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研究生:蘇又新
研究生(外文):Yu-Hsin Su
論文名稱:磁性層包覆導線之磁場分析
論文名稱(外文):Analysis of Magnetic Field of the Conducting Line with cladding layer
指導教授:張慶瑞
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:英文
論文頁數:61
中文關鍵詞:磁場分析
外文關鍵詞:analysisofmagneticfield
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Abstract
In the structure of Magnetic Random Access Memory (MRAM), there exists orthogonal conducting wires clad with high permeability magnetic materials, and the Tunneling Magnetoresistance (TMR) cells is located between
them. By passing the current into wires, they will produce two orthogonal magnetic …elds on the cells, so the magnetic moment of the free layer in TMR will rotate to parallel or antiparallel the magnetic moment of the pinned layer in order to write the cell into 0 or 1. The high permeability
magnetic materials is used to concentrate the magnetic flux, once the wires are clad with them, we can pass less current to produce the same magnetic field. It has advantages of saving the power and preventing the current over the load of the wires. The main topic of the thesis is to calculate the magnetic field produced by the conducting wires clad with high permeability magnetic
materials.
The geometry of the conducting wire and the high permeability magnetic materials is larger in one dimension (along the current direction, say z-direction) than that in the other two dimensions, so we approximately take the two dimensional real space into account. It implies that the magnetic field is independent of z-axis. According to this fact, we make use of one way which transforms the real space into the imaginary space to evaluate the magnetic field on TMR cells. That is "Schwarz-Christo¤el Transformation".
Schwarz-Christos¤fel Transrmation provides a method that maps the interior of the polygon to the upper-half plane, so we can deal with the problem in the upper-half plane. Finally, we integrate directly the current and the
image current source in the real space to obtain the magnetic field. In addition we study the features of magnetic …eld under several kinds of geometry
of cladding layer.
Contents
1 Introduction . . . . . . .. . . . . . . . . . . . .. . .11
1.1 Introduction to MRAM . . . . . . . . . . . . . . . . . . . . . . . . . . .11
1.2 Introduction to coherent rotation . . . . . . . . . . . . . . . . . . . . . . .. . 13
2 The Theory of Applied Mathematics . . . . . . . . . . . 17
2.1 Conformal Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 The Schwarz-Christo¤el Transformation . . . . . . . . . . . . . . . . . . . . . 21
3 Calculation of the Magnetic Field . . . . . . . . . . . 27
3.1 Transformthe boundary of cladding layer by S-C Transformation. . . . . . .. . . . . . .. . . . . . .. . 27
3.2 The image current distribution . . . . . . . . . . . . . . . .. . . . . . . 37
3.3 Calculation of the magnetic …field . . . . . . . . . . . . . . . . . . . . . . . .. . 39
3.4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Summary. . . . . . . . . . . . . . . . . . . . . . . . .55
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