K-means clustering analysis is applied to frequency-domain thermoreflectance (FDTR) hyperspectral image data to rapidly screen the spatial distribution of thermophysical properties at material interfaces. Performing FDTR while raster scanning a sample consisting of 8.6 μ m of doped-silicon (Si) bonded to a doped-Si substrate identifies spatial variation in the subsurface bond quality. Routine thermal analysis at select pixels quantifies this variation in bond quality and allows assignment of bonded, partially bonded, and unbonded regions. Performing this same routine thermal analysis across the entire map, however, becomes too computationally demanding for rapid screening of bond quality. To address this, K-means clustering was used to reduce the dimensionality of the dataset from more than 20 000 pixel spectra to just K = 3 component spectra. The three component spectra were then used to express every pixel in the image through a least-squares minimized linear combination providing continuous interpolation between the components across spatially varying features, e.g., bonded to unbonded transition regions. Fitting the component spectra to the thermal model, thermal properties for each K cluster are extracted and then distributed according to the weighting established by the regressed linear combination. Thermophysical property maps are then constructed and capture significant variation in bond quality over 25 μ m length scales. The use of K-means clustering to achieve these thermal property maps results in a 74-fold speed improvement over explicit fitting of every pixel.
Bonding diamond to the back side of gallium nitride (GaN) electronics has been shown to improve thermal management in lateral devices; however, engineering challenges remain with the bonding process and characterizing the bond quality for vertical device architectures. Here, integration of these two materials is achieved by room-temperature compression bonding centimeter-scale GaN and a diamond die via an intermetallic bonding layer of Ti/Au. Recent attempts at GaN/diamond bonding have utilized a modified surface activation bonding (SAB) method, which requires Ar fast atom bombardment immediately followed by bonding within the same tool under ultrahigh vacuum (UHV) conditions. The method presented here does not require a dedicated SAB tool yet still achieves bonding via a room-temperature metal-metal compression process. Imaging of the buried interface and the total bonding area is achieved via transmission electron microscopy (TEM) and confocal acoustic scanning microscopy (C-SAM), respectively. The thermal transport quality of the bond is extracted from spatially resolved frequency-domain thermoreflectance (FDTR) with the bonded areas boasting a thermal boundary conductance of >100 MW/m2·K. Additionally, Raman maps of GaN near the GaN-diamond interface reveal a low level of compressive stress, <80 MPa, in well-bonded regions. FDTR and Raman were coutilized to map these buried interfaces and revealed some poor thermally bonded areas bordered by high-stress regions, highlighting the importance of spatial sampling for a complete picture of bond quality. Overall, this work demonstrates a novel method for thermal management in vertical GaN devices that maintains low intrinsic stresses while boasting high thermal boundary conductances.
3D integration of multiple microelectronic devices improves size, weight, and power while increasing the number of interconnections between components. One integration method involves the use of metal bump bonds to connect devices and components on a common interposer platform. Significant variations in the coefficient of thermal expansion in such systems lead to stresses that can cause thermomechanical and electrical failures. More advanced characterization and failure analysis techniques are necessary to assess the bond quality between components. Frequency domain thermoreflectance (FDTR) is a nondestructive, noncontact testing method used to determine thermal properties in a sample by fitting the phase lag between an applied heat flux and the surface temperature response. The typical use of FDTR data involves fitting for thermal properties in geometries with a high degree of symmetry. In this work, finite element method simulations are performed using high performance computing codes to facilitate the modeling of samples with arbitrary geometric complexity. A gradient-based optimization technique is also presented to determine unknown thermal properties in a discretized domain. Using experimental FDTR data from a GaN-diamond sample, thermal conductivity is then determined in an unknown layer to provide a spatial map of bond quality at various points in the sample.
In this report we detail demonstration of temperature dependent effects on grayscale intensity imaged in Focused Ion Beam (FIB) microscope, as well as secondary electron (SE) dependence on temperature in the Auger Electron Spectroscopy (AES) and a Scanning Electron Microscope (SEM). In each instrument an intrinsic silicon sample is imaged at multiple temperatures over the course of each experiment. The grayscale intensity is shown to scale with sample temperature. Sample preparation procedures are discussed, along with hypothesized explanations for unsuccessful trials. Anticipated outcomes and future directions for these measurements are also detailed.
A method is developed to calculate the length into a sample to which a Frequency Domain Thermoreflectance (FDTR) measurement is sensitive. Sensing depth and sensing radius are defined as limiting cases for the spherically spreading FDTR measurement. A finite element model for FDTR measurements is developed in COMSOL multiphysics and used to calculate sensing depth and sensing radius for silicon and silicon dioxide samples for a variety of frequencies and laser spot sizes. The model is compared to experimental FDTR measurements. Design recommendations for sample thickness are made for experiments where semi-infinite sample depth is desirable. For measurements using a metal transducer layer, the recommended sample thickness is three thermal penetration depths, as calculated from the lowest measurement frequency.
In order to predict material failure accurately, it is critical to have knowledge of deformation physics. Uniquely challenging is determination of the conversion coefficient of plastic work into thermal energy. Here, we examine the heat transfer problem associated with the experimental determination of β in copper and stainless steel. A numerical model of the tensile test sample is used to estimate temperature rises across the mechanical test sample at a variety of convection coefficients, as well as to estimate heat losses to the chamber by conduction and convection. This analysis is performed for stainless steel and copper at multiple environmental conditions. These results are used to examine the relative importance of convection and conduction as heat transfer pathways. The model is additionally used to perform sensitivity analysis on the parameters that will ultimately determine b. These results underscore the importance of accurate determination of convection coefficients and will be used to inform future design of samples and experiments. Finally, an estimation of convection coefficient for an example mechanical test chamber is detailed as a point of reference for the modeling results.
In this work, a finite element analysis model was developed to predict the frequency domain thermal response to heat input from a gaussian heat source for arbitrary 2-dimensional geometries. The model was used for geometric parameter fitting of samples experimentally measured using Frequency Domain Thermoreflectance (FDTR). Inverse fitting was performed to on experimental data to extract characteristic geometries of samples with feature sizes smaller than the Il e 2 radius of the laser used to probe the system. Further simulations were done to demonstrate the ability of the system to detect a variety of feature types. Silicon wafers with 50 nm to 1 pm of wet thermal oxide were measured and fit. Finally, microparticles suspended in epoxy were imaged using FDTR.