在Kane量子電腦中邊界和電場對於電子波函數的影響

The effects of boundaries and electric fields on the donor electron wave function in the Kane quantum computing scheme

李宗諺(Zong-Yan Li)

指導教授 ： 管希聖

國立臺灣大學/理學院/物理研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.10129

摘要

Knae量子電腦，在量子電腦領域內被廣泛的討論研究。在Knae的模型裡面，在純的矽晶體裡面參雜一顆磷原子。磷原子較矽原子多出一顆電子而原子核也多出一顆質子，這個多出來的質子和電子都可以被當作一個量子位元使用。藉由加電場和磁場的方式，我們可以操縱這顆多出來的電子。讓電子和磷原子之間的自旋交互作用，和兩個相鄰之間的電子自旋交互作用可以被操控來達成量子邏輯閘的運算的目的。在這篇論文當中，我們將會研究邊界和電場的存在對電子波函數造成的效應。我們考慮一個磷原子被掺雜在矽晶體當中，而矽晶體之上有一層絕緣的二氧化矽存在。兩個平行電板夾著二氧化矽和矽晶體，並利用平行電板來產生均勻的電場。在低溫的時候這個多出來的電子的波函數可以用矽晶體在傳導帶最低點附近的波函數來展開。
我們使用不等向性等效質量理論來計算這個多出來電子的波函數。由於二氧化矽是絕緣體，所以電子的機率密度必須要是零在二氧化矽和矽晶體的介面上。變形的氫原子波函數乘上一個可以使波函數在邊界上是零的函數，當作我們的嘗試性的電子波函數，我們也考慮了映像電子的效應。我們計算了特徵電場的值，特徵電場的意義在於當所加的電場值大於特徵電子時電子將會被游離。我們也計算了穿隧時間和超精細交互作用對於外加電場強度的關係。

關鍵字

量子電腦 ； 等效質量理論 ； 穿隧時間 ； 超精細交互作用 ； 特徵電場

並列摘要

The silicon-based donor spin quantum computer, also known as the Kane quantum computer, is one of the most promising solid-state quantum computing proposals. In this Kane scheme, P donor atoms are placed in an array embedded in a pure 28Si crystal. The spin of either the extra electron or the extra proton of the P donor atom can be defined as quantum bits (qubits). By applying electric fields (voltage) and magnetic fields, the donor wave function can be deformed and manipulated. As a result, the hyperfine interaction between the nuclear spin and electron spin as well as the exchange interaction between two neighboring electron spins may be controlled to construct logical quantum gate operations. In this thesis, we investigate the effect of boundaries and electric fields on the donor electron wave function in the Kane quantum computer scheme. The device that we consider has a donor atom embedded in a silicon crystal, and the electric field is generated by two parallel conducting plates sandwiching the silicon crystal with a silicon-dioxide (SiO2) insulator layer in between on each side. At low temperature the donor electron wave function can be approximately expanded by the Bloch states of six conduction band minima (valleys) of the silicon lattice as silicon is an indirect band-gap semiconductor.
We use the anisotropic effective mass theory to calculate the donor electron wave function and consider the single-valley case and six-valley case. Because SiO2 is an insulator, the donor electron wave function and donor electron density are expected to be zero at SiO2-Si boundary. The deformed hydrogen wave functions multiplied by a term which vanishes at the boundary are thus used as our trial envelope wave functions. The effects of image charges of the donor electron and nucleus are also investigated. We calculate the values of the characteristic electric field, Fc, at which the donor electron is about to be ionized to the interface region , for different donor depths. We also calculate the tunneling time and the hyperfine interaction as a function of the electric field strength.

並列關鍵字

Kane quantum computer ； anisotropic effective mass theory ； tunneling time ； hyperfine interaction ； characteristic electric field

參考文獻

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