Acoustic-phonon-assisted Quantum Control Of Qubits Based On Donor Electron Spins In Silicon

In this thesis, we have investigated the quantum control of qubits based on donor electron spins between the donor and the Si/SiO₂ (001) interface, i.e., the shuttling of donor electrons. The donor electron is shuttled to the interface to measure the qubit state. In practical devices, electron-acoustic-phonon interaction plays an important role in determining the functionality of devices. Hence, in our theoretical model, we have considered the interface, longitudinal, and transverse acoustic phonons to investigate their contributions to the shuttling process. We have also studied the influence of energy valley interference in silicon, the lattice temperature, and the screening effect of the metallic gate on the shuttling process. The present investigations are of importance to the design and manipulation of the qubit devices.Firstly, the mechanism of acoustic-phonon-assisted shuttling of donor electrons is proposed: the quantum transition of a donor electron caused by the electron-phonon interaction leads to the space transfer of the electron between the donor and the interface. For the donor-interface system under an electric field, the interface potential well near the interface appears. The electron shuttling is in fact the space transfer of the electron between the two potential wells. In this coupled double-well potential, the ground state and the first excited state of an electron are located in different potential wells in certain condition. The electron-phonon interaction causes the quantum transition of the electron between the two states, leading to the space transfer of the electron. The main transition of an electron is that from the first excited state to the ground state. Obviously, the shuttling time (i.e., the transition time) is a very important parameter. In calculating electronic states, we begin with single-valley effective-mass approximation. Calculation results show that the contributions of interface, longitudinal and transverse acoustic phonons to the electron shuttling are different at different electric field strengths or different donor depths. The relationship between the shuttling time and electric field strength or donor depth exhibits a double-valley feature. The value of the shuttling time is the biggest at critical electric field or critical donor position. Our results also give an important conclusion that in realistic devices, to guarantee a successful shuttling of an electron the donor should be located in the range about from 21 nm to 32 nm to the interface.Secondly, considering the conduction band structure of silicon, we have investigated the effect of valleys interference on the electron shuttling. In interface well, the energies in the valley perpendicular to the interface are lower than those in other valleys due to the presence of the Si/SiO₂ (001) interface. Furthermore, the potential experienced by electrons between the donor and the interface does not cause the coupling between the valleys in differenct directons. Hence, we use two-valley effective-mass approximation to calculate the electronic states. Calculation results show that valley interference does not change the double-valley feature of the relationship between the shuttling time and electric field strength. However, it causes that the shuttling time oscillates with donor depgh. In a fixed field, the shuttling time is maximum at crictial position. At critical electric fields, the trend of the variation of shuttling time with donor depth is increasing. Within the range from ? 10.0 meV to ? 1.0 meV, the variation of interface valley-orbit coupling parameter has a small influence on the shuttling time. The influence of lattice temperature on the shuttling time varies with electric field strength, and it is the strongest at critical electric field. When the electric field strength deviates far from crictical field, the influence of the lattice temperature vanishes.Finally, we have studied the influence of screening effect of metallic gates on the shuttling process. The screening effect associlates closely with the thickness of the SiO₂ layer separating the metallic gate from silicon. When the SiO₂ thickness is larger than 10 nm, it has no influence on electronic states and the shuttling time. In practical devices, the SiO₂ layer is a few nanometers thick. The wave functions and energy levels of an electron relates closely to the SiO₂ thickness. For a fixed donor depth, the inflencen of the variation of the SiO₂ thickness on the shuttling time varies with electric field strength, and it is the strongest at critical elecrric field.