The study, published in Frontiers in Carbon, explores the growth dynamics of single-crystal diamond in what the researchers call a pocket holder, a machined substrate holder that physically surrounds the growing crystal during microwave plasma-assisted chemical vapor deposition, or MPACVD. The pocket effect is twofold. First, it enhances the linear dimension and area of the epitaxial layer through a process known as epitaxial lateral outgrowth, or ELO, in which the crystal expands sideways as well as upward. Second, it suppresses a parasitic phenomenon called polycrystalline diamond rim formation, a ring of useless polycrystalline material that typically deposits at the edges of the substrate and eats into the useful lateral area of the resulting epi-layer. By suppressing the rim, the pocket allows pure single-crystal lateral outgrowth to proceed.

The experimental setup is a classic MPACVD configuration. A gas mixture of methane and hydrogen is fed into a quartz dome inside an electromagnetic cavity, and a 2.45-gigahertz microwave signal ignites and sustains a plasma at 240 Torr. The plasma dissociates the precursor gases, producing methyl radicals and atomic hydrogen as the main species for diamond growth. Methyl radicals deliver carbon to the growing surface, while atomic hydrogen selectively etches away graphite, keeping the deposition purely diamond. Substrates are type Ib high-pressure high-temperature diamond seeds, cleaned in a sequence of sulfuric, nitric, and hydrochloric acids and solvents before loading. Growth temperatures ranged from roughly 760 to 1,020 degrees Celsius depending on the reactor geometry, with vertical growth rates controlled to approximately 25 micrometers per hour and input microwave power between 2 and 3 kilowatts. The holder is actively water-cooled to regulate substrate temperature throughout depositions lasting from 3 to 60 hours.

A total of 13 samples were grown across two reactor configurations to examine how manipulating the substrate-to-pocket constraints affects outgrowth. The researchers varied pocket width, depth, and the initial gap between the substrate edge and the pocket wall. In all cases, the wider the initial gap, the more lateral gain the crystal achieved, because a larger gap permitted a larger influx of methyl radicals to the growing crystal corners. The most useful optimization variable, once the optimal pocket depth of 2.5 to 3 millimeters was found, proved to be the gap distance. A setup with a gap of 1.5 to 1.75 millimeters allowed CVD diamond to gain up to 1 millimeter on a single crystal edge after 48 hours of growth at a vertical rate of around 25 to 28 micrometers per hour.

To understand what was happening at the gas-solid interface, the team performed computational modeling of the reactor in COMSOL, calculating three-dimensional methyl radical distributions at the start of growth and after the growing film had quadrupled in thickness, equivalent to 60 hours of deposition. The modeling revealed something elegant. At the beginning of growth, the methyl radical flux is uniformly suspended over the substrate in the pocket, driving standard out-of-plane vertical growth. But as the crystal thickens, it perturbs the incoming flux, which now arrives at an angle toward the crystal corners. This angled flux enables the gas-to-solid transformation that produces lateral outgrowth. In other words, the pocket is not merely a mechanical constraint; it is a direct manipulator of the methyl radical flux near the growing diamond surface, and therefore a direct manipulator of the phase transformation kinetics themselves.

From the modeling, the researchers parametrized the growth within the classical framework of first-order exponential decay, using an Avrami-type equation for the temporal lateral gain function. The equation captures the growth in both symmetric and asymmetric cases across both reactors with striking fidelity. The lateral gain rate slows exponentially as the distance between the growing crystal and the pocket side wall reduces. The parametrization yielded a maximum lateral gain, a characteristic decay time, and growth rate coefficients for every sample. The ratio of lateral to vertical growth rates ranged from 0.09 to 1.65 depending on the holder design and growth time, with the widest pockets and shortest growth times producing the most accelerated lateral outgrowth. Generally, the wider the pocket, the wider the lateral size and the longer the decay time.

But the exponential decay scenario revealed a fundamental limitation of the traditional box-like pocket. Lateral outgrowth in such a design can never be sustained; it always decays as the crystal approaches the wall. The team therefore asked whether the holder-substrate system could be engineered to lessen the constraint, ideally achieving a best-case scenario in which lateral outgrowth does not decay but remains constant. Their answer was a new generation of angled pockets with a fixed wall angle, where the traditional vertical wall corresponds to 90 degrees and a fully open pocket to 0 degrees. The hypothesis was that polycrystalline or graphite deposition on the pocket slope would not influence the growth behavior of the CVD diamond so long as the angle remained between 0 and 90 degrees, and that the crystal could then show a linear, undecayed outgrowth profile.

A series of angled pocket designs were fabricated with different combinations of inner and outer pocket width, step length, inner and total pocket depth, and wall angle, with angles of 37 and 60 degrees chosen as intuitively clear candidates near the midpoint of the allowed range. The inner pocket depth was fixed at 1 millimeter to expose the top 200 to 400 micrometers of the substrate to the methyl radical flux, and the inner width at around 4 millimeters to keep the substrate centered. All growths were done at 980 degrees Celsius with a vertical growth rate of around 25 micrometers per hour, giving an upper growth time limit of approximately 64 hours before the crystal would fill the upper pocket. The results discriminated sharply between designs. The strongest constraint, closest to the traditional pocket, yielded smooth growth but very limited outgrowth governed by exponential decay. A large 60-degree angle with no step demonstrated the most severe constraining regime, where no lateral outgrowth was attained and the crystal actually shrank inward. A combination of a step and a small 37-degree angle proved too permissive, allowing the polycrystalline rim to form aggressively and forcing growth to be stopped after 24 hours.

The breakthrough came from two intermediate designs providing similar effective in-pocket spacing, which allowed the largest lateral gains of the entire study. One of them showed the perfect hypothesized relationship: a nearly linear relationship between lateral gain and time, indicating a constant growth rate. Because the pockets are now semi-open, some polycrystalline deposition is expected to form on the slope, closing the effective gap from 37 degrees toward 45 degrees and thereby inducing quasi-linear outgrowth. The demonstration made it possible to maintain equal vertical and lateral gains such that the ratio of lateral to vertical growth rate equals 1. With that single demonstration, the linear size of the homoepitaxially grown CVD crystals can be doubled and the area quadrupled, a gain that compounds with each sequential growth cycle.

The implications reach well beyond the laboratory. Epitaxial lateral outgrowth by MPACVD is a simple sequential single-substrate process, requiring no bonding, no slicing, and no exotic equipment beyond the CVD reactor itself. Because each growth cycle can double the linear dimension and quadruple the area, repeated cycles constitute a self-replicating industrial process for producing 1 to 2 inch single-crystal diamond wafers. The work also provides a general design principle: the pocket geometry is the means of manipulating gas-to-solid phase transformation kinetics, and the wall angle is the major optimization variable for attaining constant-rate outgrowth. As demand surges for diamond power electronics, quantum devices, and heat-spreading substrates, the ability to grow large, high-quality single crystals at scale could finally unlock the material’s potential. The Michigan State team’s angled pocket may prove to be the engineering trick that brings diamond from the laboratory bench to the wafer fab.

Subject of Research: Diamond growth dynamics in a constrained system

Article Title: Diamond growth dynamics in a constrained system

Article References: Diamond growth dynamics in a constrained system. (n.d.). https://doi.org/10.3389/frcrb.2024.1367715

Image Credits: AI Generated

DOI: 10.3389/frcrb.2024.1367715

Keywords: Diamond, growth, dynamics, constrained, system, scientific research