Kevin R. Bagnall

Thermal Spreading Resistance and Heat Source Temperature in Compound Orthotropic Systems With Interfacial Resistance

In this paper, a new and more general solution for thermal spreading resistance in compound, orthotropic systems with interfacial resistance is considered. This new solution, which extends beyond previously published results, is obtained for a finite rectangular heat source of uniform strength arbitrarily located on a rectangular substrate. By means of superposition, one can obtain the temperature field in the source plane for multiple heat sources as well as the source mean and centroid temperatures. By means of orthotropic transformations, systems containing orthotropic materials can be easily modeled. Extension of the present solutions using a computationally efficient influence coefficient method is also given, such that the effects of large numbers of heat sources are superimposed. The application of these closed-form expressions for the temperature rise is demonstrated with calculations for Gallium nitride (GaN) high electron mobility transistors (HEMTs). These solutions are shown to be more flexible than previously reported analytical expressions and much more computationally efficient than 3-D finite element analysis, especially for a large number of discrete heat sources associated with multifinger GaN HEMTs.

Analytical Solution for Temperature Rise in Complex Multilayer Structures With Discrete Heat Sources

Temperature rise and thermal spreading resistance in multilayered structures are an important research topic in several branches of the thermal-fluid sciences, including thermal management of electronics and contact resistance. Previous work in developing analytical solutions for the temperature rise and thermal spreading resistance has been limited to relatively few layers and simple conditions at the interfaces. Recent development of multilayer epitaxial structures for high power electronics has led to the need for more general and flexible analytical solutions because numerical methods, such as the finite element method, are often computationally inefficient. This paper presents a closed-form, analytical solution for the temperature distribution in a rectangular structure with rectangular isoflux heat sources, any number of layers of arbitrary thermal conductivity, and perfect interfacial contact or finite interfacial conductance. Extensions are also presented for convective boundary conditions in the source and sink planes. The proposed analytical solution is demonstrated and validated to study gallium nitride (GaN)-based epitaxial structures in realistic device configurations. The capability to explore the parametric space in a computationally efficient manner provides the ability to understand the key dependencies of the temperature rise on the properties of the structure, such as the substrate thickness in GaN-on-diamond epitaxial structures. Our results show that reduction of the thickness of diamond substrates may actually increase the device temperature in a realistic device configuration due to the importance of thermal spreading within the first ~100 μm of the heat source.

Application of the Kirchhoff Transform to Thermal Spreading Problems With Convection Boundary Conditions

Thermal management and thermal analysis of microelectronic devices and packages are critical in ensuring the performance, reliability, and lifetime of todays electronic systems. When the thermal conductivity of a semiconductor or packaging material depends strongly on temperature, the use of a constant thermal conductivity value may significantly underestimate the temperature rise and thermal resistance. The Kirchhoff transform provides a convenient way of linearizing the heat conduction equation to use computationally efficient analytical solutions to calculate the device or package temperature. In the past, the application of the Kirchhoff transform has been restricted to temperature and heat flux boundary conditions in thermal spreading problems. In this paper, we developed an approximate solution for the application of the Kirchhoff transform to thermal spreading problems with convection in the sink plane and show the technique to be accurate to within 1% for relevant problems in device-level thermal analysis. The proposed technique is combined with a recently developed analytical solution for temperature rise in complex, multilayered structures in which a finite heat transfer coefficient in the sink plane needs to be considered. These analytical expressions and the Kirchhoff transform are valuable tools for accurately predicting the temperature in high-power, wide bandgap electronics, such as gallium nitride power amplifiers.

Nanoporous evaporative device for advanced electronics thermal management

We report the design, fabrication and modeling of a thin film evaporation device for cooling of high performance electronic systems. The design uses a membrane with pore diameters of ~100 nm to pump liquid via capillarity to dissipate the high heat fluxes. Viscous losses are minimized by using a thin membrane (~200 nm) which is supported by a ridge structure that provides liquid supply channels. As a result, the external pumping requirements are low, enabling an integrated cooling device with a large coefficient of performance. By integrating the cooling solution directly into the substrate, the thermal resistance of the spreader and interface material are removed entirely. Pentane is used as the working fluid based on its dielectric properties, surface tension and latent heat of vaporization. We first developed a model to capture the heat and fluidic transport within the membrane and supporting ridge structure using conservation of mass, momentum and energy. Using the model, we conduct a parametric sweep of the ridge and membrane geometries to elucidate their influence on thermal performance. We then show how the temperature of hot spots can be managed with a customized cooling solution while independently managing the temperature of background heated regions through variation in the membrane porosity over a realizable range of 10 - 50%. This work provides design guidelines for the development of a high performance evaporator device capable of dissipating the extreme heat fluxes (> 1 kW/cm2) required for next generation high power electronic devices.

Analytical thermal model for HEMTs with complex epitaxial structures

Although wide bandgap solid state devices are one of the most promising technologies for high power, high frequency applications, high device temperatures often lead to degraded performance and reliability. Thus, accurately predicting and maintaining device temperature at an acceptable level is a key to realizing the full potential of wide bandgap electronics. In this work, we present a closed-form analytical solution to the steady-state heat equation applicable to compound semiconductor high electronic mobility transistors (HEMTs), such as those based on gallium nitride (GaN). While numerical techniques are widely used to predict device temperature, our analytical solution is more computationally-efficient and can account for complex multi-layer structures, internal heat sources, and a variety of thermal interface conditions. Through a Fourier series-based solution and recursive relations for the Fourier coefficients in adjacent layers, we report manageable expressions for the Fourier coefficients. We also demonstrate that these solutions are two orders of magnitude more efficient than state of the art semi-analytical techniques for complex 3D structures. In addition, we have validated the model with high spatial resolution micro-Raman thermography measurements on GaN device structures.

Contributed Review: Experimental characterization of inverse piezoelectric strain in GaN HEMTs via micro-Raman spectroscopy.

Micro-Raman thermography is one of the most popular techniques for measuring local temperature rise in gallium nitride (GaN) high electron mobility transistors with high spatial and temporal resolution. However, accurate temperature measurements based on changes in the Stokes peak positions of the GaN epitaxial layers require properly accounting for the stress and/or strain induced by the inverse piezoelectric effect. It is common practice to use the pinched OFF state as the unpowered reference for temperature measurements because the vertical electric field in the GaN buffer that induces inverse piezoelectric stress/strain is relatively independent of the gate bias. Although this approach has yielded temperature measurements that agree with those derived from the Stokes/anti-Stokes ratio and thermal models, there has been significant difficulty in quantifying the mechanical state of the GaN buffer in the pinched OFF state from changes in the Raman spectra. In this paper, we review the experimental technique of micro-Raman thermography and derive expressions for the detailed dependence of the Raman peak positions on strain, stress, and electric field components in wurtzite GaN. We also use a combination of semiconductor device modeling and electro-mechanical modeling to predict the stress and strain induced by the inverse piezoelectric effect. Based on the insights gained from our electro-mechanical model and the best values of material properties in the literature, we analyze changes in the E2 high and A1 (LO) Raman peaks and demonstrate that there are major quantitative discrepancies between measured and modeled values of inverse piezoelectric stress and strain. We examine many of the hypotheses offered in the literature for these discrepancies but conclude that none of them satisfactorily resolves these discrepancies. Further research is needed to determine whether the electric field components could be affecting the phonon frequencies apart from the inverse piezoelectric effect in wurtzite GaN, which has been predicted theoretically in zinc blende gallium arsenide (GaAs).

Transient thermal dynamics of GaN HEMTs

Although GaN high electron mobility transistors (HEMTs) are one of the most promising semiconductor technologies for high power and high frequency applications, high device temperatures often lead to degraded performance and reliability. Most reports on the thermal characterization of GaN HEMTs have focused on the steady state temperature rise in spite of the prevalence of time-dependent power dissipation in aerospace, defense, and communications applications. In this work, we utilize analytical solutions to the transient heat conduction equation to investigate the thermal time constants associated with self-heating in GaN HEMTs. In contrast to previous reports and commonly held notions in the GaN device industry, we demonstrate that one or two thermal time constants does not adequately describe transient self-heating. Due to aggressive heat spreading from the small heat source in GaN HEMTs, a wide range of thermal time constants up to ≈10 ms are important for devices on sapphire substrates. These theoretical arguments are supported with transient temperature measurements obtained by time-resolved micro-Raman spectroscopy for a GaN-on-sapphire ungated HEMT.

Electric field dependence of optical phonon frequencies in wurtzite GaN observed in GaN high electron mobility transistors

Due to the high dissipated power densities in gallium nitride (GaN) high electron mobility transistors (HEMTs), temperature measurement techniques with high spatial resolution, such as micro-Raman thermography, are critical for ensuring device reliability. However, accurately determining the temperature rise in the ON state of a transistor from shifts in the Raman peak positions requires careful decoupling of the simultaneous effects of temperature, stress, strain, and electric field on the optical phonon frequencies. Although it is well-known that the vertical electric field in the GaN epilayers can shift the Raman peak positions through the strain and/or stress induced by the inverse piezoelectric (IPE) effect, previous studies have not shown quantitative agreement between the strain and/or stress components derived from micro-Raman measurements and those predicted by electro-mechanical models. We attribute this discrepancy to the fact that previous studies have not considered the impact of the electric...

High heat flux evaporation from nanoporous silicon membranes

We investigated the evaporative cooling performance of a nanoporous membrane based thermal management solution designed for ultra-high heat flux dissipation from high performance integrated circuits. The biporous evaporation device utilizes thermally-connected, mechanically-supported, high capillarity membranes that maximize thin film evaporation and high permeability liquid supply channels that minimize viscous pressure losses. The 600 nm thick membrane was created on a silicon on insulator (SOI) wafer, fusion-bonded to a separate wafer with larger liquid channels. Overall device performance arising from non-uniform heating and evaporation of methanol was captured experimentally. Heat fluxes up to 412 W/cm2 over an area of 0.4×5 mm, at a temperature rise of 24.1 K from the heated substrate to ambient vapor, were obtained. These results are in good agreement with a high-fidelity coupled fluid convection and solid conduction compact model that incorporates non-equilibrium and sub-continuum effects at the liquid-vapor interface. This work provides a proof-of-concept demonstration of our biporous evaporation device. Simulations of the validated model at optimized operating conditions and with improved working fluids, predict heat dissipation in excess of 1 kW/cm2 with a device temperature rise under 30 K, for this scalable cooling approach.

Simultaneous measurement of temperature, stress, and electric field in GaN HEMTs with micro-Raman spectroscopy

As semiconductor devices based on silicon reach their intrinsic material limits, compound semiconductors, such as gallium nitride (GaN), are gaining increasing interest for high performance, solid-state transistor applications. Unfortunately, higher voltage, current, and/or power levels in GaN high electron mobility transistors (HEMTs) often result in elevated device temperatures, degraded performance, and shorter lifetimes. Although micro-Raman spectroscopy has become one of the most popular techniques for measuring localized temperature rise in GaN HEMTs for reliability assessment, decoupling the effects of temperature, mechanical stress, and electric field on the optical phonon frequencies measured by micro-Raman spectroscopy is challenging. In this work, we demonstrate the simultaneous measurement of temperature rise, inverse piezoelectric stress, thermoelastic stress, and vertical electric field via micro-Raman spectroscopy from the shifts of the E2 (high), A1 longitudinal optical (LO), and E2 (low) optical phonon frequencies in wurtzite GaN. We also validate experimentally that the pinched OFF state as the unpowered reference accurately measures the temperature rise by removing the effect of the vertical electric field on the Raman spectrum and that the vertical electric field is approximately the same whether the channel is open or closed. Our experimental results are in good quantitative agreement with a 3D electro-thermo-mechanical model of the HEMT we tested and indicate that the GaN buffer acts as a semi-insulating, p-type material due to the presence of deep acceptors in the lower half of the bandgap. This implementation of micro-Raman spectroscopy offers an exciting opportunity to simultaneously probe thermal, mechanical, and electrical phenomena in semiconductor devices under bias, providing unique insight into the complex physics that describes device behavior and reliability. Although GaN HEMTs have been specifically used in this study to demonstrate its viability, this technique is applicable to any solid-state material with a suitable Raman response and will likely enable new measurement capabilities in a wide variety of scientific and engineering applications.