Hall effect measuring technique

In crystalline semiconductors, the most common technique for the measurement of carrier mobility involves the Hall effect. However, in noncrystalline materials, experimental data are both fragmentary and anomalous (see, for example. Ref. [5]). Measured HaU mobility is typically of the order of 10 - 10 cm A /s and is frequently found to exhibit an anomalous sign reversal with respect to other properties providing information concerning the dominant charge carrier. Thus, apart from some theoretical interest, the Hall effect measurements are of minimal value in the study of macroscopic transport in amorphous semiconductors. 

The number of characterization techniques that are sufficiently sensitive for this material and preferably impurity species or defect structure specific is rather small. Variable temperature Hall effect measurements in the Van der Pauw (1958) configuration allow the determination of (NA - ND). The... 

At the end of the discussion of electrochemical measurement techniques, let us, however, briefly mention that there are other techniques that are not exclusively electrochemical in nature but related to the above methods such as thermoelectric measurements and Hall-effect measurements. Both techniques are extremely helpful in combination with conductivity experiments as they then allow the splitting of the conductivities into carrier concentration and mobilities. The first method relies on the emf formed as a sheer consequence of temperature differences (crosseffects in the thermal and chemical flux-force relations), while the second technique refers to concentration changes upon application of magnetic fields. Both techniques are particularly worked out for electronic carriers but are more tricky and much less straightforward for ionic carriers. For more details the reader is referred to Ref.16 301 302... 

Wurtzite-structure ZnO thin films grown by a variety of deposition techniques, as well as commercially available single crystal bulk samples are discussed. Furthermore, data for ZnO thin films intermixed with numerous elements are reviewed. Most of the results are obtained by SE, which is a precise and reliable tool for measurements of the DFs. The SE results are supplemented by Raman scattering and electrical Hall-effect measurement data, as well as data reported in the literature by similar or alternative techniques (reflection, transmission, and luminescence excitation spectroscopy). 

Hall effect measurements indicate mobilities of— 10-1 cm2 V-Isec-1 for both electrons (Dresner, 1980) and holes (E>resner, 1983). Tiedje et al. (1981) have measured drift mobilities of 1 cm2 V-1 for electrons and 10-3 cm2 V-1 sec-1 for holes. However, Silver et al. (1982) have estimated that the electron mobility is s 100 cm2 V-1 sec-1 by using the reverse recovery technique. 

Eor the experimental determination of the temperature dependence, the whole sample with the electrical leads has to be in temperature equilibrium at least for the time ofmeasure-ment. Due to the sniall size of the samples, the van der Pauw technique is particularly suited for such measurements and some corresponding measurement systenns are equipped with an integrated temperature chamber. A very flexible and convenient temperature control can be realized with a vacuum chamber, with the sample cooled by the Joule-Thompson effect (expansion cooling of N2 from a capillary nozzle), or heated by a resistive heater. In this way, temperature dependent measurements in the range between 80 and 580 K can be performed and the temperature can be set very accurately, which is also an important precondition for the Hall measurement (Section Hall effect measurement ). Simpler systems are using a cryostat with liquid nitrogen or helium, which allows measurements at temperatures down to 77 and 4 K, respectively. 

At very high frequencies, the current is measured by assessing one of the effects that it produces. Several techniques are possible, e.g. (1) measuring the temperature rise when the current flows through a known resistance or (2) using a Hall-effect probe to measure the electromagnetic field created by the current. 

In Section 1 we will use the theory developed in Appendix A to discuss the various measurement and analysis techniques that have been applied to SI GaAs. We will also discuss the precautions that must be observed in apparatus design, and present an automated Hall-effect and photo-electronic system capable of measuring high resistivity samples. 

Automated computer-controlled measurement techniques for Hall effect, photoconductivity, and photo-Hall measurements in semi-insulating... 

AlGaN alloys doped with Si have been grown by electron cyclotron resonance (ECR) MBE at temperatures between 700 and 800°C [23,24], These layers were found to have net carrier concentrations of 1016 to 1019 cm 3 as measured by the Hall effect technique. The carrier concentration varies only slightly on alloying up to 25% Al. The samples were found to be smooth and free from cracks. Murakami et al also reported crack-free surfaces of Si doped Alo.1Gao.9N with a carrier concentration of up to 2 x 1018 cm 3 [25],... 

The methods by which the phenomenon of interconfiguration fluctuations may be studied are (i) determination of lattice constant, (ii) magnetic susceptibility measurements, (iii) Mossbauer spectroscopy, (iv) measurement of electrical resistivity, (v) Hall effect, (vi) X-ray absorption spectroscopy and (vii) X-ray photoelectron emission spectroscopy. It is useful to note that a suite of techniques must be used to detect ICF phenomenon in a system. Nuclear magnetic resonance is sparingly used because not all the systems exhibiting ICF contain magnetically active nuclei. 

There are four experimental techniques that are commonly used to gain information about the electronic transport in a-Si H dc conductivity, the drift mobility, thermopower, and the Hall effect. Sections 7.1 and 7.2 describe these measurements and how the information about electronic conduction in Sections 7.3 and 7.4. 

X-ray and electron diffraction methods are applied in order to measure atomic distances in the crystal lattice and their changes. Hence, the diffraction methods are also basically suitable for measuring the strain/stress behaviour in thin films. However, since the film thickness and the crystallite size in thin films are small, some line broadening already arises from this. In order to determine what contribution the mechanical stresses have on the diffuse lines, careful analysis of the line profiles must be undertaken [148, 151]. This method is less suitable for routine determination of stresses in thin films. In some cases, it is possible though rarely applied to determine the stresses in the films through their influence on other, known film properties, at least approximately. Such properties are, for example, the position of an absorption edge [152], the Hall effect [153], electron spin resonance spectra [155] and in the case of superconducting films, variations in the critical transition temperature [156]. However, these effects can, unfortunately, also arise for other reasons, and thus these techniques can usually only be used as supplemental experiments. 

The main experimental effects are accounted for with this model. Some approximations have been made a higher-level calculation is needed which takes into account the fact that the charge distribution of the trapped electron may extend outside the cavity into the liquid. A significant unknown is the value of the quasi-free mobility in low mobility liquids. In principle, Hall mobility measurements (see Sec. 6.3) could provide an answer but so far have not. Berlin et al. [144] estimated a value of fiqf = 27 cm /Vs for hexane. Recently, terahertz (THz) time-domain spectroscopy has been utilized which is sensitive to the transport of quasi-free electrons [161]. For hexane, this technique gave a value of fiqf = 470 cm /Vs. Mozumder [162] introduced the modification that motion of the electron in the quasi-free state may be in part ballistic that is, there is very little scattering of the electron while in the quasi-free state. 

M-S is an electrochemical impedance spectroscopy (EIS) technique [10-12] that can be difficult to perform and interpret if the system is not ideal. When the measurement is successful, it is able to determine both the fb and the free charge carrier density (donors or acceptors, A/Dopant) of the photoelectrode. Efb, along with the band gap (Eg) and the A dopant. can be used to determine the band structure of a photoelectrode and if it possesses the proper alignment with respect to the water splitting potentials (see chapter Introduction ). The A dopant also plays a role in the bulk and surface semiconductor properties such as the width of the depletion layer and rate of recombination. The conductivity type is also revealed by M-S analysis. The M-S plot will possess a negative slope for p-type materials and a positive slope for n-type materials (positive slope). In the case that the M-S measurement is not successful, then other techniques such as Hall Effect can still yield conductivity and A dopant for materials which can be deposited onto non-conductive substrates such as quartz. 

Carrier densities and carrier mobilities were obtained for polypyrrole via the Hall effect technique. The apparatus was also used to measure conductivities. The analysis was performed for polypyrrole containing three different counterions p-toluenesulfonate, perchlorate, and tetrafluoroborate. The carrier density was found to vary by one order of magnitude, from 1019 to 1020 cm-3. The carrier mobility, on the other hand, remained constant with respect to counterion, at 1 cm2V-lsec-l. In order to ensure that any solvent from preparation of the polymer was not affecting the results, one polymer, polypyrrole-p-toluenesulfonate, was subjected to vacuum dehydration for varying periods of time, followed by re-analysis. It was found that the carrier density changes very little with dehydration. There was no affect on the carrier mobility. 

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