Carbon nanotubes (CNTs) provide an ideal medium for testing the behavior of one-dimensional electron systems and are promising candidates for electronic applications such as sensors or field-effect transistors. This thesis describes the use of low frequency resistance fluctuations to measure both the properties of the one-dimensional electron system in CNTs, and the sensitivity of CNT devices to their environment.

Low frequency noise was measured in CNTs in field effect transistor (FET) geometry. CNTs have a large amount of surface area relative to their volume and are expected to be strongly affected by their environment, leading to speculation that CNTs should have large amounts of 1/f noise. My measurements indicate that the noise level is in the same range as that of traditional FETs, an encouraging result for possible electronic applications. The temperature dependence of 1/f noise from 1.2 K to 300 K can be used to extract the characteristic energies of the fluctuators responsible for the noise. The characteristic energies allows for the elimination of structural and electronic transitions within the CNT itself as possible sources of 1/f noise in CNTs, leaving the motion of defects in the gate dielectric, or possibly strongly physisorbed species, as the likely culprits.



 Another form of low frequency noise found in CNTs is random telegraph signal (RTS), which manifests as the alternation between two current states at a stable voltage bias. In CNTs, this phenomenon occurs due to the tunneling of electrons into and out of the CNT from a nearby defect, and thus provides a way to probe the tunneling density of states of the CNT itself.  The tunneling density of states in turn provides information on the strength of the electron-electron interaction in CNTs. Due to the one-dimensional structure of CNTs their electronic state is expected to be a Luttinger liquid, which should manifest as a power-law suppression of the tunneling density of states at the Fermi energy.   The power law exponent is measured in both the temperature dependence and energy dependence of the tunneling rates.  In agreement with theory, the power-law exponent is significantly larger in semiconducting CNTs than found in previous experiments on metallic CNTs.  The RTS can also be used as a "defect thermometer" to probe the electron temperature of the CNT. The effect of the bias voltage on the electron temperature provides a means to determine the energy relaxation length for the electrons in the CNT.