CN111597767A - Random nanowire network topology analysis and electrical property simulation method - Google Patents

Random nanowire network topology analysis and electrical property simulation method Download PDF

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CN111597767A
CN111597767A CN202010354087.8A CN202010354087A CN111597767A CN 111597767 A CN111597767 A CN 111597767A CN 202010354087 A CN202010354087 A CN 202010354087A CN 111597767 A CN111597767 A CN 111597767A
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赵志伟
翁正进
方勇
吴锦东
江和龙
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Abstract

The invention discloses a method for topology analysis and electrical property simulation of a random nanowire network, which comprises the following steps: 1. constructing a random nanowire network microscopic model; 2. describing the random nanowire network microscopic model by using a graph theory idea and a double-node model to obtain a matrix representation of a graph; 3. carrying out topology analysis on the random nanowire network diagram; 4. establishing a random nanowire network circuit topological graph and establishing a corresponding network branch admittance matrix; 5. the electric network is analyzed and calculated by means of a node voltage method. The invention provides a more reliable and more complete method for analyzing the topology of the random nanowire network and simulating the electrical properties, which can analyze the topology of the random nanowire network by considering basic physical quantities such as segment resistance, junction resistance, tunnel effect junction resistance and the like, and adopts a systematic and automatic method to construct and solve a circuit equation, thereby realizing the simulation and the simulation of the electrical properties of the random nanowire network through a computer.

Description

Random nanowire network topology analysis and electrical property simulation method
Technical Field
The invention belongs to the technical field of advanced nano material design and analysis, and particularly relates to a random nanowire network topology analysis and electrical property simulation method.
Background
Nanowires (tubes) with one-dimensional morphology have been extensively studied for their unique structure and excellent physical properties. However, the construction and application of single nanowires in nano devices are not ideal. In contrast, a random nanowire network (such as a carbon nanotube, a silver nanowire, a copper nanowire, a gold nanowire and a metal alloy nanowire network) formed by assembling nanowires has the advantages of good photoelectric performance, flexible mechanical response, low cost, suitability for large-scale production and the like, is paid much attention to by people, and has a very wide application prospect in the fields of transparent conductive electrodes, flexible sensing, touch control, display and the like.
The electrical property is one of important physical properties of the random nanowire network, is an index for measuring and evaluating the performance of the random nanowire network, and is a very important parameter in designing and optimizing the random nanowire network and the application of the random nanowire network in photoelectric devices. However, the electrical mechanism of the random nanowire network faces more complicated problems, especially the electrical anisotropy caused by random distribution, the conduction and conduction characteristics caused by percolation networks, the breakdown phenomenon caused by the action of electrical stress, and the like. Therefore, a proper mathematical model and equation need to be established, and the conduction and conduction process of the random nanowire network is expressed in the model by proper mathematical and physical languages, so that the simulation and emulation of the electrical properties of the random nanowire network are realized by a computer by means of a numerical simulation method.
Up to now, the percolation conduction conductivity of the random nanowire network has been mainly studied through typical work, and the influence of basic physical quantities such as the distribution, length, diameter, length-diameter ratio, section resistance, node contact resistance and the like of the nanowires on the conductivity of the random nanowire network has been studied. However, due to the complexity of the random nanowire network theory and system research, the existing numerical simulation and emulation models have the following constraints:
if no good simulation method is available, the influence of the random nanowire network geometry and basic physical quantity on the electrical properties of the random nanowire network can be completely researched. The lattice model is effective in predicting the percolation threshold of a random nanowire network, but does not take into account the shape of the nanowires. The Junction-doped evaluation (JDA) provides a simple and convenient method for calculating the square resistance of the random nanowire network, but usually ignores the segment resistance of the nanowires, and cannot accurately estimate the actual square resistance of the random nanowire network after the Junction resistance between the nanowires is reduced to dozens of ohms through a proper welding process.
For example, the geometric topological structure of the nanowire network cannot be intuitively reflected and well described by a mathematical language in a simulation model, the seepage conduction of the nanowire network is researched more, and the judgment of the full conduction state is less.
For example, the current density and voltage drop of important nodes in the random nanowire network are difficult to reflect in a simulation model, and the current density and voltage drop are not related to the geometric topology of the random nanowire network, so that the corresponding voltage distribution is obtained.
For example, a large-scale random nanowire network cannot provide a systematic and automatic method for constructing an electrical network equation and rapidly solving each node voltage.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method for analyzing the topology of a random nanowire network and simulating electrical properties, which can accurately perform topology analysis on the geometric structure of the random nanowire network by considering the basic physical quantities such as the length, distribution, aspect ratio, segment resistance, junction resistance, and tunneling junction resistance, and determine the fully conducting state while solving the percolation threshold, and construct a large-scale electrical network equation according to the obtained topological relationship of the nanowire network to solve the network conductivity, the current density and the voltage drop of each node.
In order to achieve the purpose, the technical scheme provided by the invention is as follows: a random nanowire network topology analysis and electrical property simulation method comprises the following steps:
step 1, analyzing the structural characteristics of a random nanowire network, and establishing a microscopic random nanowire network structural model corresponding to the structural characteristics by using a Monte Carlo method to obtain a basic information matrix of random nanowires;
step 2, describing the geometric topological structure of the random nanowire network by using a graph theory thought and a double-node model based on a seepage theory and a quantum tunneling theory to obtain directed graph matrix representation of the nanowire network;
step 3, carrying out topology analysis on the random nanowire network diagram;
step 4, establishing a random nanowire network circuit topological graph according to an electric network theory, and establishing a corresponding network branch admittance matrix;
and 5, analyzing and calculating the electric network by a node voltage method.
Further, geometric topology transformation and matrix characterization of the graph of the random nanowire network: describing the random nanowire network by using the relation between a vertex and an edge by means of a graph theory algorithm; establishing two potential vertexes for the intersection points in the random nanowire network by using a double-node model, wherein each vertex is positioned on each nanowire related to a contact point; and numbering the vertexes and the edges, and obtaining an incidence matrix of the random nanowire network diagram according to the relation between the vertexes and the edges.
Further, converting the incidence matrix of the random nanowire network diagram into an adjacent matrix; judging the connectivity of the network according to a connectivity algorithm of the graph, solving the number of connected blocks of the graph, and indicating which connected block each vertex belongs to respectively so as to obtain the seepage probability and the total conduction critical density of the random nanowire network; from the weight matrix of the graph of the random nanowire network, the general center of the graph can be determined.
Further, the random nanowire network topology is formalized into a circuit model through parameter extraction. Static simulation analysis is carried out on the random nanowire network pure resistance model, a large-scale linear equation set is established according to the incidence matrix and the branch admittance matrix of the random nanowire network graph by adopting a classical node analysis method, and voltage values of all circuit nodes are obtained by solving the linear equation set, so that the voltage drop, the current density and the like of each node can be further analyzed.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a more reliable and more complete method for analyzing the topology of a random nanowire network and simulating the electrical properties, which can analyze the topology of the random nanowire network graph by considering the basic physical quantities of the nanowire length, the distribution, the length-diameter ratio, the segment resistance, the junction resistance, the tunnel effect junction resistance and the like, and adopts a systematic and automatic method to construct and solve a circuit equation, thereby realizing the computer simulation and simulation of the electrical properties of the random nanowire network under the complex physical condition by a computer, and providing necessary verification and basis for designing and optimizing the random nanowire network.
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The invention will be described in further detail below with reference to the attached drawing figures, wherein:
FIG. 1 is a schematic flow chart of a two-dimensional random nanowire network model simulation method of the present invention;
FIG. 2 is a schematic diagram of a two-dimensional random nanowire network model of the present invention;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to specific embodiments below.
The invention provides a method for topology analysis and electrical property simulation of a random nanowire network, which comprises the following steps:
step 1, establishing a random nanowire network microstructure model:
selecting a model according to the form of the random nanowire network: a two-dimensional model is used for random nanowire network simulation applied to two-dimensional film materials such as transparent conductive films; a three-dimensional model is used for random nanowire network simulation of three-dimensional materials such as conductive composite materials.
a. Establishing a two-dimensional random nanowire network model as shown in FIG. 2; initially establishing a null of size (L)x+L)×(Ly+ L) and then adding straight, penetrable nanowires in the generated domain using the Monte Carlo method, wherein the nanowiresHas a length L, a diameter D and a number N. The spatial position of the nanowire is defined by the midpoint coordinate (x)i,0,yi,0) And the direction angle thetaiDetermining that the size of the midpoint coordinate in the model in the generation domain is Lx×LyThe generated positions in the region of (a) are set to be random, and the nanowires are randomly distributed in space.
b. Establishing a three-dimensional random nanowire network model: initially establishing a null of size (L)x+L)×(Ly+L)×(Lz+ L), then generating nanowires one by one in an empty three-dimensional generation domain by using a MATLAB tool, each nanowire calculating a gap with the previously generated nanowire, rejecting the nanowire to regenerate if the gap is less than 0 until a set number of nanowires is reached, and adding straight impenetrable nanowires in the generation domain, wherein the nanowires have a length of L, a diameter of D and a number of N. The spatial position of the nanowire is defined by the midpoint coordinate (x)i,0,yi,0,zi,0) Angle of orientation thetaiAnd a pitch angle
Figure BDA0002472875660000041
Determining that the size of the midpoint coordinate in the model in the generation domain is Lx×Ly×LzThe generated positions in the region of (a) are randomly arranged, and the nanowires are randomly distributed in space.
Step 2, abstracting the nanowire network in the analysis domain into a graph to obtain a matrix representation of the nanowire network graph; first, the analysis domain (a. two-dimensional model generation domain size is L'x×L′y(ii) a b. L 'is the size of the three-dimensional model generation domain'x×L′y×L′z) Between nanowires and at their intersections with the boundaries of the analytical domains. The relationship between the nanowires and their boundaries is then described by means of graph theory: the intersections between the nanowires and the boundary are regarded as vertexes in the graph, and the relationship between the intersections is regarded as an edge. And counting the intersection points, and numbering the intersection points in sequence. It should be noted that if the distance d between the nanowires is less than or equal to the sum of the tunneling distance and the diameter of the nanowires, the nanowires are also considered to intersect. The intersection point between each nanowireThe vertices are numbered in the order of 1, 2, N +1, N +2, N2 for intersections within the nanowires, the vertices for intersections between boundaries and nanowires (lower boundary: N2+1, N + 2+ p + p; upper boundary: N2+ p +1, N2+ p + N2+ N; left boundary: N2+ N +1, N2+ N + p; right boundary: N2+ N + p +1, N2+ N + p + N2+ N), the numbering is done sequentially from left to right and from top to bottom1，v2，…，vnH, edge set E2{ E1，e2，...，emAnd the weight on the edge is f (v)ivj) Where i, j ═ 1, 2, …, n.n ═ N1 × 2+ N2+ N3. to obtain a correlation matrix M0(G) and a weight matrix w of the nanowire map, where the row j of M0(G) represents a point and the column k represents an edge, the correlation matrix M0(G) ═ Mjk)n×mElement m ofjkIs defined as
Figure BDA0002472875660000051
Weight matrix w ═ dij)n×nIs defined as
Figure BDA0002472875660000052
In particular, if the vertex v isiAnd vjIf there is an edge between them, the weight on the edge is the distance between the two vertexes; if the vertex v isiAnd vjThere is no edge between them, the weight of the edge, i.e. the distance between the two vertices, is infinite.
Step 3, carrying out topology analysis on the nanowire network graph; converting the correlation matrix M0(G) of the nanowire map into the adjacency matrix a (G) ═ aij)n×nWherein a isijRepresenting a vertex viAnd vertex vjThe number of edges between is 0 or 1. Defining P (G) as the reachable matrix P (G) of the adjacent matrix calculation chartij)n×nElement p of (1)ijIs composed of
Figure BDA0002472875660000053
Whether the nanowire network forms a seepage conduction path or not can be determined through the reachable matrix. In addition, the number of connected blocks of the nanowire directed graph can be found by the adjacency matrix of the graph, and it is indicated to which connected block each vertex belongs. If the number of the connected blocks is 1, the nanowire network is in a full conduction state. Knowing the weight matrix of the graph of the nanowire network, the general center of the graph can be determined.
Step 4, establishing a random nanowire network circuit topological graph, and establishing a corresponding network branch admittance matrix; the random nanowire network graph forming the percolation conduction path is regarded as an electric network, edges are called branches, and points are called nodes. The sizes of the nanowire segment resistance, the junction resistance and the tunneling junction resistance are obtained according to a formula, and corresponding resistance values are given to the branches (the branch between intersection points formed by lapping different nanowires is the junction resistance, and the branch between adjacent nodes of the same nanowire is the segment resistance). Then, a corresponding element admittance matrix Y is establishede，YeIs a diagonal matrix whose elements are the element admittances of the branches. When there is no controlled source and mutual inductance, the branch admittance matrix YbComponent admittance matrix Ye. I.e. without controlled source, the branch admittance matrix, i.e. the element admittance matrix, is a diagonal matrix.
Step 5, analyzing and calculating the electric network by means of a node voltage method, specifically as follows:
firstly, a node in the graph G is selected as a reference node, a row of the node in the incidence matrix M0(G) can be drawn, and the matrix after drawing the row is called a reduced order incidence matrix and is represented by M (G).
The number of the circuit nodes is n, n-1 nodes outside the reference node are analyzed and calculated according to a formula Yn-1＝MYbMTConstructing an (n-1) × (n-1) order node admittance matrix Yn-1I.e. a network conductance matrix, where MTIs the transpose of the reduced order correlation matrix M. Then, a node voltage equation is established according to a node analysis method: y isn-1Vn-1＝Jn-1Wherein (n-1) × 1 order 1 matrix Vn-1Is a circuit node voltage vector of (n-1) × 1 order matrix Jn-1Is a vector of current sources injected into the node.
The node voltage response under the static model of the circuit can be obtained by solving the node voltage equation through a direct solution or an iterative solution, so that the voltage drop and the current density of each node can be further analyzed, and the equivalent resistance of the circuit network can be calculated according to the ohm's law. For the two-dimensional model, the optical transmittance of the corresponding network can be calculated according to a transmittance formula, and the relation between the resistivity and the transmittance of the random nanowire network is obtained.
The above description is only for illustrating the present invention, but the scope of the present invention is not limited thereto. Any person skilled in the art can make appropriate changes or modifications within the technical scope of the invention, and such changes or modifications are intended to be included within the scope of the invention.

Claims (4)

1. A random nanowire network topology analysis and electrical property simulation method is characterized by comprising the following specific steps:
step 1, analyzing the structural characteristics of a random nanowire network, and establishing a microscopic random nanowire network structural model corresponding to the structural characteristics by using a Monte Carlo method to obtain a basic information matrix of random nanowires;
step 2, describing the geometric topological structure of the random nanowire network by using a graph theory thought and a double-node model based on a seepage theory and a quantum tunneling theory to obtain directed graph matrix representation of the nanowire network;
step 3, carrying out topology analysis on the random nanowire network diagram;
step 4, establishing a random nanowire network circuit topological graph according to an electric network theory, and establishing a corresponding network branch admittance matrix;
and 5, analyzing and calculating the electric network by a node voltage method.
2. The method for random nanowire network topology analysis and electrical property simulation of claim 1, wherein the matrix characterization of the graph of the random nanowire network is:
describing the random nanowire network by using the relation between a vertex and an edge by means of a graph theory algorithm; establishing two potential vertexes for the intersection points in the random nanowire network by using a double-node model, wherein each vertex is positioned on each nanowire related to a contact point; and numbering the vertexes and the edges, and obtaining an incidence matrix of the random nanowire network diagram according to the relation between the vertexes and the edges.
3. The random nanowire network topology analysis and electrical property simulation method of claim 1, wherein the topology analysis is performed on a random nanowire network graph:
judging the connectivity of the network according to the matrix representation and connectivity algorithm of the graph, solving the number of the connected blocks of the graph, and indicating which connected block each vertex belongs to respectively so as to obtain the seepage probability and the total conduction critical density of the random nanowire network, and determining the general center of the graph according to the weight matrix of the graph of the random nanowire network.
4. The method for random nanowire network topology analysis and electrical property simulation of claims 1 to 3, wherein a graph theory and an electrical network theory are combined, a node admittance matrix is constructed and a node voltage equation is established for electrical network analysis and calculation:
the method comprises the steps of establishing a random nanowire network model, establishing a circuit model by using a random nanowire network topological structure, performing static simulation analysis on the random nanowire network model by using a parameter extraction method, establishing a large-scale linear equation set according to an incidence matrix and a branch admittance matrix of a random nanowire network graph by using a classical node analysis method, and obtaining voltage values of all circuit nodes by solving the linear equation set, so that the voltage drop, the current density and the like of each node can be further analyzed.
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