Magnetoresistance technique for determining cross-plane mobility in superlattice devices

Abstract

The cross-plane mobility, in the direction perpendicular to the planes of a superlattice, is critical for the computation of the figure of merit (ZT) in a thermoelectric device. The measurement of cross-plane mobilities in thermoelectric superlattice structures cannot be performed by conventional techniques such as the van der Pauw method. Therefore, alternative techniques must be used to obtain this important parameter. Magnetoresistance is the increase in material resistivity due to a lengthened path for charge carriers in a perpendicular magnetic field. The magnetoresistance is related to the magnetic field strength as (µB) 2 in the standard configuration, but the field dependence is also influenced by device geometry. This work focuses on measuring superlattice samples of composition Bi 2 Te 3 /Sb 2 Te 3 that are removed from their growth substrate and mounted on metal-coated substrates. This resulting mesa structure has a 100-µm-square contact metallization. Technical issues related to the sample preparation for the measurement are discussed. The magnetoresistance effect is expected to be small due to the anticipated low mobilities in Bi 2 Te 3 -based materials. Magnetoresistance studies with such superlattice thermo-elements were attempted using a dc magnetic field, but the sensitivity was insufficient. An ac magnetoresistance with lock-in detection can yield improved sensitivity. IntroductionMagnetoresistance is the increase in sample resistance due to the presence of a magnetic field. It may be useful for determining mobility when the sample structure does not permit van der Pauw contacts typically used for Hall-effect mobility measurements. The increased resistance induced by an applied magnetic field is due to both resistivity changes in the semiconductor sample and geometrical effects. First, the physical magnetoresistance effect (PMR) is related to conduction-process anisotropy, multi-carrier-type conduction, and energy-dependent carrier scattering. [1,2] If the sample is a long, thin rectangular bar with an applied transverse magnetic field, Lorentz forces on the carriers are balanced by the Hall electric field developed across the bar. PMR occurs when carriers with energy above and below the average energy are under-and over-compensated by this Hall field and result in increased resistivity.[2] If the sample consists of a thin plate with metallic contacts on the large faces, then the Hall field due to the transverse magnetic field would effectively be shorted out by the contacts. With no Hall field, the current flows at the Hall angle and magnetoresistance is observed even with no PMR. This effect is geomagnetoresistance (GMR), and it can be a much larger effect than PMR. [2] Long, rectangular samples with contacts at the ends of the long sample have a large length-to-width ratio (L/W), and the magnetoresistance effect is very small. [1] As L/W approaches zero, as it is for the Corbino disk, the magnetoresistance effect increases.[1] The resistance ratio of sample resistance in a magnetic f...