鉛和銅之間的晶格不匹配約為36.7%，為何在如此大的不匹配度之下，實驗仍然發現到鉛原子會取代表層的銅原子？而由STM實驗所觀測到在覆蓋率高於0.75後，會有部份鉛原子會取代表層銅原子。為了更進一步探討此現象，本論文利用密度泛函理論來計算不同覆蓋率的鉛原子在銅(110)面上之穩定結構。藉由提出鉛取代及吸附模型來進行比較。因為此二系統總原子數目不一，於此藉由計算形成能量來驗證實驗所推斷的穩定結構。
在計算結果中，我們可以得出覆蓋率為0.8時，為p(5×1)的結構，部分鉛原子會取代表層的銅原子的形成能量相較於鉛吸附的模型低0.3 eV，而覆蓋率在0.75(結構為p(12×1))以及0.778(結構為p(9×1))時，也會得到鉛原子取代表層銅原子會有較低的形成能量，相較於吸附模型分別低0.1 eV和0.2 eV，意即鉛取代較容易發生。另外可以發現在形成能量的差值會隨著覆蓋率的增加而增加。
在觀察電子密度分佈時，可以觀察到鉛原子的電子幾乎沒有和銅原子有作用。另外在觀察鍵長時發現，三種覆蓋率鉛原子和銅原子之間的鍵長都很相近，而鉛原子之間的鍵長會隨覆蓋率增加而減少。而取代型鉛原子和鄰近的鉛原子距離增加，使得系統趨於穩定。

關鍵字：密度泛函理論、銅表面、鉛原子、取代、吸附

Lattice mismatch between lead and copper is approximatively 36%, but why does the STM data show that lead atoms substitute for copper atoms, instead of adsorption on the surface. In order to answer this question, Density Functional Theory was used in this thesis to verify the stable structure of lead on copper (110) surface in different coverage by comparing lead substitution and lead adsorption models. Since the total the number of atoms in both lead substitution and lead adsorption models are different we use formation energy to determine the stability of the two model.
The simulation results show that the coverage 0.8, p(5×1) unit cell, of substitution case is the most stable one among all of models; the formation energy of the Pb substitution models is 0.03 eV lower than the Pb adsorption model. The same trend is observed in the cases of the coverage equal to 0.75, p(12×1) unit cell, and 0.778,p(9×1) unit cell: the Pb substitution for Cu is more stable than the Pb adsorption case. In addition, with the increase of the Pb coverage, we have found the difference of formation energy between the Pb substitution and adsorption models increases slightly. We also examine their charge density and the outcomes disclose that there is no charge transfer between the lead and copper atoms. Concerning their bond length variation, the bond distances between Cu and Pb is almost the same under the three coverage models; the Pb-Pb bond length decreases with the increase of Pb coverage on Cu (110) surface. We found that the Pb-Pb bond length of substitution model is larger than the Pb-Pb bond length of adsorption model.

Keyword: Density Functional Theory, Cu surface, Pb atom, adsorption, substitution

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