Silicon (Si) is one of the most popular semiconductors and is used extensively in the fields of energy, photoelectronic imaging, and remote sensing owing to its abundant reserves, low cost, and compatibility with standard complementary metal-oxide-semiconductor (CMOS) technology^[1–3]. To meet current needs, crystalline Si with high absorption coefficients across a broad range of wavelengths and subbandgap photon sensitivity is required, which can potentially fulfill the rising demand for higher photovoltaic conversion efficiency in solar cells, as well as elevated photoelectric conversion efficiency in photodetectors. In order to realize this, promising methods such as pulsed laser irradiation and ion implantation have been applied to achieve hyperdoping of impurities far beyond the solubility limit of a semiconductor and enhance its spectral responsivity over a wide spectral range^[4]. During ion implantation, the introduction of high-energy particles will inevitably result in the formation of a large number of lattice defects. Consequently, pulsed laser melting is always employed as a means of restoring the induced defects^[5]. Furthermore, black Si (b-Si) processed using ultrafast laser irradiation has emerged as a compelling all-Si material owing to its microstructured and hyperdoped surface. As a result, b-Si demonstrates exceptional optical and electronic properties^[6–9], making it a promising material for applications in Si photonics and Si optoelectronics^[10,11].

Ultrafast laser irradiation can induce surface microstructures and hyperdoping of impurities, leading to an antireflection effect and the formation of intermediate levels in Si, which enhance broadband spectral absorption. Among them, chalcogen and transition metals are the commonly used dopants^[12–15]. However, the high electroactivity of chalcogens in Si always results in a high concentration of free carriers, which has a limited contribution to the subbandgap photoelectric conversion and even leads to a high noise current^[16,17]. Additionally, the thermal instability of chalcogens in b-Si results in reduction of the subbandgap absorption after indispensable thermal annealing, which further compromises device performance^[18]. Conversely, transition metals have gained significant attention as dopants for Si owing to their low electroactivity, deep-level impurity property, and high thermal stability in Si^[15,16]. As a stable transition metal dopant, Ti has a donor energy level of 0.34 eV above the valence band maximum of Si^[19], making it a promising deep-level impurity beneficial for optoelectronic applications^[20]. However, simulation studies on the properties of Ti-hyperdoped Si are particularly scarce, and systematic research on the comprehensive performance of Ti-hyperdoped b-Si remains rather limited^[21].

In this Letter, density functional theory (DFT) was employed to investigate the electronic and optical properties of Ti-hyperdoped Si. The simulated results indicated that interstitial Ti with low formation energy could introduce a broad intermediate band within the bandgap of Si, which probably resulted in the observed stable subbandgap absorption. According to the simulated results, Ti-hyperdoped black silicon (b-Si:Ti) was experimentally fabricated through Ti film deposition followed by femtosecond laser irradiation. The fabricated b-Si:Ti samples exhibited broad spectral absorption ranging from visible to infrared wavelengths (400–2500 nm). Additionally, it also offered stable subbandgap absorption after undergoing an optimized rapid thermal annealing (RTA) process to improve the lattice quality. Based on the advantages of high absorption over a broadband spectrum and good thermal stability, this enhancement demonstrates an effective hyperdoping of Ti in Si. The experimental findings align well with the simulated results, providing insight into the underlying physical mechanisms of Ti-hyperdoped Si and thus promoting the future application of b-Si:Ti in Si photonics.

The hyperdoping of Ti can introduce intermediate levels in the bandgap, resulting in distinctive electrical and optical properties. In order to verify the band structure and optical properties of Ti-hyperdoped Si, DFT computations were performed using the VASP 5.4.4 simulation package by employing the projector augmented wave (PAW) method. The exchange-correlation potential was determined using the HSE06 hybrid functional to align the simulated results with the experimental findings. This provided more accurate results for the band structure by minimizing the bandgap underestimation effect associated with DFT, in comparison to the generalized gradient approximation (GGA) calculations^[22,23]. The cutoff energy for the plane-wave basis was set at 500 eV. The atomic coordinates were relaxed with a convergence criterion of force on each atom smaller than 0.005 eV/Å. The energy convergence threshold was 10−5eV/atom. The samplings of the irreducible Brillouin zone were conducted using Γ-centered 3×3×3 grids. The hyperdoped models with different positions of Ti were created based on a 2×2×2 supercell structure of the conventional Si8 cubic unit cell. Substitutional Ti (TiSiSi63) models in which the host Si atoms are replaced by Ti atoms and interstitial Ti (TiiSi64) models in which foreign Ti atoms occupy the interstitial sites were established, with a high doping concentration of 1.56%. Additionally, a structure of undoped crystal Si (Si64) was also simulated and investigated for comparison. The atomic configurations for Si64, TiSiSi63, and TiiSi64 are shown in Figs. 1(a)–1(c), respectively.

The electronic band structures of the materials with relaxed structures were determined following the self-consistent-field calculations and are also presented in Fig. 1. Specifically, the Si64 structure exhibited an indirect bandgap property with a bandgap of 1.20 eV, as illustrated in Fig. 1(d). This closely aligned with the actual band structure and absorption characteristics of crystalline Si.

It can be seen in Fig. 1(e) that the energy difference between the valence band maximum (VBM) and the conduction band minimum (CBM) for the TiSiSi63 compound increased to 1.44 eV upon substitution of an Si atom by a Ti atom, which was slightly higher than 1.20 eV that was observed for Si64. Furthermore, the substitution by Ti atoms can form an intermediate band within the bandgap of TiSiSi63. The intermediate band has a bandwidth of 0.52 eV, with its lowest energy level being 0.23 eV lower than the CBM, indicating an overlap with the conduction band. Consequently, the bandgap of the TiSiSi63 compound was 1.21 eV separated by the valence band and the intermediate band. The intermediate band originated from the eg doublet, resulting from the crystal field splitting of the Ti 3d electrons imposed by the tetrahedral environment. The high energy t2g triplet state was strongly hybridized with the conduction band alongside the eg doublet state^[24], which led to band structure distortion, thereby increasing the width of the bandgap. At lower doping concentrations, narrowing and separation of the intermediate band from the conduction band may be achieved. It is worth noting that the bandgap of TiSiSi63 was found to be almost identical to that of Si64, which pointed towards a minimal contribution of the substitutional Ti to the subbandgap absorption.

The six second-nearest Si atoms can form an octahedral crystal field upon implantation of an interstitial Ti atom at the geometric center of a tetrahedral structure formed by four host Si atoms. This field can then split the 3d levels into a low-energy t2g triplet state and a high-energy eg doublet state^[25]. The octahedral crystal field may have a greater impact compared to the tetrahedral crystal field from the four nearest Si atoms^[26]. Consequently, the electronic and energy band structures of the TiiSi64 compound differ significantly and become more complex compared to that of the TiSiSi63 structure. The band structure of the relaxed TiiSi64 compound exhibited an energy difference of 1.52 eV between the VBM and the CBM, as shown in Fig. 1(f). The increase in the bandgap was attributed to the addition of interstitial Ti atoms, which can exert pressure and distort the crystal structure. Furthermore, the t2g triplet and eg doublet states formed intermediate bands within the bandgap of the TiiSi64 compound. The minimum of the intermediate band was 0.38 eV higher than the VBM, indicating a deep-level characteristic. Consequently, subbandgap absorption can be enhanced significantly, highlighting the crucial role of hyperdoping interstitial Ti atoms in the enhancement of the subbandgap absorption.

The band structures showed that implanting Ti atoms can form intermediate bands or broaden the conduction band, which indicated its potential to broaden the spectral absorption range. To analyze the optical behavior of Ti-hyperdoped Si, the absorption coefficients for Si64, TiSiSi63, and TiiSi64 obtained from the dielectric function were closely examined, the results of which are presented in Fig. 2. The absorption characteristics of bulk Si64, as derived from the calculated absorption spectrum, align with previous experimental results, except for discrepancies arising from indirect transitions. After Ti hyperdoping, an enhancement in the absorption coefficients of TiSiSi63 and TiiSi64 was achieved over a broader spectral range. In particular, TiSiSi63 exhibited an enhanced absorption coefficient with an absorption peak centered around 2.5 eV due to hybridization of the impurity energy band with the conduction band, resulting in the availability of additional electronic states. Nevertheless, the substitutional Ti atom provided a limited contribution to the subbandgap absorption, which is consistent with the band structure results. In contrast, the TiiSi64 compound exhibited an enhanced absorption coefficient with an extended spectral absorption range. The absorption band edge was broadened to less than 0.5 eV. The deep impurity bands formed by the interstitial Ti atoms facilitated the transition of the subbandgap photons from the valence band to the intermediate band and from the intermediate band to the conduction band. This is critical for the transition and absorption of subbandgap photons.

Finally, the formation energies (Ef) for two kinds of Ti implantations were estimated from the total energies and were defined as Ef[TiSiSi63]=E[TiSiSi63]−6364E[Si64]−13E[Ti3]=2.14eV,(1)Ef[TiiSi64]=E[TiiSi64]−E[Si64]−13E[Ti3]=1.80eV,(2)where E[Si64], E[TiSiSi63], E[TiiSi64], and E[Ti3] refer to the total energies of Si64, TiSiSi63, TiiSi64, and crystalline Ti, respectively. The formation energies of TiSiSi63 and TiiSi64 were calculated to be 2.14 and 1.80 eV, respectively. These values corresponded to the energy consumption required for the formation of a substitutional and an interstitial Ti atom. The formation energy of TiiSi64 was significantly lower (0.34 eV) compared to the TiSiSi63 compound. Therefore, interstitial Ti atoms can be incorporated more readily into the Si lattice with a higher concentration, forming a stable structure than the substitutional Ti atoms.

The simulated results showed that interstitial Ti atoms can be used to extend the spectral absorption of Si, while also offering low formation energy, thus making it a stable dopant state. Therefore, Ti can be considered an excellent dopant for the hyperdoping of Si owing to its potential to extend the absorption range into the subbandgap region with good thermal stability. Following the simulated results, the experimental fabrication of b-Si:Ti was achieved using femtosecond laser irradiation after the Ti film deposition process.

In the experiment, the n-type monocrystalline Si substrate ⟨100⟩ with a resistivity of around 3000–5000 Ω·cm and a thickness of 410 µm was first cleaned using the standard RCA process. Thereafter, a Ti film with a thickness of about 50 nm was sputtered onto it via thermal resistance evaporation. Subsequently, the b-Si:Ti samples were prepared in an inert Ar environment at a pressure of 0.1 MPa using a regeneratively amplified Ti: sapphire femtosecond laser that delivered 120-fs pulses at a wavelength of 800 nm with a 1 kHz repetition frequency. The scanning speed of the laser was set to 1 mm/s, with a scanning line spacing of 50 µm. The average fluence of the laser was adjusted continuously using a combination of a half-wave plate and a Glan–Taylor polarizer. The laser pulses were focused onto the surface of the Ti-covered Si substrates using a converging lens with a focal length of 50 cm, thereby achieving an average beam diameter of 100 µm. An RTA process was then applied at different temperatures for 10 min to repair the laser-induced lattice defects and evaluate the thermal stability of the hyperdoped Ti atoms in Si.

The absorption spectra of b-Si:Ti were measured in a range of 400–2500 nm by employing a Hitachi U-4100 UV-VIS-NIR spectrophotometer equipped with an integrating sphere detector. The absorptance (A) values were derived from the directly measured plots of diffuse reflectance (R) and transmittance (T) and are mathematically related as A=1−R−T. The obtained results are exhibited and compared in Fig. 3. A detailed analysis of the results revealed that the absorptance characteristics of the prepared b-Si-Ti samples were affected by different mechanisms within the in-bandgap and subbandgap region. The enhancement of the in-bandgap absorption primarily depends on the light-trapping effect from the surface microstructures, which enables the incident photons to reflect and absorb multiple times on the surface of the b-Si:Ti samples, thereby increasing their absorptance. Meanwhile, the increase in subbandgap absorptance can be attributed to a combination of the surface microstructures and the impurity-assisted photon transition. The impurity levels formed by the Ti hyperdoping facilitate the transition of subbandgap photons, and surface microstructures promote and enhance this process further.

The absorption curves for b-Si:Ti measured at different laser fluences are shown in Fig. 3(a), and all the samples have been processed using RTA treatment at a temperature of 600°C. It was revealed that all the b-Si:Ti samples exhibited a significant enhancement in their absorption properties throughout the entire measured spectral range in comparison to the Si substrate. Specifically, the in-bandgap (400–1100 nm) absorptance was enhanced distinctly with an increase in the laser fluence. On the other hand, the absorptance remained quite competitive in the subbandgap range (1100–2500 nm) for fluence values lower than 1.2kJ/m2, but then dropped sharply as the fluence was increased to 2.5kJ/m2. However, the absorption in the subbandgap range rose again as the laser fluence was increased further. Although a stronger laser influence can induce larger-sized surface microstructures, it also results in stronger ablation effects and explosions on the surface concurrently, removing the surface of the deposited Ti, and thus lowering its doping concentration. This may lead to a decrease in the subbandgap absorption as the laser fluence is increased initially. However, the high-intensity light trapping effect at higher laser fluences can lead to enhanced subbandgap absorption again.

The absorption spectra of b-Si:Ti under different RTA temperatures at a laser fluence of 1.2kJ/m2 are provided in Fig. 3(b). The change in absorption at 1550 nm with temperature is demonstrated by the plot provided in the inset of the figure. The in-bandgap absorption surpassed 80% and then remained constant after thermal treatment, which confirmed that the in-bandgap absorption was due to the thermally insensitive surface microstructures. The absorption of the b-Si:Ti sample in the subbandgap range decreased from nearly 60% to about 45% after an RTA treatment at 500°C. However, raising the temperature further hardly affected the subbandgap absorption. The b-Si:Ti sample demonstrated significant absorption even after undergoing a 10-min high-temperature RTA treatment, which indicated higher thermal stability of Ti in Si compared to chalcogens^[27]. Based on the simulation results, the interstitial Ti atoms exhibited a low formation energy and deep-level impurity properties in Si. These factors played a crucial role in achieving the stable subbandgap absorption in b-Si:Ti that was experimentally observed.

The spectral absorption of b-Si is directly influenced by the morphology of the irradiated microstructures. In general, femtosecond laser irradiation forms ripple structures during the initial evolutionary process of the laser–material interaction, after which the droplets and the cones start to appear, with the size and the periods of the microstructures determined by laser-induced periodic surface structures. Therefore, the microstructures formed at the surface of b-Si:Ti were characterized using a field-emission scanning electron microscope (FE-SEM). The results and their corresponding high-magnification images at a rotation angle of 45° are presented in Fig. 4.

Micro-droplets with heights and spacings of about 1–2 µm began to appear with ripple structures beneath them at a low laser fluence of 1.2kJ/m2, as shown in Fig. 4(a). The incident laser was focused by the surface microstructures with an increase in the laser fluence and then was concentrated at the valleys of the micro-droplets, thereby removing the sides of the droplets. This resulted in larger surface microstructures, which in turn facilitated the concentration of the incident laser beam, thus accelerating the material removal process. Therefore, with an increase in the incident laser fluence to a value of 2.5kJ/m2, the size of the surface micro-droplets increased to about 3 µm and the ripple structures disappeared simultaneously, as shown in Fig. 4(b). As the laser fluences were increased further, the surface micro-droplets evolved into conical structures as a result of the violent ablation and removal of the materials. For laser fluences of 4.5 and 6.8kJ/m2, the size and period of the microstructures further increased to more than 5 µm, as shown in Figs. 4(c) and 4(d), respectively. The evolution of microstructures can be seen more clearly in the single microcone images provided in Figs. 4(e)–4(h).

Femtosecond laser irradiation enables the formation of surface microstructures and hyperdoping of the Ti element. The maximum concentration of Ti in b-Si:Ti, as measured by secondary ion mass spectrometry (SIMS) reached as high as 2.17×1020 for a laser fluence of 1.2kJ/m2. This was the origin of subbandgap absorption, and the density was in close agreement with the simulated model. Nevertheless, violent interaction between the laser pulses and the material can lead to a high density of lattice defects, restricting the performance of b-Si:Ti and devices based on it. In this circumstance, a suitable thermal annealing treatment becomes essential to promote lattice relaxation, reduce interfacial defects, and enhance the lattice quality of b-Si:Ti. Therefore, Raman spectroscopy measurements were performed using a Renishaw inVia instrument with an Ar-ion laser operating at a wavelength of 514 nm to analyze the effect of laser fluence and RTA treatment on the b-Si:Ti samples. The results are presented in Fig. 5.

The Raman spectra for the b-Si:Ti samples prepared by irradiation under different laser fluences are presented in Fig. 5(a). The prominent Si-I peak near 520cm−1 and the broadband peak near 300cm−1 were observed in all samples, which indicated a high degree of crystallinity^[28]. Following the femtosecond laser irradiation process, broadband peaks around 475cm−1 and broadened peaks near 300cm−1 were observed, which were ascribed to the amorphization of crystalline Si as well as lattice damages induced by the ultrafast ablation and the resolidification process. Additionally, an increase in the incident laser fluence led to an increase in the amorphous phase (α−Si) peaks near 475cm−1 and a significant enhancement of the peak near 300cm−1. Concurrently, the peak position of Si-I redshifted from 517.92 to 516.02cm−1, and the full width at half-maximum (FWHM) broadened from 8.36 to 10.42cm−1 as the laser fluence was increased from 1.2 to 6.8kJ/m2, which were also related to deterioration in the lattice quality^[16]. The results showed that the lattice quality of b-Si:Ti could be determined directly by the ablation strength, where a higher laser fluence induced a larger density of lattice defects and amorphous phase, causing more serious surface damage.

The Raman spectra of the b-Si:Ti samples after RTA treatment at different temperatures are presented in Fig. 5(b). The broadband peak around 475cm−1 and the broadening near the 300cm−1 peak were suppressed after thermal annealing, indicating an effective repairing effect of the α-Si phase and the pressure-induced lattice damages induced by the femtosecond laser ablation process. At the same time, the repairing effect was enhanced with the increase in annealing temperature at low annealing temperatures. As the annealing temperature was elevated further beyond 600°C, the repairing effect hardly showed any non-change, according to the Raman spectra. However, excessively high annealing temperatures inevitably lead to the thermal diffusion of the hyperdoped impurities and suppress the concentration of hyperdoping. The Raman spectral results displayed a similar tendency to the subbandgap absorption, indicating that the decrease in subbandgap absorption may be related to the mitigation of structural defects that were responsible for the infrared absorption.

The electronic properties of the annealed b-Si:Ti samples were investigated using Hall effect measurements based on the Van der Pauw technique. All b-Si:Ti samples exhibited n-type surfaces, indicating the presence of Ti as a donor dopant in Si. For samples fabricated by laser fluences ranging from 1.2 to 6.8kJ/m2 and subsequently subjected to a 600°C RTA treatment, the sheet carrier densities were found to be within a range of 1011–1012cm−2. The sheet carrier densities of the b-Si:Ti samples were orders of magnitude lower compared to other b-Si samples^[17]. These low free-carrier concentrations indicated a low electroactivity of hyperdoped Ti in Si, which can significantly reduce noise in the prepared devices. Besides, the carrier mobilities fluctuated within the range of 280–430 cm2V−1s−1 owing to the increase in activated carriers and enhancement of the impurity scattering process. The carrier mobilities of b-Si:Ti samples exhibited a significantly higher value than those of other hyperdoped b-Si compounds^[27]. The results of the study provide sufficient evidence to suggest that the b-Si:Ti material is more suitable for energy and information applications in comparison to other hyperdoped b-Si materials.

In this work, deep-level impurity and low formation energy properties of interstitial Ti in Si have been verified by first-principle simulations. This is believed to be responsible for the stable subbandgap absorption of Ti-hyperdoped Si. Subsequently, b-Si:Ti materials were fabricated by Ti film deposition followed by femtosecond laser irradiation and rapid thermal annealing. The resulting b-Si:Ti samples exhibited high lattice quality, low free-carrier density, and large carrier mobilities. Furthermore, high absorption was achieved in both the visible and the subbandgap ranges, as confirmed by the simulation results as well as the experimental results. The combination of high lattice quality, unique energy band structure, and high subbandgap absorptance with good thermal stability, renders Ti as an ideal dopant for Si. The unique characteristics of b-Si:Ti open up new opportunities for applications in all-Si devices, particularly those that require room-temperature infrared photon sensitivity and CMOS compatibility. Therefore, this study is significant for the in-depth understanding of hyperdoped Si and for improving its performance for potential applications in Si photonics and Si optoelectronics.