Lu掺杂AlN的电子结构和光学性质的第一性原理研究

张瑞亮 卢胜尚 肖清泉 谢 泉

(贵州大学大数据与信息工程学院新型光电子材料与技术研究所，贵阳 550025)

With the rapid development of electronic informa‑tion technology,the performance requirements of semi‑conductor materials are getting higher[1].As a classic Ⅲ‑Ⅴ compound semiconductor material,AlN has attracted much attention because of its advantages,such as a wide direct bandgap[2],high electron mobility,high thermal conductivity[3],low thermal expansion coefficient[4],good chemical stability and mechanical strength,and good resistance to high temperature and corrosion.Therefore,AlN can be used as substrate material for ultraviolet LEDs,ultraviolet lasers,detec‑tors,and other devices.AlN has great market applica‑tion prospects in various optoelectronics devices,because of its good optical and mechanical properties[5].

Rare earth elements have been widely used in electronics,petrochemical,and other fields.Due to the low melting points of rare earth metals,with a unique electron shell of rare‑earth metal atoms,the doping of rare‑earth elements can effectively adjust the photo‑electric properties of AlN.Doping has been used to change the conductive type of semiconductors and elec‑tronic structure,produce new impurity energy levels and different types of carriers,and then change the optical and electrical properties of the material.Sc[6],La,Er[7],Mg[8],Cr[9],Tm[10],Tb,Ce,or Eu[11]doped AlN has been investigated by experimental and theoretical research.Generally,the bandgap of AlN decreases with the increase of rare‑earth element doping concen‑trations,and the absorption in the visible light region is enhanced,thereby expanding the absorption region of AlN.

Lu is the hardest and densest metal element in rare earth elements,it can be used as a catalyst for chemical synthesis and the preparation of scintillation crystals.Li et al.[12]discussed the effect of Lu3+addition on the microstructure and optical properties of phos‑phor through experiments,the results showed that the Lu‑doped samples had higher luminescence intensity.This suggests that Lu doping could improve the optical properties of the crystal.To our knowledge,few theoret‑ical data have been reported on the electronic structure and optical properties of Lu‑doped AlN.Therefore,the‑oretical research about the electronic structure and optical properties of Lu‑doped AlN (denoted as Al1-xLuxN,wherexis the atomic fraction of Lu)is nec‑essary.In this paper,the effects of Lu doping concen‑trations on the bandgap,density of states,and optical properties of AlN are studied by first‑principles,which provide a theoretical basis for the preparation of vari‑ous AlN‑related electronic devices.

1.1 Theoretical models

In this work,AlN is a hexagonal fiber zinc ore structure,the spatial point group isP63mc(No.186),and the lattice constants area=b=0.311 2 nm,c=0.497 9 nm.

A 2×2×2 AlN supercell consisting of 16 Al atoms and 16 N atoms was constructed.The doping process was to substitute Al atoms with Lu atoms,and the doping concentrations were 0.062 5,0.125,and 0.187 5,respectively.Fig.1 shows the crystal structures of Al1-xLuxN(x=0,0.062 5,0.125,0.187 5)supercells with different Lu doping concentrations after geometry optimization,In Fig.1a,x=0,so it is the actual super‑cell of intrinsic AlN.The number of Al or Lu indicates the positions of atoms in the supercell.For example,Al5 represents the position of the fifth Al atom in the supercell,and Lu10 means that a Lu atom occupied the tenth position.When the doping concentration is 0.125,the expression(2,6)means the occupancy of the second and sixth places by Lu atoms.Therefore,when the concentration of Lu doping is 0.125 and 0.187 5,Fig.2 shows the energy after optimization of different Lu doping positions.By comparing the energy of the crystal structure when the doped atoms are in dif‑ferent positions,the preferred position of the doped atoms in the crystal structure can be determined.The crystal structure is more stable if its energy is lower.Therefore,the calculations in this work were based on the two structures shown in Fig.1.

Fig.1 Supercell models of Al1-xLuxN：(a)x=0,(b)x=0.062 5,(c)x=0.125,(d)x=0.187 5

Fig.2 Lowest energy plots of different doped positions of Al1-xLuxN：(a)x=0.125,(b)x=0.187 5

1.2 Calculation details

The calculations used for this work were carried out in the Cambridge Serial Total Energy Package(CASTAT)module of Materials Studio (Accelrys Company,2019 Version)software package,a quantum mechanical program based on density functional theory that calculates from scratch.The BFGS(Broyden‑Fletcher‑Goldfarb‑Shanno)algorithm was used to geo‑metrically optimize the crystal geometry model,and then the electronic structure and optical properties of the geometrically optimized structure were calculated.The generalized gradient approximation (GGA)of Perdew‑Burke‑Ernzerhof(PBE)was selected to deal with the exchange‑correlation potential.The base group used by the atom was the plane wave base group,and the method of plane wave ultrasoft pseudopotential was used to deal with the interaction between ions and electrons in the paper.The plane‑wave cutoff energy was optimized to be 500 eV,and 8×8×4 K‑point grids were selected to sample the Brillouin zone.The calcu‑lation parameters were set as follows：the energy con‑vergence accuracy was 5×10-7eV per atom,the maxi‑mum interaction force was 0.1 GPa,the convergence accuracy of interatomic forces was 0.1 eV·nm-1,the maximum interaction force was 0.05 GPa,and the max‑imum displacement was 2×10-4nm.The calculation of energy was performed in the inverted space.The valence electrons involved in the calculations were N：2s22p3,Al：3s23p1,and Lu：4f145s25p65d16s2.

2.1 Electronic structure

The supercell volume and bandgap of Al1-xLuxN with different Lu doping concentrations after geometry optimization were shown in Table 1.Obviously,with the increase of Lu doping concentration,the supercell volume increases,and the bandgap decreases.Since the atomic radius of Lu is larger than that of Al,as Al atoms are substituted by Lu atoms,the supercell volume of AlN increases.Although a larger supercell volume should be obtained with a higher doping concentration,it is difficult to obtain a doping concen‑tration higher than 0.187 5 due to the limitation of Lu solid solubility.

Table 1 Supercell lattice constant and bandgap of Al1-xLuxN

The top of the valence band and the bottom of the conduction band of intrinsic AlN are located at the same point in the Brillouin zone,as shown in Fig.3,which indicates the intrinsic AlN is a direct bandgap semiconductor,the bandgap value is 3.890 eV,the results of this work do not differ significantly from those of Zou et al[13].The calculated bandgap of the intrinsic AlN is much smaller than the experimental value of 6.2 eV[14],which is consistent with other litera‑ture due to the underestimation within GGA[15].The bandgap value calculated by the GGA method is much smaller than the experimental value,and the relevant theoretical calculations show that the bandgap error calculated by the GGA method has a positive correla‑tion trend with the bandgap value of the material itself.As a result,the bandgap error for a material calculated using the GGA method will be very small when the band gap is zero.The bandgap error for a material calculated using the GGA method will also be very large when the bandgap is large.For Ⅲ‑Ⅴ main group compound semiconductors,the discontinuity of the wave function at CBM and VBM is the main reason for the small bandgap calculated by the GGA method[16].This is a common problem in many articles[13,17‑18],but it does not affect our qualitative analysis of AlN.

Fig.3 Band structures of Al1-xLuxN：(a)x=0,(b)x=0.062 5,(c)x=0.125,(d)x=0.187 5

The top of the valence band and the bottom of the conduction band of Al1-xLuxN (x≠0)are located at points F and G in the Brillouin zone,respectively,which indicates the Al1-xLuxN(x≠0)is an indirect band‑gap semiconductor.As the doping concentration increases,the bottom of the conduction band moves downwards,the band gap width narrows,and the band curve of the doped system becomes denser.This is due to the incorporation of rare earth elements,which cause lattice distortion and introduce new impurity energy levels into the energy band.

The bandgap is related to the electronic structure,so the electronic structure of Al1-xLuxN(x=0,0.062 5,0.125,0.187 5)was further investigated by calculating the electronic density of states(DOS)as shown in Fig.4.

Fig.4 Electronic density of states(DOS)of Al1-xLuxN：(a)x=0,(b)x=0.062 5,(c)x=0.125,(d)x=0.187 5

The total DOS(TDOS)spectrum shows three regions：the lower valence band(LVB)region at-15 to-11 eV,the upper valence band(UVB)region at-6 to 0 eV,and the conduction band(CB)region at 0 to 20 eV.For the intrinsic AlN,the TDOS is dominated by N2s,N2p,and Al3pstates.In the TDOS of Al1-xLuxN(x=0,0.062 5,0.125,0.187 5),LVB is mainly contrib‑uted by N2sstates,the UVB is mainly contributed by N2pand Lu4fhybrid orbitals,and the CB is dominated by Al3s,Al3p,and Lu5dstates.In addition,an addition‑al peak around-24 eV dominated by Lu5pis observed.With the increase of Lu doping concentration,the con‑tributions of N2pstate orbital hybridization to UVB gradually decrease,while the contribution of Lu4fstate orbital hybridization to UVB increases.In the CB part,the bottom of the conduction band moves towards the lower energy.Therefore,the bandgap of AlN decreases with the increase of Lu doping concentration.

2.2 Optical properties

The optical properties of AlN are related to the transition of electrons between energy levels,and the probability and intensity of electronic transitions can be conducted by the study of the dielectric function.The dielectric function is expressed as[19]：

where the imaginary part of the dielectric functionε2(ω)can be obtained by calculating the matrix ele‑ments of the wave function in the unoccupied state,as shown below[20]：

Where C and V are the conduction band and valence band,respectively;kandωare the reciprocal lattice vector and angular frequency,respectively;BZ is the first Brillouin zone;e·MCV(k)is the matrix element of momentum warp;EC(k)andEV(k)are the intrinsic ener‑gy level of the conduction band and valence band,respectively.

The real partε1(ω)can be derived from the imagi‑nary partε2(ω)through the Kramers‑Kronig relation：

wherePis the value of principal integration.

The real and imaginary parts of the dielectric function for Al1-xLuxN are shown in Fig.5.The real part is the static dielectric constant under the electrostatic field.As shown in Fig.5a,the static dielectric constantε1(0)are 4.50,4.86,5.17,and 5.46,respectively,when the energy value is zero andx=0.062 5,0.125,0.187 5.Theε1(0)increases with the increase of Lu doping concentration due to the increase of system energy and volume.

Fig.5 Dielectric function of Al1-xLuxN：(a)real part,(b)imaginary part

The imaginary part mainly reflects the optical absorption characteristics of the semiconductor.As shown in Fig.5b,the peaks of the imaginary part are all lower than the intrinsic AlN,but its peaks increase with the increase of Lu doping concentration,and whenx=0,0.062 5,0.125,and 0.187 5,the corresponding peaks are 8.28,7.79,7.93,and 7.95 eV,respectively.In addition,Lu doping makes the imaginary part of the dielectric function for AlN move towards the lower energy direction as a whole.This is mainly due to the incorporation of Lu impurity level,and Lu5d,N2p,and Al3pwork together at the top of the valence band,so the bandgap width of the system decreases with the increase of Lu doping concentration,and the electron transition is more prone to occur.Furthermore,the degree of the red shift is enhanced with the increase of Lu doping concentrations,which corresponds to the decrease in the bandgap of AlN.

The optical properties such as reflectivityR(ω),absorption coefficientα(ω),energy‑loss spectrumL(ω),and photoconductivity were calculated using relations given by earlier workers.Fig.6a shows the reflectivity of Al1-xLuxN(x=0,0.062 5,0.125,0.187 5).Al1-xLuxN shows high reflectivity in the ultraviolet region,and the strength of the reflection peak in the ultraviolet region decreases with the increase of Lu doping concentra‑tions and shifts to the lower energy.

Fig.6 Optical properties of Al1-xLuxN：(a)reflective index R(ω),(b)absorption coefficient α(ω)

The absorption spectrum is the percentage of time‑intensity decay of light waves propagating per unit dis‑tance in a semiconductor medium.As shown in Fig.6b,the absorption coefficients of Al1-xLuxN(x=0,0.062 5,0.125,0.187 5)are all at 105cm-1level,indicating that they all have good absorption performance.In the deep ultraviolet region,the peak intensity decreases gradual‑ly with the increase of Lu doping concentration.While in the visible and infrared regions,the absorption coef‑ficients increase with the increase of Lu doping concen‑tration.The illustration on the upper right shows that the absorption edges of AlN, Al0.9375Lu0.0625N,Al0.875Lu0.125N,Al0.8125Lu0.1875N are equal to 2.43,1.98,1.66,and 1.53 eV,respectively,which are consistent with the change of the bandgap.Compared with intrin‑sic AlN,Al1-xLuxN(x≠0)has an extra absorption peak at 30 eV.Since the energy level of generated impuri‑ties is in the bandgap,the absorption of visible light increases,and the absorption zone broadens.

The energy loss when the electron passes through the uniform dielectric can be further deduced from the dielectric function.The energy ‑lossL(ω)spectra of Al1-xLuxN(x=0,0.062 5,0.125,0.187 5)are shown in Fig.7,and its characteristic peak is related to plasma oscillation[21].The peak values are 17.68,8.94,5.01,and 2.87,respectively.The peaks of Al1-xLuxN(x≠0)are lower than that of intrinsic AlN,indicating that the emissivity of secondary electrons is extremely high after doping.In addition,the peak position exhibits a blue shift with the increase of doping concentration,indicating that Lu doping into AlN enhances the elec‑tronic transition of the upper valence band.

Fig.7 Energy‑loss spectra of Al1-xLuxN

The real and imaginary parts of the photoconduc‑tivity of Al1-xLuxN(x=0,0.062 5,0.125,0.187 5)are shown in Fig.8.The real part is observed that photocon‑ductivity increases sharply in the low‑energy region with the increase of energy,which confirms that there are more free electron transitions in the conduction band.The imaginary part of the photoconductivity of Al1-xLuxN(x=0,0.062 5,0.125,0.187 5)is 0 at the initial position.Lu doping makes the imaginary part of the photoconductivity for AlN move toward the lower energy direction.The minimum value gradually becomes larger,while the maximum value gradually becomes smaller.After the energy is greater than 60 eV,the con‑ductivity overlaps and is relatively stable.

Fig.8 Photoconductivity of Al1-xLuxN：(a)real part,(b)imaginary part

Detailed first‑principles investigations have been done on the electronic structure and optical properties of Al1-xLuxN(x=0,0.062 5,0.125,0.187 5)with differ‑ent Lu doping concentrations.The results show that the conduction band moves down and the bandgap becomes narrower with the increase of Lu doping con‑centration.Therefore,it is easier for electrons to transi‑tion from the valence band to the conduction band,resulting in the redshift of reflectivity,and absorption coefficient.The static dielectric constant increases with the increase of Lu doping concentration,however,the peak intensities of reflectivity,absorption coeffi‑cient,energy loss function,and photoconductivity decrease with the increase of Lu doping concentration.Lu doping enhances the absorption coefficient of AlN in the visible and infrared regions,which would make AlN a potential candidate in the photoelectrochemical application.

Acknowledgments:The work was supported by the Foundation for Sci‑tech Activities for the Returned Overseas Chinese Scholars of Guizhou Province,China(Grant No.[2018]09),the High‑level Creative Talent Training Program of Guizhou Province,China(Grant No.[2015]4015),and the Construction Project of Intelligent Manufacturing Industry and Education Integration Innovation Platform and Graduate Joint Training Base of Guizhou University,China(Grant No.2020520000‑83‑01‑324061).

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