZ). In this work, we report the analytical approach used to attain the phase profile across the split HOLZ line. The phase profile is studied for three different atomic displacement fields in the Si substrate at 80nm away from its interface with Si/Si0.8Ge0.2 superlattices.

Aberration-corrected self-interference of split higher order Laue zone line for measuring the z-dependent strain profile

Abstract

Mapping of Strain Fields in GaAs/GaAsP Core-Shell Nanowires with Nanometer Resolution.

We report the nanoscale quantification of strain in GaAs/GaAsP core-shell nanowires. By tracking the shifting of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction patterns, we observe unique variations in HOLZ line separation along different facets of the core-shell structure, demonstrating the nonuniform strain fields created by the heterointerface. Furthermore, through the use of continuum mechanical modeling and Bloch wave analysis we calculate expected HOLZ line shift behavior, which are directly matched to experimental results. This comparison demonstrates both the power of electron microscopy as a platform for nanoscale strain characterization and the reliability of continuum models to accurately calculate complex strain fields in nanoscale systems.

Determination of three-dimensional strain state in crystals using self-interfered split HOLZ lines

An experimental method to measure the strain through the thickness of a crystal is demonstrated. This enables the full three-dimensional stress–strain state of a crystal at the nanoscale to be determined taking the current practice from two-dimensional strain state determination. Knowing the 3D strain state is desired by crystal growers in order to improve their crystal's quality. This method involves combining electron diffraction with electron interferometry in a transmission electron microscope. The electron diffraction uses a split higher order Laue zone (HOLZ) line and the electron interferometry uses an electron biprism.

Correlating stress generation and sheet resistance in InAlN/GaN nanoribbon high electron mobility transistors

We report the nanoscale characterization of the mechanical stress in InAlN/GaN nanoribbon-structured high electron mobility transistors (HEMTs) through the combined use of convergent beam electron diffraction (CBED) and elastic mechanical modeling. The splitting of higher order Laue zone lines in CBED patterns obtained along the [540] zone axis indicates the existence of a large strain gradient in the c-direction in both the planar and nanoribbon samples. Finite element models were used to confirm these observations and show that a passivating layer of Al2O3 can induce a tensile stress in the active HEMT layer whose magnitude is dependent on the oxide layer thickness, thus, providing important ramifications for device design and fabrication.

Automated characterization of bending and expansion of a lattice of a Si substrate near a SiGe/Si interface by using split HOLZ line patterns

A method to determine lattice parameters and parameters characterizing the bending strain of the lattice, the direction and magnitude of the displacement field of the bending strain, by using higher-order Laue zone (HOLZ) reflection lines observed in convergent-beam electron diffraction patterns is proposed. In this method, all of the parameters are simultaneously determined by a fit of two Hough transforms of experimental and kinematically simulated HOLZ line patterns. This method has been used to obtain two-dimensional maps of lattice parameter a, the direction and relative magnitude of the displacement field in a Si substrate near a SiGe/Si interface.

Effect of WC or NbC addition on lattice parameter of surrounding structure in Ti(C 0.7N 0.3)–Ni cermets investigated by TEM/CBED

The changes in the lattice parameters of the solid solutions in the Ti(C 0.7N 0.3)–WC–Ni and Ti(C 0.7N 0.3)–NbC–Ni systems were first shown quantitatively by the CBED (Convergent Beam Electron Diffraction) technique together with TEM (Transmission Electron Microscopy) microstructure characterization. The extent of the changes in the lattice parameters between core and rim differs in the case of WC and NbC additions. No change in the lattice parameters is observed in the Ti(C 0.7N 0.3)–WC–Ni cermets, in contrast to the Ti(C,N)–NbC–Ni cermets where significant changes in the lattice parameters are observed. The difference in the parameters is correlated with the core/rim structure, which disappears in the Ti(C,N)–NbC–Ni cermets when a large amount of NbC is added, and is discussed based on thermodynamic arguments. Large strain in the core and rim structure, especially near the core/rim interface, is also observed from the HOLZ (High Order Laue Zone) line splitting.

HANSIS software tool for the automated analysis of HOLZ lines

A software tool, named as HANSIS (HOLZ analysis), has been developed for the automated analysis of higher-order Laue zone (HOLZ) lines in convergent beam electron diffraction (CBED) patterns. With this tool, the angles and distances between the HOLZ intersections can be measured and the data can be presented graphically with a user-friendly interface. It is capable of simultaneous analysis of several HOLZ patterns and thus provides a tool for systematic studies of CBED patterns.

Convergent beam electron diffraction measurements of relaxation in strained silicon using higher order Laue zone line splitting

Convergent beam electron diffraction patterns of silicon from blanket wafers of ∼50 nm Si0.85Ge0.15 on Si and ∼126 nm Si0.79Ge0.21 on Si and from a complementary metal-oxide-semiconductor transistor with recessed Si0.82Ge0.18 stressors were analyzed at zone axes slightly off ⟨110⟩. It was shown that certain higher order Laue zone lines split near the SiGe/Si interfaces, indicating that considerable relaxation occurred during the preparation of the transmission electron microscopy specimens. The variation in splitting as a function of distance from the interface and sample thickness is described. A simple method was used to estimate the relaxation and was compared to behavior predicted by linear elastic finite element modeling of the structures. These methods showed reasonable agreement for the structures that were examined.

Quantitative and easy estimation of a crystal bending effect using low-order CBED patterns

The quantitative measurement of a crystal bending effect is performed using low-order zone-axis convergent beam electron diffraction (CBED) patterns. Although the accuracy of the present method is inferior to that of the method of using split higher order Laue zone lines, this method enables us to estimate the crystal bending effect at a region very close to the interface and to easily judge whether the crystal bending effect results in a tensile bend or a compressive bend. As an application of the present method, the crystal bending effect at a region close to the SiGe/Si interface was measured. It was found that the crystal bending effect is due to a thin-foil relaxation of almost 0.3 degrees at a region that is approximately 10 nm away from the interface.

Lattice parameter measurement in single crystalline LiCoO 2 particles by convergent beam electron diffraction

Convergent beam electron diffraction (CBED) is a powerful method for the measurement of lattice parameters in small specimen volumes, such as single crystalline particles or different regions of one particle. In this article we investigate the suitability of the CBED method for measurements in LiCoO 2 and correlate small changes in c-lattice parameters to variations in Li content. We find that higher order Laue zone (HOLZ) lines at the [001] zone axis are well suited to monitor the c-lattice parameter and demonstrate that the best achievable accuracy is about 0.003 Å. Comparison between HOLZ line patterns of as-received LiCoO 2 particles to HOLZ line patterns obtained of delithiated particles illustrates the effect of decreasing Li content on HOLZ line positions and provides insight into inhomogeneities in the delithiated sample.

Simple Method for Estimating Relaxation in Silicon from Higher Order Laue Zone Line Splitting

Extended abstract of a paper presented at Microscopy and Microanalysis 2008 in Albuquerque, New Mexico, USA, August 3 – August 7, 2008

Distortion Measurement of Multi-Finger Transistor Using Split Higher-Order Laue Zone Lines Analysis

A distortion measurement in a region close to the interface between different materials in LSI is performed using a convergent beam electron diffraction (CBED) pattern. Split higher-order Laue zone (HOLZ) lines emerge in the CBED pattern so that a stressing region is observed close to the interface. The calculation method of the split HOLZ lines based on kinematical approximation with the sample's deformation model well reflects the experimental results. As a result of split HOLZ line analysis using the present method, it is found that there is distortion depending on the external form of a multi-finger transistor.

Determination of c Lattice Parameter of LiCoO2 by Convergent-Beam Electron Diffraction

The convergent-beam electron diffraction technique of transmission electron microscopy was applied to the determination of the c lattice parameter of LiCoO2. [0001] orientation which showed a sufficient number of high-order Laue zone (HOLZ) lines was found to be suitable to the work. The ratio of the distances between {0551} HOLZ line family and the interceptions of {2641} family at [0001] orientation was able to allow the c to be determined. The accuracy of the technique was high enough to assess the homogeneity of the material and to investigate the change of the c lattice parameter with variation of lithium content in the material.

Strain analysis of arsenic-doped silicon using CBED rocking curves of low-order reflections

Local lattice strains of semiconductor devices have been so far examined using higher order Laue zone (HOLZ) line patterns of convergent-beam electron diffraction (CBED). Recently, strain analyses in highly strained regions near interfaces have been reported using split HOLZ line patterns. In the present paper, it is demonstrated for arsenic-doped silicon that the use of CBED rocking curves of low-order reflections provides a promising new tool for the determination of strain distributions of highly strained specimen areas. That is, the anomalous intensity increase in the CBED rocking curves of low-order reflections is explained using a model structure with a strain gradient in the electron beam direction, which is similar to the models used for the split HOLZ line patterns.

On the Splitting of High Order Laue Zone Lines in CBED Analysis of Stress in Silicon

Convergent beam electron diffraction (CBED) on cross-sectional transmission electron microscopy (TEM) specimens can map stress in the Si substrate of microelectronics devices with high spatial resolution. However, at shallow depths below the interface the diffraction lines within a CBED pattern are split, rendering pattern interpretation impossible in the classical way. This effect is believed to derive from a bending of the diffracting planes through the sample thickness. In this work, a variety of specimens, ranging from polycrystalline to epitaxial and amorphous materials, have been systematically analyzed. A similar qualitative distribution of the splitting effects is present in each case, but quantitative differences are observed which can be related to the stress induced by the different materials. Capping layers can partially avoid the splitting but seem to modify the strain distribution. The surface relaxation in the thin TEM specimen foil is modelled by finite elements simulations as well as with an epitaxial-layer model. The results predict well the experimental magnitude of the splitting but fail to simulate the intensity of the secondary lines. Possible explanations for such discrepancies are discussed and critically assessed.

An algorithm for refinement of lattice parameters using CBED patterns

A new algorithm for calculation of lattice parameters from convergent beam electron diffraction (CBED) patterns has been developed. Like most of the previous approaches to the problem, it is an optimization procedure matching geometric elements of high order Laue zone (HOLZ) lines in experimental patterns to corresponding elements of kinematically simulated patterns. The procedure uses an original objective function based directly on the underlying algebraic equation of the HOLZ lines. Although the new approach requires crystal orientation parameters to be fitted alongside the strain components, it is easier to implement than methods used previously. It is also straightforward to apply to strain determination from multiple patterns. Numerical tests on dynamically simulated patterns show that in the case of one or two patterns, the new procedure gives results that are more reliable than the established method based on HOLZ line intersections. As an example application, the a and c parameters of a TiAl alloy are determined.

Local Strain Characterization on Strained-Si/SiGe Heterostructures with Convergent Beam Electron Diffraction and Finite Element Simulation

We introduce a novel and reliable method to quantify local strain variation in microelectronic device structures based on convergent beam electron diffraction (CBED) and finite element (FE) calculation. The match of the finite element calculation results with the experimental data not only validated the parameters used for the finite element simulations, but also gives us insights into the origin of high order Laue zone (HOLZ) line splitting in a lattice-mismatched heterostructure. The 2D and 3D calculations showed that the residual strain measured from clean and sharp CBED patterns deviate from the initial strain. The effect of a SiO2 layer on the strain in a TEM sample was also investigated by FE simulation and we found that a SiO2 layer can suppress some of the elastic deformation making it possible to obtain clean and sharp CBED patterns. The here proposed novel method uses the elastic deformation to determine the initial strain in microelectronic devices structures by combining FE simulations and CBED patterns.

Local Strain Measurement on Strained Si/SiGe Heterostructures Using Convergent Beam Electron Diffraction Analysis

Local strain variations in microelectronic device structures have been investigated with convergent beam electron diffraction (CBED). The analysis has been improved with a series of tasks: high order Laue zone (HOLZ) line detection by the Hough transform, HOLZ line position simulation with the kinematic theory, lattice parameter refinement by the examination of least square fitting, and theoretical strain state calculation with finite element (FE) modeling. The goal of this paper is to demonstrate the procedure of this strain measurement analysis. The actual strain variation in a TEM foil of a CMOS device structure was shown, followed by the FE in a strain Si/SiGe heterostructure. The strain data will not be included in this paper, but will be added later.

Analysis of Nanoscale Stress in Strained Silicon Materials and Microelectronics Devices by Energy-Filtered Convergent Beam Electron Diffraction

The convergent beam electron diffraction (CBED) technique of transmission electron microscopy (TEM) has excellent capabilities for strain detection at high spatial resolution. Here we report strain measurements in a bulk s-Si/SiGe/Si wafer and in a strained 35nm PMOS device in which SiGe acts as the source and drain. CBED measurements of the composition of the relaxed SiGe buffer are in quantitative agreement with Raman spectroscopy. For the PMOS device, CBED measured a uniaxial compressive stress of 1.12GPa in the channel. However, it was found that even in the cross-sectional TEM samples with thicknesses greater than 300nm, the intrinsic surface strain relaxation was often so severe that no recognizable high-order Laue zone lines in the CBED patterns could be collected. The amorphorization of both free surfaces of the TEM sample to a range of about 80nm is proposed to minimize the impact of surface strain relaxation for future study.