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Abstract
To reduce the wide bandgap of diamond and expand its applications in the photovoltaic fields, a diamond-based intermediate-band (IB) material C-Ge-V alloy was designed by first-principles calculations. By replacing some C with Ge and V in the diamond, the wide bandgap of the diamond can be reduced sharply and a reliable IB, which is mainly formed by the d states of V, can be formed in the bandgap. With the increase of Ge content, the total bandgap of the C-Ge-V alloy will be reduced and close to the optimal value of an IB material. At a relatively low atomic concentration of Ge (below 6.25%), the IB formed in the bandgap is partially filled and varies little with the concentration of Ge. When further increasing the content of Ge, the IB moves close to the conduction band and the electron filling in the IB increases. The 18.75% content of Ge might be the limitation to form an IB material, and the optimal content of Ge should be between 12.5% and 18.75%. Compared with the content of Ge, the distribution of Ge has a minor effect on the band structure of the material. The C-Ge-V alloy shows strong absorption for the sub-bandgap energy photons, and the absorption band generates a red-shift with the increase of Ge. This work will further expand the applications of diamond and be helpful to develop an appropriate IB material.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Hyperdoping deep-level dopant in the surface of the semiconductor to improve its optoelectronic properties has been one of the research focuses in the optoelectronics and microelectronics fields [1–10]. The hyperdoping of deep-level dopant can change the electronic structure of the semiconductor remarkably, e.g., it can form an intermediate-band (IB) in the bandgap of the host material [1,2]. Because of this IB, sub-bandgap energy photons can be absorbed and generate additional carriers through the transitions of electrons from valance band (VB) to the IB and from IB to the conduction band (CB) [11–14]. In addition, the formation of the IB can inhibit the non-radiative recombination [11,14], which was confirmed by the experiments [15]. In this way, a heterojunction can be formed between the hyperdoped layer and the substrate of the semiconductor and can be used directly in the photovoltaic devices [3]. The conversion efficiency limit of the IB solar cells is much higher than that of single-gap solar cells operating under the same conditions [11,16], which attracted broad attention and interest in the recent years. According to the research of Luque et al., an optimal IB material should have a total bandgap of about 1.95 eV and two sub-bandgaps of about 0.71 eV and 1.24 eV [11]. Therefore, find a host semiconductor with appropriate bandgap is the key to prepare a high efficiency IB solar cell.
Recently, a novel optoelectronic material based on diamond was reported [17–24]. The material is prepared by irradiating the surface of the chemical vapor deposition (CVD) diamond with femtosecond laser pulses and it is called “black diamond” due to its black appearance [17–24]. The black diamond overcomes the disadvantages of the common diamond, such as the wide bandgap (5.47 eV) and transparent for the visible and infrared light [25], it exhibits a strong sub-bandgap absorption in the visible and near-infrared wavelength range [20,22]. According to the computational study, the black diamond is an IB material, and the formation of the IB is attributed to the vacancies formed in the diamond during the preparation [26]. Subsequently, to further optimize the properties of the black diamond, a deep-level-impurity hyperdoped diamond was engineered by using first-principles calculations [27]. For the hyperdoped diamond, the characteristics of the band structure can be better regulated by changing the dopant types and concentrations. However, the total bandgap of the hyperdoped diamond is still too large to meet the conditions of an optimal IB material and it does not change obviously with the doping conditions.
To make the diamond applicable for the IB material, we currently substituted Ge atoms for several C atoms of the diamond and implanted deep-level dopant V in the material to form a reliable IB in the bangap. The substitution of Ge for C can dramatically reduce the wide bandgap of both the diamond and the diamond-based IB material. In addition, the bandgap and the character of the IB of the material can be well regulated by changing the content of Ge, which would be likely to make the material to meet the condition of an optimal IB material. Based on these findings, we engineer a bandgap-regulable IB material C-Ge-V by co-implanting Ge and deep-level dopant V in the diamond through DFT calculations. In this paper, the variations of the electronic structure and optical absorption of the material with the content and distribution of Ge are investigated. To study the dynamic stability of the material, phonon dispersion was computed and first-principles molecular dynamics (FPMD) were carried out for some of the configurations in this work.
2. Computational methods
The calculations carried out in this work are mainly based on the density-functional theory (DFT) under the CASTEP code [28–30]. The generalized gradient approximation (GGA) through the Perdew, Burke, and Ernzerhof (PBE) functional was used to treat the exchange-correlation potential [31]. The core electrons were treated with the ultrasoft pseudopotential [30]. The Broyden, Fletcher, Goldfarb, and Shanno (BFGS) algorithm was performed for the geometry optimization [32]. A planewave energy cutoff of 580 eV was used to optimize the configurations and calculate the electronic and optical properties. A k-point sampling of 3 × 3 × 3 in a Monkhorst-Pack grid was used for the geometry optimization, and a 8 × 8 × 8 k-point grid was used for the calculations of electronic and optical properties. The convergence condition used to optimize the electronic structure was set at 5 × 10−7 eV/atom. The convergence conditions for the geometry optimization were set as follows: the maximum energy change was 5 × 10−6 eV/atom, the maximum atomic force was 0.01 eV/ Å, the maximum stress was 0.02 GPa, and the maximum atomic displacement was 5 × 10−4 Å. With these calculational setups, the lattice constants of the pure diamond after geometry optimization is a = 3.5657 Å, which is well consistent with the experimental mearsurements: a = 3.5666 ± 0.0001 Å at T = 4.2 K and a = 3.5669 ± 0.0001 Å at T = 300 K [33].
The configurations of the C-Ge-V alloy in this study were derived from the 2 × 2 × 2 supercell of the conventional C8 unit cell. For convenience, we used “C63-xGexV” to represent the alloy in the following. In the C63-xGexV configurations, the total number of the atoms is 64, and (1 + x) C atoms were replaced by x Ge atoms and one V atom. To determine the most stable site and distribution of Ge and V, we calculated the formation energies of these configurations by employing the following equation:
where [C], [Ge] and [V] are the chemical potentials of one C atom, one Ge atom, and one V atoms, respectively ([C] = E[C64]/64, [Ge] = E[Ge64]/64, and [V] = E[Vpri]).The FPMD calculations were carried out in the NVT ensemble with a Nose-Hoover thermostat at a temperature of 350 K. The total simulation time was 2 ps: the time step was set to 1 fs and the simulations were run for 2000 timesteps. In the phonon dispersion calculation of the conventional unit cell of the C56Ge8 configuration, the core electrons were treated with the norm conserving pseudopotential [34]. A planewave energy cutoff of 1000 eV and a k-point sampling of 6 × 6 × 6 in a Monkhorst-Pack grid were used to optimize the configuration and calculate the phonon dispersion.
Considering the underestimation of the DFT-GGA method for the bandgap of semiconductor, we calculated the band structure of the conventional unit cell of the C56Ge8 configuration by using HSE06 functional [35,36] and GGA-1/2 method [37] as a comparison. The GGA-1/2 method is a semi-empirical method and can substantially improve the bandgaps for many semiconductors [37,38]. In addition, considering that the doping of V atom may lead to magnetism for the alloy, we add the spin polarization when calculating the band structure of one configuration by using GGA-1/2 method. In the HSE06 calculation, the norm conserving pseudopotential [34] was used to treat the core electrons, the planewave energy cutoff and the k-point sampling were the same to that in the phonon dispersion calculation. In the GGA-1/2 calculations, the linear combinations of atomic orbitals (LCAO) in Atomistix Toolkit (ATK) were used to expand the wave functions of valence states.
The optical properties of the material were studied by means of its absorption coefficient derived from the dielectric function. The imaginary part of the dielectric function is obtained from the momentum matrix elements between the occupied and unoccupied wave functions with selection rules [39]. The real part is calculated from imaginary part by using the Kramers-Kronig relations.
3. Results and discussion
We first calculated the formation energies of the substitutional and interstitial configurations of Ge (C63GeS and C64GeI) using the Eq. (1). The formation energies of the C63GeS and C64GeI configurations are 22.58 eV and 6.45 eV, respectively. The results indicate that the substitutional configuration of Ge is more stable than the interstitial one, which is the same as the case of V in our previous report. Thus both of the Ge and V atoms tend to locate at the substitutional site in the diamond at the equilibrium state.
Then, we considered two possible double substitutional configurations of Ge: close GeS-GeS distance configuration (C62Ge2C) and remote GeS-GeS distance configuration (C62Ge2R). The formation energies of the C62Ge2C and C62Ge2R alloys are 14.81 and 12.47 eV, respectively, which indicate that the Ge atoms would be separate from each other in the diamond at the equilibrium state. In addition, the formation energy of the close GeS-VS distance configuration (C62GeVC) (13.65 eV) is slightly lower than that of the remote GeS-VS distance configuration (C62GeVR) (13.99 eV). Even so, considering that the formation energy difference is very small and the Ge and V are the minority in the alloy, the configuration with separate Ge and V atoms should be the main part in the alloy.
Therefore, we constructed six C63-xGexV (x = 1, 2, 4, 8, 12, 16) alloys with separate Ge and V atoms in this work. The atomic concentrations of V are 1.56% for all of the alloys, and the atomic concentrations of Ge are 1.56%, 3.13%, 6.25%, 12.5%, 18.75%, and 25%, respectively. The distributions of Ge and V atoms in these alloys are shown in Figs. 1(a)-(f). In all of these configurations, the V atoms are uniformly distributed. For the C62GeV and C55Ge8V alloys [Figs. 1(a) and (d)], the distribution of Ge is uniform (the C55Ge8V configuration was derived from the 2 × 2 × 2 supercell of the conventional C7Ge unit cell). While for other configurations, we directly substituted the C with Ge in the 2 × 2 × 2 supercell and make the distribution of Ge approximately uniform. The lattice constants of these configurations are shown in Table 1. Compared with the lattice constants of the pure diamond (7.13 Å of the 2 × 2 × 2 supercell), we can find that the alloying with Ge and V would increase the size of the diamond cell. Figure 1(g) shows the variation of the total band gap (the energy difference between VB maximum and CB minimum) of these alloys with the atomic concentration of Ge. For comparison, the total bandgap of the host C64-xGex are also given in Fig. 1(g). It can be found that the incorporation of Ge could significantly reduce the bandgap of the diamond, and the bandgap reduces with the increase of the content of Ge. The variation trend of the C63-xGexV alloy with the content of Ge is similar to that of the host C64-xGex. At the same content of Ge, the total bandgap of the C63-xGexV alloy is smaller than that of the host C64-xGex, i.e., the implantation of V could further reduce the total bandgap of the material. In addition, at a lower content of Ge (below 6.25%), the total bandgaps of the C63-xGexV alloy and the host C64-xGex reduce repidly, but the bandgap reduction is slowed down at higher content of Ge. The details of the bandgaps for the host C64-xGex and the C63-xGexV are listed in Table 2.
Fig. 1. Configurations of the (a) C62GeV, (b) C61Ge2V, (c) C59Ge4V, (d) C55Ge8V, (e) C51Ge12V, and (f) C47Ge16V in 2 × 2 × 2 supercell. The yellow (small), green (medium), and blue (big) balls represent the C, Ge, and V atoms, respectively. (g) Variation of the total bandgap of the C63-xGexV and the C64-xGex alloys with the content of Ge.
Table 1. Lattice constants of the C63-xGexV configurations. The values are given in Å.
Table 2. Total bandgaps of the C64-xGex and C63-xGexV (x = 1, 2, 4, 8, 12, 16). The values of the bandgaps are given in eV.
Figure 2 shows the band structures of the C63-xGexV (x = 1, 2, 4, 8, 12, 16) alloys, and the details are listed in Table 3. From Table 3 we can find that, with the increase of Ge content, the width of the IB presents less variation, while the energy differences between the VB and IB, IB and CB reduce. At relatively low atomic concentration of Ge (below 6.25%), a narrow partially filled IB is formed in the middle of the bandgap and the occupation of the IB hardly changes with the content of Ge. In addition, with the increase of Ge content, the reduction of δE[VB-IB] is faster than that of the δE[IB-CB], i.e., the IB shifts to the VB. When the content of Ge further increases, as shown in Figs. 2(d)-(f), the bottom of the CB begin to split and move close to the IB, while the top of the VB remains nearly constant. Even so, there is still an isolated and partially filled IB in the bandgap at an atomic concentration of Ge up to 12.5%. Nevertheless, when the atomic concentration of Ge is more than 18.75%, the electron filling of the IB increases and the IB is quite close to the CB. Especially for the C47Ge16V alloy, the IB is nearly fully filled and does not meet the conditions of an IB material. Therefore, the 18.75% content of Ge might be the limitation to form an IB material. In addition, considering that the sub-bandgap from the VB to the IB is almost twice larger than that from the VB to the IB [11,13], it can be speculated that the optimal content of Ge should be between 12.5% and 18.75%. Based on the calculational results, the change rule of the band stucture of the C63-xGexV alloy with the content of Ge can be well understood, and then the characteristic of the band structure of the material can be well regulated by changing the content of Ge in the material.
Fig. 2. Electronic band structures of the (a) C62GeV, (b) C61Ge2V, (c) C59Ge4V, (d) C55Ge8V, (e) C51Ge12V, and (f) C47Ge16V alloys in 2 × 2 × 2 supercell.
Table 3. Electronic structure information of the C63-xGexV (x = 1, 2, 4, 8, 12, 16) alloys. The values are given in eV.
For the configurations in Fig. 1, the V atom was placed in the supercell randomly and all of the dopants were separated from each other. Nevertheless, the actual situation should be more complicated due to the high content of dopant. To get a fuller picture of the material, we changed the distribution of the dopant in the diamond and studied its impact on the electronic structure of the alloy. Figure 3(a) shows the configuration that contains two Ge atoms with close distance and a separated V atom (C61Ge2CV). Figure 3(b) shows the configuration of C62GeVC, which contains a Ge and a V with close distance. We changed the position of the V atom in the C55Ge8V alloy and used C55Ge8V2 to represent [Fig. 3(c)]. We also altered the distribution of Ge in the C55Ge8V alloy and used C55Ge8VN to represent [Fig. 3(d)]. In the two configurations of C55Ge8V2 and C55Ge8VN, the V and Ge atoms were separated from each other in the supercell. The band structures are shown in Figs. 3(e)∼3(h), and the details of the band structure information are shown in Table 4. The results show that the C61Ge2CV configuration exhibits similar IB character to the C61Ge2V one, which indicates that the bonding between Ge atoms may have less influence on the character of the IB. Nevertheless, the bonding between Ge and V broadens the IB and increases the electron filling in the IB. In addition, the bonding of the dopants (Ge-Ge and Ge-V) would decrease the total bandgap of the material. By comparing with the band structure of the C55Ge8V alloys in Fig. 2 and Tables 2 and 3, we can find that the band structure of the C55Ge8V2 alloy has barely changed. It is means that the position of V has less effect on the band structure of the alloy. While for the C55Ge8VN alloy, the band structure is slightly different from that of the C55Ge8V alloy. For instance, for the C55Ge8VN alloy, the energy difference between the IB maximum and the CB minimum is slightly reduced and its total band gap is slightly smaller than that of the C55Ge8V alloy. Even so, the influence of the distribution of Ge on the band structure of the alloy is minimal relative to the influence of the Ge content. Considering the complexity of the alloy in practical preparation, further theoretical and experimental researches are needed to determine the dopant distribution and its effect on the properties of the alloy.
Fig. 3. (a) Configuration of C61Ge2CV that contains two Ge atoms with close distance and a separated V atom. (b) Configuration of C62GeVC that contains a Ge and a V with close distance. (c) Configuration of the C55Ge8V alloy with a V atom located at another position, which is represented as C55Ge8V2. (d) Configuration of the C55Ge8V alloy with nonuniform distribution of Ge, which is represented as C55Ge8VN. (e)∼(h) Electronic band structures of C61Ge2CV, C62GeVC, C55Ge8V2, and C55Ge8VN alloys.
Table 4. Electronic structure information of the C61Ge2CV, C62GeVC, C55Ge8V2, and C55Ge8VN alloys. The values are given in eV.
It is known that the atomic radiuses of Ge and V are much larger than that of C. Therefore, lattice distortion would be larger and will increase with the increase of the content of Ge, and the structure of the alloy might be not stable for practical applications. To determine the dynamic stability of the material, the phonon dispersion calculation and FPMD simulations were performed in this work. We computed the phonon dispersion of the C7Ge unit cell and performed FPMD simulations on the C55Ge8V and C47Ge16V alloys. It should be noted that the C56Ge8 configuration in Fig. 1(d) was the 2 × 2 × 2 supercell of the C7Ge unit cell. Therefore, the stability of the C56Ge8 can be fully demonstrated by phonon dispersion of the C7Ge. However, the C7Ge configuration is not necessary the conventional unit cell of the C56Ge8, which contains much more space phases considering the random distribution of Ge in C. To determine the stability of the C55Ge8V configuration, we also simulated the FPMD of the C55Ge8VN configuration, which contains nonuniform distributed Ge atoms, as shown in Fig. 3(d). The phonon dispersion and FPMD results are shown in Fig. 4. From Fig. 4(a), it can be found that no imaginary phonon modes appear in the whole Brillouin zone, which indicates that the host C56Ge8 alloy is dynamically stable. The FPMD simulations indicate that there are nearly no structure changes after 2 ps for the C55Ge8V, C55Ge8VN, and C47Ge16V alloys. All of the results show that these alloys are thermal stable at 350 K. The configurations have high content of Ge and exhibit good stability, which indicates that the alloys with much lower content of Ge should be also stable at the temperature.
Fig. 4. (a) Phonon dispersion for the C7Ge unit cell. (b) FPMD simulations of the C55Ge8V, C55Ge8VN, and C47Ge16V alloys at 0 ps and 2 ps at 350 K.
From the partial density of states (PDOS) of the C63-xGexV (x = 1, 4, 8, 12) alloys as shown in Fig. 5, we can find that the IB in the bandgap is mainly formed by the d states of the V atom, which is the same as the V-implanted diamond without the incorporation of Ge [27]. While the s and p states of C atom contribute less to the formation of the IB, and the contribution of the s and p states of Ge atom is negligible. In addition, for all of the four configurations, the top of the VB is mainly composed of the p state of C atom, while the bottom of the CB is mainly composed of the s and p states of C atom together with the d states of V atom. It should be noted that the contribution of the s and p states of Ge for the CB bottom should not be ignored for the C51Ge12V alloy. When the content of Ge is higher, such as the C55Ge8V and C51Ge12V alloys, it can be found clearly that the s and p states of C and the d states of V in the bottom of the CB are split and move toward the IB, which leads to the split and shift of the CB bottom. Based on these results, the formation of the IB in bandgap is attributed to the implantation of V in the diamond. The incorporation of Ge in the diamond can reduce the bandgap obviously but has less effect on the character of the IB. With the increase of Ge content, the interaction among the C, Ge, and V is enhanced and the lattice distortion is increased, which lead to a great change for the band structure of the material.
Fig. 5. Partial density of states (PDOS) of the (a) C62GeV, (b) C59Ge4V, (c) C55Ge8V, and (d) C51Ge12V in 2 × 2 × 2 supercell.
To investigate the optical properties of the material, we calculated the optical absorption coefficient of the C63-xGexV (x = 1, 2, 4, 8, 12, 16) alloys and the results are shown in Fig. 6. For the alloys with lower content of Ge, such as the C62GeV, C61Ge2V, and C59Ge4V, a sub-bandgap absorption peak appears, which should be attributed to the transitions of electrons from the VB to the IB and from the IB to the CB. With the increase of the Ge content, the sub-bandgap absorption peak generates red-shift, which is due to the decrease of the sub-bandgaps from the VB to the IB and from the IB to the CB. When further increase the content of Ge, it can be found that the character of the sub-bandgap absorption changes obviously. For instance, for the C55Ge8V alloy, the shift of the sub-bandgap absorption peak is increased, while for the C51Ge12V and C47Ge16V alloys, the sub-bandgap absorption peak vanished and replaced by a broad absorption band. These changes of the sub-bandgap absorption are related to the variation of the band structure, such as the reduction and split of the CB and the increase of the electron occupancy. In addition, for the alloys with lower content of Ge (below 6.25%), such as the C62GeV, C61Ge2V, and C59Ge4V, there is a small and narrow absorption peak appears around zero eV, which is due to the transition of electrons in the partially filled IB. When the content of Ge is higher than 12.5%, the sub-bandgap absorption would extend to the visible and infrared regions, and the small peak around zero eV disappeares (see the inset figure). Besides the sub-band absorption, the absorption of photons with energies above the bandgap also shifts to longer wavelength regions with the increase of Ge, which is due to the reduction of total bandgap between VB and CB. Based on the results, a regulation for optical response regions would be achieved by changing the content of Ge in the alloy.
Fig. 6. Optical absorption coefficients of the C63-xGexV (x = 1, 2, 4, 8, 12, 16) alloys. The optical absorption coefficient of the pure diamond is also given for comparison.
It is well known that the bandgap of a semiconductor would be underestimated by the traditional GGA method. To determine the true bandgaps of these alloys, the band structure of the conventional unit cell (C7Ge) of the C56Ge8 configuration was calculated by using HSE06 functional [35,19] and GGA-1/2 method [37] [see Figs. 7(a) and 7(b)], which can predict much better electronic structure properties than the traditional GGA method. The results show that the band structures of the C56Ge8 alloy calculated by HSE06 and GGA-1/2 methods are similar. The bandgaps are 3.5 eV and 3.75 eV calculated by HSE06 and GGA-1/2, respectively, 1.05 eV and 1.3 eV larger than the result calculated by the traditional GGA method. The results indicate that the GGA-1/2 method has the similar accuracy to the HSE06 method in calculating the bandgap of the diamond-based semiconductor. Considering that the doping of V atom may lead to magnetism for the alloy, we took the C62GeV alloy as research object and add the spin polarization when calculating its band structure by using GGA-1/2 method. The Spin-up and spin-down band structures of the C62GeV alloy are shown in Figs. 7(c) and 7(d). It can be found that the total bandgap of the C62GeV alloy is about 4.72 eV for both spin-up and spin-down results, which is 1.14 eV larger than that calculated by the traditional GGA method. In addition, the IB is partially filled and in the middle of the bandgap for the spin-up band structure, while it is empty and in the upper half of the bandgap for the spin-down one. Based on the results, the true bandgaps of the alloy should be a little more than 1 eV larger than the GGA results in Table 2. It can be found that the total bandgap of the C63-xGexV alloys is close to the optimal value of an IB material with the increase of the content of Ge.
Fig. 7. Electronic band structure of the conventional unit cell (C7Ge) of the C55Ge8 alloy (inset) calculated by (a) HSE06 and (b) GGA-1/2 methods. (c) Spin-up and (d) spin-down band structures of the C62GeV alloys calculated by GGA-1/2 method.
Based on the results, the C63-xGexV alloy would be an appropriate IB material in theory, while there remain some problems. So far, the incorporation of Ge in diamond is mainly achieved by means of CVD and high-pressure and high-temperature (HPHT) techniques, which can form Ge-vacancy color centers in the diamond [40,41]. Nevertheless, the concentration of Ge in diamond obtained by these methods is much lower than that in our simulations. In addition, the C-Ge alloy with high content of Ge prepared in experiment is generally amorphous [42–45]. Therefore, the preparation of the zinc-blende C-Ge alloy is the key to implementing the application of the IB material and needs further investigation. As for the incorporation of V in the alloy, the ion implantation and pulsed laser ablation/melting method could be used, which were widely used for hyperdoping silicon with transition metals [4,46–48]. To eliminate additional vacancies produced in the process of preparation, thermal annealing should be necessary after the preparation. Therefore, finding out the optimal annealing conditions is also important for the C63-xGexV alloy to apply efficiently as an IB material.
4. Conclusion
In this work, a diamond-based IB material C63-xGexV (x = 1, 2, 4, 8, 12, 16) alloy was engineered by first-principles calculations. The total bandgap of the C63-xGexV alloy is much smaller than that of the pure diamond and can be regulated by changing the content of Ge atoms. With the increase of Ge content, the total bandgap of the C-Ge-V alloy will be reduced and close to the optimal value of an IB material. At a lower atomic concentration of Ge (below 6.25%), there is a narrow partially filled IB formed in the bandgap for the C63-xGexV alloy and it shifts to the VB with the increase of Ge. In this range of concentration of Ge, the width and occupation of the IB have barely changed. The C55Ge8V alloy (12.5% of Ge content) seems to be a critical state, the bottom of the CB begin to split and move toward the IB. Nevertheless, great changes would take place in the band structures when the atomic concentration of Ge is higher than 18.75%, i.e., the electron filling of the IB increases and the IB is quite close to the CB. The 18.75% content of Ge might be the limitation to form an IB material, and the optimal content of Ge should be between 12.5% and 18.75%. The PDOS results indicate that the formation of the IB in bandgap is attributed to the implantation of V (the d state of V) in the diamond. The incorporation of Ge in the diamond has less effect on the character of the IB. The C63-xGexV alloy can absorb the sub-bandgap photons obviously, and the sub-bandgap absorption peak generates red-shift with the increase of the Ge content. The calculations in this work will be helpful to develop a novel and high-efficiency IB photovoltaic material.
Funding
National Natural Science Foundation of China (62275074, 12274117); Science Foundation for the Excellent Youth Scholars of Henan Province (202300410226); Scientific and Technological Innovation Program of Henan Province’s Universities (20HASTIT026); project funded by China Postdoctoral Science Foundation (2022M711078).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. C. B. Simmons, A. J. Akey, J. P. Mailoa, D. Recht, M. J. Aziz, and T. Buonassisi, “Enhancing the infrared photoresponse of silicon by controlling the Fermi level location within an impurity band,” Adv. Funct. Mater. 24(19), 2852–2858 (2014). [CrossRef]
2. M. Wang, E. García-Hemme, Y. Berencén, R. Hübner, Y. Xie, L. Rebohle, C. Xu, H. Schneider, M. Helm, and S. Zhou, “Silicon-based intermediate-band infrared photodetector realized by Te hyperdoping,” Adv. Opt. Mater. 9(4), 2001546 (2021). [CrossRef]
3. M. Wang, Y. Berencén, E. García-Hemme, S. Prucnal, R. Hübner, Y. Yuan, C. Xu, L. Rebohle, R. Böttger, R. Heller, H. Schneider, W. Skorupa, M. Helm, and S. Zhou, “Extend infrared photoresponse in Te-hyperdoped Si at room temperature,” Phys. Rev. Appl. 10(2), 024054 (2018). [CrossRef]
4. J. P. Mailoa, A. J. Akey, C. B. Simmons, D. Hutchinson, J. Mathews, J. T. Sullivan, D. Recht, M. T. Winkler, J. S. Williams, J. M. Warrender, P. D. Persans, M. J. Aziz, and T. Buonassisi, “Room-temperature sub-band gap optoelectronic response of hyperdoped silicon,” Nat. Commun. 5(1), 3011 (2014). [CrossRef]
5. W. Yang, A. J. Akey, L. A. Smillie, J. P. Mailoa, B. C. Johnson, J. C. McCallum, D. Macdonald, T. Buonassisi, M. J. Aziz, and J. S. Williams, “Au-rich filamentary behavior and associated subband gap optical absorption in hyperdoped Si,” Phys. Rev. Mater. 1(7), 074602 (2017). [CrossRef]
6. J. M. Warrender, “Laser hyperdoping silicon for enhanced infrared optoelectronic properties,” Appl. Phys. Rev. 3(3), 031104 (2016). [CrossRef]
7. M. Wang, A. Debernardi, W. Zhang, C. Xu, Y. Yuan, Y. Xie, Y. Berencén, S. Prucnal, M. Helm, and S. Zhou, “Critical behavior of the insulator-to-metal transition in Te-hyperdoped Si,” Phys. Rev. B 102(8), 085204 (2020). [CrossRef]
8. K. Wang, H. Shao, K. Liu, S. Qu, Y. Wang, and Z. Wang, “Possible atomic structures responsible for the sub-bandgap absorption of chalcogen-hyperdoped silicon,” Appl. Phys. Lett. 107(11), 112106 (2015). [CrossRef]
9. K. Wang, P. Liu, S. Qu, Y. Wang, and Z. Wang, “Optical and electrical properties of textured sulfur-hyperdoped silicon: a thermal annealing study,” J. Mater. Sci. 50(9), 3391–3398 (2015). [CrossRef]
10. H. H. Gandhi, D. Pastor, T. T. Tran, S. Kalchmair, L. A. Smilie, J. P. Mailoa, R. Milazzo, E. Napolitani, M. Loncar, J. S. Williams, M. J. Aziz, and E. Mazur, “Gold-hyperdoped germanium with room-temperature sub-band-gap optoelectronic response,” Phys. Rev. Appl. 14(6), 064051 (2020). [CrossRef]
11. A. Luque, A. Martí, and C. Stanley, “Understanding intermediate-band solar cells,” Nat. Photonics 6(3), 146–152 (2012). [CrossRef]
12. Y. Okada, N. J. Ekins-Daukes, T. Kita, R. Tamaki, M. Yoshida, A. Pusch, O. Hess, C. C. Phillips, D. J. Farrell, K. Yoshida, N. Ahsan, Y. Shoji, T. Sogabe, and J.-F. Guillemoles, “Intermediate band solar cells: Recent progress and future directions,” Appl. Phys. Rev. 2(2), 021302 (2015). [CrossRef]
13. A. Datas, E. López, I. Ramiro, E. Antolín, A. Martí, and A. Luque, “Intermediate band solar cell with extreme broadband spectrum quantum efficiency,” Phys. Rev. Lett. 114(15), 157701 (2015). [CrossRef]
14. C. T. Crespo, “Effect of band occupations in intermediate-band solar cells,” Sol. Energy 178, 157–161 (2019). [CrossRef]
15. E. Antolín, A. Martí, J. Olea, D. Pastor, G. González-Díaz, I. Mártil, and A. Luque, “Lifetime recovery in ultrahighly titanium-doped silicon for the implementation of an intermediate band material,” Appl. Phys. Lett. 94(4), 042115 (2009). [CrossRef]
16. E. Ghorbani, D. Barragan-Yani, and K. Albe, “Towards intermediate-band photovoltaic absorbers: theoretical insights on the incorporation of Ti and Nb in In2S3,” npj Comput. Mater. 6(1), 93 (2020). [CrossRef]
17. M. Mastellone, A. Bellucci, M. Girolami, V. Serpente, R. Polini, S. Orlando, A. Santagata, E. Sani, F. Hitzel, and D. M. Trucchi, “Deep-subwavelength 2D periodic surface nanostructures on diamond by double-pulse femtosecond laser irradiation,” Nano Lett. 21(10), 4477–4483 (2021). [CrossRef]
18. A. F. Sartori, S. Orlando, A. Bellucci, D. M. Trucchi, S. Abrahami, T. Boehme, T. Hantschel, W. Vandervorst, and J. G. Buijnsters, “Laser-induced periodic surface structures (LIPSS) on heavily boron-doped diamond for electrode applications,” ACS Appl. Mater. Interfaces 10(49), 43236–43251 (2018). [CrossRef]
19. A. Bellucci, P. Calvani, M. Girolami, S. Orlando, R. Polini, and D. M. Trucchi, “Optimization of black diamond films for solar energy conversion,” Appl. Surf. Sci. 380, 8–11 (2016). [CrossRef]
20. M. Girolami, A. Bellucci, M. Mastellone, S. Orlando, V. Valentini, R. M. Montereali, M. A. Vincenti, R. Polini, and D. M. Trucchi, “Optical characterization of double-nanotextured black diamond films,” Carbon 138, 384–389 (2018). [CrossRef]
21. M. Girolami, L. Criante, F. Di Fonzo, S. Lo Turco, A. Mezzetti, A. Notargiacomo, M. Pea, A. Bellucci, P. Calvani, V. Valentini, and D. M. Trucchi, “Graphite distributed electrodes for diamond-based photon-enhanced thermionic emission solar cells,” Carbon 111, 48–53 (2017). [CrossRef]
22. P. Calvani, A. Bellucci, M. Girolami, S. Orlando, V. Valentini, R. Polini, and D. M. Trucchi, “Black diamond for solar energy conversion,” Carbon 105, 401–407 (2016). [CrossRef]
23. M. Girolami, A. Bellucci, M. Mastellone, S. Orlando, A. Orsini, S. Salvatori, and D. M. Trucchi, “Transport properties of photogenerated charge carriers in black diamond films,” Ceram. Int. 45(7), 9544–9547 (2019). [CrossRef]
24. S. Amoruso, A. Andreone, A. Bellucci, C. Koral, M. Girolami, M. Mastellone, S. Mou, S. Orlando, G. P. Papari, D. Paparo, R. Polini, A. Rubano, A. Santagata, V. Serpente, V. Valentini, and D. M. Trucchi, “All-carbon THz components based on laser-treated diamond,” Carbon 163, 197–201 (2020). [CrossRef]
25. R. S. Balmer, J. R. Brandon, S. L. Clewes, H. K. Dhillon, J. M. Dodson, I. Friel, P. N. Madgwick, M. L. Markham, T. P. Mollart, N. Perkins, G. A. Scarsbrook, D. J. Twitchen, A. J. Whitehead, J. J. Wilman, and S. M. Woollard, “Chemical vapour deposition synthetic diamond: materials, technology and applications,” J. Phys.: Condens. Matter 21(36), 364221 (2009). [CrossRef]
26. X. Dong, Y. Wang, and X. Song, “Physical mechanisms for the optical properties of the femtosecond-lasertreated black diamond,” Journal of Physics: Condens. Matter 32, 165502 (2020). [CrossRef]
27. X. Dong, T. Wang, Y. An, and Y. Wang, “Deep-level impurities hyperdoped diamond: a first-principles calculations,” J. Phys.: Condens. Matter 33(11), 115502 (2021). [CrossRef]
28. P. Hohenberg and W. Kohn, “Inhomogeneous electron gas,” Phys. Rev. 136(3B), B864–B871 (1964). [CrossRef]
29. W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140(4A), A1133–A1138 (1965). [CrossRef]
30. D. Vanderbilt, “Soft self-consistent pseudopotentials in a generalized eigenvalue formalism,” Phys. Rev. B 41(11), 7892–7895 (1990). [CrossRef]
31. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996). [CrossRef]
32. B. G. Pfrommer, M. Côté, S. G. Louie, and M. L. Cohen, “Relaxation of crystals with the quasi-Newton method,” J. Comput. Phys. 131(1), 233–240 (1997). [CrossRef]
33. V. V. Brazhkin, E. A. Ekimov, A. G. Lyapin, S. V. Popova, A. V. Rakhmanina, S. M. Stishov, V. M. Lebedev, Y. Katayama, and K. Kato, “Lattice parameters and thermal expansion of superconducting boron-doped diamonds,” Phys. Rev. B 74(14), 140502 (2006). [CrossRef]
34. D. R. Hamann, M. Schlüter, and C. Chiang, “Ab initio norm-conserving pseudopotentials,” Phys. Rev. Lett. 43(20), 1494–1497 (1979). [CrossRef]
35. J. Heyb, G. E. Scuserial, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118(18), 8207–8215 (2003). [CrossRef]
36. J. Heyb, G. E. Scuserial, and M. Ernzerhof, “Erratum: “Hybrid functionals based on a screened Coulomb potential,” [J. Chem.Phys. 118, 8207, (2003)],” J. Chem. Phys. 124(21), 219906 (2006). [CrossRef]
37. L. G. Ferreira, A. Marques, and L. K. Teles, “Slater half-occupation technique revisited: the LDA-1/2 and GGA-1/2 approaches for atomic ionization energies and band gaps in semiconductors,” AIP Adv. 1(3), 032119 (2011). [CrossRef]
38. X. Dong, Y. Li, T. Wang, Y. An, and Y. Wang, “Insulator-to-metal transition in intermediate-band materials: insights from temperature-dependent transmission computations,” New J. Phys. 25(3), 033008 (2023). [CrossRef]
39. J. Sun, X. Zhou, Y. Fan, J. Chen, and H. Wang, “First-principles study of electronic structure and optical properties of heterodiamond BC2N,” Phys. Rev. B 73(4), 045108 (2006). [CrossRef]
40. V. Sedov, A. Martyanov, S. Savin, A. Bolshakov, E. Bushuev, A. Khomich, O. Kudryavtsev, V. Krivobok, S. Nikolaev, and V. Ralchenko, “Growth of polycrystalline and single-crystal CVD diamonds with bright photoluminescence of Ge-V color centers using germane GeH4 as the dopant source,” Diamond Relat. Mater. 90, 47–53 (2018). [CrossRef]
41. E. A. Ekimov, S. G. Lyapin, K. N. Boldyrev, M. V. Kondrin, R. Khmelnitskiy, V. A. Gavva, T. V. Kotereva, and M. N. Popova, “Germanium-vacancy color center in isotopically enriched diamonds synthesized at high pressures,” JETP Lett. 102(11), 701–706 (2015). [CrossRef]
42. X. Che, Z. Liu, Y. Li, and N. Wang, “Effects of hydrogen and substrate temperature on the chemical bonding and optical properties of germanium carbon films deposited by reactive sputtering,” Appl. Surf. Sci. 258(17), 6212–6216 (2012). [CrossRef]
43. X. Che, Z. Liu, Y. Li, and T. Tan, “Effects of radio frequency power on the optical and electrical properties of germanium carbon films,” J. Alloys Compd. 577, 15–18 (2013). [CrossRef]
44. J. Szmidt, M. Gazicki-Lipman, H. Szymanowski, R. Mazurczyk, A. Werbowy, and A. Kudla, “Electrophysical properties of thin germanium/carbon layers produced on silicon using organometallic radio frequency plasma enhanced chemical vapor deposition process,” Thin Solid Films 441(1-2), 192–199 (2003). [CrossRef]
45. L. G. Jacobsohn and F. L. Freire Jr., G. Mariotto, “Investigation on the chemical, structural and mechanical properties of carbon-germanium films deposited by dc-magnetron sputtering,” Diamond Relat. Mater. 7(2-5), 440–443 (1998). [CrossRef]
46. E. Garcia-Hemme, G. García, P. Palacios, D. Montero, R. García-Hernansanz, G. Gonzalez-Diaz, and P. Wahnon, “Vanadium supersaturated silicon system: a theoretical and experimental approach,” J. Phys. D: Appl. Phys. 50(49), 495101 (2017). [CrossRef]
47. Y. Zhou, F. Liu, and X. Song, “The insulator-to-metal transition of Co hyperdoped crystalline silicon,” J. Appl. Phys. 113(10), 103702 (2013). [CrossRef]
48. J. Olea, M. Toledano-Luque, D. Pastor, G. González-Díaz, and I. Mártil, “Titanium doped silicon layers with very high concentration,” J. Appl. Phys. 104(1), 016105 (2008). [CrossRef]
