# Growth strategies for widening thick heavily boron-doped (113)-oriented CVD diamond

R. Mesples-Carrère, R. Issaoui, A. Valentin, L. Banaigs, O. Brinza, F.

Bénédic, Jocelyn Achard

► To cite this version:

R. Mesples-Carrère, R. Issaoui, A. Valentin, L. Banaigs, O. Brinza, et al. Growth strategies for widening thick heavily boron-doped (113)-oriented CVD diamond. Diamond and Related Materials, 2024, 149, pp.111659. 10.1016/j.diamond.2024.111659. hal-05246758

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# Growth strategies for widening thick heavily boron-doped (113)-oriented CVD diamond

R. Mesples-Carrère, R. Issaoui, A. Valentin, L. Banaigs, O. Brinza, F. Bénédic, J. Achard*

LSPM, CNRS, Université Sorbonne Paris Nord, 99 avenue J.B. Clément, 93460, Villetaneuse, France

## ARTICLE INFO

**Keywords:**

Single crystal CVD diamond
Boron-doping
Surface widening
Free-standing CVD plate

## ABSTRACT

In the present study, a growth strategy allowing widening thick heavily boron doped (113)-oriented diamonds is proposed. It relies on a geometrical model developed at the LSPM, which is used to visualize the evolution of the deposited crystal shape. This model helped us to identify the specific growth parameters allowing to slow down the growth rate along (113) direction and, at the same time, continuously increase the area of this crystalline face. Depositions have been carried out and has resulted in a significant increase of 145% of the top-surface area, giving a functional surface of 3.7mm in diameter after a growth of 930µm, starting from 2.3mm. The resistivity, measured by four-point probe system, reaches a value as low as 5mΩ.cm, which is comparable to the best results obtained on thick layers grown on the conventional (100) orientation.

## 1. Introduction

Diamond has long been recognized as a very promising material for high-performance electronics in virtue of its exceptional properties. Nevertheless, developing elementary electronic components, and especially bipolar ones, remains a significant challenge insofar that it requires thick and heavily boron-doped films, ideally with a top surface as large as possible. These layers are usually deposited through the classical (100) orientation [1] since the boron-doped (111)-oriented films do not exhibit an optimal crystalline quality [2,3] and remain extremely difficult to thicken. Unfortunately, results described in the literature demonstrated that n-doped (100)-oriented layers suffered from a high compensation rate and moderated carrier mobility [4], which is severely limiting the development of efficient vertical bipolar components on this orientation. Nevertheless, it has been recently reported [4] that the use of (113)-oriented crystals favours a decrease of the compensation rate and an increase of the electron mobility, leading to a growing interest in the synthesis of diamond CVD layers on this specific orientation [5-8]. Furthermore, a recent paper showed encouraging results concerning the feasibility of thick boron-doped (113)-oriented diamond layers [9], paving the way for the development of more efficient vertical components. Although the properties of deposited (113)-oriented layers are promising, limiting factors are still slowing down its widespread implementation in the world of diamond community. Indeed, the lack of commercially available (113)-oriented substrates involves costly and

time consuming operations such as laser cutting and polishing processes [10]. Moreover, maximizing the number of components produced per CVD sample implies the development of wider functional areas on this orientation. The main objective of this article consists in producing heavily boron doped (113)-oriented substrate with a widened top-surface area. To reach this goal, a preliminary numerical analysis using a 3D geometrical model has been carried out to determine the most favourable growth conditions, and a series of experiments has been led in order to validate the obtained theoretical results. Finally, an industrialization would necessitate the growth protocol determined to be both reliable and reproducible, which constitutes the corollary achievement of this study.

## 2. Experimental details

The (113)-oriented substrates have been obtained by laser cutting and polishing operations, starting from 1.5 mm thick High Pressure High Temperature (HPHT) Ib substrates with all faces oriented along the (100) direction as described in previous works [10]. The final substrates are cylinders of approximately 2 mm in diameter and 0.5 mm thick. Each substrate received a H₂/O₂ plasma pre-treatment of 20 min in order to remove the damaged top surface and to avoid, as well as possible, the propagation of dislocations from the HPHT substrate to the deposited CVD layers [11].

Microwave Plasma Assisted Chemical Vapour Deposition (MPACVD)

<figure><img src="image_2.png" /></figure>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: jocelyn.achard@lspm.cnrs.fr (J. Achard).</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 1. Morphology diagram of the shapes of crystals composed of {100}, {110}, {111} and {113} faces. The coexistence domains of the different facets are circumscribed by boundaries that depend on α, β and γ parameters [13].</figcaption></figure>

has been used as the growth process, with parameters determined by a geometrical model that will be described in paragraph 3. The substrate temperature was monitored by a two-colour pyrometer and a constant total gas flow rate of 200sccm was maintained throughout the growth process. The depositions have been achieved with hydrogen and methane purities of respectively 9N and 5N5, and boron doping has been accomplished by the addition of a mixture of diborane (B₂H₆) and hydrogen in the gas phase. Several depositions have been carried out in order to ensure the reproducibility of the process.

The doping levels of the growth samples were characterized by Raman spectroscopy using a Horiba HR800 Raman spectrometer with a 473nm excitation line at room temperature [12]. The surface morphology and widenings of these samples were observed and quantified using a Keyence VK-9700 laser scanning microscope (LSM) for the samples A1, A2 and B1; and using a Zeiss GeminiSEM scanning electron microscope (SEM) for the samples A3, B2, C and D (cf. Table 2). Finally, the electrical resistivity measurements were performed using a Keithley 4200-SCS system, equipped with a collinear four-point probe (FPP) configuration with a 1mm spacing, placed in direct contact with the diamond sample.

### 3. Geometrical model

A geometrical model has been developed a few years ago in order to predict the crystal morphology, depending on the growth parameters α, β and γ, the deposition time and the initial shape, orientation and dimensions of the substrate. Only 3 growth parameters have been defined taking into account the stable crystalline faces observed for CVD diamond. These growth parameters are proportional to the ratio of the growth rate of {100} planes and, respectively, the growth rate of {111}, {110} and {113} planes, as showed in Eq. (1) [13,14].

$$ \alpha = \sqrt{3} \times \frac{V_{\{100\}}}{V_{\{111\}}}; \beta = \sqrt{2} \times \frac{V_{\{100\}}}{V_{\{110\}}}; \gamma = \sqrt{11} \times \frac{V_{\{100\}}}{V_{\{113\}}} \quad (1) $$

The relative values of these parameters allow the model to predict the final crystal morphology at a given deposition time, knowing that the final shape is defined by the faces which have the lowest growth rate [13,15].

In this study, the aim is the widening of (113)-oriented substrate, so the {113} faces must have a slow growth rate, and especially compared to {111} and {110} faces. Consequently, the first sine qua non conditions to fulfil is specified as follows: $V_{\{113\}} < V_{\{111\}}$ and $V_{\{113\}} < V_{\{110\}}$. It can be noticed that the growth rate of the {100} faces is not taken into account as its value is used as the numerator in the calculation of each

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 2. Simulated evolution of the top-surface area as a function of (a) the growth parameter α, (b) the growth parameter β, and (c) the growth parameter γ.</figcaption></figure>

growth parameter, as shown above in Eq. (1). Thus, it has no influence on the proportionality between the α, β and γ parameters. Beyond the first conditions, the growth has to take place in the domain of existence of {113} faces in order to stabilize them throughout the entire deposition. Thus, another prerequisite to satisfy is $γ ≥ (11α/5)$, as shown in Fig. 1, which corresponds to an α parameter of 2.2 usually obtained in
<table><caption>**Table 1**
Summary of the samples used to define the experimental growth parameters α, β and γ.</caption><thead><tr><th>Sample</th><th>Substrate orientation</th><th>Growth rate (µm/h)</th><th>Corresponding growth parameters</th></tr></thead><tbody><tr><td>RMR.abg.100</td><td>&lt;100&gt;</td><td>4.4</td><td>/</td></tr><tr><td>RMR.abg.110</td><td>&lt;110&gt;</td><td>9.6</td><td>β = 0.6</td></tr><tr><td>RMR.abg.111</td><td>&lt;111&gt;</td><td>9.4</td><td>α = 0.8</td></tr><tr><td>RMR.abg.113</td><td>&lt;113&gt;</td><td>4.5</td><td>γ = 3.2</td></tr></tbody></table>

our optimized growth conditions for intrinsic (100)-oriented diamond material.

The top-surface area of the deposited layers was calculated with Gauss's area formula (also known as shoelace formula or surveyor's formula [16]), that allows to determine the area of an arbitrary 2D polygon based on the Cartesian coordinates of its vertex, as showed in Eq. (2).

$$ \Delta = \frac{1}{2} \left\{ \begin{vmatrix} x_0 & x_1 \\ y_0 & y_1 \end{vmatrix} + \begin{vmatrix} x_1 & x_2 \\ y_1 & y_2 \end{vmatrix} + \dots + \begin{vmatrix} x_{n-2} & x_{n-1} \\ y_{n-2} & y_{n-1} \end{vmatrix} + \begin{vmatrix} x_{n-1} & x_0 \\ y_{n-1} & y_0 \end{vmatrix} \right\} \quad (2) $$

where Δ is the area of the polygon and $(x_i, y_i)$ are the Cartesian co-ordinates of each vertex, which are numbered counter clockwise around the perimeter of the polygon.

Fig. 2 shows the time evolution of the top surface area for growth parameter α in Fig. 2a, β in Fig. 2b and γ in Fig. 2c. It demonstrates that the β parameter does not have a strong influence on the top-surface area when it is maintained under a value of 1.1, threshold value below which

all curves are merged, as shown in Fig. 2b. However, the situation is quite different for α and γ parameters. Indeed, for a standard value of γ in the case of a (113)-oriented substrate growth, the increase of α leads to a gradual decrease of the top surface area throughout a deposition of 200 hours, from 7.5 to 2 mm², as illustrated in Fig. 2a so an α value lower than 2 is desirable. Conversely, the increase of γ leads to a strong increase of the area, from 0 to 7.5mm², as demonstrated in Fig. 2c and the value of this parameter must be kept higher than 3. The results obtained on the last figure indicate that the most favourable set of parameters is {α = 1.5; β = 0.8; γ = 3.5}, i.e. when the γ/α ratio is the closest to the value of 11/5. Thus, to widen the functional area, the γ parameter has to be maximized and the α parameter has to be minimized, with a γ/α ratio maintained above 11/5.

In previous studies, it has been reported that the addition of a low amount of oxygen in plasma leads to the development of {113} faces when (100)-oriented substrates were used to grow boron doped films [17]. More recently, a set of parameters leading to thick (113) boron-doped films were reported by Tallaire et al. [9]. Considering these studies, adapted growth parameters were used in order to stabilize and thicken (113)-oriented faces. The temperature of the substrate has been maintained around 850°C during the whole growth process, with a plasma phase composed of 6% of methane, 0.25% of oxygen and 5000ppm of (B/C)gas, using diborane diluted in hydrogen. Finally, a couple pressure/microwave power was fixed to 200mbar/3kW [12] in order to maximize the crystalline quality of the deposited films [18,19].

<table><caption>**Table 2**
Summary of the CVD samples studied in this work.</caption><thead><tr><th>Sample</th><th>A1</th><th>A2</th><th>A3</th><th>B1</th><th>B2</th><th>C</th><th>D</th></tr></thead><tbody><tr><td>Thickness (µm)</td><td>—</td><td>—</td><td>930</td><td>—</td><td>745</td><td>645</td><td>647</td></tr><tr><td>Top-surface area (mm²)</td><td>4.69</td><td>4.94</td><td>10.7</td><td>4.75</td><td>7.6</td><td>7.09</td><td>8.08</td></tr><tr><td>Widening factor (w<sub>f</sub>)</td><td>1.08</td><td>1.13</td><td>2.45</td><td>1.09</td><td>1.85</td><td>1.73</td><td>1.97</td></tr><tr><td>Time of deposition (h)</td><td>45</td><td>70</td><td>260</td><td>50</td><td>195</td><td>185</td><td>155</td></tr><tr><td>Estimated boron con-centration (at.cm<sup>-3</sup>)<sup>a</sup></td><td>—</td><td>—</td><td>5 × 10<sup>20</sup></td><td>—</td><td>7 × 10<sup>20</sup></td><td>6 × 10<sup>20</sup></td><td>4 × 10<sup>20</sup></td></tr><tr><td>Resistivity (Ω.cm)</td><td>—</td><td>—</td><td>0.014</td><td>—</td><td>0.011</td><td>0.016</td><td>0.005</td></tr><tr><td>Characterizations</td><td>LSM</td><td>LSM</td><td>SEM<br>Raman<br>FPP</td><td>LSM</td><td>SEM<br>Raman<br>FPP</td><td>SEM<br>Raman<br>FPP</td><td>SEM<br>Raman<br>FPP</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>**Fig. 3.** (a)(b) Top-surface areas respectively of the samples A1 and A2, observed by LSM. (c) Top-surface area of the sample A3 observed by SEM. The dashed white lines represent the surface of the HPHT substrate used for this deposition.</figcaption></figure>

<footnote>a Estimation of the boron concentration based on the algorithm developed by the Czech Academy of Science [20].</footnote>
<figure><img src="image_8.png" /><figcaption>Fig. 4. (a) Top-surface area of the sample B1 observed by LSM. (b) Top-surface area of the sample B2 observed by SEM. The dashed white lines represent the surface of the HPHT substrate used for this deposition.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 5. Top-surface morphologies of (a) the sample A3, (b) the sample B2, (c) the sample C and (d) the sample D, observed by SEM.</figcaption></figure>

# 4. Experimental results and discussion

## 4.1. Determination of the experimental growth parameters

The first step of the experiments was the validation of the selected growth conditions by measuring the experimental growth rates of the four families of faces. These growth rates allow the calculation of experimental growth parameters $α, β$ and $γ$, which are necessary to

confirm or deny the choice of using these growth conditions. To carry out this part of the study, a deposition was performed on each substrate's orientation, i.e. the {100}, {111}, {110} and {113} ones, starting from HPHT substrates. The thicknesses of deposited films have been measured in order to calculate the corresponding speed rates and, finally, determine the experimental growth parameters. Each deposition has been executed strictly in the same conditions as those determined above, and for an exact duration of 5 h in order to limit as much as
<figure><img src="image_10.png" /><figcaption>Fig. 6. Comparison between the simulated evolution of the top-surface area (blue curve) and the experimental measurements as a function of the growth time.</figcaption></figure>

possible a potential temperature drift.

The results obtained, summarized in Table 1, show that the (100) and (113)-oriented samples have the slowest growth rates as expected and are quite low compared to those of the (110) and (111)-oriented ones, which satisfies the first condition specified above ($V_{(113)} < V_{(111)}$ & $V_{(113)} < V_{(110)}$). Furthermore, these growth conditions theoretically allow the stabilization of {113} faces throughout a long deposit insofar as the ratio $γ/α$ is around 4, which is much higher than the prerequisite of 11/5. Thus, this set of growth conditions fulfils all the requirements and will be used to widen the (113)-oriented substrates in the rest of this study.

## 4.2. Deposition on (113)-oriented substrates

After the validation of the growth conditions defined previously, four (113)-oriented samples have been deposited, as detailed in Table 2. In order to observe the evolution of the functional surface area throughout the growth, the deposition of the samples A has been stopped twice and the one of the sample B has been stopped once. During these

interruptions, the samples have been characterized by laser and electronic microscopy for the purposes of evaluating the widening of the samples. Finally, the samples C and D have been deposited with the aim of ensuring the reproducibility of the process used in this study.

A factor $w_f$ has been defined in order to quantify the widening of the (113)-oriented functional surface area. It is calculated as follows in Eq. (3):

$$w_f = \frac{\mathcal{A}_f}{\mathcal{A}_i} \qquad (3)$$

where $\mathcal{A}_f$ represents the surface area after growth, and $\mathcal{A}_i$ the initial surface area.

As shown in Fig. 3, after 45 hours of growth, the enlargement of the top-surface area of the sample has increased by a factor of 1.08, but, the first appearance of crystallographic planes on the cylindrical surface can be observed. The surface area then reached 1.13 times the initial one after 70 hours of depositions, which is a negligible improvement compared to the previous step. Thus, it has been decided to grow much longer before removing the sample from the reactor another time, which
<figure><img src="image_11.png" /><figcaption>Fig. 7. Normalized Raman spectra of the samples A3, B2, C and D, acquired with a 473 nm excitation line at room temperature.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 8. Photography of a laser-cut and polished (113)-oriented self-supporting sample with an inner diameter of 3 mm.</figcaption></figure>

allowed a significant increase of the functional surface area. Indeed, after a deposit of 260 hours, the final surface area is 145% wider than the substrate's one. In other terms, the original top-surface area has been multiplied by a factor of 2.45, with a functional diameter increased from 2.3 to 3.7 millimetres. The sample B, as illustrated in Fig. 4, has been removed from the reaction chamber after 50 and 195 hours, in order to obtain intermediate values of the enlargement of the functional surface area. A $w_f$ of 1.09 has been observed after 50 hours of deposition, which perfectly corroborates the results obtained with the sample A. Finally, after 195 hours of growth, the final the widening factor reached 1.85, which totally corresponds to the outcome of the previous deposition. Finally, the growth of the samples C and D allowed ensuring the reliability of the process as this crystal has an extremely similar shape to the sample B, as demonstrated in Fig. 5. Indeed, after respectively 185 and 155 hours of deposition, the crystallographic planes on the periphery of this sample are exactly the same as those on the sample B.

The characterizations of these films allowed collecting data necessary to compare the experimentations to the predictions of the geometrical model. The time of deposition and the functional surface area are sufficient parameters to draw a comparison between the simulation and the results obtained. As presented on Fig. 6, the experimental trend curve is slightly above the curve relative to the growth

parameters previously determined. This disharmony is due to the widenings of the samples A3 and D, which are slightly high, compared to their growth times. This could be explained by a gradual drift in substrate temperature throughout growth which is always a critical point for very long deposition duration. However, all the other reference points tend to corroborate the results provided by the simulation since, taking into account measurement uncertainties in the identification of the experimental growth parameters which are estimated around 10%, most of experimental points are included in the corresponding blue area.

After having achieved the objective of widening the samples and proving the reproducibility of the process developed, the properties of the deposited layers were evaluated in order to determine their potential as doped substrates for power electronics vertical structures.

As illustrated in Fig. 7, normalized Raman spectra of the samples show the appearance of a strong Fano effect, which is a visible dissymmetry of the bases lines on either side of the diamond peak. This effect, combined to very high values of their full widths at half maximum ($5\text{cm}^{-1}$ for the sample D, $6\text{cm}^{-1}$ for the samples A and C, and even $10\text{cm}^{-1}$ for the sample B), is characteristic of a strong boron-doping level [21]. The four-point probes measurements completely corroborate this idea insofar as the resistivity is around $10\text{ mΩ.cm}$ for the samples A, B and C, and reaches $5\text{ mΩ.cm}$ for the sample D. Such low values imply that the crystals are close to their metallic transitions [21], which is related to a very high concentration of doping elements inside the diamond layers. The results provided by the Raman Analysis Tool, developed by the Czech Academy of Science [20], confirm this hypothesis by showing a boron concentration above $10^{20}\text{at.cm}^{-3}$ for each sample.

After having obtained such results, one objective will be to clone these crystals and enlarge them further after another growth step. This would allow multiplying the number of substrates and optimizing the functional surface area. As an illustration, Fig. 8 shows a freestanding crystal obtained after a laser cutting and polishing processes starting from sample D, which has a thickness of $450\text{µm}$ and an average functional diameter of 3mm.

## 5. Conclusion

The widening of thick boron-doped (113)-oriented diamond films obtained by MWPACVD has been successfully achieved, reaching after eleven days of growth, 2.45 times the initial functional surface area. The growth conditions determined in this study appear to fall within a very favourable window for {113} faces' development. The thicknesses which can be attained (close to the millimetre) are very satisfying and adequate to clone the samples via laser cutting operations, allowing self-sufficiency in terms of (113)-oriented substrates supply in the future. Raman spectroscopy and the four-point probes are consistent with a heavy boron-doping level, with a resistivity measured as low as $5\text{mΩ.cm}$, in the most advantageous case. Moreover, microscopic analyses showed functional surfaces totally free of crystalline defects. These results point to the possibility of using this process for the development of elementary vertical electronic components, such as Schottky or PIN diodes for example. In the latter case, the (113) orientation could be particularly useful for the n-type doping with phosphorus which is still very limiting on (100) orientation and offer a good compromise between the (100) and (111) orientations for the elaboration of vertical power devices.

### CRediT authorship contribution statement

**R. Mesples-Carrère:** Writing – original draft, Software, Investigation, Conceptualization. **R. Issaoui:** Writing – review & editing, Validation, Supervision, Project administration, Funding acquisition, Conceptualization. **A. Valentin:** Writing – review & editing, Software.

**L. Banaigs:** Investigation. **O. Brinza:** Validation, Methodology. **F. Bénédic:** Writing – review & editing, Validation. **J. Achard:** Writing –
review & editing, Validation, Supervision, Investigation, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Data availability

Data will be made available on request.

Acknowledgments

This work benefited from State funding managed by the French National Research Agency (ANR) under the investment programme LAPIN113 (ANR-19-CE29-0017-04) and the investment programme for future Equipex e-Diamant (ANR-21-ESRE-0031). The SEM characterizations were mainly carried out by the Microscopy Department of the LSPM, and especially by M. Konstantakopoulou and F. Amendola.

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