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In this dissertation, split-gate tunnel barriers in enhancement-mode silicon metal- oxide-semiconductor (MOS) device structures are characterized electrically at liquid helium temperatures (T = 4.2 K) using transport spectroscopy. Tunnel barriers with different gate geometries and barriers implanted with a small number of antimony donor atoms are characterized. Low disorder MOS tunnel barriers are demonstrated and compared to the implanted cases. The ”clean” MOS tunnel barriers are an important proof of principle that disorder free tunnel barriers can be achieved in MOS. The implanted cases provide an important reference for the effects of donors and shallow traps on a MOS tunnel barrier. To analyze these different geometries and cases with varying degrees of disorder, we propose a compact model for multi-electrode tunnel barriers. The model is based on a 1D barrier that is parameterized in terms of a barrier height and width and on two mathematical frameworks: the Landauer-Büttiker formalism and transfer matrices. The model is arrived at after considering a wide range of commonly used models such as Simmons, WKB and Fowler-Nordheim models that typically have deficiencies because of the wide range of voltages examined and the consideration of low dimensions and temperatures. The proposed models are used to extract effective barrier heights and widths from the experimental data for a wide range of voltages. This provides a method to quantitatively describe how the barrier changes with voltage and a way to compare different gate geometries. It also provides a way to do energy spectroscopy on shallow trap levels (i.e., order of 1-50 meV below the conduction band). We find that the barrier height shows several regimes of voltage dependence, either linear or approximately exponential offering functional forms for relatively simple parameterization for these different regimes of operation. These results are compared to electrostatic simulations and are found to agree qualitatively. Overall, this work offers critical insights about the details of electrostatic multi-electrode tunnel barriers at low temperatures, including a new way to characterize the shallow disorder potential in MOS barriers and a relatively rapid way to model them for extensions to multi-barrier device structures.