二元化合物半导体的晶格动力学和热力学性质的第一性原理研究
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摘要
在Ⅲ-Ⅴ族半导体中,由于氮化物(BN,AlN和GaN)具有优良的机械和热学性质,例如:高硬度、高熔点、高热导和大的体模量,因此近些年在科学研究和技术应用上引起了人们极大的兴趣。这些材料已被广泛用在短波发光二极管、激光二极管、光学探测器和其它的高温、高能、和高频装置上。Ⅱ-Ⅵ族半导体ZnS和ZnSe属于宽带隙半导体,它们在图像显示装置上具有广泛的应用。
本文基于密度函数理论和密度函数扰动理论,用第一性原理计算了:(1)闪锌矿结构和纤锌矿结构AlN和GaN的电子结构、晶格动力学和介电性质。这些性质包括晶格常数、体弹模量和弹性常数;以及利用线性响应方法计算的波恩有效电荷、高频介电常数和声子频率。(2)闪锌矿结构和纤锌矿结构AlN和GaN的弹性、介电和动力学性质与压力的关系。(3)闪锌矿结构BN的热力学性质,包括PTV状态方程,不同压力下的热膨胀系数等;纤锌矿结构GaN的热膨胀系数和定压摩尔比热随温度的变化关系。(4)闪锌矿结构ZnS和ZnSe的声子频率与压力的关系,以及热膨胀系数和定压比热随温度的变化关系。
本文的研究结果表明:
1.本次计算的闪锌矿结构和纤锌矿结构AlN和GaN的晶格常数、弹性常数、波恩有效电荷、介电常数与可利用的实验结果有比较好的一致。由于元素Al和Ga具有不同的电负性和原子半径,使AlN和GaN具有不同的共价键强度,这导致了闪锌矿结构和纤锌矿结构AlN和GaN的基态性质的差异。
2.闪锌矿结构AlN和GaN的C_(11)、C_(12),以及C_(11)、C_(12)、C_(13)和C_(33)随着压力的变化发生明显的变化,但无论闪锌矿结构还是纤锌矿结构,C_(44)都不如其它弹性张量对压力敏感。通过Martin变换,可以从闪锌矿结构的弹性常数得到纤锌矿结构的弹性常数。比较通过Martin变换和密度函数扰动理论得到的弹性常数,发现此次通过密度函数扰动理论得到的结果优于Martin变换结果。
3.除了纤锌矿结构AlN与c轴平行的波恩有效电荷有一例外外,其它的闪锌矿结构和纤锌矿结构的介电张量和波恩有效电荷张量均随着压力的增加单调的减小。这个例外可能是由于四角相变形的退杂化造成。总的来说,GaN的压力依赖性更明显,这是因为在AIN中有更强的共价键。
4.闪锌矿结构和纤锌矿结构AlN和GaN布里渊区中心Γ点的横向光学声子频率(TO)和纵向声学声子频率(LO)均随着压力的增加而单调的增加。光学声子支的所有振动模相当相似,并不与AlN和GaN的结构有关。
5.利用声子频率,从自由能得到了闪锌矿结构BN的压力-温度-体积(PTV)状态方程。从状态方程得到的295K下晶格常数与实验值之间的差异小于计算的基态晶格常数与实验值之间的差异。通过计算得到压力作用可用来减小热膨胀系数。
6.用密度函数理论计算了各向异性的纤锌矿结构GaN热膨胀系数,计算表明沿a轴方向的热膨胀系数在整个温区范围内高于沿c轴方向的热膨胀系数。无论对纤锌矿结构GaN,还是闪锌矿结构ZnS和ZnSe,在极低温状态下它们的热膨胀系数均为负,这可能是由于在极低温条件,激发的声子模主要是横向声学声子模,而这类声子模具有负的Gr(u|¨)neisen参数,导致热膨胀系数为负值。
7.本次计算了闪锌矿结构ZnS和ZnSe,以及纤锌矿结构GaN的定压摩尔热容。总的来说,在低温范围,计算的结果与实验值有比较好的一致,但在高温范围,计算值和实验值相差较大,这是由于非谐作用,以及样品本身在高温会产生较多的缺陷等原因所致。
Among theⅢ-Ⅴsemiconductors,the nitrides(BN,AlN,and GaN) have attracted both scientific and technological interest in recent years. This is due to the fascinating mechanical properties of them,such as hardness,high melting point,high thermal conductivity,large bulk modules.These materials can therefore be used for short-wavelength light-emitting diodes,laser diodes,and optical detectors,as well as for high-temperature,high-power,and high-frequency devices,zinc-blende zinc sulfide(ZnS) and zinc selenide(ZnSe) are wide bandⅡ-Ⅵsemiconductor.They are extremely useful in the manufacture of semiconductor devices.They are also the most important materials for image display applications.
Based on the density-function theory(DFPT) and density-function perturbation theory(DFPT),we report first-principles calculation of structure,lattice-dynamical and dielectric properties for zinc-blende and wurtzite AlN and GaN,i.e.(1) the lattice constants,the bulk moduli,and the elastic constants.A linear-response approach is used to derive the Born effective charge,the high-frequency dielectric constant,and the frequencies in ground state.(2) the structure,elastic properties and lattice-dynamical properties under hydrostatic pressure for zinc-blende and wurtzite AlN and GaN.(3) the thermodynamic properties of zinc-blende BN including the PTV equation of state and thermal expansion coefficient and heat capacity at constant pressure with temperature for wurtzite GaN.(4) the phonon frequencies with pressure, the thermal expansion coefficient and heat capacity at constant pressure with pressure for zinc-blende ZnS and ZnSe.Above these properties are performed using a pseudopotential plane wave method。
The results of this paper show that:
(1) The results for lattice constants,elastic constants,Born effective charges,dielectric constant are in good agreement with the experimental data available.Owing to different electronegative and atomic radius for atom Al and Ga,which resulting in different relative and absolute strengths of the ionic versus the covalent bonding,this results in different properties for zinc-blende and wurtzite AlN and GaN in ground state.
(2) The C_(11),C_(12) in zinc-blende AlN and GaN,and the C_(11),C_(12),C_(13) and C_(33) in wurtzite AlN and GaN depend significantly on hydrostatic pressure.Much weaker dependence on pressure has been observed for C_(44) elastic constant in both zinc-blende and wurtzite phases.It is possible to obtain elastic constants of wurtzite material from the zinc-blende ones applying the so-call Murtin's transformation.Comparing the results of Murtin's transformation and DFPT,the result using DFPT in this calculation is advantages to one of Martin's transformation.
(3) Except for the Born effective charge along c axis for wurtzite AlN, the other Born effective charges and high-frequency dielectric constants for both zinc-blende and wurtzite AlN and GaN decrease with rising pressure.This exception is likely due to the dehybridization that accompanies the tetrahedron deformation.In general,the pressure(and hence,volume)dependence is more pronounce for GaN because of stronger covalent bonding in AlN.
(4) The longitudinal optic(LO) and transverse optic(TO) phonon frequencies in Brillouin zone center for the zinc-blende and wurtzite AlN and GaN are monotonic increase with rising hydrostatic pressure.The pressure dependences of all vibrational modes related to optical phonon branches are rather similar and independent of the polytype of the nitride. Small deviation between GaN and AlN can be traced back to stronger covalent bonding in AlN.
(5) We obtain the PTV equation of state of zinc-blende BN from the free energy using phonon dispersion.The room temperature values of lattice constant is in better agreement with the experimental than T=0Kcalculated value.The effect of pressure is to reduce the thermal expansion coefficient.
(6) The anisotropic thermal expansion of wurtzite GaN is studied by density-function perturbation theory.The thermal expansion coefficient along a axis is always larger than one along c axis.For zinc-blende ZnS and ZnSe,wurtzite GaN,the thermal expansion coefficient are negative at low temperature,which can be explained as follow:in the quasiharmonic approximation(DHA),the thermal expansion coefficient at low temperature,the excited phonon modes are predominantly of transverse acoustic type which have negative Gr(u|¨)neisen parameter, giving negative values of thermal expansion coefficient.
(7) The calculated result of heat capacity at constant pressure of zinc-blende ZnS,ZnSe and wurtzite GaN are compared with the available experimental data in a wide temperature range.Generally in low temperature range,they have good agreement.But in high temperature range,due to anharnonic effect and the samples themselves forming more defects,lead to large errors between theoretical results and available experimental data.
本文基于密度函数理论和密度函数扰动理论,用第一性原理计算了:(1)闪锌矿结构和纤锌矿结构AlN和GaN的电子结构、晶格动力学和介电性质。这些性质包括晶格常数、体弹模量和弹性常数;以及利用线性响应方法计算的波恩有效电荷、高频介电常数和声子频率。(2)闪锌矿结构和纤锌矿结构AlN和GaN的弹性、介电和动力学性质与压力的关系。(3)闪锌矿结构BN的热力学性质,包括PTV状态方程,不同压力下的热膨胀系数等;纤锌矿结构GaN的热膨胀系数和定压摩尔比热随温度的变化关系。(4)闪锌矿结构ZnS和ZnSe的声子频率与压力的关系,以及热膨胀系数和定压比热随温度的变化关系。
本文的研究结果表明:
1.本次计算的闪锌矿结构和纤锌矿结构AlN和GaN的晶格常数、弹性常数、波恩有效电荷、介电常数与可利用的实验结果有比较好的一致。由于元素Al和Ga具有不同的电负性和原子半径,使AlN和GaN具有不同的共价键强度,这导致了闪锌矿结构和纤锌矿结构AlN和GaN的基态性质的差异。
2.闪锌矿结构AlN和GaN的C_(11)、C_(12),以及C_(11)、C_(12)、C_(13)和C_(33)随着压力的变化发生明显的变化,但无论闪锌矿结构还是纤锌矿结构,C_(44)都不如其它弹性张量对压力敏感。通过Martin变换,可以从闪锌矿结构的弹性常数得到纤锌矿结构的弹性常数。比较通过Martin变换和密度函数扰动理论得到的弹性常数,发现此次通过密度函数扰动理论得到的结果优于Martin变换结果。
3.除了纤锌矿结构AlN与c轴平行的波恩有效电荷有一例外外,其它的闪锌矿结构和纤锌矿结构的介电张量和波恩有效电荷张量均随着压力的增加单调的减小。这个例外可能是由于四角相变形的退杂化造成。总的来说,GaN的压力依赖性更明显,这是因为在AIN中有更强的共价键。
4.闪锌矿结构和纤锌矿结构AlN和GaN布里渊区中心Γ点的横向光学声子频率(TO)和纵向声学声子频率(LO)均随着压力的增加而单调的增加。光学声子支的所有振动模相当相似,并不与AlN和GaN的结构有关。
5.利用声子频率,从自由能得到了闪锌矿结构BN的压力-温度-体积(PTV)状态方程。从状态方程得到的295K下晶格常数与实验值之间的差异小于计算的基态晶格常数与实验值之间的差异。通过计算得到压力作用可用来减小热膨胀系数。
6.用密度函数理论计算了各向异性的纤锌矿结构GaN热膨胀系数,计算表明沿a轴方向的热膨胀系数在整个温区范围内高于沿c轴方向的热膨胀系数。无论对纤锌矿结构GaN,还是闪锌矿结构ZnS和ZnSe,在极低温状态下它们的热膨胀系数均为负,这可能是由于在极低温条件,激发的声子模主要是横向声学声子模,而这类声子模具有负的Gr(u|¨)neisen参数,导致热膨胀系数为负值。
7.本次计算了闪锌矿结构ZnS和ZnSe,以及纤锌矿结构GaN的定压摩尔热容。总的来说,在低温范围,计算的结果与实验值有比较好的一致,但在高温范围,计算值和实验值相差较大,这是由于非谐作用,以及样品本身在高温会产生较多的缺陷等原因所致。
Among theⅢ-Ⅴsemiconductors,the nitrides(BN,AlN,and GaN) have attracted both scientific and technological interest in recent years. This is due to the fascinating mechanical properties of them,such as hardness,high melting point,high thermal conductivity,large bulk modules.These materials can therefore be used for short-wavelength light-emitting diodes,laser diodes,and optical detectors,as well as for high-temperature,high-power,and high-frequency devices,zinc-blende zinc sulfide(ZnS) and zinc selenide(ZnSe) are wide bandⅡ-Ⅵsemiconductor.They are extremely useful in the manufacture of semiconductor devices.They are also the most important materials for image display applications.
Based on the density-function theory(DFPT) and density-function perturbation theory(DFPT),we report first-principles calculation of structure,lattice-dynamical and dielectric properties for zinc-blende and wurtzite AlN and GaN,i.e.(1) the lattice constants,the bulk moduli,and the elastic constants.A linear-response approach is used to derive the Born effective charge,the high-frequency dielectric constant,and the frequencies in ground state.(2) the structure,elastic properties and lattice-dynamical properties under hydrostatic pressure for zinc-blende and wurtzite AlN and GaN.(3) the thermodynamic properties of zinc-blende BN including the PTV equation of state and thermal expansion coefficient and heat capacity at constant pressure with temperature for wurtzite GaN.(4) the phonon frequencies with pressure, the thermal expansion coefficient and heat capacity at constant pressure with pressure for zinc-blende ZnS and ZnSe.Above these properties are performed using a pseudopotential plane wave method。
The results of this paper show that:
(1) The results for lattice constants,elastic constants,Born effective charges,dielectric constant are in good agreement with the experimental data available.Owing to different electronegative and atomic radius for atom Al and Ga,which resulting in different relative and absolute strengths of the ionic versus the covalent bonding,this results in different properties for zinc-blende and wurtzite AlN and GaN in ground state.
(2) The C_(11),C_(12) in zinc-blende AlN and GaN,and the C_(11),C_(12),C_(13) and C_(33) in wurtzite AlN and GaN depend significantly on hydrostatic pressure.Much weaker dependence on pressure has been observed for C_(44) elastic constant in both zinc-blende and wurtzite phases.It is possible to obtain elastic constants of wurtzite material from the zinc-blende ones applying the so-call Murtin's transformation.Comparing the results of Murtin's transformation and DFPT,the result using DFPT in this calculation is advantages to one of Martin's transformation.
(3) Except for the Born effective charge along c axis for wurtzite AlN, the other Born effective charges and high-frequency dielectric constants for both zinc-blende and wurtzite AlN and GaN decrease with rising pressure.This exception is likely due to the dehybridization that accompanies the tetrahedron deformation.In general,the pressure(and hence,volume)dependence is more pronounce for GaN because of stronger covalent bonding in AlN.
(4) The longitudinal optic(LO) and transverse optic(TO) phonon frequencies in Brillouin zone center for the zinc-blende and wurtzite AlN and GaN are monotonic increase with rising hydrostatic pressure.The pressure dependences of all vibrational modes related to optical phonon branches are rather similar and independent of the polytype of the nitride. Small deviation between GaN and AlN can be traced back to stronger covalent bonding in AlN.
(5) We obtain the PTV equation of state of zinc-blende BN from the free energy using phonon dispersion.The room temperature values of lattice constant is in better agreement with the experimental than T=0Kcalculated value.The effect of pressure is to reduce the thermal expansion coefficient.
(6) The anisotropic thermal expansion of wurtzite GaN is studied by density-function perturbation theory.The thermal expansion coefficient along a axis is always larger than one along c axis.For zinc-blende ZnS and ZnSe,wurtzite GaN,the thermal expansion coefficient are negative at low temperature,which can be explained as follow:in the quasiharmonic approximation(DHA),the thermal expansion coefficient at low temperature,the excited phonon modes are predominantly of transverse acoustic type which have negative Gr(u|¨)neisen parameter, giving negative values of thermal expansion coefficient.
(7) The calculated result of heat capacity at constant pressure of zinc-blende ZnS,ZnSe and wurtzite GaN are compared with the available experimental data in a wide temperature range.Generally in low temperature range,they have good agreement.But in high temperature range,due to anharnonic effect and the samples themselves forming more defects,lead to large errors between theoretical results and available experimental data.
引文
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