Carrier recombination and diffusion in high-purity diamond after electron irradiation and annealing

The design of semiconductor devices requires the control of carrier-transport parameters, which is commonly accomplished by in situ doping. Electron irradiation (EI) is an alternative approach to optimizing the high-frequency response in an accurate cost-efficient way.¹ In this technique, vacancies (V) and interstitials (I) produced during the inelastic collisions of electrons with lattice atoms act as recombination centers. If a starting carrier lifetime is sufficiently long, a desired value is achieved by exposing the device to a well-calibrated dose of electrons at a chosen energy. Both V and I, however, can be relatively mobile at elevated temperatures, leading to the formation of secondary clusters or complexes with other impurities. In Si, for example, the evolution of divacancy-related defects during annealing remains an active research topic, despite decades of investigation.^2,3

The study of EI-created defects in diamonds has its roots in high-energy particle detectors exposed to high irradiation doses. It has been found that the direct annihilation of the V–I pairs in this material has very low probability at <1900 °C, owing to the large energy barrier of the process⁴ and the different activation energies in their mobility.^5,6 In annealing, these defects migrate and form a variety of secondary defects, which show up in the visible absorption spectrum and have been used in the color treatment of diamond specimens.^7–9 In recent years, the evolution of the nitrogen-vacancy (NV) center has attracted significant interest for applications ranging from biolabeling to quantum computing, owing to its quantum optical properties.¹⁰ 

Despite extensive research, the effect of EI on the diamond lifetime and other transport parameters is virtually unknown, likely because the challenges of n-type doping have frustrated the development of commercially viable electronic devices. However, diamond has tremendous potential in photoconductive (PC) switching applications,¹¹ where bulk device structures are predicted to take full advantage of its excellent carrier mobility, breakdown electric field, and thermal conductivity. These applications capitalize on advances in the chemical vapor deposition (CVD) growth of thick homoepitaxial crystals, in which impurity levels can be reduced to several ppb. Lifetimes reaching several microseconds have been reported in high-purity CVD diamond,^12–14 affording a broad range in tailoring of this parameter.

In this work, we investigate the systematic transformation of carrier recombination and diffusion mechanisms using EI under well-defined low-irradiation doses. Carrier dynamics is studied using two pump–probe techniques and correlated with data from various spectroscopy methods. Our findings suggest that lifetimes in diamond can be altered predictably over many orders of magnitude. Annealing increases lifetimes, with the most significant difference observed at the highest temperature, 1450 °C. We show that the latter changes are related to the thermal diffusion and agglomeration of V defects, which still provide adequate control of photoconductive properties.

A set of six CVD-grown samples with dimensions of 2 × 2 × 0.5 mm³ was purchased from Element Six. All samples were assigned by the supplier to the electronic grade specified as containing <5 ppb of nitrogen (N) and <1 ppb of boron (B).¹⁵ The N content in the samples measured by secondary-ion mass spectroscopy showed levels at or below the detection limit of 10¹⁴ cm⁻³. A negligible concentration of other impurities was corroborated by various spectroscopy measurements. Sample irradiation was carried out using a linear electron accelerator with an electron flux in the range of (1–2.5) × 10¹² cm⁻² s⁻¹. The total dose Φ in each of the six samples was evenly distributed in the range of 2 × 10¹²–10¹⁶ cm⁻². A Faraday cup was used for dose calibration. To provide uniform distribution of the irradiation-created defects across the 0.5 mm thickness of the samples, 6 MeV energy electrons were chosen, having been shown to have a mean propagation path of 8 mm along the [100] crystallographic axes in diamond.¹⁶ 

After irradiation, samples were exposed to four annealing temperatures, T, chosen according to the following considerations: (1) at 600 °C, I mobility is fully inhibited;^4–6 (2) at 900 °C, the early signs of V thermal diffusion are detected; (3) at 1000 °C, most of the features related to the single V⁰ defects are suppressed;^17,18 and (4) at 1450 °C, complexes and aggregates related to the original V defects are shown to form stable structures.^19–21 Annealing at each temperature was performed for 1 h using the procedure described in Ref. 22. After each annealing step, samples were etched in a chromic acid solution for 30 s to remove graphitization and other possible contamination from sample surfaces before characterization. All annealing was done in an Ar atmosphere except at 1450 °C, which was performed in a vacuum.

First, the lifetime was investigated using the pump–probe technique based on the free carrier absorption (FCA) principle.^12,14 This approach allows an electronically controlled delay between the pump and the probe, which is advantageous in detecting relatively slow lifetimes in EI diamond. Carriers were excited using 10 ps duration pulses with an energy density of 50 mJ/cm² at 353 nm. According to the two-photon absorption (TPA) coefficient of 0.2 cm/GW reported for this wavelength,²³ the pulses were sufficient to generate an average carrier concentration of ΔN₀ = 4 × 10¹⁶ cm⁻³ across a sample. Lifetimes extracted from the measured FCA decays are summarized in Fig. 1 for different Φ and T values. Before annealing, a decrease in the lifetime becomes apparent at Φ ∼5 × 10¹³ cm⁻², and the reduction reaches two orders of magnitude at Φ = 10¹⁶ cm⁻². Note that the 300 °C data are almost overlaid by the 600 °C data. Under following annealing, gradual recovery of the lifetime is observed.

It has been demonstrated^3,24,25 that lifetime dependence vs Φ in EI semiconductors can be described using the following expression:

where τ₀ is the lifetime in the unirradiated material, s is the power parameter, and K_τ is the lifetime radiation damage coefficient. Data fit using Eq. (1) is shown in Fig. 1 by solid lines, and corresponding parameters are presented in Table I. Before annealing, the s = 1 slope, i.e., linear dependence, typical for EI semiconductors is observed, and the extracted K_τ is comparable to those reported for bulk Si and Ge.^25,26 Under initial annealing, the s = 1 slope is maintained, but abruptly reduced to s = 0.7 at 1450 °C.

Next, carrier dynamics were investigated using the transient grating (TG) technique, based on the spatial modulation of excited carriers.¹⁴ Excitation conditions were the same as in FCA measurements, except that the pump was split into two equal beams to produce an interference pattern for carrier generation. The main advantage of this technique is simultaneous extraction of lifetime τ and the diffusion coefficient D from the TG decay time, τ_G, according to the relation,

where Λ is the spatial period of the modulated fringes. TG decays are obtained by measuring the first-order diffraction efficiency (DE) of the probe at different Λ values, according to

where n_eh is the proportionality factor related to a single electron–hole pair, d is the effective absorption depth, λ is the excitation wavelength, and ΔN₀ is the initial concentration of excited carriers.

At t = 0, DE (labeled as DE₀) is also directly proportional to (ΔN₀)², providing insight into the carrier-generation mechanisms. Figure 2(a) shows DE₀ measurements vs excitation density in samples with different Φ values. In the unirradiated sample (black symbols), the dependence with the power of p = 4 is revealed on the log –log plot (solid line) over the whole excitation range, as expected for the TPA-generation process. In the irradiated samples, an additional DE₀ component with a p = 2 slope emerges at lower excitations, indicating the presence of monopolar carrier generation. The square root of the new component's amplitude, which is proportional to ΔN₀, according to Eq. (3), has the linear dependence on Φ, as shown in the inset of Fig. 2(a). This suggests that monopolar generation is related to an extrinsic carrier-generation mechanism originating from an EI-induced defect. Under annealing, the p = 2 component is suppressed, as shown in Fig. 2(b), but the amplitude decrease is not monotonic with annealing temperature, as shown in the inset. Moreover, at 1450 °C, the decrease is reversed and correlates with the transition into the sublinear p = 1 excitation dependence, shown as a dashed line in Fig. 2(b). Annealing results are demonstrated using the Φ = 5 × 10¹⁵ cm⁻² sample, chosen because it exhibits the largest ambient lifetime in this sample. The same sample is used as the example in the rest of the text.

Lifetimes τ and diffusion coefficients D were extracted at excitations covering both the TPA and the monopolar generation. Lifetime results for the four samples with the highest irradiation dose are shown in Fig. 2(c). In the p = 4 generation range, the TG results agree well with the FCA data reproduced from Fig. 1. In the p = 2 generation range, TG data reveal a drop in lifetimes by almost two orders of magnitude. The solid curves are guidelines to suggest an s-shape dependency, which is preserved between different samples but shifts to lower lifetimes with increasing irradiation. The result contrasts starkly with the dependency in non-irradiated high-quality diamond (dashed gray area), where the lifetime decrease is observed at high excitations and attributed to excitonic effects.^14,27

Under annealing at up to 1000 °C, TG-detected lifetimes became longer in a manner consistent with Fig. 1, while maintaining s-shape dependency as illustrated in Fig. 2(d). Under subsequent annealing to 1450 °C, the transition into fast lifetimes at low excitations has vanished. To confirm this finding, lifetimes in all irradiated samples were remeasured using the FCA technique, which is better suited for tracking slow-decay components. The result is summarized in Fig. 2(d) by the solid symbols, confirming longer excitation-independent lifetimes.

Diffusion coefficients for the four samples with the highest irradiation values are shown in Fig. 2(e). In the p = 4 range, the D coefficients agree well with the trend in the non-irradiated diamond (gray curve), where the gradual decrease at large excitations is explained by the same excitonic effects.¹⁴ In the p = 2 range, the coefficients reveal a significant reduction, with the measured values approaching zero at the highest Φ value. Under annealing, reduction prevailed with small shape variations at different temperatures, as shown in Fig. 2(f).

Photoluminescence (PL) measurements at 77 K were used to track defects responsible for the observed carrier transport changes. The main findings are summarized in Fig. 3(a), which shows the only prominent peak at 741.15 nm, detected in the as-irradiated sample. This peak has been identified as the zero-phonon line (ZPL) of the neutral state V⁰, commonly referred to as the GR1 intrinsic line.^7,17,18,28 The width of the GR1 peak of 0.8 ± 0.1 meV is smaller than the 1.3–7.5 meV range reported for IIa diamonds under high irradiation doses.^6,28–30 This indicates that V⁰ can be treated as a point defect unaffected by inhomogeneous stress of the surrounding crystal lattice. Under annealing, the V⁰ peak continued to dominate in the PL spectrum up to 1000 °C. At that point, the V⁰ peak lost strength considerably and became accompanied by the ZPL of the divacancy V₂ line at 733.1 nm and its phonon satellite at 738 nm.¹⁸ At 1450 °C, both V⁰ and V₂ lines disappeared and were replaced by a doublet at 736.6/736.9 nm, identified as the SiV complex.^7,18 Several additional observations were made beyond the spectral range shown in Fig. 3(a): the carbon di-interstitial line TR12 at 470.1 nm (Refs. 5, 7, and 28) emerged at 600 °C, but disappeared afterward; and the ZPL of the NV⁰ center at 575 nm appeared above 900 °C and peaked in intensity at 1000 °C.

PL measurements suggest that V⁰ is the most likely defect to explain carrier recombination changes in an as-irradiated diamond. It dominates the PL spectrum, and its peak strength increases linearly with Φ, as shown in the inset of Fig. 3(a), in agreement with the linear lifetime decrease in Fig. 1. Moreover, the amphoteric nature of the vacancy can explain the carrier lifetime decrease at low excitations. Both 0/− and 0/+ charge transitions are possible from the V⁰ state within the diamond bandgap.³¹ However, only the 0/− level at ∼2 eV above the valence band is directly accessible using the pump–probe photons of 3.53 eV. This extrinsic optical transition produces free holes that remain bound to a negative vacancy V⁻, owing to the Coulomb attraction. Carrier localization leads to enhanced hole recombination and shorter lifetimes. Under higher excitations, on the other hand, free carriers of both types are generated by the TPA process. Recombination in this case involves both 0/− and 0/+ transitions and must follow charge-conservation equations.³² Much longer lifetimes may be observed in this case if capture cross sections of the 0/− and 0/+ transitions are substantially different. In addition, the free-hole localization is consistent with observed diffusivity loss at low excitations.

Extrinsic carrier generation at low excitations through the excited V⁰ states is also supported by optical-absorption measurements. Figure 3(b) shows the room-temperature spectrum of the as-irradiated sample (red curve) where the intrinsic ZPL of V⁰ at 1.673 eV is overtaken by the phonon-assisted transitions forming an absorption band at ∼2 eV.⁵ The band is followed by an absorption shoulder at higher energies. The inset of Fig. 3(b) shows that both the 2 eV band and the shoulder at the pump energy of 3.53 eV increased linearly with Φ, in agreement with the monopolar DE₀ component in Fig. 2(a). This points to the similar origin of all phenomena.

The absorption spectrum also allowed the extraction of the V⁰ concentration using the previously calibrated expression N_V0 = (α_2.0 eV/1.71) × 10¹⁷ cm⁻³, where α_2.0eV corresponds to the absorption coefficient at the peak of the 2 eV band.³³ For the Φ = 5 × 10¹⁵ cm⁻² sample, N_V0 = 1.2 × 10¹⁶ cm⁻³ is obtained yielding the production rate N_V0 (cm⁻³)/Φ(cm⁻²) = 2.4 cm⁻¹, which is close to the theoretical estimate of 2.85 cm⁻¹ for 5 MeV electrons¹⁶ and the experimental value of 2.15 cm⁻¹ for 2 MeV electrons.²⁸ Assuming that V⁰ acts as a single recombination center, the capture cross section of the defect, σ_V, was estimated from 1/τ = v_thσ_VN_V0, where v_th = 2× 10⁷ cm/s is the thermal carrier velocity. Using the τ = 6.8 ns value from Fig. 1, we obtained σ_V = 6.3 × 10⁻¹⁶cm², which is higher than the σ_N = 1 × 10⁻¹⁶cm² value reported for the neutral nitrogen center N⁰.¹⁴ This indicates that V⁰ is an effective lifetime killer.

Under annealing, recombination through other evolving defects must be considered. Visualizing the correlation between carrier recombination and the observed PL, Fig. 3(c), displays the recombination rate 1/τ taken from the data in Fig. 1 and compares it with the normalized highest PL intensity in Fig. 3(d) at the same temperature. Due to the negligible 1/τ change at 600 °C, the role of interstitials and their complexes can be disregarded. In the range of 900–1000 °C, the divacancy V₂ takes over the recombination process, as the significant loss of V⁰ in this range is not accompanied by an equivalent 1/τ drop. Like the monovacancy V, the divacancy V₂ is an amphoteric defect with 0/− charge transition levels showing up at very similar energies.³¹ This explains the small changes in carrier recombination and diffusion excitation dependencies despite the defect transformation. The explanation for decreasing DE₀ amplitude is less obvious, but most likely related to a weakness in the absorption cross section of the divacancy.

Figure 3(d) shows that at 1450 °C, SiV becomes the main compensating factor for the V₂ loss, as 1/τ in Fig. 3(c) remains relatively unchanged compared to 1000 °C. This assumption, however, is contradicted by the Φ-dependence of this defect, as shown in Fig. 3(e). The dominant recombination center is expected to have a linear increase in amplitude like that of the V₂ trace emerging at high Φ. The SiV shape, in contrast, appears saturated after emerging at moderate Φ. The other detected defect, NV⁰, is even a less likely candidate as its concentration is already decreasing at 1450 °C as shown in Fig. 3(d). The latter defect also had an unsystematic Φ-dependence as shown in Fig. 3(e).

We propose that all changes at 1450 °C are related to the formation of V multi-clusters. These defects are not detectable by PL measurements but produce the “brown” coloration in natural high-quality diamonds. The main characteristic of this coloration is the featureless absorption spectrum above 1.5 eV caused by the gradually ramping transitions into empty defect states above the Fermi level.¹⁹ Figure 3(b) shows that exactly this type of spectrum develops at 1450 °C, in contrast to the 600 °C and 1000 °C spectra, which are just smaller-amplitude replicas of the spectrum before annealing. While the exact configuration of multivacancy defects is still under debate, their presence is clearly revealed by reports of positron-annihilation spectroscopy.^20,21 The unusual s = 0.7 power parameter in Fig. 1 and the sublinear p = 1 excitation dependence in Fig. 2(b) hint to a defect with a complicated internal structure. To demonstrate that these agglomerates can, nevertheless, act as adequate recombination centers in PC devices, we measured the steady-state PC in all samples, using lateral surface contacts and a 220 nm illumination source. The open symbols in Fig. 1 confirm that the PC response follows the 1450 °C lifetime data. This confirms that free carriers generated through an intrinsic band-to-band absorption process recombine predominantly through the irradiation- and annealing-created defect.

In summary, we measured carrier recombination and diffusion in high-purity CVD diamond irradiated with 6 MeV electrons in the dose range up to 10¹⁶ cm⁻². Immediately after irradiation, carrier lifetimes reaching a few nanoseconds were demonstrated in the case of bipolar carrier generation. The neutral monovacancy was revealed as the most likely recombination center, with a quite large capture cross section of σ_V = 6.3 × 10⁻¹⁶cm². Under annealing, lifetimes gradually increased and achieved excitation-independent behavior at 1450 °C. We attribute these changes to thermal diffusion and aggregation of V into the V-clusters. The fitness of the latter defects for use in tailoring the properties of switching devices was demonstrated using PC measurements.

The authors thank V. Kazuchits for the steady-state PC measurements. This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and was supported by the LLNL-LDRD Program under Project No. 17-ERD-050 (No. LLNL-JRNL-813961).