Implementation of the Quantum Hall Effect based precision resistance measurement system

Maboko, Mporome Brian

Implementation of the Quantum Hall Effect based precision resistance measurement system

Master Thesis

2019

Abstract

The integer Quantum Hall Effect (QHE) occurs when a two-dimensional electron gas (2DEG) is subjected to a strong perpendicular magnetic field and when the system is cooled to low temperatures. The QHE harbours a wealth of unique phenomena. Of interest is the existence of the Quantum Hall Resistance (QHR) which had found to be related to two fundamental constants of nature via the von Klitzing constant h e 2 , where e is the charge of the electron and h Planck’s constant. This thesis investigates the properties of the QHE in a low dimensional electron gas system. The von Klitzing constant is determined as well as the electron density n2D and mobility µ of the material measured. The results are compared to the accepted value of the von Klitzing constant as determined by the metrological community. The average von Klitzing constant obtained is 25 783.637 Ω within an accuracy of 1.13 × 10−12. Our results are further interpreted using the Landau quantum mechanical model of electron transport in perpendicular magnetic field. The measurement of standard resistances utilising a standard DC resistance measurement system were also undertaken at the National Metrology Institute of South Africa (NMISA). This ties in with the ongoing project of NMISA to develop an in-house quantum Hall measurement system to provide the full traceability for resistance standard measurements in the Republic of South Africa. The device measured utilised a GaAs/AlGaAs heterostructure structure, grown via Molecular Beam Epitaxy (MBE). A micron sized Hall bar with Ohmic contacts was patterned using standard clean room procedures. Magnetotransport measurements at low temperatures, sub 200 mK were carried out on the device. The transverse and longitudinal resistances were obtained and plotted against the perpendicular magnetic field. Quantum Hall plateaus and Shubnikov de-Haas (SdH) oscillations were observed. Properties of the heterostructure such as the electron density (n2D) and mobility (µ) were determined. The n2D obtained was 2.27 × 1011 cm−2 with µ at 3.5 × 105 cm2V−1 s −1 . All results were compared to current literature values.

Keywords

Physics

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