| Tunneling of an electron is one of the well-studied phenomena. It also found many commercial applications including tunnel diodes. In top-gated semiconductor quantum dot spin qubits, the voltage controlled tunnel barriers formed by top gates are the fundamental building block to build qubit. Moreover, energy dependence of the tunnel rate in such barriers is well utilized in many qubit measurements including single shot read out of a spin. There have been only a few studies in energy dependent tunneling in top-gated quantum dot devices. Also there has not been much study on the tunnel barrier itself. The barrier information such as height, length, and shape of the barrier is important to understand the dot system and to understand the energy dependent tunneling, which is critical in qubit operation. In this thesis research, we studied the tunnel barrier in a top gated Si/SiGe quantum device. We measured temperature dependence of the tunneling conductance, where we determined the height of the barrier by activation energy. Using the experimentally determined height of the barrier, we developed simple, empirical two-dimensional (2D) barrier models based on molecular coherent tunneling theory. The calculated tunneling conductance well fit to the experimental conductance. Using the developed models, we determined energy dependent tunneling coefficients, which agree well with experimental values that determined from pulsed gate tunnel rate measurements, performed in a dot using similar Si/SiGe heterostructure. The results suggest that the shape of the barrier is parabolic as we expected. Finally, we compared the barrier shape with conventional 1D models to check the impact of the dimensionality. |
