Properties for Thermally Conductive Interfaces with Wide Band Gap Materials

The goal of this study is to determine how bulk vibrational properties and interfacial structure affect thermal transport at interfaces in wide band gap semiconductor systems. Time-domain thermoreflectance measurements of thermal conductance G are reported for interfaces between nitride metals and group IV (diamond, SiC, Si, and Ge) and group III–V (AlN, GaN, and cubic BN) materials. Group IV and group III–V semiconductors have systematic differences in vibrational properties. Similarly, HfN and TiN are also vibrationally distinct from each other. Therefore, comparing G of interfaces formed from these materials provides a systematic test of how vibrational similarity between two materials affects interfacial transport. For HfN interfaces, we observe conductances between 140 and 300 MW m–2 K–1, whereas conductances between 200 and 800 MW m–2 K–1 are observed for TiN interfaces. TiN forms exceptionally conductive interfaces with GaN, AlN, and diamond, that is, G > 400 MW m–2 K–1. Surprisingly, interfaces formed between vibrationally similar and dissimilar materials are similarly conductive. Thus, vibrational similarity between two materials is not a necessary requirement for high G. Instead, the time-domain thermoreflectance experiment (TDTR) data, an analysis of bulk vibrational properties, and transmission electron microscopy (TEM) suggest that G depends on two other material properties, namely, the bulk phonon properties of the vibrationally softer of the two materials and the interfacial structure. To determine how G depends on interfacial structure, TDTR and TEM measurements were conducted on a series of TiN/AlN samples prepared in different ways. Interfacial disorder at a TiN/AlN interface adds a thermal resistance equivalent to ∼1 nm of amorphous material. Our findings improve fundamental understanding of what material properties are most important for thermally conductive interfaces. They also provide benchmarks for the thermal conductance of interfaces with wide band gap semiconductors.


Atomic Force Microscopy Scans
. AFM scan on 2 μm x 2 μm area of the Diamond sample with (100) orientation purchased from Element Six. RMS roughness observed ≈1 nm.

Metal Thickness and Thermal Conductivity Analysis
The thicknesses of the nitride metal layers were determined in two ways. First, by picosecond acoustics observed on a control sample of nitride metal/SiO2/Si stack 1 . The control samples were deposited at the same time as the samples of interest. To interpret picosecond acoustic signals, we assume average longitudinal speeds of sound in TiN and HfN to be ~10 nm/ps 2 and ~5.5 nm/ps.
We derived the value for the speed of sound in HfN from elastic constant data 3 . We also measured film thickness by treating it as a fit parameter when analyzing TDTR data collected on control likely due to differences in the polycrystalline grain sizes. When analyzing our TDTR data, we account for variation in electrical transport by using the WF-law to predict for each sample, see Table 1. We assume phonon thermal conductivities are sample independent. This latter assumption may not be rigorously valid. However, the sensitivity of our measurements to of the nitride-metal is small.  Uncertainty in the total thermal conductivity of the sputtered nitride metal films was of concern to us. For our measurements of the interface conductance to be as accurate as possible, we want the thermal resistance of the metal film to be small. If the thermal resistance of the metal film is small, the temperature evolution of the sample surface will be governed by the interface conductance. In our initial experiments, we deposited TiN films with a thickness of 55-60 nm. But we found that for samples with high , our TDTR signals had a small amount of sensitivity to the thermal conductivity of the nitride, which led to larger error bars for . To eliminate sensitivity to the TiN thermal conductivity, we prepared samples with thinner TiN layers. We found preparing samples with a TiN layer with a thickness between 30 and 40 nm effectively eliminates sensitivity

Substrate Thermal Conductivity
To determine the thermal conductivity of the bulk substrates, we performed TDTR on SiC 4H, SiC 6H, Si, Ge and ceramic AlN with ~80 nm of Al as the transducer. We used picosecond acoustic analysis to determine the thickness of the DC sputtered aluminum film, with an uncertainty of 5%.
The thermal conductivity and heat capacity of Al, heat capacities of the substrates 4-14 and thicknesses of the constituent layers were the input parameters for the thermal model. We fit the thermal model to the TDTR data by using the thermal conductivity of the substrate as the fitting parameter. Table S2 lists the best-fit values of the thermal conductivity of the substrates. The error bars indicate the range of thermal conductivity values within 5% RMS error due to the uncertainty in the thickness of the aluminum film. These measured substrate thermal conductivities were then used as input parameters for nitride metal/bulk substrate (SiC 4H, SiC 6H, Si, Ge and ceramic AlN) data. Overall, the TDTR measured thermal conductivities are in good agreement with literature values.  Figure S11.  For SiC-3C film on (100) Si and GaN film on (0001) Sapphire from MTI Corporation, the thermal conductivity of the thermally thick films was used as a fit parameter along with the interface conductance for TiN/SiC 3C and TiN/GaN samples. This was possible since the model is sensitive to the thermal conductivity of the film and the interface conductance at different time delays, allowing us to fit for both parameters, see Figure S12. We measured the thermal conductivity of GaN and SiC 3C to be 100 ± 10 W m -1 K -1 and 90 ± 20 W m -1 K -1 , respectively. The measured thermal conductivities for GaN and SiC 3C are only ∼ 50% and ∼ 25% of bulk thermal conductivity values, respectively. Epi-layer films often have lower thermal conductivity than bulk single crystals due to defects, e.g. dislocations. Finally, the sensitivity plots in Figure S13 indicate that the thermal model is not sensitive to the thermal conductivities of the thin-film AlN for all three substrates: CVD AlN epilayers from

DOWA, CVD AlN epilayers from Kyma Technologies and MBE grown AlN from Cornell
University. This is because AlN has high thermal conductivity and the AlN films are not thick enough for effects of its thermal resistance to be measured at picosecond time-scales. Since the sensitivity to the thin-film AlN is low, it is not possible to accurately fit for the thermal conductivities of these films. Due to the low sensitivity however, our best-fit values for the interface conductance for all three samples does not depend on the thermal conductivity of the AlN thin-films.

Raman Spectroscopy
Raman spectroscopy (Renishaw inVia) measurements were performed on HfN and TiN deposited on Si and MgO substrates in the backscattering configuration using 633 nm (red) laser excitation wavelength.
[1] The cutoff frequency is 110 cm -1 . The results are shown in Figure S14 and Figure S15. In both plots, the black and blue curves correspond to the Raman spectra of bare Si and MgO substrates, respectively. Silicon has only one Raman-active mode at ~520 cm -1 which is attributed to the LO/TO phonon polarization branches 21 23 . As seen in Figure S14 and Figure S15, the spectra collected from the pristine MgO substrate (blue curves) do not exhibit any peaks confirming that the crystal is almost defect free.
In case of HfN/Si and HfN/MgO structures ( Figure S14, red and green curves), a broad peak is observed at ~170 cm -1 . The peak is attributed to the first-order acoustic bands activated by the presence of nitrogen vacancy in HfN 23 . In case of TiN, no Raman peaks are detected in the shown frequency range. The latter confirms the deposition of stochiometric TiN on both substrates.

Isotropic Quadratic Dispersion Relation
We assumed a simple isotropic quadratic dispersion relationship to evaluate the phonon irradiance per Kelvin for TiN, HfN, group IV materials and III-V materials.
Here ( ) is the phonon density of states, is the phonon group velocity and is the wave vector.
Here is the sound velocity in the material and is a constant, is the reduced Debye wave vector, = (6π 2 ) 1/3 (4) Here 0 is the lattice constant.  Figure S17. Schematic of the HEMT device geometry we used as an example of how nitride/diamond interface conductance will affect device performance.

calculation Parameters
Thermal parameters used for modelling the temperature rise in a GaN/Diamond HEMT are detailed in figure S17. We used the interface conductance of AlN/GaN 24 for G AlGaN/GaN , since AlGaN is vibrationally similar to AlN, with some of the Al atoms substituted by Ga atoms. The analytical solution from ref 25 includes a 50 um SnAg die-attach layer and a convective heat transfer coefficient of 6.5 × 10 5 W m -2 K -1 in the source plane to model the thermal resistance of the die attach and high-performance microchannel cooler.
The analytical solution predicts a resistance R sub = 4.5 m 2 K GW -1 for the thermal resistances from the diamond substrate, die-attached layer and convective boundary at the bottom of the die.
The interface conductance between GaN and diamond adds in parallel with the rest of the device's resistance. Therefore, the device temperature rise is given by, where is the power density and is the total device thermal resistance, Here, ℎ is the thickness of the layer, Λ is the thermal conductivity of the material and G is the interface conductance between the respective layers. 26