In this blog, we provide an overview of thermal boundary resistance, why understanding it is critical when engineering semiconductor devices, and some critical challenges for interfacial thermal metrology.
What is thermal boundary resistance?
Thermal boundary resistance is simply a measure of resistance to heat flow at the interface between two materials. It is also commonly referred to as interfacial thermal resistance (ITR). This measure is sometimes called “Kapitza resistance,” (after Soviet physicist Pyotr Kapitza), although this term technically refers to resistance for an atomically perfect interface. In realistic devices, small deviations from an ideally perfect interface can lead to defects, diffusion, and other non-idealities creating a region of finite thickness. Thus, the thermal resistance of this interfacial region is the ITR.
When energy-carrying phonons or electrons transfer heat across interfaces and interfacial regions between two materials, scattering at the interface and in this interfacial region lead to additional temperature drops and thermal resistance that cannot be described from any characteristics of the electron or phonon properties of a single material. Thus, the thermal boundary conductance, G, which relates the heat flux, Q, across the interface to this interfacial temperature drop, DT, given by
is a property of the interfacial region between the two materials in contact. As a result, this property G is not an intrinsic material property but is related to some combination of the intrinsic electron and phonon properties and processes in each material and in the interfacial region. In the equation above, R is the ITR, which is the inverse of G.
Understanding the interfacial thermal resistance of materials is critical when the characteristic length scales of materials comprising composites or devices become on the order of or less than the Kapitza length. The Kapitza length represents the thickness of a material that has the same thermal resistance as the interface it is adjacent to. This Kapitza length, Lk, is given by
where k is the thermal conductivity of the material. Kapitza lengths can span from nanometers for low thermal conductivity amorphous oxides to even 100’s of micrometers for high thermal conductivity, high ITR materials and interfaces. This means that the ITR can play a major role in dictating the total thermal resistances of devices with length scales on the order of or less than 1 – 10 micrometers, which are common device length sales in a range of electronic devices, ranging from logic to power.
Semiconductors provide an instructive example to discuss the nanoscale processes that drive ITR. Thermal transport in most semiconductors is driven by phonons. Thus, for an interface between two semiconductors, we can understand the ITR based on how phonons of different energies interact with each other at the interface. Modeling approaches such as the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM) are two of the more common models to predict the ITR at interfaces based on the phononic properties of the materials comprising the interface. However, these theoretical models make simplifying assumptions about the nature and behavior of phonons in the materials, and how they interact at interfaces. For example, the phonon interactions at the inevitable atomic-scale imperfections that arise at interfaces, as previously mentioned, are not rigorously taken into account in these simplified mismatch modeling approaches. We expand on the modeling techniques used for semiconductor boundary resistances below.
Why is measuring interfacial thermal resistance so critical for semiconductors?
Because semiconductor devices must dissipate a large amount of heat, often in a very small space and across heterogeneous interfaces, understanding and calculating their ITR is vital to reliably predicting performance and specifying reliable operating limits. Crucially, today’s semiconductors have been engineered to such extraordinarily small length scales (well below the Kapitza length) that thermal resistance is mostly determined by the ITRs between materials, rather than the intrinsic properties of bulk materials.
Approaches such as molecular dynamics (MD) simulation are used to predict interfacial thermal resistances for semiconductors. This modeling-based approach can often provide results that are consistent with experimental evidence. MD approaches have proven quite powerful to study trends in how atomistic properties of interfaces can impact ITR. However, the quantitative predictive accuracy of this simulation technique is questionable for realistic materials due to the lack of suitable interatomic potentials that can correctly describe thermal interactions and thus ITR. This is an ongoing and active area of research.
Accurate parameterization of interatomic potentials for use in MD simulations often relies on comparison to experimental data. Additional routes to better refine MD simulation predictions of ITR often rely on generating potentials using first principles-based approaches, the output of which must also be verified with experimental results on real systems. Direct measurements of ITR across semiconductor interfaces are thus of utmost importance to evaluate the accuracy and help to further improve the predictive power of these atomistic approaches to calculating ITR.
Key Challenges for Interfacial Thermal Metrology in Thin Film Semiconductors
Laser Thermal’s Steady-State Thermoreflectance in Fiber Optics (SSTR-F) is a non-contact laser-based pump-probe technique that can measure interfacial thermal resistance of thin film semiconductors. The high-throughput, automated data collection and analysis allows for measurements of ITR on a wide array of semiconductor interfaces and packages. This novel thermal resistance testing technique is well suited to a number of other unique metrology challenges associated with semiconductor manufacturing. Laser Thermal’s patented design of the SSTR-F tool allows for turnkey, fully automated thermal conductivity measurements, with batch testing capabilities well suited to the high-throughput needs of semiconductor manufacturing. You can learn more about this technology in our article here.