梁啟德臺灣大學：物理研究所江育廷Jiang, Yu-TingYu-TingJiang2007-11-262018-06-282007-11-262018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/54614Abstract This dissertation describes the measurement on the electron transport in two-dimensional GaAs electron systems. We report on the transport properties of electron gas systems of AlGaAs/GaAs heterostructure in the presence of a perpen-dicular magnetic field B. 1. Resistivity law in high-mobility two-dimensional GaAs electron systems: There are many physical quantities that may be studied in a two-dimensional elec-tron gas (2DEG), and one of the most popular characteristics is magnetoresistance (MR). The two components of quantum Hall transport coefficient ρxx and ρxy in high-mobility 2DEG had been found to be related by ρxx=αB(dρxy /dB), called “resis-tivity law”. The work we do is to study the temperature and mobility effects on scal-ing parameter α at high temperatures in a standard 2DEG system of GaAs/AlGaAs heterostructure. The high mobility samples (sample T475-2 with a mobility μ =239 m2/Vs and sample T479-4 with a mobilityμ =512 m2/Vs at 0.3 K) we used are fab-ricated by molecular beam epitaxy (MBE). The measurement was performed in a top-loading 3He cryostat over the temperature 0.3K~80 K. Four-terminal magnetore-sistance was measured by using standard phase-sensitive lock-in techniques with Hall bar and Ohmic contact technique. We estimate the scaling factor α of the resistivity law at temperature T= 20~80 K under the magnetic field not too low (B> 0.5 T) and find it varying with temperature, consistent with the work of Simon and Halperin in 1994. 2. The explanation and the transport behavior of resistivity law in two-dimensional electron gas system: Since we have investigated the high-temperature properties of resistivity law in high-mobility 2DEG systems, another work we do is to study resistivity law in a low-mobility 2DEG system. The low-mobility 2DEG system (sample C1335 with a mobility μ=0.804 m2/Vs at T=0.3 K) is formed at the interface of GaAs/AlGaAs heterostructure with self-assemble InAs quantum dots. Furthermore, we discuss the theoretical explanation and details of electron transport of resistivity law that also suggested by Simon and Halperin in 1994. Their argument is based on high-mobility 2DEG systems, i.e. ρxy is much larger than ρxx with percolation network. We compare our result with their conclusion.Contents Chapter1. Introduction to low-dimensional electron system 1 1-1 GaAs two-dimensional electron systems…………………………………………1 1-2 Density of states…………………………………………………………………...2 1-3 AlGaN/GaN electron system……………………………………...……………….6 Chapter2. Background theory 9 2-1 Classical Hall effect……………………………………………………………….9 2-2 Hall bar mesa patterned in heterostructure wafer………………………………..11 2-3 Quantum Hall effect……………………………………………………………...12 2-3-1 Landau levels and Shubnnikov-de Hass oscillation………………………...13 2-3-2 Edge states…………………………………………………………………..16 2-3-3 Quantum Hall effect...………………………………………………………17 2-4 Percolation theory………………………………………………………………..19 2-4-1 Fractal dimension and correlation length…………………………………...20 2-4-2 Percolating contour…………………………………………………………23 Chapter3. Sample fabrication and experimental techniques 26 3-1 Sample fabrication……………………………………………………………….26 3-2 Cryogenic system: Sorption pumped 3He cryostat………………………………27 3-2-1 Condensation of 3He………………………………………………………...28 3-2-2 Controlling the temperature………………………………………………...28 3-3 Measurement set-up and four-terminal resistance……………………………….28 Chapter4. Resistivity law in high-mobility two-dimensional GaAs electron systems 31 4-1 Introduction………………………………………………………………………31 4-2 Large positive magnetresistance in a high-mobility two-dimensional electron gas……………………………………………………………………………………32 4-3 Resistivity law at low temperatures……………………………………………...37 4-4 Resistivity law at high temperatures……………………………………………..39 4.5 Summary…………………………………………………………………………45 Chapter5. The explanation and the transport behavior of resistivity law in two-dimensional electron gas system 47 5-1 The behavior of the scaling factor α of resistivity law theoretically…………..47 5-2 The scaling factor α of resistivity law of high mobility samples in our experiment……………………………………………………………………………49 5-3 The details of theoretical explanation of resistivity law…………………………51 5-3-1 The percolation theory 5-3-2 The effect of disorder on microscopic and macroscopic lengths 5-4 The resistivity law in a low-mobility GaAs/AlGaAs heterostructure at high tem-peratures……………………………………………………………………………...54 5-5 The fundamental relation between electric and thermoelectric transport coeffi-cients in the quantum Hall regime……………………………………………………59 Chapter6. Conclusions 643489905 bytesapplication/pdfen-US量子霍爾效應二維電子氣體電阻率定律Quantum Hall Effecttwo-dimensional electron gasresistivity lawthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54614/1/ntu-95-R93222020-1.pdf