Electron-phonon relaxation and excited electron distribution in zinc oxide and anatase

We propose a first-principles method for evaluations of the time-dependent electron distribution function of excited electrons in the conduction band of semiconductors. The method takes into account the excitations of electrons by an external source and the relaxation to the bottom of the conduction band via electron-phonon coupling. The methods permit calculations of the non-equilibrium electron distribution function, the quasi-stationary distribution function with a steady-in-time source of light, the time of setting of the quasi-stationary distribution and the time of energy loss via relaxation to the bottom of the conduction band. The actual calculations have been performed for titanium dioxide in the anatase structure and zinc oxide in the wurtzite structure. We find that the quasi-stationary electron distribution function has a peak near the bottom of the conduction band and a tail whose maximum energy rises linearly with increasing energy of excitation. The calculations demonstrate that the relaxation of excited electrons and the setting of the quasi-stationary distribution occur within a time of no more than 500?fs for ZnO and 100?fs for anatase. We also discuss the applicability of the effective phonon model to energy-independent electron-phonon transition probability. We find that the model only reproduces the trends in the change of the characteristic times whereas the precision of such calculations is not high. The rate of energy transfer to phonons at the quasi-stationary electron distribution also have been evaluated and the effect of this transfer on the photocatalysis has been discussed. We found that for ZnO this rate is about five times less than in anatase.     

Ab initio calculations of the electron-phonon interaction and characteristics of large polarons in rutile and anatase

The calculations of the electron-phonon interaction and some characteristics of excited electrons near the bottom of the conduction band of titanium dioxide in the structure of anatase and rutile have been performed. The Eliashberg function, the imaginary and real parts of the self-energy potential, as well as the band and polaron masses and width of the photoemission line, have been calculated. It has been shown that the electron-phonon interaction is primarily determined by the interaction with optical photons. Moderate values of the polaron mass (<2m _e ) correspond to large polarons. The calculated values of the spectral line width are significantly less than those observed in the experiment. Arguments have been presented in support of the assumption that the main contribution to the spectral line width corresponds to the interaction of electrons with the potential of randomly arranged oxygen vacancies.     

Dynamics of the processes of electron-hole recombination and capture of charge carriers in anatase doped with boron, carbon, or nitrogen

The first-principles investigation of the processes of nonradiative recombination of electron-hole pairs and binding of excited charge carriers with impurity atoms in anatase doped with boron, carbon, or nitrogen has been carried out using the perturbation theory method. The perturbation is provided by a dynamically screened electron-electron interaction potential calculated in the random phase approximation. It has been shown that the most probable processes occurring upon doping with boron and carbon are exchange processes in which electrons are bound with the impurity atom, whereas the most probable processes observed upon doping with nitrogen are exchange processes in which holes are bound with the impurity atom. These processes occur within a time interval of shorter than 2 fs. The next in probability are the processes of energy losses by unbound electrons and holes due to the generation of phonons. For the case of nitrogen doping, the time of this process is estimated at approximately 300 fs. For excitons formed in this case, the luminescence photon energy and the binding energy of electrons or holes with the impurity atom are estimated. The agreement between the calculated data and the results of experiments on the photocatalysis proceeding on the surface of N-doped anatase is discussed.     

C掺杂锐钛矿相TiO2吸收光谱的第一性原理研究

运用第一性原理,对C掺杂锐钛矿相TiO₂的电子结构进行了研究,从能带结构理论解释了C掺杂TiO₂吸收光谱的一些实验现象.发现在C掺杂后的锐钛矿相TiO₂的禁带宽度增大,并且在带隙中出现了杂质能级,这些杂质能级主要是由C 2p轨道上的电子构成的,它们之间是独立的,正是这些独立的杂质能级使TiO₂掺杂后可以发生可见光响应.价带上的电子可以吸收一定能量的光子跃迁到杂质能级,而杂质能级上的电子也可以吸收一定能量的光子跃迁到导带,所以从理论上可以计算出掺杂后的TiO₂在可见光范围内存在两个吸收边,与实验中所得到的现象相一致. 关键词： C掺杂 2')" href="#">锐钛矿TiO₂ 能带结构 吸收光谱     

Electron heating through a set of random levels in the conduction band of insulators induced by femtosecond laser pulses

We develop a theory describing the heating of electrons in crystalline insulators irradiated by high-intensity laser pulses. In agreement with photoelectron yield versus intensity measurements, we assume that electrons are excited into the conduction band from defect layers and traps. The electron dynamics due to direct inter-branch transitions within the conduction band is simulated by solving of time-dependant Schr?dinger equation. The set of levels for this equation is supposed to be random with a distribution function equal to the density of states in the conduction band. The influence of different parameters on the electron heating efficiency is studied. The theory is applied for diamond; the theoretical spectrum is in qualitative agreement with the experimental observations.     

Electronic structure and the optical and photocatalytic properties of anatase doped with vanadium and carbon

The electronic structures of undoped anatase and anatase doped with carbon and vanadium have been calculated using the ab initio tight-binding linear muffin-tin orbital (TB-LMTO) method in the LSDA + U approximation. It has been shown that the doping of TiO₂ leads to the formation of narrow bands of the C and Vimpurity states in the band gap. The calculations of the imaginary part of the dielectric function have made it possible to estimate the intensity of the optical absorption. It has been established that the doping with vanadium and carbon leads to optical absorption in the visible range and to an increase in the absorption in the ultraviolet range up to 4 eV. This should result in an increase in the photocatalytic activity on the surface of the doped anatase. The experimental determination of the photocatalytic activity of whiskers of the anatase doped with carbon and vanadium in the reaction of hydroquinone oxidation has confirmed the increase in the activity of the doped materials under exposure to ultraviolet, visible, and blue light. The phenomenon of dark catalysis in the anatase doped with carbon and vanadium has been interpreted within the concept of low-energy electronic excitatio ns between the impurity levels of carbon.     

Electronic and optical properties of pure and Mo doped anatase TiO2 using GGA and GGA+U calculations

Comparative GGA and GGA+U calculations for pure and Mo doped anatase TiO₂ are performed based on first principle theory, whose results show that GGA+U calculation provide more reliable results as compared to the experimental findings. The direct band gap nature of the anatase TiO₂ is confirmed, both by using GGA and GGA+U calculations. Mo doping in anatase TiO₂ narrows the band gap of TiO₂ by introducing Mo 4d states below the conduction band minimum. Significant reduction of the band gap of anatase TiO₂ is found with increasing Mo doping concentration due to the introduction of widely distributed Mo 4d states below the conduction band minimum. The increase in the width of the conduction band with increasing doping concentration shows enhancement in the conductivity which may be helpful in increasing electron–hole pairs separation and consequently decreases the carrier recombination. The Mo doped anatase TiO₂ exhibits the n-type characteristic due to the shifting of Fermi level from the top of the valence band to the bottom of the conduction band. Furthermore, a shift in the absorption edge towards visible light region is apparent from the absorption spectrum which will enhance its photocatalytic activity. All the doped models have depicted visible light absorption and the absorption peaks shift towards higher energies in the visible region with increasing doping concentration. Our results describe the way to tailor the band gap of anatase TiO₂ by changing Mo doping concentration. The Mo doped anatase TiO₂ will be a very useful photocatalyst with enhanced visible light photocatalytic activity.     

第一性原理研究Ni、V、Zr、N、P、S单掺杂及其共掺杂锐钛矿物相TiO_2的电子结构和吸收光谱

采用基于密度泛函理论(density functional theory,DFT)的Castep(MS 5.5)软件包进行计算,计算方法为广义梯度近似(generalized gradient approximation,GGA)下的Predew-Burke-Ernzerhof交换关联泛函和投影缀加平面波方法,构建2×2×1锐钛矿相二氧化钛单掺杂Ni、V、Zr、W等金属原子及N、P、S等非金属原子的晶胞模型,对掺杂锐钛矿相二氧化钛的能带结构、态密度和吸收光谱进行了计算.计算结果表明:Ni、V、Zr、W、P、N、S单掺杂二氧化钛的带隙宽度,除了W元素,其它掺杂元素都使带隙变窄,吸收光谱发生一定程度的红移.同时计算结果也表明,在金属和非金属共掺杂的作用下,由于共掺杂元素的引入,均使得带隙降低,其中P-V和S-Ni共掺杂的带隙最小,光学性质显示S-Ni共掺杂吸收边带最宽,对可见光的利用率最高,理论上S-Ni共掺杂锐钛矿二氧化钛具有良好的光致阴极保护效果.     

M- (Sm, Pr, Ga) 掺杂TiO2带隙及电子结构的第一原理研究

采用密度泛函理论对M-（Sm、Pr、Ga）掺杂锐钛矿型TiO2能带和电子性质进行了系统的理论研究. 计算结果表明,通过Sm和Pr的掺杂可以降低TiO2的带隙进而使其产生吸收边红移,通过Ga的掺杂能使带隙稍增加. 这主要是由于Sm和Pr的掺杂使Sm和Pr上的4f层电子与原子相邻O原子上的2p层电子相互作用,形成的杂质能级影响了Ti-O的能带结构,从而降低带隙,提高TiO2的可见光吸收性能.     

Relaxation of femtosecond photoexcited electrons in a polar indirect band-gap semiconductor nanoparticle

A model calculation is given for the energy relaxation of a non-equilibrium distribution of hot electrons (holes) prepared in the conduction (valence) band of a polar indirect band-gap semiconductor, which has been subjected to homogeneous photoexcitation by a femtosecond laser pulse. The model assumes that the pulsed photoexcitation creates two distinct but spatially interpenetrating electron and hole non-equilibrium subsystems that initially relax non-radiatively through the electron (hole)-phonon processes towards the conduction (valence) band minimum (maximum), and finally radiatively through the phonon-assisted electron-hole recombination across the band-gap, which is a relatively slow process. This leads to an accumulation of electrons (holes) at the conduction (valence) band minimum (maximum). The resulting peaking of the carrier density and the entire evolution of the hot electron (hole) distribution has been calculated. The latter may be time resolved by a pump-probe study. The model is particularly applicable to a divided (nanometric) polar indirect band-gap semiconductor with a low carrier concentration and strong electron-phonon coupling, where the usual two-temperature model [1-4] may not be appropriate.     

ZnS:Cu,Nd, Cl薄膜直流电致发光的激发态寿命和光谱强度

在真空中用共蒸发方法制的直流电致发光薄膜ZnS:Cu,Nd,Cl,实验中测量了它的可见和红外发射。本文研究了Nd3+离子的各个激发态的寿命各个辐射波长的发射强度与温度和外加电压的关系,发现导带中参与电致发光激发过程的热电子能量分布遵从玻尔兹曼函数,热电子平均能量是0.16eV左右,这个值和能量转换效率测量结果相一致。     

A model of hopping and band DC photoconduction in doped crystals

Expressions for the screening length and the ambipolar diffusion length are derived, for the first time, for the case where hopping conduction and band conduction coexist in semiconductors with hydrogen-like impurities. A method is proposed for calculating the diffusion coefficient of electrons (holes) hopping between impurity atoms from data on the Hall effect, in the case where the hopping and band conductivities are equal. An interpretation is given of available experimental data on hopping photoconduction between acceptors (Ga) and donors (As) in p-Ge at T=4.2 K doped by a transmutation method. It is shown that the relative magnitude of the mobilities of electrons hopping between donors and holes hopping between acceptors can be found from the hopping photoconductivity measured as a function of the intensity of band-to-band optical carrier excitation.     

Investigation of the Occupation Function of Localized States in Amorphous Semiconductors Under Infrared-Light Excitation

The occupation function of localized states in a-Si:H under i.r. light excitation is directly calculated from the observed infrared-stimulated photocurrent spectra. The calculated occupation function in dual-beam and one-beam excitation cases are compared. The overshot phenomenon in the dual-beam experiment is explained as the result of the difference of the initial condition between two cases when i.r. light is turned on. In the dual-beam excitation case, at the beginning, in the upper part of the band gap, there are many trapped electrons to be excited into the conduction band to cause the photoconductivity overshot.     

Sb、Ce掺杂Mg2Ge的第一性原理研究

此文用基于密度泛函理论(DFT)的第一性原理赝势平面波方法系统的计算了Sb、Ce掺杂Mg₂Ge的能带结构、态密度以及光学性质,获得了Mg₂Ge掺杂Sb后,费米面进入导带,呈现n型导电;Mg₂Ge掺杂Ce后,上自旋电子在费米能级附近处的价带和导带有一部分重叠,呈现半金属特性,进入导带电子数目增多,导电性增强. Sb、Ce掺杂Mg₂Ge后,其主要吸收峰都小于未掺杂Mg₂Ge,在可见光区域的透过率增大;Sb掺入后,在能量低于2.6 eV反射谱出现红移,Ce掺入后Mg₂Ge的吸收范围明显宽于本征Mg₂Ge;掺杂改善了Mg₂Ge对红外光子的吸收等有益结果.     

Stark Effect of Polarons in Parabolic Quantum Wells

We report the study of Stark effect of polarons in infinite parabolic quantum wells under an electric field, taking into account the effects of interaction with bulk LO-phonons. The electron-phonon interaction and the.effective mass in the plane perpendicular to the growth direction for excited states of free polarons have been calculated as functions of the degree of confinement. The general behavior of the excited states is found to be in agreement with previous works on the ground state. It is shown that in the limit of strong confinement the differences in electron-phonon interaction and effective mass between the ground state and excited states vanish. Although the applied electric field has no effect on the electronphonon interaction or the effective mass of a free polaron system, our numerical results for an AlGaAs parabolic quantum well have demonstrated its significance in determining the coupling of electrons with bulk LO-phonons of bound polaron systems.     

Electron-phonon interaction inP-doped silicon at low temperatures

In this present work, we explain the thermal conductivity results ofP doped silicon for impurity concentration 4.7×10¹⁷ and 1.0×10¹⁸ cm^–3 by applying the theory of scattering of phonons by electrons in the mixed state i.e. both in the localised state and in the metallic state. Using Mikoshiba's inhomogeneity model we calculated the number of electrons in the bound region and in the conduction band region and using the relaxation rates of both bound electron-phonon scattering and Ziman-Kosarev theory of free electron-phonon scattering, we explain the thermal conductivity values from 2 to 40 K. The values of density-of-states effective mass and dilatation deformation potential are found to be in agreement with the experimental values for silicon, for the electron concentration in the conduction band. We have also taken into account the effect of impurity scattering due to doped impurities, along with isotope scattering.     

过渡金属(Fe,Co,Ni,Zn)掺杂金红石TiO2的电子结构和光学性质

采用基于密度泛函理论的第一性原理方法对未掺杂以及不同浓度过渡金属Fe,Co,Ni,Zn掺杂金红石TiO₂的超晶胞体系进行了几何优化,并讨论了其晶格常数,电子能带结构和光学性质.研究结果表明:掺杂前后的晶格参数与实验值偏差在3.6%以下;适量的过渡金属掺杂不但影响体系能带结构,拓宽光吸收范围,而且扮演着俘获电子的重要角色,有利于光生电子-空穴对的有效分离以及增强光吸收能力;Fe,Co,Ni,Zn最佳理论掺杂体系分别为Ti_0.75Fe_0.25O₂,Ti_0.75Co_0.25O₂,Ti_0.75Ni_0.25O₂,Ti_0.83Zn_0.17O₂;Fe,Co,Ni3d态分裂为t_2g和e_g态,分别贡献于价带高能级和导带低能级部分,促进了电子-空穴对的生成,从而可提高TiO₂的光催化性能;Zn3d态电子成对填满轨道,不易被激发,故光催化活性无明显提高.     

第一性原理研究掺杂及未掺杂(TiO2)3团簇的电子性质

为了研究金属掺杂团簇时带隙的变化趋势，本文用Cr, Mo, V, Nb四种元素掺杂 (TiO2)3团簇，并用密度泛函理论下的广义梯度近似（GGA）方法计算。不同掺杂位置的结果表明最好的掺杂位置是3-配位的钛位置。所有掺杂后(TiO2)3团簇的HOMO-LUMO带隙都要比未掺杂时要小，对应高能区态密度峰值左移0.1eV；HOMO的电子云分布主要占据了氧原子的位置，当掺杂团簇被激发时，电子从末端氧原子位置跃迁到掺杂原子。此外，我们进一步的计算表明Cr和Mo是降低(TiO2)3团簇带隙较好的掺杂元素。为了进一步的研究掺杂(TiO2)3团簇的性质以及它在光催化，清洁能源等方面的应用，还需要我们进行实验和理论相结合的研究。     

A comparative ab initio study of the structural,mechanical, electronic and optical behaviors of ZnO:Ni thin films with nanometer scale

The electronic and optical properties of undoped and Ni–doped ZnO thin films with nanometer scale have been studied in the wurtzite phase, by first–principle approach. Density functional theory has been employed to calculate the fundamental properties of the films using full–potential linearized augmented plane–wave method. Ni doping was found to reduce the bandgap value of the material. Additionally, DOS effective mass of the electrons was evaluated. It was revealed that the effective mass of the electrons at the bottom of conduction band increased with Ni doping. Decrease of reflectance for thin films with nanometer scale in the UV–vis region was observed. The substitution by Ni decreased the intensity of the peaks, and a red shift was observed in the absorption peak. Moreover, the static dielectric constant, and static refractive index decreased with Ni content. Energy loss function of the modeled compounds was also evaluated. All calculated parameters were compared with the available experimental and other theoretical results.     

Optical and electric properties of Nb-doped anatase TiO2 single crystal

Nb-doped anatase TiO₂ single crystal has been grown by chemical vapour transport method. Raman spectra shows that the obtained crystal with Nb of 0.08 wt% has typical anatase structure. An absorption band was observed at around 2.2 eV, which seems to be due to the d-d transition in the conduction band. The electron paramagnetic resonance and electric resistivity measurements show that the doped niobium makes quite shallow donor level whose orbital is d_xy-like centered at the titanium position of anatase.