Luke Yates

Invited Review Article: Error and uncertainty in Raman thermal conductivity measurements

Error and uncertainty in Raman thermal conductivity measurements are investigated via finite element based numerical simulation of two geometries often employed—Joule-heating of a wire and laser-heating of a suspended wafer. Using this methodology, the accuracy and precision of the Raman-derived thermal conductivity are shown to depend on (1) assumptions within the analytical model used in the deduction of thermal conductivity, (2) uncertainty in the quantification of heat flux and temperature, and (3) the evolution of thermomechanical stress during testing. Apart from the influence of stress, errors of 5% coupled with uncertainties of ±15% are achievable for most materials under conditions typical of Raman thermometry experiments. Error can increase to >20%, however, for materials having highly temperature dependent thermal conductivities or, in some materials, when thermomechanical stress develops concurrent with the heating. A dimensionless parameter—termed the Raman stress factor—is derived to identify when stress effects will induce large levels of error. Taken together, the results compare the utility of Raman based conductivity measurements relative to more established techniques while at the same time identifying situations where its use is most efficacious.

Thermal Boundary Resistance in GaN Films Measured by Time Domain Thermoreflectance with Robust Monte Carlo Uncertainty Estimation

ABSTRACT In this work, we investigate the thermal boundary resistance and thermal conductivity of GaN layers grown on Si with 100 nm AlN transition layers using time domain thermoreflectance (TDTR). The GaN layers ranged from 0.31 to 1.27 μm. Due to the challenges in determining the thermal boundary resistance of the buried interfaces found in this architecture, a new data reduction scheme for TDTR that utilizes a Monte Carlo fitting method is introduced and found to dramatically reduce the uncertainty in certain model parameters. The results show that the GaN thermal conductivity does not change significantly with layer thickness, whereas the resistance of the AlN layer decreases slightly with GaN thickness.

High Resolution Thermal Characterization and Simulation of Power AlGaN/GaN HEMTs Using Micro-Raman Thermography and 800 Picosecond Transient Thermoreflectance Imaging

Self-heating in gallium nitride based high frequency, high electron mobility power transistors (GaN HEMTs) is inspected using micro-Raman thermography and 800 picosecond transient thermoreflectance imaging. The two methods provide complementary temperature information inside the semiconductor and on top metal layers of the GaN HEMT. Self heating is measured under both steady-state and ultra-fast pulsed transient operation with submicron spatial resolution, 50 milliKelvin temperature resolution, and nanosecond time resolution. Fine grain electrothermal modeling of the HEMT steady state and transient self-heating are presented alongside measurements. Large spatial and temporal temperature gradients are quantified. Deviations due to unknown parameters are discussed.

Direct visualization of thermal conductivity suppression due to enhanced phonon scattering near individual grain boundaries

Understanding the impact of lattice imperfections on nanoscale thermal transport is crucial for diverse applications ranging from thermal management to energy conversion. Grain boundaries (GBs) are ubiquitous defects in polycrystalline materials, which scatter phonons and reduce thermal conductivity (κ). Historically, their impact on heat conduction has been studied indirectly through spatially averaged measurements, that provide little information about phonon transport near a single GB. Here, using spatially resolved time-domain thermoreflectance (TDTR) measurements in combination with electron backscatter diffraction (EBSD), we make localized measurements of κ within few μm of individual GBs in boron-doped polycrystalline diamond. We observe strongly suppressed thermal transport near GBs, a reduction in κ from ∼1000 W m-1 K-1 at the center of large grains to ∼400 W m-1 K-1 in the immediate vicinity of GBs. Furthermore, we show that this reduction in κ is measured up to ∼10 μm away from a GB. A theoretical model is proposed that captures the local reduction in phonon mean-free-paths due to strongly diffuse phonon scattering at the disordered grain boundaries. Our results provide a new framework for understanding phonon-defect interactions in nanomaterials, with implications for the use of high-κ polycrystalline materials as heat sinks in electronics thermal management.

Probing Growth-Induced Anisotropic Thermal Transport in High-Quality CVD Diamond Membranes by Multifrequency and Multiple-Spot-Size Time-Domain Thermoreflectance

The maximum output power of GaN-based high-electron mobility transistors is limited by high channel temperature induced by localized self-heating, which degrades device performance and reliability. Chemical vapor deposition (CVD) diamond is an attractive candidate to aid in the extraction of this heat and in minimizing the peak operating temperatures of high-power electronics. Owing to its inhomogeneous structure, the thermal conductivity of CVD diamond varies along the growth direction and can differ between the in-plane and out-of-plane directions, resulting in a complex three-dimensional (3D) distribution. Depending on the thickness of the diamond and size of the electronic device, this 3D distribution may impact the effectiveness of CVD diamond in device thermal management. In this work, time-domain thermoreflectance is used to measure the anisotropic thermal conductivity of an 11.8 μm-thick high-quality CVD diamond membrane from its nucleation side. Starting with a spot-size diameter larger than the thickness of the membrane, measurements are made at various modulation frequencies from 1.2 to 11.6 MHz to tune the heat penetration depth and sample the variation in thermal conductivity. We then analyze the data by creating a model with the membrane divided into ten sublayers and assume isotropic thermal conductivity in each sublayer. From this, we observe a two-dimensional gradient of the depth-dependent thermal conductivity for this membrane. The local thermal conductivity goes beyond 1000 W/(m K) when the distance from the nucleation interface only reaches 3 μm. Additionally, by measuring the same region with a smaller spot size at multiple frequencies, the in-plane and cross-plane thermal conductivities are extracted. Through this use of multiple spot sizes and modulation frequencies, the 3D anisotropic thermal conductivity of CVD diamond membrane is experimentally obtained by fitting the experimental data to a thermal model. This work provides an improved understanding of thermal conductivity inhomogeneity in high-quality CVD polycrystalline diamond that is important for applications in the thermal management of high-power electronics.

Thermal conductivity measurements on suspended diamond membranes using picosecond and femtosecond time-domain thermoreflectance

We report on the room temperature in-plane thermal conductivity measurements on a 1-micrometer thick suspended diamond membrane grown by chemical vapor deposition using two different time domain thermoreflectance (TDTR) setups. The first setup is at Stanford University and the second is at Georgia Institute of Technology. Despite the differences between the two setups and the difficulty associated with diamond membranes thermal measurements, we demonstrate excellent repeatability from each setup and a very good agreement between the two setups. The paper outlines steps considered by both groups to minimize the measurement uncertainty and achieve such agreement. The measurement results show that the thermal conductivity displays a large variability across the membrane. The sensitivity and uncertainty analyses suggest that this variability could be a result of the nonuniformity in the diamond and aluminum coating thicknesses across the sample.

Characterization of the Thermal Conductivity of CVD Diamond for GaN-on-Diamond Devices

Diamond films grown by chemical vapor deposition have the potential to improve the thermal management and reliability of AlGaN/GaN high electron mobility transistors. The integration of CVD diamond with GaN involves the nucleation and growth of diamond films on GaN which induces a vertical gradient in thermal conductivity of the diamond and can result in bulk properties that depend greatly on growth conditions. Thus accurate characterization of the thermal conductivity of CVD diamond, especially the lower conductivity near the growth interface is needed to assess the impact on AlGaN/GaN HEMTs. In this work, we present measurements of the thickness dependence of CVD diamond with thicknesses ranging from 5 to 13.8 μ m in addition to bulk diamond substrates using time domain thermoreflectance. Measurements were made on the same samples in two different laboratories which showed excellent correlation between the measurements. The diamond properties were then utilized in a thermal model of a 10 finger AlGaN/GaN HEMT to predict the impact of device junction temperature. Compared to a device made on SiC operating at 5 W/mm, a junction temperature reduction of 30-40% was seen when using CVD diamond and the same device size.

The Impact of Interfacial Layers on the Thermal Boundary Resistance and Residual Stress in GaN on Si Epitaxial Layers

The development of gallium nitride (GaN) on silicon (Si) substrates is a critical technology for potential low cost power electronics. These devices can accommodate faster switching speeds, hotter temperatures, and high voltages needed for power electronics applications. However, the lattice mismatch and difference in crystal structure between 111 Si and c-axis hexagonal GaN requires the use of buffer layers in order to grow device quality epitaxial layers. For lateral high electron mobility transistors, these interfacial layers act as a potential source of increased thermal boundary resistance (TBR) which impedes heat flow out of the GaN on Si devices. In addition, these interfacial layers impact the growth and residual stress in the GaN epitaxial layer which can play a role in device reliability. In this work we use optical methods to experimentally measure a relatively low TBR for GaN on Si with an intermediate buffer layer to be 3.8 ± 0.4 m2K/GW. The effective TBR of a material stack that encompasses GaN on Si with a superlattice (SL) buffer is also measured, and is found to be 107 ± 1 m2K/GW. In addition the residual state of strain in the GaN layer is measured for both samples, and is found to vary significantly between them. Thermal conductivity of a 0.8μm GaN layer on AlN buffer is determined to be 126 ± 25 W/m-K, while a 0.84 μm GaN layer with C-doping on a SL structure is determined to be 112 ± 29 W/m-K.Copyright

Thermal rectification in thin films driven by gradient grain microstructure

As one of the basic components of phononics, thermal rectifiers transmit heat current asymmetrically similar to electronic rectifiers in microelectronics. Heat can be conducted through them easily in one direction while being blocked in the other direction. In this work, we report a thermal rectifier that is driven by the gradient grain structure and the inherent gradient in thermal properties as found in these materials. To demonstrate their thermal rectification properties, we build a spectral thermal conductivity model with complete phonon dispersion relationships using the thermophysical properties of chemical vapor deposited (CVD) diamond films which possess gradient grain microstructures. To explain the observed significant thermal rectification, the temperature and thermal conductivity distribution are studied. Additionally, the effects of temperature bias and film thickness are discussed, which shed light on tuning the thermal rectification based on the gradient microstructures. Our results show that the columnar grain microstructure makes CVD materials unique candidates for mesoscale thermal rectifiers without a sharp temperature change.As one of the basic components of phononics, thermal rectifiers transmit heat current asymmetrically similar to electronic rectifiers in microelectronics. Heat can be conducted through them easily in one direction while being blocked in the other direction. In this work, we report a thermal rectifier that is driven by the gradient grain structure and the inherent gradient in thermal properties as found in these materials. To demonstrate their thermal rectification properties, we build a spectral thermal conductivity model with complete phonon dispersion relationships using the thermophysical properties of chemical vapor deposited (CVD) diamond films which possess gradient grain microstructures. To explain the observed significant thermal rectification, the temperature and thermal conductivity distribution are studied. Additionally, the effects of temperature bias and film thickness are discussed, which shed light on tuning the thermal rectification based on the gradient microstructures. Our results show t...

Low Thermal Boundary Resistance Interfaces for GaN-on-Diamond Devices

The development of GaN-on-diamond devices holds much promise for the creation of high-power density electronics. Inherent to the growth of these devices, a dielectric layer is placed between the GaN and diamond, which can contribute significantly to the overall thermal resistance of the structure. In this work, we explore the role of different interfaces in contributing to the thermal resistance of the interface of GaN/diamond layers, specifically using 5 nm layers of AlN, SiN, or no interlayer at all. Using time-domain thermoreflectance along with electron energy loss spectroscopy, we were able to determine that a SiN interfacial layer provided the lowest thermal boundary resistance (<10 m2K/GW) because of the formation of an Si-C-N layer at the interface. The AlN and no interlayer samples were observed to have TBRs greater than 20 m2K/GW as a result of a harsh growth environment that roughened the interface (enhancing phonon scattering) when the GaN was not properly protected.