MODELING C-BN GROWTH WITH HIGH ION ENERGIES 115 It has to be noted that the existence of a high energy threshold, above which

c-BN nucleation is no longer possible, is very likely. However, further investigations regarding this matter are very difficult. As already observed by Feldermann [Fel02], the thickness of the t-BN interlayer increases with increasing ion energy, which would thus require the growth of very thick films in order to possibly detect c-BN within the sample. Figure 4.12 displays the FTIR spectra of three BN films that have been deposited with 2, 3, and 5 keV, respectively, on silicon substrates at a temperature of 250^◦C. The total deposited charge for each film wasQ= 1.3−1.4 C,

600 800 1000 1200 1400 1600

Wavenumber [cm^-1]

IR Absorption [a.u.] _{3 keV}

2 keV 5 keV

1073 cm^-1

Figure 4.12: FTIR spectra of BN films, directly deposited on silicon substrates with Eion ≥ 2 keV.

which resulted in film thicknesses of 1.2–1.6 µm, as measured using profilometry.

For the sample deposited with E_ion = 2 keV, the cubic phase content calculates to about 50%, but a further increase of the ion energy leads to a drastic decrease of sp³-bonds until eventually only t-BN films are obtained. As the use of higher temperatures is required to form c-BN with increasing ion energy, the failure to nucleate c-BN with an energy of 5 keV might also be related to an insufficiently high substrate temperature. However, in the view of the cylindrical thermal model, c-BN formation is related to the number of rearrangements in a thermal spike. Since this number strongly decreases for energy above about 3 keV, the effective c-BN growth regime is possibly limited to ion energies below 3 keV.

When depositing a BN film, ion impact on the silicon substrate initially leads to the formation of an unordered, sp²-bonded phase. If the ion energy is within the limits required to nucleate c-BN (i.e. 125 eV < E_ion < 2 keV), the incident ion beam would be capable of inducing sufficient compressive stress in the film to orient the t-BN planes perpendicular to the substrate surface. Yet, this effect is suppressed for temperatures below a specific, energy dependent value T_C, and the result would be a sample exhibiting an IR absorption spectrum as shown in figure 4.11a. This might also be due to accumulation of defects created by the impinging ions.

In the considered energy range between 125 eV and 2 keV, the range of ¹¹B⁺ and

14N⁺ ions in t-BN is in the order of a few nanometers. The distance x between the mean ion range and the maximum of the vacancy distribution is similar to the c-BN case, i.e. xc−BN(E) = xt−BN(E) = x(E). Since the ion flux for MSIB deposited films is almost constant, the diffusion time can be set to t = 0.1 s as well. To fill a formerly created vacancy (or move to the surface in the early stage of deposition) and avoid defect accumulation, an interstitial atom is again required to diffuse the distance x(E) within the time t = 0.1 s. If one assumes a random walk as diffusion mechanism as well, the diffusion constant D0 for t-BN is then given by equation (4.9). Orellana and Chacham [Ore01] investigated the ion beam induced formation of defects in boron nitride, and they stated that an interstitial boron atom in hexagonal BN is most likely to be found at an interlayer position forming metalliclike bonds with B atoms of adjacent layers. Assuming an interstitial atom resides between the basal planes and moves perpendicular to the c-axis (figure 4.13), the jump length can be estimated to a = 2.9 ˚A (assuming a distance a₀ = 1.45 ˚A between two atoms in a t-BN hexagon), which results in a diffusion constant of D₀ ≈ 1.2×10⁻² cm²/s. c-BN nucleation at a substrate temperature of T_S = 150^◦C is observed when using an ion energy of 500 eV, but not atE_ion = 800 eV (see figure 4.11). Therefore, the corresponding ion energy for a critical temperature of 150^◦C is between 500 and 800 eV, and the ion range at those energies as calculated by SRIM is about x ≈ 1.3 nm. Using equation (4.9), this results in a migration energy of W_m ≈ 0.9 eV, which is in good agreement with the reports by Albe [Alb98]. In a theoretical study, he calculated the migration energies for boron and nitrogen diffusion in h-BN and obtained a value of about 1-2 eV. This value is significantly larger than the calculated migration energy for c-BN, which would

4.6 SUMMARY 117

[0001]

a₀=1.45 Å

Figure 4.13: Schematic diagram of a simple random walk diffusion in h-BN, assuming an inter-stitial atom resides between the basal planes and moves perpendicular to the c-axis.

probably explain the need for a higher temperature for c-BN nucleation as compared to growth. If the substrate temperature is high enough, diffusion processes can be effective in annealing radiation damage. This is also in conformity with the findings by McCarty et al.. The temperature-driven diffusion of defects located between the t-BN basal planes would allow a compression of the t-BN lattice until eventually a 2:3 matching to the c-BN (111) planes is reached.

4.6 Summary

An energy-temperature dependence for c-BN nucleation has been found that ex-hibits features similar to c-BN growth. The previously assumed independence of ion energy and substrate temperature thresholds has been disproved; instead, the temperature has to be increased for increasing energies in order to nucleate the cubic phase. The simple diffusion model developed for c-BN growth at high ion energies has been applied to c-BN nucleation as well, and a diffusion constant and migration energy for self-diffusion in t-BN have been estimated to D₀ ≈ 1×10⁻² cm²/s and W_m ≈ 0.9 eV, respectively. As these values are significantly larger than for c-BN, a higher temperature at a given ion energy is required in order to nucleate c-BN as compared to its subsequent growth. Temperature-induced diffusion processes are seen responsible for annealing of radiation damage, avoiding defect accumulation

Figure 4.14: Phase diagram for BN films deposited via MSIBD, plotted as log₁₀(E) vs. 1/T. c-BN nucleation is only possible in a narrow energy window ranging from 125 eV to about 2 keV.

For higher ion energies the temperature has to be increased slightly in order to nucleate the cubic phase. c-BN growth on the other hand is possible for a wider range of both substrate temperature and ion energy. The low energy threshold is atEion≈60 eV. For ion energies up to about 5 keV, TS ≈RT is sufficient to grow c-BN, but for higher energies the temperature has to be increased according to equation (4.9).

and providing the boundary conditions required to nucleate the cubic phase.

With the available data it is now possible to extend the phase diagram for MISB deposited BN films (figure 3.1.1), and the revised diagram is shown in figure 4.14.

Nucleation of c-BN is possible only within a narrow energy window ranging from 125 eV to about 2 keV. Increasing the ion energy requires a slight increase in substrate temperature as well; the respective dependence has been estimated from the obtained values forW_m andD₀ for t-BN. Cubic BN growth, on the other hand, can be maintained for a broader range of ion energies and substrate temperatures.

The low energy threshold is around 60 eV, and up to an energy of about 3–5 keV the growth process seems to be relatively temperature-independent. For energies

4.6 SUMMARY 119