<p> In this thesis, the conventional four-point measurement technique and the van der Pauw (vdP) method are systematically investigated in the presence of non-ideal conditions, namely, non-uniform carrier density distribution and absence of ohmic contacts, which are nonetheless commonly encountered in semiconductor characterizations. Upon understanding the challenges in the conventional methods, novel characterization techniques are developed to address these challenges. </p><p> A longitudinal magnetoresistance asymmetry method was developed to study the carrier density non-uniformity in two-dimensional samples. By analyzing the asymmetric longitudinal magnetoresistance under positive and negative <i> B</i>-fields, an analytical model based on a linear density gradient across the sample was deduced to quantitatively describe the asymmetry. Based on the theoretical model, a practical method was described which enabled one to experimentally measure the density gradient within a single sample. The method requires only measurements of longitudinal resistances <i>R<sub> xx</sub></i> and <i>R<sub>yy</sub></i> under both positive and negative <i>B</i>-fields, and equations have been provided to extract both the angle and the magnitude of density gradients from the measured resistances. The method was demonstrated in a GaAs quantum well wafer at cryogenic temperatures and <i>n</i>-GaAs bulk-doped wafer at room temperature. In both systems, the density gradient vectors extracted with our method matched well with the interpolated density gradient vectors estimated from actual density distribution maps as a base comparison set, suggesting that our method can be a universal extension of the vdP method to extract density gradients in various systems. The method also allows one to uncover the true local longitudinal resistivity ρ<i><sub>xx</sub></i> at the center of the sample, which the conventional vdP method cannot describe in the presence of non-uniform densities. The ability to find ρ<i><sub>xx</sub></i> makes it possible to study interesting physics in semiconductors such as interaction-induced quantum corrections to resistivity and valley filtering in multi-valley systems. </p><p> To extend the vdP method to cases where ohmic contacts are not available, a capacitive contact technique was introduced which sends current and senses voltage capacitively. A capacitive contact is formed between the buried conducting layer and the contact metal which is simply evaporated onto the sample. Systematic studies of four-point measurements with ohmic and/or capacitive contacts were conducted on a test sample and a Hall bar sample to demonstrate the effectiveness of the capacitive contact method. With a pre-defined capacitive scaling factor γ and a measurement frequency band (<i>f<sub>L</sub></i> ∼ <i> f<sub>H</sub></i>), it was shown that capacitive contacts could extract the same four-point resistance as ohmic contacts, establishing the validity of the capacitive contact technique. </p><p> Built on the idea of capacitive coupling with capacitive contacts, a contactless electrical characterization probe was proposed. On the probe head, there are two types of metal gates: depletion gates to define a test region and separate the contacts, and capacitive contacts to conduct four-point measurements. To characterize a piece or a region on a wafer hosting a buried conducting layer, one brings the probe onto the sample, conducts the electrical measurements with the capacitive contacts, and removes the probe. The sample remains untouched and can be reused. The contactless probe should provide a fast and nondestructive way of semiconductor characterization.</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10160475 |
| Date | 06 October 2016 |
| Creators | Zhou, Wang |
| Publisher | Northwestern University |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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