4.1.3. Optimizing Diamond CVD for Thermal Management Applications

The initial layers of a diamond film typically feature small grains and feature a correspondingly low κ. This effect, combined with the *TBR* at the diamond/dielectric interface, may contribute to an additional *TBR* of 10 m<sup>2</sup> ·K/GW [79]. The importance of the quality of the diamond nucleation layer was highlighted in a recent work by Song et al. [169], who showed that the *R*th of a 12 finger/30 µm gate pitch GaN-on-diamond HEMT dissipating 5 W/mm would lower from 13.0 to ≈11.0 K·mm/W in the absence of phonon scattering by external defects in the GaN layer and interface (a value ≈49% lower than that of a state-of-the-art similar GaN-on-SiC structure). If the κ of the diamond nucleation layer were the same as its bulk conductivity, the *R*th of this devices would further decrease to ≈10.0 K·mm/W (≈54% lower than the *R*th of a similar GaN-on-SiC HEMT). Following the same trend, in the case of a HEMT with one finger gate, if the *TBR* at the GaN/diamond interface decreased from 13 to 3 m<sup>2</sup> ·K/GW, the device *R*th would go from 2.8 to 1.9 K·mm/W, which corresponds to a ≈30% reduction in the peak operating temperature at a given power level [73].

The morphology and properties of the diamond nucleation layer are intrinsically related with the process of depositing diamond films on non-diamond substrates. The deposition of diamond on a foreign substrate requires a seeding step, during which the substrate surface is enriched with diamond nanoparticles (DNP). Different techniques can be used for this purpose, such as ultrasonic agitation in a suspension containing DNP or spin-coating of a solution saturated with the same. Once exposed to diamond growth conditions, the diamond seeds grow three-dimensionally and eventually coalesce, forming a closed diamond film. At this stage the individual crystallites start growing perpendicularly to the surface, following the Van der Drift model [170], until growth terminates. The incubation time for the onset of the formation of diamond crystallites can be 15–45 min, depending on the growth parameters.

The growth of the diamond crystals from individual diamond seeds translates in the existence of a so-called diamond nucleation region which contains a high concentration of defects and grain boundaries that increase the phonon scattering and consequently decrease the thermal conductance. The thickness of this nucleation layer ranges typically between 10 and 50 nm, depending on the seeding method and deposition conditions, and its κ can be as low as 3 W/(m·K) [78]. The appearance of voids at the diamond/substrate interface at the locations where the enlarged diamond seeds touch one another is also common. This effect is represented schematically in Figure 22a [84]. Figure 22b shows a high-angle annular dark-field STEM (HAAD-STEM) image of the interface where such voids can be easily identified.

The size of the diamond grains is typically a few nm close to the substrate and increases with the thickness of the film. The evolution of the grain size has been studied computationally [171,172] and experimentally [173]; it has been shown that, depending on the growth conditions, the lateral size of the grains and their aspect ratio are strongly changing with the film thickness. As a consequence, the grain boundary density varies with the depth of the PCD layer, translating into an inhomogeneous κin-plane. On the other hand, in columnar PCD films κout-of-plane is typically higher than κin-plane [174]. However, this condition does not necessarily hold true in the nucleation region, where κin-plane can be higher than κout-of-plane and vice-versa for a given PCD film thickness [175]. The grain size dependence of κ, which is especially pronounced near the nucleation region, is therefore a critical parameter for maximizing the heat-spreading capabilities of PCD films on hybrid diamond/GaN devices. The dependence of the in-plane and out-of-plane κ with the PCD film thickness is shown in Figure 23. W/(m∙K)

µm gate

–

**Figure 22.** (**a**) Schematic of diamond film growth with low nucleation density; (**b**) HAAD-STEM image of the interface where the voids are clearly seen (reprinted from [84]; permission conveyed through CCBY 4.0: https://creativecommons.org/licenses/by/4.0/ (accessed on 7 October 2021)). 

 printed, with permission, from J. Anaya, et al., "Thermal management of GaN diamond near nucleation region," in – **Figure 23.** Evolution of in-plane and out-of-plane κ with diamond film thickness (© 2016 IEEE. Reprinted, with permission, from J. Anaya, et al., "Thermal management of GaN-on-diamond high electron mobility transistors: Effect of the nanostructure in the diamond near nucleation region," in 15th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), 2016, pp. 1558 1–8 [175]).

4.1.3.1. Impact of the Seeding Procedure

It is obvious that the deposition conditions (CH4/H<sup>2</sup> ratio, substrate temperature, and pressure) impact directly the growth rate as well as the macro-level characteristics/quality of the diamond deposits. Similarly, the seeding step has a considerable impact on the quality of the diamond film in the nucleation region, close to the interface with the substrate.

Increasing the seeding density has been the motto of researchers during the past years. Given their small size, which allows for homogeneous and high density seeding, DND seeds are the most frequently used diamond particles. The seeding methods that lead to the highest seeding densities include the ultrasonic agitation in a suspension containing DND seeds and the enhancement of the electrostatic attraction between the DND seeds and the substrate.


Despite leading to the highest reported seeding densities, DND particles may not be the best choice for thermal management applications, which rely on the minimization of the *TBR* between diamond and substrate. DND particles possess an amorphous shell [182], which may contribute to the increase of sp<sup>2</sup> bonds close to the interface, which in turn will enhance phonon scattering, thus compromising the thermal transport across the interface. In addition, while it is true that a high seeding density guarantees a lower coalescence time, it is not absolutely clear that this is an advantage for thermal applications. A very high density of seeds means that they are not allowed to grow significantly before they coalesce with each other; as a consequence the amount of defects and grain boundaries further increases—and so does the scattering of the phonons.

If seeding is performed with larger sized particles, the grain/grain boundaries ratio might be maximized. Following this reasoning, in 2017 Liu and co-workers evaluated the effect of seeding GaN substrates with a 30 nm-thick SiN protective layer with 30 and 100 nm diamond seeds [81]. Unlike what happened with the smaller 30 nm particles, seeding with 100 nm particles damaged the SiN layer, which resulted in the etching of the GaN surface and appearance of pin holes during diamond growth. More recently, Bai et al. [183] evaluated the impact of seeding with 4 and 20 nm seeds on the κ of diamond films deposited in Si substrates. Seeding with the larger 20 nm seeds resulted in a smaller seeding density (7 <sup>×</sup> <sup>10</sup><sup>9</sup> cm−<sup>2</sup> in contrast with 3 <sup>×</sup> <sup>10</sup><sup>11</sup> cm−<sup>2</sup> with the 4 nm seeds) but resulted in larger-sized grains near the interface region, and in a correspondingly higher in-plane κ as measured by Raman thermography.

In order to overcome the limitations of the standard seeding procedures, Smith et al. [76] proposed a two-step electrostatic spray technique to seed 130 nm-thick AlN films deposited on Si substrates. Using this method, the surface of the AlN was initially seeded with 2 µm diamond particles with smooth facets, which guaranteed a large contact area with the AlN surface and favored the thermal transport across the AlN/diamond interface. Following this step, the substrate was electrostatically sprayed again with 3.3 nm DNP, which filled in the gaps between the larger seeds and prevent the formation of voids. The schematic diagram explaining the rationale for the two-step seeding is shown in Figure 24. The advantages of this method are twofold: the microparticles of diamond guarantee a lower grain boundary ratio (when compared to conventional seeding with DND particles) and the DNP fill the voids between the larger particles, protecting the AlN surface from the plasma. This layer of electrosprayed seeds replaces the highly defective diamond nucleation layer

characteristic of heteroepitaxial diamond films. Using this method, an extremely low *TBR* of 1.47 m<sup>2</sup> ·K/GW (close to the theoretical minimum of 0.8 m<sup>2</sup> ·K/GW [84]) was obtained at a diamond/AlN interface.

W. Smith et al., "Mixed amond onto GaN and AlN", pp. 620– **Figure 24.** Rationale behind the two-step seeding: seeding with (**a**) ND particles alone, (**b**) diamond microparticles alone, and (**c**) diamond microparticles followed by ND (reprinted from Carbon, vol 167, E. J. W. Smith et al., "Mixed-size diamond seeding for low-thermal-barrier growth of CVD diamond onto GaN and AlN", pp. 620–626 [76], Copyright 2020, with permission from Elsevier).
