半导体异质结中的电子迁移率及其压力效应
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摘要
本文采用记忆函数法,分别以Ⅲ-Ⅴ族异质结半导体和Ⅱ-Ⅵ族应变型异质结半导体为研究对象,从理论上讨论半导体单异质结中平行界面方向的电子迁移率及其压力效应.
首先以Ⅲ-Ⅴ族Al_xGa_(1-x)As/GaAs异质结为研究对象,考虑有限深势垒与导带弯曲的实际异质结势的影响,同时计入电子向异质结势垒层的隧穿效应,利用变分法和记忆函数法,讨论在体纵光学声子(LO)和界面光学声子(IO)的散射下,界面附近电子迁移率随温度、Al组分和电子面密度的变化关系及其压力效应.结果显示:电子迁移率随温度、压力的增加而减小;随Al组分和电子面密度的增加而非线性增加.且两种光学声子的散射作用均随压力增强,IO声子的变化幅度更为显著.同时发现,在光学声子散射下,电子迁移率随Al组分的缓慢增加,主要是由IO声子决定的;而电子迁移率随电子面密度增加的变化则由LO声子决定.
为进一步深入讨论异质结中电子的带间散射提供依据,采用三角势近似异质结的导带弯曲效应,通过数值计算方法求解薛定谔方程,研究流体静压力影响下有限深势垒ZnSe/Zn_(1-x)Cd_xSe应变异质结的本征态问题,同时与无应变的情形进行了比较分析.发现平面双轴应变使电子的能级降低,能级间距减小,且静压效应加剧了该下降趋势.同时,应变导致波函数的隧穿几率增加.
在上述工作的基础上,进一步改进理论模型:同时考虑沟道区及垒区存在自由应变时对半导体物理参数的调制作用,以及运用简化相干势近似(SCPA)计算Ⅱ-Ⅵ族三元混晶效应,讨论Cd组分、电子面密度的改变对电子本征态的影响.结果显示,随着Cd组分的增大,能级和能级间距增大,波函数隧穿进入垒区的几率逐渐减小。而且发现,随着电子面密度的增大,波函数隧穿几率增加,同时本征能量也随之增大,而能级间距逐渐减小.
基于已有应变异质结中电子本征态的研究结果,以Ⅱ-Ⅵ族ZnSe/Zn_(1-x)Cd_xSe异质结为研究对象,采用三角势近似并计入有限深势垒的限制效应,运用记忆函数方法,研究光学声子作用下应变异质结体系中电子的迁移率及其压力效应,分别讨论了带内散射及带间散射对迁移率的贡献.结果表明:内部平面双轴应变效应降低电子的迁移率,且外部流体静压力加剧了这种下降趋势.因此,讨论电子在应变型异质结构中的散射问题时,需要计入材料间由于晶格不匹配而产生的应变效应的影响.同时发现,电子迁移率的变化主要来自于沟道区LO声子的贡献.另外,带间散射和带内散射对于压力条件下的电子迁移率同样重要,而不容忽略.
In this thesis,a memory function approach(MFA) is adopted to discuss theoretically the electron mobility parallel to the interfaces in heterojunctions consisting ofⅢ-Ⅴgroup semiconductors and in strained heterojunctions consisting ofⅡ-Ⅵgroup semiconductors,and the pressure effect on the mobility is also been investigated.
Firstly,a variational method and the MFA are adopted to investigate the electron mobility in an Al_xGa_(1-x)As/GaAs heterojunction composed ofⅢ-Ⅴgroup materials under pressure effect by considering the scattering from LO and IO phonons.The influence of a realistic interface potential in a heterojunction with a finite barrier and conduction band bending are taken into account.Meanwhile,the tunneling of electrons into the barrier is also considered.The properties of electron mobility versus temperature,Al concentration and electronic density are given and discussed, respectively.The results show that the electron mobility decreases obviously as the increase of temperature and pressure,whereas increases nonlinearly with A1 concentration and electronic density.The scatterings from the IO and LO phonons increase with pressure and the former becomes more obvious than the latter. Furthermore,the variation of electron mobility with A1 concentration and electronic density are dominant by the IO and LO phonons,respectively.
Secondly,for the further discussion of the intersubband scattering of electrons in heterojunctions,the eigenvalues of an electron and its corresponding eigenfunctions in a ZnSe/Zn_(1-x)Cd_xSe strained heterojunction with a finite barrier under hydrostatic pressure are obtained by solving the Schrodinger equation.A triangle potential approximation is adopted and the electronic penetrating into the barrier is also taken into account.The numerical results with and without strain effect are compared and analyzed.It is shown that the strain lowers the electronic eigen-energy levels and decreases the seperations between the energy-levels,and pressure effect strengthens this tendency of the drop.Meanwhile strain enhances the penetration probability of eigenfunctions.
On the basis of above discussion,the theoretical model is improved to consider the effect of the free strain on both the barrier and the channel side,at the same time, a simplified coherent potential approximation(SCPA) is adopted to calculate the parameters of the ternary mixed crystals composed ofⅡ-Ⅵgroup materials.The Cd concentration and the electronic density influence,,;on the eigenstates of the electrons are discussed,respectively.The results indicate that the electronic eigen-energy levels and its seperations increase while the penetration probability of eigenfunctions decreases with increase of Cd concentration.Moreover,the eigen-energy levels and the penetration probability increase while the seperations between the energy-levels decrease with the electronic density.
Lastly,based on the results of the ZnSe/Zn_(1-x)Cd_xSe strained heterojunction composed ofⅡ-Ⅵgroup materials,the electron mobility parallel to the interface under hydrostatic pressure is investigated with the MFA by considering the intersubband and intrasubband scatterings from the optical phonons.A triangle potential approximation is adopted to simplify the potential of the conduction band bending and the electronic penetrating into the barrier is considered by a finite interface potential in our model.It is shown that the strain effect lowers the mobility of electrons while the hydrostatic pressure effect is more obvious to decrease the mobility.The contribution induced by the LO phonons in the channel side is dominant to decide the mobility.Compared with the intrasubband scattering,the effect of intersubband scattering is also important and is not negligible for the material studied.Thus,it indicates that the biaxial strain effect needs to be considered when one discusses the scattering problems of an electron in a strained heterojunction.
首先以Ⅲ-Ⅴ族Al_xGa_(1-x)As/GaAs异质结为研究对象,考虑有限深势垒与导带弯曲的实际异质结势的影响,同时计入电子向异质结势垒层的隧穿效应,利用变分法和记忆函数法,讨论在体纵光学声子(LO)和界面光学声子(IO)的散射下,界面附近电子迁移率随温度、Al组分和电子面密度的变化关系及其压力效应.结果显示:电子迁移率随温度、压力的增加而减小;随Al组分和电子面密度的增加而非线性增加.且两种光学声子的散射作用均随压力增强,IO声子的变化幅度更为显著.同时发现,在光学声子散射下,电子迁移率随Al组分的缓慢增加,主要是由IO声子决定的;而电子迁移率随电子面密度增加的变化则由LO声子决定.
为进一步深入讨论异质结中电子的带间散射提供依据,采用三角势近似异质结的导带弯曲效应,通过数值计算方法求解薛定谔方程,研究流体静压力影响下有限深势垒ZnSe/Zn_(1-x)Cd_xSe应变异质结的本征态问题,同时与无应变的情形进行了比较分析.发现平面双轴应变使电子的能级降低,能级间距减小,且静压效应加剧了该下降趋势.同时,应变导致波函数的隧穿几率增加.
在上述工作的基础上,进一步改进理论模型:同时考虑沟道区及垒区存在自由应变时对半导体物理参数的调制作用,以及运用简化相干势近似(SCPA)计算Ⅱ-Ⅵ族三元混晶效应,讨论Cd组分、电子面密度的改变对电子本征态的影响.结果显示,随着Cd组分的增大,能级和能级间距增大,波函数隧穿进入垒区的几率逐渐减小。而且发现,随着电子面密度的增大,波函数隧穿几率增加,同时本征能量也随之增大,而能级间距逐渐减小.
基于已有应变异质结中电子本征态的研究结果,以Ⅱ-Ⅵ族ZnSe/Zn_(1-x)Cd_xSe异质结为研究对象,采用三角势近似并计入有限深势垒的限制效应,运用记忆函数方法,研究光学声子作用下应变异质结体系中电子的迁移率及其压力效应,分别讨论了带内散射及带间散射对迁移率的贡献.结果表明:内部平面双轴应变效应降低电子的迁移率,且外部流体静压力加剧了这种下降趋势.因此,讨论电子在应变型异质结构中的散射问题时,需要计入材料间由于晶格不匹配而产生的应变效应的影响.同时发现,电子迁移率的变化主要来自于沟道区LO声子的贡献.另外,带间散射和带内散射对于压力条件下的电子迁移率同样重要,而不容忽略.
In this thesis,a memory function approach(MFA) is adopted to discuss theoretically the electron mobility parallel to the interfaces in heterojunctions consisting ofⅢ-Ⅴgroup semiconductors and in strained heterojunctions consisting ofⅡ-Ⅵgroup semiconductors,and the pressure effect on the mobility is also been investigated.
Firstly,a variational method and the MFA are adopted to investigate the electron mobility in an Al_xGa_(1-x)As/GaAs heterojunction composed ofⅢ-Ⅴgroup materials under pressure effect by considering the scattering from LO and IO phonons.The influence of a realistic interface potential in a heterojunction with a finite barrier and conduction band bending are taken into account.Meanwhile,the tunneling of electrons into the barrier is also considered.The properties of electron mobility versus temperature,Al concentration and electronic density are given and discussed, respectively.The results show that the electron mobility decreases obviously as the increase of temperature and pressure,whereas increases nonlinearly with A1 concentration and electronic density.The scatterings from the IO and LO phonons increase with pressure and the former becomes more obvious than the latter. Furthermore,the variation of electron mobility with A1 concentration and electronic density are dominant by the IO and LO phonons,respectively.
Secondly,for the further discussion of the intersubband scattering of electrons in heterojunctions,the eigenvalues of an electron and its corresponding eigenfunctions in a ZnSe/Zn_(1-x)Cd_xSe strained heterojunction with a finite barrier under hydrostatic pressure are obtained by solving the Schrodinger equation.A triangle potential approximation is adopted and the electronic penetrating into the barrier is also taken into account.The numerical results with and without strain effect are compared and analyzed.It is shown that the strain lowers the electronic eigen-energy levels and decreases the seperations between the energy-levels,and pressure effect strengthens this tendency of the drop.Meanwhile strain enhances the penetration probability of eigenfunctions.
On the basis of above discussion,the theoretical model is improved to consider the effect of the free strain on both the barrier and the channel side,at the same time, a simplified coherent potential approximation(SCPA) is adopted to calculate the parameters of the ternary mixed crystals composed ofⅡ-Ⅵgroup materials.The Cd concentration and the electronic density influence,,;on the eigenstates of the electrons are discussed,respectively.The results indicate that the electronic eigen-energy levels and its seperations increase while the penetration probability of eigenfunctions decreases with increase of Cd concentration.Moreover,the eigen-energy levels and the penetration probability increase while the seperations between the energy-levels decrease with the electronic density.
Lastly,based on the results of the ZnSe/Zn_(1-x)Cd_xSe strained heterojunction composed ofⅡ-Ⅵgroup materials,the electron mobility parallel to the interface under hydrostatic pressure is investigated with the MFA by considering the intersubband and intrasubband scatterings from the optical phonons.A triangle potential approximation is adopted to simplify the potential of the conduction band bending and the electronic penetrating into the barrier is considered by a finite interface potential in our model.It is shown that the strain effect lowers the mobility of electrons while the hydrostatic pressure effect is more obvious to decrease the mobility.The contribution induced by the LO phonons in the channel side is dominant to decide the mobility.Compared with the intrasubband scattering,the effect of intersubband scattering is also important and is not negligible for the material studied.Thus,it indicates that the biaxial strain effect needs to be considered when one discusses the scattering problems of an electron in a strained heterojunction.
引文
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