New insights into the mechanism of CVD diamond growth: Single crystal diamond in MW PECVD reactors

Abstract

CVD Diamond can now be deposited either in the form of single crystal homoepitaxial layers, or as polycrystalline films with crystal sizes ranging from mm, μm or nm, and with a variety of growth rates up to 100s of μm h^− 1 depending upon deposition conditions. We previously developed a model which provides a coherent and unified picture that accounts for the observed growth rate, morphology, and crystal sizes, of all of these types of diamond. The model is based on competition between H atoms, CH₃ radicals and other C₁ radical species reacting with dangling bonds on the diamond surface. The approach leads to formulae for the diamond growth rate G and average crystallite size <d> that use as parameters the concentrations of H and CH_x (0 ≤ x ≤ 3) near the growing diamond surface. We now extend the model to show that the basic approach can help explain the growth conditions required for single crystal diamond films at pressures of 100–200 Torr and high power densities.

Introduction

Diamond films can be deposited using a chemical vapour deposition (CVD) process involving the gas-phase decomposition of a gas mixture containing a small quantity of a hydrocarbon in excess hydrogen [1]. A typical gas mixture uses 1% CH₄ in H₂, and this produces polycrystalline films with grain sizes in the micron or tens of micron range, depending upon growth conditions, substrate properties and growth time. It is generally believed [2], [3] that the main growth species in standard diamond CVD is the CH₃ radical, which adds to the diamond surface following hydrogen abstraction by H atoms. Thus, a high concentration of atomic H at the surface in addition to CH₃ radicals is a prerequisite for successful microcrystalline diamond (MCD) deposition. By increasing the ratio of methane in hot filament (HF) CVD reactors from the standard 1% CH₄/H₂ gas mixture to ~ 5% CH₄/H₂, the grain size of the films decreases, and eventually becomes of the order of hundreds down to tens of nm. Such nanocrystalline diamond (NCD) films (often termed ‘cauliflower’ or ‘ballas’ diamond) are smoother than the microcrystalline ones, but have larger numbers of grain boundaries that contain substantial graphitic impurities. With further addition of CH₄, the films become graphitic.

Recently, so-called ultrananocrystalline diamond (UNCD) films have become a topic of great interest, since they offer the possibility of making smooth, hard coatings at relatively low deposition temperatures, which can be patterned to nm resolution [4], [5]. These differ from NCD films [6] since they have much smaller grain sizes (~ 2–5 nm). Most reports of the deposition of these films describe using a microwave (MW) plasma CVD reactor and gas mixture of 1% CH₄ in Ar, usually with addition of 1–5% H₂ [4]. We have previously reported the use of similar Ar/CH₄/H₂ gas mixtures to deposit NCD (or UNCD) in a hot filament (HF) reactor [7], with the compositional diagram for mixtures of Ar, CH₄ and H₂ being mapped out corresponding to the type of film grown.

Originally it was suggested [8] that the C₂ radical played an important role in the growth mechanism for UNCD. However, recent work by ourselves [9], [10] and others [11] has shown that C₂ is not a dominant species. In our previous paper [10], we used a 2-dimensional model of the gas chemistry, including heat and mass transfer, in our HF reactors to understand the experimental observations. The conclusions led to a generalised mechanism for the growth of diamond by CVD which was consistent with many experimental observations, both from our group and from others in the literature [12].

The proposed mechanism involves competitive growth by all the C₁ radical species that are present in the gas mixture close to the growing (100) diamond surface. Previous models mainly considered CH₃ since this is the dominant reactive hydrocarbon radical in standard H₂-rich CVD gas mixtures. However, we found that in HFCVD reactors at high filament temperatures (e.g. T_fil ~ 2700 K) or high CH₄ concentrations, the concentration of the other C₁ radical species, in particular C atoms, near the growing diamond surface can become as high as ~ 10¹² cm^− 3, and so may contribute to the growth process. C atoms as gas-phase precursors of diamond films have been considered before for HFCVD [13], microwave CVD [14] and plasma arc jet reactors [13], [15], [16], [17].

In most growth models, abstraction of surface H atoms by gas-phase atomic H are the reactions which drive the chemistry of growth. These reactions create two main types of surface radical sites on the reconstructed (100) − (2 × 1) diamond surface [18] (see Fig. 1), monoradical sites (a single dangling bond on a surface carbon) and biradical sites (defined as two surface radical sites on adjacent carbons). There are different variants of these bi- and monoradical sites, depending upon the local surface geometry, and the most important for growth have been labelled as A1, A2, etc., in Fig. 1. For typical diamond CVD conditions, the fraction of available biradical sites (of all types) is ~ 10 times lower than that of the monoradical sites (see section 1.4, below).

According to quantum-mechanical calculations [18] for a diamond (100) surface, CH₃ can add to dimer sites (both mono and biradical) but CH₃ cannot add to bridge and dihydride surface sites because of the strong steric repulsion among H atoms of the CH₃ group and the surrounding surface H atoms. In our previous studies [9], [10], [12] we have considered only addition of CH₃ to biradical dimer sites as the primary process by which carbon is added to the diamond lattice. Since the biradical sites have an adjacent dangling bond already present, the CH₃ adduct does not have to wait for a suitable abstraction reaction to occur before it can link in to the lattice. Thus, the reaction that forms the bridging CH₂ group readily occurs before the CH₃ can desorb. In ref. [12], [17], [19] we derived an equation for the growth rate contribution, G (in μm h^− 1) from CH₃ via this biradical channel as:

$$G_{\text{bi}}=3.8\times {10}^{-14}{T}_{\text{s}}^{0.5}\left[{\text{CH}}_3\right]R^2$$

where T_s is the substrate temperature in K, [CH₃] is the methyl gas-phase concentration in cm^− 3 at the substrate surface, and R is the fraction of surface monoradical sites (see section 1.4).

A modification to this previous model is that we now consider that, in addition to the biradical channel, CH₃ can also attach to monoradical dimer sites [18], [20], thereby terminating the ‘dangling bond’ and forming a pendant CH₃ adduct. There are then two competing processes which determine the fate of this adduct. One is that the adduct can simply desorb back into the gas phase (which is likely to be quite a facile process) and reform the monoradical site, and this can be quantified by a desorption rate, k_d. Alternatively, a suitable H abstraction reaction might occur on a neighbouring lattice position (or on an H atom from the CH₃ adduct) during the time the CH₃ remained attached to the surface followed by fast H atom transfer from the pendant CH₃ to this vacant site [18]. This suitable H abstraction reaction would depend upon the gas-phase atomic hydrogen concentration above the surface, [H], and the rate would be given by k_a[H], where k_a is the rate constant for abstraction. Then, the pendant CH₂ will create a dangling bond to the adjacent carbon of the same dimer (as a result of a β-scission reaction) and thus, the pendant CH₂ will be incorporated into the lattice as a bridging CH₂ group [18]. Thus, for successful incorporation of CH₃ into the diamond lattice via monoradical sites, the rate of H abstraction must be comparable with or higher than the CH₃ desorption rate, i.e. k_a[H] ≥ k_d. We have now included this mechanism by adding two monoradical channels to Eq. (1). The channels involve two main monoradical sites during regular growth, a dimer–dimer pair (A1 in Fig. 1) and a dimer–bridge pair (A3 in Fig. 1). We also assume that time-averaged fraction of these sites are 50%, and the rate of the CH₃ absorption on these monoradical dimer sites is the same as for biradical sites [12] (8.3 ×10^− 12 cm^− 3 s^− 1 for T_s = 1200 K). To derive an expression for the growth rate, G_mono, via monoradical dimer channels similar to that in Eq. (1), we should change R² (the probability of the surface site becoming a biradical site) in Eq. (1) to R (the probability of the monoradical surface site), and multiply by the probability of CH₃ incorporation via monoradical channels, given by k_a[H]/(k_a[H] + k_d). Thus, we will have

$$G_{\text{mono}}=3.8\times {10}^{-14}{T}_{\text{s}}^{0.5}\left[{\text{CH}}_3\right]\times R\times 0.5·k_{\text{a}}\left[\mathrm{H}\right]\{1/(k_{\text{a}}\left[\mathrm{H}\right]+k_{\text{d}}\left(\text{A}1\right))+1/(k_{\text{a}}\left[\mathrm{H}\right]+k_{\text{d}}\left(\text{A}3\right)\left)\right\}$$

and the total growth rate due to CH₃ can now be expressed as

$$G_{\text{CH}3}=3.8\times {10}^{-14}{T}_{\text{s}}^{0.5}\left[{\text{CH}}_3\right]·R·\{0.5·k_{\text{a}}[\text{H}]·(1/\left(k_{\text{a}}\right[\mathrm{H}]+k_{\text{d}}(\text{A}1\left)\right)+1/(k_{\text{a}}[\mathrm{H}]+k_{\text{d}}(\text{A}3\left)\right))+R\}$$

where k_d(A1) and k_d(A3) refer to the rates of desorption of CH₃ from A1 and A3 sites, respectively. R is the fraction of surface monoradical sites given by R = C_d^⁎/(C_d^⁎ + C_dH), where C_d^⁎ and C_dH are the respective densities of open- and hydrogen-terminated surface sites. This fraction, R, mainly depends on the rate constants for the surface H abstraction and addition reactions. Neglecting the effects of CH_x upon radical site density R, we obtain [9]

$$R=1/\{1+0.3\mathrm{e}\mathrm{x}\mathrm{p}(3430/T_{\text{s}})+0.1\mathrm{e}\mathrm{x}\mathrm{p}(-4420/T_{\text{s}}\left)\right[{\text{H}}_2]/[\text{H}\left]\right\}$$

where [H] and [H₂] are the atomic and molecular hydrogen gas-phase concentrations at the substrate surface, respectively.

We can now estimate the relative importance of the monoradical and biradical growth processes for CH₃ for different diamond CVD conditions. Using the values of k_a from ref. [12], and k_d(A1) and k_d(A3) from ref. [18] for a typical substrate temperature of T_s = 1200 K, we see that the CH₃ incorporation rate via the monoradical dimer sites A1 and A3 will be equal to the biradical incorporation rate when [H] = 2Rk_d(A1)/((1 − R)∙k_a) and when [H] = 2Rk_d(A3)/((1 − R)∙k_a), respectively. For R ~ 0.1 (see later) this condition will occur when [H] = 1.8 × 10¹⁴ cm^− 3 for the A1 site (k_d = 5300 s^− 1 [18]) and when [H] = 5.2 × 10¹⁵ cm^− 3 for the A3 site (k_d = 1.5 × 10⁵ s^− 1 [18]).

Our simulations show that [H] ~ 10¹⁴ – 10¹⁵ cm^− 3 for typical MCD growth conditions in HFCVD and MW PECVD reactors, therefore CH₃ incorporation via biradical and monoradical sites could be comparable for this case. In contrast, for SCD growth in high power MWCVD reactors [H] ~ 10¹⁶ cm^− 3, and thus, CH₃ incorporation via monoradical sites will now be the dominant mechanism. However, we note that accurate estimation of the contributions from both channels (mono and biradical) requires reliable values of [H] (and k_d for the monoradical channel) and its substrate temperature dependences.

As well as CH₃ addition, we assume that CH_x (x < 3) species, (C atoms, CH radicals, and also CH₂ although its number density close to the substrate surface is much lower) could also adsorb onto the surface. CH_x species can readily attach to both surface biradical sites and monoradical sites. These CH_x radicals differ from CH₃ in that after bonding to the surface they still have at least one ‘spare’ dangling bond and thus remain highly reactive. In the case of monoradical sites, once attached, the reactive adduct does not have to wait for a subsequent H abstraction reaction — it simply utilizes its spare dangling bond to react with an adjacent carbon and link into the lattice. This will also occur on biradical sites in much the same way. Therefore, CH_x species can be readily incorporated into the diamond lattice via both monoradical and biradical sites. The result of this is that even for low CH_x concentrations [CH_x]/[CH₃] ~ R + k_a[H]/(k_a[H] + k_d), their contribution to the growth rate can become important since they can readily add to the more abundant radical sites.

In a similar manner to Eqs. (2), (3), it is possible to estimate the contribution to the growth rate, G (in μm h^− 1), of these CH_x species, using formulae stated in refs. [12], [17], [19]:

$$G_{\text{CH}x}=3.9\times {10}^{-14}{T}_{\text{s}}^{0.5}\left[{\text{CH}}_x\right]R$$

where CH_x is for x = 0,1,2.

We now consider the fate of the bridging CH₂ groups. From the stable bridging structures, further hydrogen abstraction reactions allow the CH₂ groups to migrate across the surface until they meet a step-edge, at which point they will extend the diamond lattice, leading to large regular crystals [10], [12], [18]. In contrast, many of the bridging structures created following addition of C and CH species would remain reactive since they still contain at least one dangling bond. The most likely fate for such reactive surface sites, considering that they are surrounded by a gas mixture containing a high concentration of H atoms, is that they are rapidly hydrogenated to CH₂. If so, the subsequent reactions will be indistinguishable from attachment and growth by methyl, as described above. The rate of these hydrogenation reactions can be estimated by reference to an analogous gas-phase reaction, such as: C₂H₄ + H +M → C₂H₅ C₂H₅ + M. The high-pressure limit of this reaction rate is k⁎[M] ~ 5 × 10^− 12 cm³s^− 1 at T ~ 1000 K [21]. The characteristic time of this reaction (given by τ ~ (k[M][H])^− 1) for typical MCD growth conditions ([H] ~ 2 × 10¹⁴ cm^− 3, [CH₃] ~ 10¹³ cm^− 3, T_s = 1200 K and R ~ 0.1) is τ ~ 1 ms, which is comparable with the characteristic time for H abstraction τ ~ (k_a[H])^− 1 ~ 0.8 ms and much lower than that for CH₃ adsorption τ ~ (k_ad[CH₃]R)^− 1 ~ 120 ms.

However, when the atomic H concentration is low, other possible fates for the reactive surface adducts are possible, such as reaction with other gas-phase hydrocarbon radicals, further bridging or cross-linking leading to restructuring of the surface, or even renucleation of a new, misoriented crystallite. These processes are proposed to be one route by which the size of crystallites is prevented from becoming larger.

For the typical conditions used to deposit MCD/NCD and UNCD in a variety of different diamond CVD reactors (including MW and HF CVD reactors), the reactions of the surface adducts with atomic hydrogen which lead to continuous normal diamond growth are much more frequent events than the surface reactions which might ultimately lead to renucleation. As long as the surface migration of CH₂ (induced by H abstractions) is much faster than adsorption of CH₃, the aggregation of CH₂ bridge sites into continuous chains (void filling) will provide normal layer-by-layer {100} diamond growth [18]. But as the ratio of gaseous CH_x/H increases, the initiation of next layer growth could proceed before all the voids in the current layer are filled. Thus, depending upon the gas mixture and reaction conditions used, the relative concentrations of each of these species close to the growing diamond surface (e.g. [H]/[CH₃], [H]/[C], [H]/[H₂]) determine the probability of a renucleation event occurring and the average equilibrium crystal sizes, <d>, and hence the morphology of the subsequent film.

We extended these ideas [12] to derive quantitative estimations of <d>. Fig. 2 shows the percentage of both types of open sites for different substrate temperatures and [H₂]/[H] ratios, and helps to explain the diamond growth behaviour observed at different temperatures. At standard CVD growth temperatures of ~ 1200 K, and values of [H₂]/[H] = 1000 (typical of CVD diamond growth [9]), ~ 12% of the diamond surface is covered with monoradical sites, but only ~ 1.5% of the surface has the biradical sites necessary for CH₃ addition via the biradical channel (Fig. 2(b)).

The relative contributions for incorporation of CH₃ via monoradical and biradical channels depend mainly on the substrate temperature and on [H]. As can be seen from Eqs. (1), (2), the following trends should be observed: high [H] will promote the monoradical channel, whereas higher desorption rates k_d will reduce the monoradical channel contribution.

The percentages for R and R² shown in Fig. 2(b) highlight why diamond CVD is often a slow process under conditions where CH₃ is the only possible growth species. These percentages are a sensitive function of temperature, however, and for lower temperatures, the number of radical sites (of both types) falls rapidly. The MCD growth rate, G, has an activation energy E ~ 20–30 kcal mol^− 1 [22] (G ~ exp(− E/(0.001987 T_s)) at T_s < 1200 K and drops an order of magnitude for each ~ 200 K decrease in T_s (e.g. for T_s ~ 1000 K, ~ 800 K). The percentage of biradical sites drops accordingly with decreasing T_s and, in addition, CH₃ concentrations are reduced at low temperatures because of three-body recombination of CH₃ with H atoms. Note, however, that UNCD and NCD can be deposited (slowly) in MW PECVD reactors in 1% CH₄/Ar mixtures at temperatures down to ~ 700 K [5]. Here the other C₁ species (C atoms) could be the main contributors to growth [10], because these only require monoradical sites with corresponding activation energy E ~ 6.9 kcal mol^− 1 (G ~ R ~ exp(− E/(0.001987 T_s)), Eqs. (4), (5). R has a small but non-zero value (R ~ 3%), even at these low temperatures: for higher [H₂]/[H] ratios (e.g. Fig. 2(c)), the value of R² at all temperatures is too low for growth by CH₃ alone, but R is sufficient that growth from the other C₁ species is still possible, even down to temperatures as low as T_s ~ 700 K. This is consistent with the fact that literature reports of low temperature growth often describe that the films consist of low quality, defective, small grains, with high sp² carbon content, and/or NCD-type material [23], [24]. It should be noted that experimentally observed values of E are in the range E ~ 2–8 kcal mol^− 1 [5].

Conversely, for the very low [H₂]/[H] values ~ 100 that might occur in high power plasmas, R and R² values (Fig. 2(a)) can both become too high, resulting in localised cross-linking and restructuring of the diamond surface, which ultimately lead to graphitisation and/or amorphisation of the surface. This can largely be prevented, however, by growing at lower substrate temperatures < 1000 K, where the R and R² values are sufficient to create the appropriate number of open sites (R ~ 10%, R² ~ 1%), but not enough to initiate amorphisation.

Turning now to the question of crystallite size, by comparing the frequency of CH₂ surface migration processes with those for CH_x addition, we can estimate the average crystal size corresponding to varying deposition conditions. Assuming that the ratio of [H]/[H₂] near the substrate is not extremely low (e.g. [H]/[H₂] > 0.001, as will be the case for the vast majority of CVD deposition reactors), the average crystal size in nm, is given by [12]:

$$<d>=\{2+0.6\mathrm{e}\mathrm{x}\mathrm{p}(3430/T_{\text{s}}\left)\right\}\times \left\{\right[\text{H}]/\sum {\text{CH}}_x\}(x<4)$$

This equation predicts that the average crystal size is a linear function of the ratio of the concentration of atomic H to those of the C₁ growth species, close to the growing surface. Previously, [12] we used Eqs. (1), (5), (6) to model the growth rate, G, and maximum crystal size <d> for films grown under various conditions in hot filament CVD reactors. We showed that the predictions of these equations for both G and <d> compared favourably with the experimental values under both MCD and NCD growth conditions. However, when the nucleation rate approached that required for UNCD growth, the model became less accurate — although it still predicted grain sizes to within an order of magnitude, as well as the trends in growth rate and grain size with distance from the filament.

One process which has not been included in the model so far, and which would affect the rate of defect formation on the surface, is that of surface reconstruction or cross-linking. This was mentioned earlier as one possible fate for reactive surface adducts when there are insufficient H atoms nearby to rapidly hydrogenate any dangling bonds to form stable CH₂ bridges. Thus, the likelihood of a surface defect being created – possibly leading to formation of a new crystallite with different symmetry to the underlying lattice – will be directly related to the concentration (or adsorption reaction probability) of CH_x (x < 4) and/or more complex hydrocarbon radicals C_yH_z (y > 1), but inversely related to the concentration of H close to the surface. Thus, Eq. (6) can be multiplied by an additional factor to give:

$$<d{>}_{\text{new}}=\{2+0.6\exp (3430/T_{\text{s}}\left)\right\}\times \left\{\right[\text{H}]/\sum [{\text{CH}}_x\left]\right\}\times \left[\text{H}\right]/\left\{f_1\right(\left[{\text{CH}}_x\right])+f_2(\left[{\text{C}}_y{\text{H}}_z\right]\left)\right\}$$

for x < 4, y > 1 and where f₁ and f₂ are ‘efficiency functions’ which determine how efficient these defect creation processes are. As a first approximation, since these functions are unknown and might be a function of deposition conditions, in this paper we shall consider only the effect of CH_x (f₂ = 0) and shall assume that f₁([CH_x]) = Σ[CH_x].

We should make it clear that the value of <d>_new calculated here would be the equilibrium, ultimate or limiting value that would be achieved after the growth had occurred for sufficient length of time that any effects due to the substrate material, surface topology, and nucleation methods can be neglected. For SCD this is not an issue since columnar growth does not occur and crystallite size is independent of growth time. It is also not an issue with cauliflower NCD or UNCD, where renucleation occurs continually and there is no increase in crystallite size with growth time. However, when columnar growth occurs, such as during MCD deposition, the crystal size increases with growth time. Thus, in comparing our predictions with experimental data for MCD, we must be careful to ensure that the growth time was sufficiently long that that an equilibrium between the rate of secondary nucleation and the rate of crystal size increase had been reached.

Fig. 3 shows the predictions of Eq. (7) as a function of [H]/[ΣCH_x], plotted on a log-scale to allow all the diamond growth regions to be displayed on the same graph. The figure demonstrates that the type of film (SCD, MCD, NCD or UNCD) is determined simply by the [H]/[ΣCH_x] ratio near the growing diamond surface. Low [H]/[ΣCH_x] ratios and elevated substrate temperatures will favour smaller crystal sizes, and thereby promote NCD and UNCD deposition. However, should the atomic H concentration fall too low, then diamond growth ceases (<d> → 0), as observed in our and other experiments [7]. For [H]/[ΣCH_x] values less than ~ 1, <d> becomes < 10 nm, which is consistent with UNCD. For [H]/[ΣCH_x] between 1 and 3, <d> is between 10 and 100 nm, which is NCD. For [H]/[ΣCH_x] values higher than 3, the crystal size approaches a few μm, so this is the MCD regime. And, extrapolating the graph, for [H]/[ΣCH_x] > ~ 60 the crystallite size becomes > 100 μm, which is approaching SCD. It should be noted that some other mechanism of crystal size limitation could occur for UNCD deposition in MW PECVD reactors in methane–hydrogen mixtures in excess (up to 99%) Ar (e.g. renucleation due to C₂ [5] and thus f₂ ≠ 0 in Eq. (7) for this case). Preliminary simulations of UNCD growth in 0.5% CH₄/1% H₂/Ar mixtures of our MW PECVD reactor show that C atoms are the dominant species above the substrate. The calculated concentrations [C] ~ 10¹² cm^− 3 and [H] ~ 10¹⁵ cm^− 3 provide growth rates G ~ 0.1 μm h^− 1, which are close to those experimentally observed.

In this paper we shall concentrate on the SCD regime, and a full report of the results of the model for all other types of diamond film will be given elsewhere. From Fig. 3 we would predict that in order to achieve the <d> values of the order of many μm or even mm that are necessary for SCD growth, we require a very large ratio of [H]/[ΣCH_x]. However, in order to get a reasonable growth rate, [CH₃] also needs to be large, which can be achieved using a high proportion of CH₄ in the gas mixture (2–10%) and higher pressures than the 20 Torr that are typical for HFCVD, such as 100–200 Torr. But in order to obtain the required [H]/[CH₃] ratio at these higher pressures and methane concentrations, extremely high MW power densities (~ 40–150 W cm^− 3) [25] would be required to create a high density plasma. The high gas temperatures (~ 3000–3400 K) this would produce should greatly increase the dissociation rate of H₂, leading to a larger concentration of atomic H at the growing surface (compared with that in the lower power plasmas used for depositing MCD). This high [H] ensures that any C₁ species that attach to the surface will be rapidly hydrogenated to CH₂ before they have chance to restructure the surface. This allows rapid growth (since every adsorbed C₁ species contributes to growth), together with essentially no renucleation, which leads to large crystal sizes. Thus, single crystal diamond should be grown – even at these high CH₄ concentrations – so long as the power density is high enough to maintain a very high [H] that is uniformly distributed above the substrate, and the (100) substrate itself is defect-free and cooled efficiently and uniformly to prevent overheating [26].

These predictions are all borne out by the experimental conditions reported by the few groups who have successfully grown SCD to date. For example, 270 μm-thick single crystal diamond films of area of 2.5 × 2.5 mm have been grown by the group at Hasselt University, at 700 °C using 10% CH₄ [27]. The same group has reported epitaxial diamond growth yielding sub-nm smooth surfaces for films with thicknesses up to 730 μm [28]. Using similar conditions, freestanding diamond films of area 4 × 4 mm² and thickness between 390 and 690 μm were reported by workers from Element Six [29]. Recently, a group based at the Carnegie Institute in Washington has grown single crystal diamond up to 4.5 mm in thickness at growth rates as much as two orders of magnitude higher than conventional polycrystalline CVD methods [30], [31]. These single crystals can be fashioned into brilliant cut ‘gemstones’ using standard techniques. There are already companies (e.g. Apollo Diamond [32]) beginning to exploit the deposition conditions to produce CVD diamonds for the commercial gemstone market.

In this paper we seek to test our model using the key reactor parameters and conditions used for SCD growth on (100) substrates reported by Bogdan et al. [28]. They used a MW plasma reactor at a gas pressure of 180 Torr and methane concentration of 10% in H₂ with a total gas flow of 360 sccm, a substrate temperature of 973 K, input power of 600 W (giving an energy loading of 25 eV/molecule). They reported growth rates ~ 3–4 μm h^− 1, and although the film surfaces were generally smooth with a very low quantity of defects, some round-shaped growth structures with heights up to 0.5 μm and widths up to 100 μm occurred in some parts of the smooth samples, sometimes with a small number (< 2 mm^− 2) of square-shaped inverted pits with fourfold symmetry of size < 50 μm. Thus, their growth conditions are near SCD, but are not quite perfect.