低维纳米结构中声学声子的输运性质研究
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摘要
近几十年来,半导体低维量子结构因其新颖的物理性质和广泛的应用前景,已成为凝聚态物理和材料科学中的重要前沿领域。同时,分子束外延等超薄生长技术和精细束加工技术的日益完善和迅猛发展也为量子器件的不断推陈出新给予了重要的技术支持。在本文中,我们对半导体低维纳米结构中的热输运和热导作了较深入的探索,并获得了一些有意义的结果,以期能为相关量子器件的设计和制造提供理论依据。
首先,我们在连续弹性近似模型下,利用转移矩阵方法,研究了扩散层和缺陷层在多层薄膜结构中对声学声子输运的影响,计算结果表明:不同频率的声学声子,大多数都能很好地穿透该结构,但也有若干频率的声学声子只有较低的透射系数而在图像中形成相应的波谷;波谷处的声学声子频率的大小与扩散层和缺陷层的厚度、含Al浓度、薄膜周期数的变化没有关系;声学声子通过该结构的透射系数,与扩散层和缺陷层的厚度、含Al浓度、薄膜周期数有密切关系,有些声学声子的透射系数对结构参数的变化十分敏感。这些结论,一方面,告诉我们可以通过改变以上结构参数来调节和控制声学声子通过该结构的透射系数;另一方面,可以为声子器件的设计和相应的实验研究提供理论上的参考。
接着,我们利用连续介质弹性模型和散射矩阵方法,研究了四垂直波导中的热输运,计算结果揭示了一些有趣的性质:总透射系数对约化频率的透射谱展示了一系列共振的峰谷结构。当四垂直波导中的一个弯曲高度大于或等于该量子波导中声子通道的最小维度时,透射谱中就会出现禁止频隙;当弯曲高度足够大时,透射谱中会出现一个或多个禁止频隙。有些具有较大弯曲高度的四垂直波导,它们对应的禁止频隙的宽度反而更窄,禁止频隙的数目可能更少。在波导的弯曲部分只有0模时,可以看到声子的透射系数随弯曲高度成周期性改变。在弯曲区域的高度和长度较小时,四垂直波导的热导对弯曲区域的高度和长度的变化十分敏感。随着温度的升高,四垂直波导的热导先减小,达到最小值后再增大。第一个连接在单个波导上的四垂直波导会抑制透射系数的增大和形成禁止频隙。在四垂直波导系列上每增加一个四垂直波导,就会在透射谱上增加二个共振峰。这些结论对人工控制热导和声子器件的设计具有指导意义。
我们也对低温下四通道量子结构的声子输运和热导进行了数值分析。计算的结果表明:当声学声子通过对称四通道量子结构时,声学波将在区域II的边界发生多重反射,这些声学波在区域II相互干涉形成具有一定波长和周期的驻波。不同的声学声子模在对称四通道量子结构中能够自动选择性地进入不同的输运通道。声学声子模的选择输运特性依赖于区域II的的宽度和长度、不同通道的横向宽度和相对位置。通过适当调谐该纳米结构的几何参数,可以加强或者削弱声子在不同通道中的输运强度。当声学声子通过非对称四通道量子结构时,不同的声学声子模也能够自动选择性地进入不同的输运通道。不同声子通道在低温下的热导是非整数量子化的。因此,该半导体四通道纳米结构在低温下可以用作声子模的分离器,或用于控制声学声子输运。
最后,我们研究了两种不同性质的双缺陷对纳米线中的声学声子热输运的影响,研究结果表明:当声学声子通过内含双缺陷的纳米线时,总透射系数( T )随约化声子频率(ω/? )的变化图像呈现一系列的峰―谷结构;由于缺陷和纳米线的边缘对声波的多重反射,声波在该纳米线中相互干涉可以形成驻波。在有真空缺陷的纳米线中,当T→0时,声子透射系数趋近于1 ;当双缺陷是硬材料时,在纳米线中传播的声学声子,其频率必须大于其阈限频率。这两种缺陷对热导的影响有本质的不同。若双缺陷是真空,当T→0时,可以看到普适的量子化热导和热导平台。然而,若双缺陷是硬材料,当T→0时,纳米线的热导为0 ,激发0模必须大于其阈限温度。这些结论既让人们获得了一些有关缺陷的重要性质,又为实现人工控制热导和声子器件的设计提供了又一新的思路。
In the last several decades, the semiconductor low-dimensional quantum structureshave become one of frontier research topics in condensed matter physics and materialscience as they exhibit some novel physical properties and potential application values.Simultaneously, the rapid advances and maturing in the ultrathin growth, such as molecu-lar beam epitaxy, and nanoscale lithography techniques have made it possible to fabricatevarious nano-devices. In this thesis, we deeply investigate the features of acoustic phonontransmission and thermal conductance in low-dimensional nanostructures and some use-ful results are obtained. It is expected to be helpful theoretically for the design and man-ufacture of quantum devices.
At first, by using the continuum elastic approximation model and the transfer matrixmethod, we investigate the effect of diffusion layers and defect layer on acoustic phononstransport through the structure consisting of different films. Our work show that mostacoustic phonons can easily pass the structure, but some only have much less transmissionprobabilities and form corresponding dips in the transmission spectrum. With the changeof the structure parameters such as the width of diffusion layers and defect layer, thenumber of unit cell and the density of containing Al in diffusion layers and defect layer,the magnitude of the frequencies of acoustic phonons corresponding to the dips almostremain unchanged, but the transmission coefficients corresponding to the dips change atdifferent degree, and the transmission probabilities of some frequencies are very sensitiveto the variation of the above-mentioned structure parameters. These results can providesome references in controlling the transmission coefficients of acoustic phonons, devisingparts of acoustic apparatus and theoretical investigation related.
Then, we investigate acoustic phonon transmission and thermal conductance in afour-perpendicularity-bend quantum waveguide at low temperatures using the scatteringmatrix method. The calculated results show some interesting features. The transmis-sion spectrum of the quantum waveguide displays a series of resonant peaks and dips;and when one of the bend heights is larger than or equal to the minimum of the dimen-sions of the phonon channel in the quantum waveguide, a stop-frequency gap will ap-pear; and some single four-perpendicularity-bend quantum waveguides with larger bendheights exhibit narrower width or smaller number of the stop-frequency gaps than thatwith smaller bend heights. When only the mode 0 is excited in the bend section, the transmission spectra can be seen to vary periodically with the bend heights. The ther-mal conductivity is much sensitive to the change of the smaller heights and longitudinallengths of the bend section; and the thermal conductivity decreases with the increasingof the temperature first, then increases after reaches a minimum. The investigations ofmultiple four-perpendicularity-bend waveguides connected in series indicate that the firstadditional four-perpendicularity-bend waveguide to the single one suppresses the trans-mission coefficient and forms stop-frequency gap; and two additional resonance peakswill be formed when each four-perpendicularity-bend waveguide is added in the series.The results could be useful for controlling thermal conductance artificially and the designof phonon devices.
The acoustic phonon transport in a four-channel quantum structure is also investigated by use of the scattering matrix method. It is found that different acoustic phonon modes transport selectively into different channels, standing waves can be formed owning to acoustic phonons interfering with each other in the quantum structure, the transmission coefficients of acoustic phonon through different channels depend sensitively on the parameters of the structure, and the channels all exhibit the noninteger quantized thermal conductance at very low temperitures due to the splitting of the quantum structure. The structure may be used as a split device for acoustic phonon modes and controlling the acoustic phonon transport.
Finally, we investigate the effect of two different kinds of double defects embeddedin a nanowire on acoustic phonon transport at low temperatures by using scattering matrixmethod. When acoustic phonons propagate through the nanowire, the total transmissioncoefficient versus the reduced phonon frequency exhibits a series of resonant peaks anddips, and acoustic waves interfere with each other in the nanowire to form standing wavewith particular wavelengths. In the nanowire with void defects, acoustic phonons whosefrequencies approach zero can transport without scattering. The acoustic phonons prop-agating in the nanowire with clamped material defects, the phonons frequencies must belarger than a threshold frequency. It is also found that the thermal conductance versustemperature is qualitatively different for different types of defects. At low temperatures,when the double defects are void, the universal quantum thermal conductance and a ther-mal conductance plateau can be clearly observed. However, when the double defectsconsist of clamped material, the quantized thermal conductance disappear but a thresholdtemperature where mode 0 can be excited emerges. The results both help people to knowsome important features on defects and give another way to control the transmission co-efficients of acoustic phonons and devise parts of acoustic apparatus.
首先,我们在连续弹性近似模型下,利用转移矩阵方法,研究了扩散层和缺陷层在多层薄膜结构中对声学声子输运的影响,计算结果表明:不同频率的声学声子,大多数都能很好地穿透该结构,但也有若干频率的声学声子只有较低的透射系数而在图像中形成相应的波谷;波谷处的声学声子频率的大小与扩散层和缺陷层的厚度、含Al浓度、薄膜周期数的变化没有关系;声学声子通过该结构的透射系数,与扩散层和缺陷层的厚度、含Al浓度、薄膜周期数有密切关系,有些声学声子的透射系数对结构参数的变化十分敏感。这些结论,一方面,告诉我们可以通过改变以上结构参数来调节和控制声学声子通过该结构的透射系数;另一方面,可以为声子器件的设计和相应的实验研究提供理论上的参考。
接着,我们利用连续介质弹性模型和散射矩阵方法,研究了四垂直波导中的热输运,计算结果揭示了一些有趣的性质:总透射系数对约化频率的透射谱展示了一系列共振的峰谷结构。当四垂直波导中的一个弯曲高度大于或等于该量子波导中声子通道的最小维度时,透射谱中就会出现禁止频隙;当弯曲高度足够大时,透射谱中会出现一个或多个禁止频隙。有些具有较大弯曲高度的四垂直波导,它们对应的禁止频隙的宽度反而更窄,禁止频隙的数目可能更少。在波导的弯曲部分只有0模时,可以看到声子的透射系数随弯曲高度成周期性改变。在弯曲区域的高度和长度较小时,四垂直波导的热导对弯曲区域的高度和长度的变化十分敏感。随着温度的升高,四垂直波导的热导先减小,达到最小值后再增大。第一个连接在单个波导上的四垂直波导会抑制透射系数的增大和形成禁止频隙。在四垂直波导系列上每增加一个四垂直波导,就会在透射谱上增加二个共振峰。这些结论对人工控制热导和声子器件的设计具有指导意义。
我们也对低温下四通道量子结构的声子输运和热导进行了数值分析。计算的结果表明:当声学声子通过对称四通道量子结构时,声学波将在区域II的边界发生多重反射,这些声学波在区域II相互干涉形成具有一定波长和周期的驻波。不同的声学声子模在对称四通道量子结构中能够自动选择性地进入不同的输运通道。声学声子模的选择输运特性依赖于区域II的的宽度和长度、不同通道的横向宽度和相对位置。通过适当调谐该纳米结构的几何参数,可以加强或者削弱声子在不同通道中的输运强度。当声学声子通过非对称四通道量子结构时,不同的声学声子模也能够自动选择性地进入不同的输运通道。不同声子通道在低温下的热导是非整数量子化的。因此,该半导体四通道纳米结构在低温下可以用作声子模的分离器,或用于控制声学声子输运。
最后,我们研究了两种不同性质的双缺陷对纳米线中的声学声子热输运的影响,研究结果表明:当声学声子通过内含双缺陷的纳米线时,总透射系数( T )随约化声子频率(ω/? )的变化图像呈现一系列的峰―谷结构;由于缺陷和纳米线的边缘对声波的多重反射,声波在该纳米线中相互干涉可以形成驻波。在有真空缺陷的纳米线中,当T→0时,声子透射系数趋近于1 ;当双缺陷是硬材料时,在纳米线中传播的声学声子,其频率必须大于其阈限频率。这两种缺陷对热导的影响有本质的不同。若双缺陷是真空,当T→0时,可以看到普适的量子化热导和热导平台。然而,若双缺陷是硬材料,当T→0时,纳米线的热导为0 ,激发0模必须大于其阈限温度。这些结论既让人们获得了一些有关缺陷的重要性质,又为实现人工控制热导和声子器件的设计提供了又一新的思路。
In the last several decades, the semiconductor low-dimensional quantum structureshave become one of frontier research topics in condensed matter physics and materialscience as they exhibit some novel physical properties and potential application values.Simultaneously, the rapid advances and maturing in the ultrathin growth, such as molecu-lar beam epitaxy, and nanoscale lithography techniques have made it possible to fabricatevarious nano-devices. In this thesis, we deeply investigate the features of acoustic phonontransmission and thermal conductance in low-dimensional nanostructures and some use-ful results are obtained. It is expected to be helpful theoretically for the design and man-ufacture of quantum devices.
At first, by using the continuum elastic approximation model and the transfer matrixmethod, we investigate the effect of diffusion layers and defect layer on acoustic phononstransport through the structure consisting of different films. Our work show that mostacoustic phonons can easily pass the structure, but some only have much less transmissionprobabilities and form corresponding dips in the transmission spectrum. With the changeof the structure parameters such as the width of diffusion layers and defect layer, thenumber of unit cell and the density of containing Al in diffusion layers and defect layer,the magnitude of the frequencies of acoustic phonons corresponding to the dips almostremain unchanged, but the transmission coefficients corresponding to the dips change atdifferent degree, and the transmission probabilities of some frequencies are very sensitiveto the variation of the above-mentioned structure parameters. These results can providesome references in controlling the transmission coefficients of acoustic phonons, devisingparts of acoustic apparatus and theoretical investigation related.
Then, we investigate acoustic phonon transmission and thermal conductance in afour-perpendicularity-bend quantum waveguide at low temperatures using the scatteringmatrix method. The calculated results show some interesting features. The transmis-sion spectrum of the quantum waveguide displays a series of resonant peaks and dips;and when one of the bend heights is larger than or equal to the minimum of the dimen-sions of the phonon channel in the quantum waveguide, a stop-frequency gap will ap-pear; and some single four-perpendicularity-bend quantum waveguides with larger bendheights exhibit narrower width or smaller number of the stop-frequency gaps than thatwith smaller bend heights. When only the mode 0 is excited in the bend section, the transmission spectra can be seen to vary periodically with the bend heights. The ther-mal conductivity is much sensitive to the change of the smaller heights and longitudinallengths of the bend section; and the thermal conductivity decreases with the increasingof the temperature first, then increases after reaches a minimum. The investigations ofmultiple four-perpendicularity-bend waveguides connected in series indicate that the firstadditional four-perpendicularity-bend waveguide to the single one suppresses the trans-mission coefficient and forms stop-frequency gap; and two additional resonance peakswill be formed when each four-perpendicularity-bend waveguide is added in the series.The results could be useful for controlling thermal conductance artificially and the designof phonon devices.
The acoustic phonon transport in a four-channel quantum structure is also investigated by use of the scattering matrix method. It is found that different acoustic phonon modes transport selectively into different channels, standing waves can be formed owning to acoustic phonons interfering with each other in the quantum structure, the transmission coefficients of acoustic phonon through different channels depend sensitively on the parameters of the structure, and the channels all exhibit the noninteger quantized thermal conductance at very low temperitures due to the splitting of the quantum structure. The structure may be used as a split device for acoustic phonon modes and controlling the acoustic phonon transport.
Finally, we investigate the effect of two different kinds of double defects embeddedin a nanowire on acoustic phonon transport at low temperatures by using scattering matrixmethod. When acoustic phonons propagate through the nanowire, the total transmissioncoefficient versus the reduced phonon frequency exhibits a series of resonant peaks anddips, and acoustic waves interfere with each other in the nanowire to form standing wavewith particular wavelengths. In the nanowire with void defects, acoustic phonons whosefrequencies approach zero can transport without scattering. The acoustic phonons prop-agating in the nanowire with clamped material defects, the phonons frequencies must belarger than a threshold frequency. It is also found that the thermal conductance versustemperature is qualitatively different for different types of defects. At low temperatures,when the double defects are void, the universal quantum thermal conductance and a ther-mal conductance plateau can be clearly observed. However, when the double defectsconsist of clamped material, the quantized thermal conductance disappear but a thresholdtemperature where mode 0 can be excited emerges. The results both help people to knowsome important features on defects and give another way to control the transmission co-efficients of acoustic phonons and devise parts of acoustic apparatus.
引文
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