非化学计量比硫族银化物奇异磁电阻效应的机理研究
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摘要
非化学计量比的硒化银和碲化银(本文统称硫族银化物)系列材料展现出奇特的磁电阻(Magnetoresistance，MR)效应：在超宽磁场(0．1mT～55T)和超宽温度(4K～300K)范围内材料显示正MR效应，且MR效应与磁场呈线性关系。这一奇异的MR效应使该系列材料在超强磁场的测量、脉冲激光技术、磁技术和信息读取技术等领域均具有广泛的应用前景，美国能源部已将这种材料作为未来十年重点开发的材料之一。但是该系列材料的制备工艺还有待进一步地完善和优化，材料的表征和性能的研究还远远不够充分，甚至出现报道结果相互抵触的情况。至于该系列材料的机理研究尚属起步阶段，国外文献尽管有一些工作能够定性或者半定量地与实验结果吻合，但是一个公认的建立在第一性原理基础上的理论机制尚未建立。
本文就是在此背景下基于目前所有的实验事实，尤其是对材料的微观结构的观测，并且在充分调研国际上相关机理的研究后，比较深入、系统地探索了非化学计量比硫族银化物系列材料MR效应的机理。我们研究的结果是国际上最早能够与实验进行定量比较的理论模型，主要针对块材和薄膜分两个层次建立了四个理论模型。
首先，第一个层次是从唯象角度建立的模型。第一个模型是所谓的两相复合材料有效介质近似模型。模型的基本物理思想是假设材料的结构可以从整体上视为许多小的银金属沉积物镶嵌于硒化银或碲化银介质中，即所谓的两相(金属相和半导体相)复合材料。模型的关键之处在于根据材料属于窄禁带半导体的特点，基于对实验数据的观察，找到材料中载流子迁移率随温度和磁场场强的依赖关系。利用有效介质近似的自洽方程成功构建了国际上第一个理论结果与实验结果可以进行定量比较的模型。利用模型分析了块材的MR效应与磁场、温度及银金属组分浓度的变化规律。分析认为，材料内部结构的不均匀导致材料内电流的流动发生弯曲，在外磁场作用下电流的弯曲加强，从而引起材料的奇异MR效应。利用模型预测了银组分的最佳掺杂浓度，此时材料的MR效应最为显著，其相应的物理图像是此时银金属在材料内部发生逾渗。理论计算值与实验值进行比较，两者吻合较好。
在第一层次，我们建立的第二个模型是两相复合材料的双重性转换模型。第一个模型不能用于薄膜MR效应的研究，原因是薄膜的边界效应显著，导致有效介质近似自洽方程不再成立。因此，要建立薄膜MR效应的理论模型必须另辟它径。仍然假设非化学计量比的硫族银化物材料是两相复合材料，并认为银金属是一滴滴小液滴镶嵌于半导体中，无磁场时这样的两相复合材料可以用“任意小液滴”模型描述。关键在于我们需要计算有磁场条件下的非对称的二阶有效电导率张量。为此，我们利用双重性转换(Duality transformation)关系，将问题转变为在物理上完全等价的无磁场条件下的标量电导率的计算。结果表明，理论计算的MR效应的数值与实验值完全吻合。
为了能够更深入、直观地探讨材料产生MR效应的物理图像，我们在第二个层次(即半唯象的层次)建立了新的理论模型——准随机电阻网络模型，分别描述二维薄膜和三维块材的MR性质。模型的主要思想是认为材料内部电流的流动可以用电阻网络中的电流流动描述。模型中薄膜和块材分别被离散为四端口和六端口电阻单元整齐、有序排列而成的电阻网络。网络内部载流子的迁移率分布满足准随机分布，即受条件限制的高斯分布。两个物理限制条件为：分布的边界值分别为银组分和半导体组分的载流子迁移率；分布的均值与材料中银组分体积分数f有关，用复合材料的并联模型决定。对于准随机电阻网络模型进行了极其复杂的数值模拟运算，得到MR效应随磁场、温度变化规律，模拟结果与实验值极为吻合。模型的显著优点是，外电场、外磁场作用下不均匀材料内部电流的流动情况可以用网络内部电流的可视图直观反映。我们清晰地看到电流在外加磁场下发生强烈弯曲，电流流动的路径增加，使得材料的电阻增大，从而导致材料的正线性MR效应。这些工作有助于今后从第一性原理出发探寻相应的物理本质。
在实验上已经发现非化学计量比硫族银化物材料的纵向MR效应，并进行了初步地表征研究。实验结果表明，随着掺杂种类的不同，材料纵向MR效应呈现复杂的行为，有正的纵向MR效应，也有负的纵向MR效应。国际上唯一的一篇探索相关机理的文章只是给出了负的纵向MR效应的定性说明。本文则在实验观察的基础上，构建了纵向MR效应的随机电阻网络模型。基于材料内部的不均匀性和纵向MR效应的特点，对材料的电阻率张量以及网络电阻单元的六阶阻抗矩阵进行修正。研究表明，我们的模型完全能描述目前纵向MR效应的复杂行为，并且能够半定量地与实验结果吻合。尤其可贵的是，通过模拟三维电流可视图，清晰展示了样品厚度方向上的电流“喷射”现象。研究表明，材料的纵向MR效应主要是由于材料在厚度上的不均匀性造成的。
An abnormal magnetoresistance (MR) of non-stoichiometric silver selenide and telluride (called by a joint name silver chalcogenide) is found firstly in 1997. It was shown that the MR of silver chalcogenide samples exhibits a linear dependence on magnetic field from 1mT to 5.5 T in the range of temperature from 4 to 300K. Silver chalcogenide material is expected to be measuring instrument for the high magnetic field, pulse laser technology, magnetic technology and information read technology. U.S. Department of Energy plans it as one of the most attentive materials in the next decade. However, the preparation technology for the materials need be improved further more and the investigation of materials' nature is inadequate. The reports about materials are even contradiction. Driven by the experimental results, theory researchers proposed models to interpret the unusual linear MR effect. Although the theory study has achieved some progress but no model has been compared with the experimental data quantitatively. A theory based on the first principle for the MR of non-stoichiometric silver chalcogenides is not built.
Taking this into consideration, we observed the experimental fact, especially the structure of materials, and investigated the existing theory, then explored the mechanism of the MR effect of materials thoroughly and systemically. Based on two levels, we proposed four models for the MR of materials which results can be compared with the experimental results quantitatively.
A first model proposed by us is a phenomenological model on the first level. The basic physical thought of the model is that the silver chalcogenide is regard as two-component (silver metal component and semiconductor component) composition. The key of the model is that the dependence of the mobility of carriers in the materials on the temperature and magnetic field is found. Based on the effective media approximation (EMA), the model for the MR of the three-dimension bulks is proposed and the results by the model agree well with the experimental data for the first time. The model takes the MR as a function of magnetic field, temperature and the conductivity of two components without magnetic field, and works when T > 112.5K . A critical volume fraction of silver metal is found, at which the MR reaches the maximum value in the same magnetic field and temperature. We suggest that the critical volume fraction is the result of the percolation between silver particles in silver selenide and telluride bulks.
The second model on the first level is a duality transformation model of two-component composition. Since boundary effect of the thin films is remarkable, the EMA model is unsuitable for the thin films. So a new model need be proposed for the MR of thin films. We hold the supposition that the silver chalcogenide is two-component composition which can be depicted by the "random droplet" model without magnetic field. Now we must calculate the effective conductivity tensor for the films in a magnetic field. A general duality transformation is found which maps the conductivity-tensor into a new, isomorphic, well-defined conductivity tensor. It is indicated that the model predictions agree well with the available experimental data.
For discussing the physical mechanism of MR effect intuitively and thoroughly, a quasi-random network model was proposed to simulate the real material on the second level (the half-phenomenological level). The main thought of the model is that the current in the real material can be described by the current in the resistor network.The thin film is dispersed into a two-dimension resistor network which is constructed from four-terminal resistors and the bulk is dispersed into a three-dimension resistor network which is constructed from six-terminal resistors. The mobility of carriesμwithin the network has a quasi-random distribution, i.e. a Gaussian distribution with two constraint conditions. The two constraint conditions are as follows: 1) The boundary values ofμare themobility of silver metalμ_1 and semiconductorμ_2 respectively; 2) The average value ofμis described by the parallel connection model of composite. The model predicts the dependence of the MR with the magnetic field and temperature. A good agreement is found between the theoretical MR and the available experimental data. The 2D and 3D visualizations of current flow within the network are indicated: the inhomogeneous of mobility in the network induce the intense curving flowing of electric current and MR effect of materials in magnetic field. This work is helpful for the mechanism of the MR of materials based on the first principle.
The longitudinal MR of the non-stoichiometric silver chalcogenide was reported by Hu et al. It is indicated that the p-type and n-type doped materials has complicated longitudinal MR, including positive MR and negative MR. The only literature proposed a model which shows the negative MR. In this work, a random network model was proposed to investigate the complex phenomenon of longitudinal MR of materials. The resistivity tensor of material and the tensor of resistor unit in the network are corrected because of the inhomogenous nature of materials and the nonzero transverse-longitudinal coupling component of resistivity tensor. The model predictions are compared with the experimental result Semi-quantitatively. The visualizations of current flow within the network indicates the intense flowing of electric current along sample's thickness direction which analogous to the effect known as current jetting. The findings indicate that the inhomogenous nature of materials induces the complicated longitudinal MR.
本文就是在此背景下基于目前所有的实验事实，尤其是对材料的微观结构的观测，并且在充分调研国际上相关机理的研究后，比较深入、系统地探索了非化学计量比硫族银化物系列材料MR效应的机理。我们研究的结果是国际上最早能够与实验进行定量比较的理论模型，主要针对块材和薄膜分两个层次建立了四个理论模型。
首先，第一个层次是从唯象角度建立的模型。第一个模型是所谓的两相复合材料有效介质近似模型。模型的基本物理思想是假设材料的结构可以从整体上视为许多小的银金属沉积物镶嵌于硒化银或碲化银介质中，即所谓的两相(金属相和半导体相)复合材料。模型的关键之处在于根据材料属于窄禁带半导体的特点，基于对实验数据的观察，找到材料中载流子迁移率随温度和磁场场强的依赖关系。利用有效介质近似的自洽方程成功构建了国际上第一个理论结果与实验结果可以进行定量比较的模型。利用模型分析了块材的MR效应与磁场、温度及银金属组分浓度的变化规律。分析认为，材料内部结构的不均匀导致材料内电流的流动发生弯曲，在外磁场作用下电流的弯曲加强，从而引起材料的奇异MR效应。利用模型预测了银组分的最佳掺杂浓度，此时材料的MR效应最为显著，其相应的物理图像是此时银金属在材料内部发生逾渗。理论计算值与实验值进行比较，两者吻合较好。
在第一层次，我们建立的第二个模型是两相复合材料的双重性转换模型。第一个模型不能用于薄膜MR效应的研究，原因是薄膜的边界效应显著，导致有效介质近似自洽方程不再成立。因此，要建立薄膜MR效应的理论模型必须另辟它径。仍然假设非化学计量比的硫族银化物材料是两相复合材料，并认为银金属是一滴滴小液滴镶嵌于半导体中，无磁场时这样的两相复合材料可以用“任意小液滴”模型描述。关键在于我们需要计算有磁场条件下的非对称的二阶有效电导率张量。为此，我们利用双重性转换(Duality transformation)关系，将问题转变为在物理上完全等价的无磁场条件下的标量电导率的计算。结果表明，理论计算的MR效应的数值与实验值完全吻合。
为了能够更深入、直观地探讨材料产生MR效应的物理图像，我们在第二个层次(即半唯象的层次)建立了新的理论模型——准随机电阻网络模型，分别描述二维薄膜和三维块材的MR性质。模型的主要思想是认为材料内部电流的流动可以用电阻网络中的电流流动描述。模型中薄膜和块材分别被离散为四端口和六端口电阻单元整齐、有序排列而成的电阻网络。网络内部载流子的迁移率分布满足准随机分布，即受条件限制的高斯分布。两个物理限制条件为：分布的边界值分别为银组分和半导体组分的载流子迁移率；分布的均值与材料中银组分体积分数f有关，用复合材料的并联模型决定。对于准随机电阻网络模型进行了极其复杂的数值模拟运算，得到MR效应随磁场、温度变化规律，模拟结果与实验值极为吻合。模型的显著优点是，外电场、外磁场作用下不均匀材料内部电流的流动情况可以用网络内部电流的可视图直观反映。我们清晰地看到电流在外加磁场下发生强烈弯曲，电流流动的路径增加，使得材料的电阻增大，从而导致材料的正线性MR效应。这些工作有助于今后从第一性原理出发探寻相应的物理本质。
在实验上已经发现非化学计量比硫族银化物材料的纵向MR效应，并进行了初步地表征研究。实验结果表明，随着掺杂种类的不同，材料纵向MR效应呈现复杂的行为，有正的纵向MR效应，也有负的纵向MR效应。国际上唯一的一篇探索相关机理的文章只是给出了负的纵向MR效应的定性说明。本文则在实验观察的基础上，构建了纵向MR效应的随机电阻网络模型。基于材料内部的不均匀性和纵向MR效应的特点，对材料的电阻率张量以及网络电阻单元的六阶阻抗矩阵进行修正。研究表明，我们的模型完全能描述目前纵向MR效应的复杂行为，并且能够半定量地与实验结果吻合。尤其可贵的是，通过模拟三维电流可视图，清晰展示了样品厚度方向上的电流“喷射”现象。研究表明，材料的纵向MR效应主要是由于材料在厚度上的不均匀性造成的。
An abnormal magnetoresistance (MR) of non-stoichiometric silver selenide and telluride (called by a joint name silver chalcogenide) is found firstly in 1997. It was shown that the MR of silver chalcogenide samples exhibits a linear dependence on magnetic field from 1mT to 5.5 T in the range of temperature from 4 to 300K. Silver chalcogenide material is expected to be measuring instrument for the high magnetic field, pulse laser technology, magnetic technology and information read technology. U.S. Department of Energy plans it as one of the most attentive materials in the next decade. However, the preparation technology for the materials need be improved further more and the investigation of materials' nature is inadequate. The reports about materials are even contradiction. Driven by the experimental results, theory researchers proposed models to interpret the unusual linear MR effect. Although the theory study has achieved some progress but no model has been compared with the experimental data quantitatively. A theory based on the first principle for the MR of non-stoichiometric silver chalcogenides is not built.
Taking this into consideration, we observed the experimental fact, especially the structure of materials, and investigated the existing theory, then explored the mechanism of the MR effect of materials thoroughly and systemically. Based on two levels, we proposed four models for the MR of materials which results can be compared with the experimental results quantitatively.
A first model proposed by us is a phenomenological model on the first level. The basic physical thought of the model is that the silver chalcogenide is regard as two-component (silver metal component and semiconductor component) composition. The key of the model is that the dependence of the mobility of carriers in the materials on the temperature and magnetic field is found. Based on the effective media approximation (EMA), the model for the MR of the three-dimension bulks is proposed and the results by the model agree well with the experimental data for the first time. The model takes the MR as a function of magnetic field, temperature and the conductivity of two components without magnetic field, and works when T > 112.5K . A critical volume fraction of silver metal is found, at which the MR reaches the maximum value in the same magnetic field and temperature. We suggest that the critical volume fraction is the result of the percolation between silver particles in silver selenide and telluride bulks.
The second model on the first level is a duality transformation model of two-component composition. Since boundary effect of the thin films is remarkable, the EMA model is unsuitable for the thin films. So a new model need be proposed for the MR of thin films. We hold the supposition that the silver chalcogenide is two-component composition which can be depicted by the "random droplet" model without magnetic field. Now we must calculate the effective conductivity tensor for the films in a magnetic field. A general duality transformation is found which maps the conductivity-tensor into a new, isomorphic, well-defined conductivity tensor. It is indicated that the model predictions agree well with the available experimental data.
For discussing the physical mechanism of MR effect intuitively and thoroughly, a quasi-random network model was proposed to simulate the real material on the second level (the half-phenomenological level). The main thought of the model is that the current in the real material can be described by the current in the resistor network.The thin film is dispersed into a two-dimension resistor network which is constructed from four-terminal resistors and the bulk is dispersed into a three-dimension resistor network which is constructed from six-terminal resistors. The mobility of carriesμwithin the network has a quasi-random distribution, i.e. a Gaussian distribution with two constraint conditions. The two constraint conditions are as follows: 1) The boundary values ofμare themobility of silver metalμ_1 and semiconductorμ_2 respectively; 2) The average value ofμis described by the parallel connection model of composite. The model predicts the dependence of the MR with the magnetic field and temperature. A good agreement is found between the theoretical MR and the available experimental data. The 2D and 3D visualizations of current flow within the network are indicated: the inhomogeneous of mobility in the network induce the intense curving flowing of electric current and MR effect of materials in magnetic field. This work is helpful for the mechanism of the MR of materials based on the first principle.
The longitudinal MR of the non-stoichiometric silver chalcogenide was reported by Hu et al. It is indicated that the p-type and n-type doped materials has complicated longitudinal MR, including positive MR and negative MR. The only literature proposed a model which shows the negative MR. In this work, a random network model was proposed to investigate the complex phenomenon of longitudinal MR of materials. The resistivity tensor of material and the tensor of resistor unit in the network are corrected because of the inhomogenous nature of materials and the nonzero transverse-longitudinal coupling component of resistivity tensor. The model predictions are compared with the experimental result Semi-quantitatively. The visualizations of current flow within the network indicates the intense flowing of electric current along sample's thickness direction which analogous to the effect known as current jetting. The findings indicate that the inhomogenous nature of materials induces the complicated longitudinal MR.
引文
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