Ab initio design of nanostructures for solar energy conversion: a case study on silicon nitride nanowire
© Pan; licensee Springer. 2014
Received: 25 August 2014
Accepted: 20 September 2014
Published: 26 September 2014
Design of novel materials for efficient solar energy conversion is critical to the development of green energy technology. In this work, we present a first-principles study on the design of nanostructures for solar energy harvesting on the basis of the density functional theory. We show that the indirect band structure of bulk silicon nitride is transferred to direct bandgap in nanowire. We find that intermediate bands can be created by doping, leading to enhancement of sunlight absorption. We further show that codoping not only reduces the bandgap and introduces intermediate bands but also enhances the solubility of dopants in silicon nitride nanowires due to reduced formation energy of substitution. Importantly, the codoped nanowire is ferromagnetic, leading to the improvement of carrier mobility. The silicon nitride nanowires with direct bandgap, intermediate bands, and ferromagnetism may be applicable to solar energy harvesting.
As one of the green energy sources, solar energy has been widely investigated to replace the old forms of depletable energy, such as coal and oil, which are limited on earth and detrimental to global climate. It needs, therefore, to develop reliable technologies to efficiently convert solar energy to other usable energy forms, such as electricity and chemical energy. A few technologies have been developed to harvest solar energy, including photovoltaic cells (PV; converting solar energy to electrical energy), photoelectrochemical cells (PEC; converting solar energy to chemical energy), and solar thermal systems (converting solar energy to thermal energy). In all of these technologies, the fundamental element, materials, plays a dominant role to maximally utilize the sunlight. For photovoltaic cells, the optimum bandgap for the solar cell material is a compromise between a bandgap wide enough so that not too many electrons are wasted and yet narrow enough so that enough photons can be absorbed to create electron–hole pairs. For photoelectrochemical cells, the development of an efficient photocatalyst for water splitting requires (a) narrowing its bandgap that satisfies the visible light absorption and the band edge requirement of H2/H2O and O2/H2O levels[2, 3] and (b) having high contacting surface area with the electrolyte to enhance the reaction and to increase the light absorption. However, no semiconductor has a bandgap that can utilize the entire spectral distribution of sunlight. To enhance the light absorption efficiency, considerable effort has been conducted for the maximal absorption of sunlight, such as chemical doping[2–8], dye sensitization[9–11], material design[12–14], defect engineering[15–17], and structure engineering[18–20]. However, novel cell concepts are necessary for a huge increase in the efficiency. One of the concepts, hot-carrier solar cell, is to use semiconductor nanocrystals or quantum dots to capture all of the energy of hot carriers[21, 22], where hot-carrier relaxation is only possible via slower multiphonon emission because of the quantum confinement-induced discretized band states in the nanostructures. Another important concept is the intermediate band (IB) solar cell, consisting of an IB material situated between two conventional semiconductors, n- and p-types[24–26], where the IB material has a band inside the bandgap. A full electron transition from the valence band to the conduction band can be completed by means of two photons with energy below the bandgap, resulting in the increase in photocurrent. The IB can arise from the quantum confinement effects in quantum dots[27–29] or impurity states by doping bulk materials with a transition metal[30–33]. Recently, solar cells based on nanostructures have attracted considerable attention because of possible cost reduction and efficiency improvement[34–36]. Therefore, nanostructures possessing an intermediate band and quantum confinement effect may be able to enhance the efficiency and reduce the cost at the same time.
Silicon nitride (Si3N4) is a material of great technological interest in a number of applications, such as high-temperature electronics, because of its chemical inertness, high dielectric constant, large electronic gap, high resistance against radiation, and strong resistance against thermal shock. Importantly, Si3N4 is a well-known antireflection coating material in the semiconductor industry to reduce the light reflection in Si-based solar cells. Also, single-crystal Si3N4 nanowires on a Si substrate can be easily synthesized by chemical vapor deposition. It is expected that an energy-harvesting cell based on Si3N4 nanowires and the present Si technology may make the Si3N4-based energy harvesting cell possibly produced on sustainable improved efficiency and cost reduction because of the easy integration of Si3N4 into the Si technology. In this work, we explore the electronic, magnetic, and optical properties of a Si3N4 nanowire for its possible application in solar energy conversion based on first-principles calculation. Our calculations predict that the Si3N4 nanowire is a direct-band semiconductor with reduced bandgap, and IBs can be created by doping with carbon and transition metals. We further show that anion-cation codoping can improve the solubility of a transition metal in Si3N4 and its crystallinity and enhance the magnetic moment. We further predict that the ferromagnetic Si3N4 nanowire with IB is more efficient for solar energy conversion.
where is the vector defining the polarization of the incident electric field. This expression is similar to Fermi's golden rule for time-dependent perturbations, and ϵ2(ω) can be thought of as detailing the real transitions between occupied and unoccupied electronic states. The real part, ϵ1(ω), is obtained by the Kramers-Kronig relation. The loss function is calculated using Im(-1/ϵ(ω)) at zero momentum transfer from the macroscopic dielectric function ϵ(ω) (ϵ(ω) = ϵ1(ω) + iϵ2(ω)) for a periodic system.
Results and discussion
Single-element-doped β-Si3N4 nanowire
Formation energy for the various doping configurations in the β-Si 3 N 4 nanowire
Anion-cation-codoped β-Si3N4 nanowire
The codoping is realized by simultaneously substituting a cation atom with a chromium atom and an anion atom with an oxygen or carbon atom as a pair inside the nanowire. The calculated formation energies are 1.51 and 6.06 eV for CrO and CrC codoping, respectively. The formation energy of CrO codoping is much lower than that of Cr doping because of the electrostatic attraction of the two dopants with opposite charge states[31, 32], which indicates that the Cr substitution can be greatly enhanced in the presence of O doping and results in the enhancement of solubility of Cr in the nanowire and improvement of crystallinity. However, the CrC codoping is unstable because of electrostatic repulsion between the two dopants, as indicated by the high formation energy, and will not be discussed. The Cr-N, Si-O, and Cr-O bond lengths in the CrO-codoped nanowire are 1.889, 1.703, and 1.996 Å, respectively.
Magnetic properties of Cr-doped and CrO-codoped β-Si3N4 nanowires
To investigate the magnetic properties of the doped nanowires, spin-polarized calculations are performed. To study the magnetic coupling between metal dopants, two neighboring Si atoms in the nanowire are substituted by two Cr atoms (Cr2) for the Cr-doped nanowire, and two neighboring Si atoms and one N atom bonded with them are replaced by two Cr atoms and one O atom (Cr2O) for the codoped nanowire. The calculated exchange energies, defined by the energy difference between the antiferromagnetic and ferromagnetic states (Eexch = EAFM - EFM), are 135 and 293 meV for the Cr2-doped and Cr2O-codoped nanowires, respectively, indicating that the nanowires with doping are ferromagnetic. Importantly, the exchange energy of the codoped nanowire is much larger than that of the Cr-doped nanowire, leading to a much stable ferromagnetic state and higher transition Curie temperature of the codoped nanowire. The calculated magnetic moments per Cr atom are 1.85 and 2.29 μB for the Cr-doped and CrO-codoped nanowires, respectively. Clearly, the codoping enhances not only the exchange energy but also the magnetic moment.
The calculated electronic structures (Figure 9) further reveal the enhancement of the sunlight absorption in the doped nanowires because of the formation of IBs within the bandgap. Importantly, the diluted magnetic semiconductors (DMSs) with IBs can have the desired optical properties and prevent radiative transition by taking the advantage of spin selection rules on IB transition. The carrier mobility/lifetime is greatly enhanced because the spin degeneracy of the bands is lifted in DMSs and the unwanted recombinations are impeded by spin selection rules or by low occupancy of states involved in the allowed recombinations[53, 54]. All of these advantages lead to the enhancement of the conversion efficiency of magnetic β-Si3N4 nanowires.
In summary, a first-principles design of nanostructures is carried out to investigate their applications in solar energy harvesting. The calculated results show that the band structures of bulk materials can be engineered by reducing their size. Bulk Si3N4 is an indirect-bandgap semiconductor, while Si3N4 nanowire is a direct one. We show that the band structure of the nanowire can be further controlled by doping. Intermediate bands within its bandgap can be created by doping. The calculated optical property shows that the intermediate bands play an important role in the enhancement of visible light absorption. We also show that anion-cation codoping is easier than single-element doping because of the electrostatic attraction of the anion and cation. We further demonstrate that the ferromagnetic nanowire can be realized by codoping, where spin polarization can efficiently improve carrier mobility due to spin selection rules. The designed nanowire with a controllable band structure engineered by doping and size reduction shows efficient sunlight absorption and improved mobility and may find applications in solar energy harvesting.
Hui Pan thanks the supports of the Science and Technology Development Fund from Macao SAR (FDCT-076/2013/A) and Multi-Year Research Grant (MYRG2014-00159-FST) and Start-up Research Grant (SRG-2013-00033-FST) from the Research & Development Office at the University of Macau. The DFT calculations were performed at the High-Performance Computing Cluster (HPCC) of the Information and Communication Technology Office (ICTO) at the University of Macau.
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