本論文分成兩部分︰電磁學與量子力學的第一原理計算。在電磁學的第一原理計算方面，我們計算光子晶體的光子能帶結構與態密度﹔由於電磁幅射可被周遭環境改變，控制光子晶體的光學性質近年來引起高度的重視。光子的態密度在光子晶體內不均勻分佈，可以產生有趣的光與原子的交互作用﹔對於一維的光子晶體，我們利用轉換矩陣法計算，在TM模式中，我們可以得到布魯斯特角，δ函數模型則否﹔對傳播模式與消散模式的態密度歸一化，可以了解自發性幅射在一維的光子晶體中的情形﹔二維的光子晶體方面，我們使用有限元素法求得能帶結構，並與平面波展開法結果比較，發現能隙只有其估計的65%﹔並且我們也研究全方位角入射並找到一個有效率的方法來判斷完全的能隙是否存在。
在量子力學的第一原理計算方面，我們用密度泛函理論計算不同原子吸附在陰極表面之功函數與表面能﹔一般來說，原子吸附在金屬表面會影響功函數，若是正電性的原子會降低功函數，負電性則反之﹔我們研究材料是金屬-鎢，由於其可以操作在較高的溫度，大約在1000度以上，但其功函數過高，而使表面電流密度太小。一般吸附鹼金族或鹼土族元素可降低功函數，我們計算研究功函數的降低跟吸覆原子的排列方式與吸覆率之影響﹔在鹼土族中，除了金屬-鈹吸附在鎢的表面會使功函數上升，其餘的皆降低，最後，我們也計算表面電荷密度與電偶極密度分佈，來解釋與理解功函數的變化。

This dissertation is divided into two parts, ab initio calculations of electromagnetics (EM) and quantum mechanics (QM). For ab initio calculations of EM, we calculate the photonic band structures and photon density of states of photonic crystals. As the emission of electromagnetic radiation can be modified by the environment, controlling the optical properties of photonic crystals has attracted much attention in recent years. Due to the non-uniform distribution of the photon density of states, there are many interesting photon-atom interactions. For the study of one-dimensional photonic crystals, the transfer matrix method is used. By comparison, the Brewster’s angle for TM modes can be obtained in our model, but the Dirac δ-function model cannot. To understand the spontaneous emission in a one-dimensional photonic crystal, we normalize the density of states for both radiative modes and evanescent modes. For two-dimensional photonic crystals, the finite element method is used to solve dispersion relations. The band gap we predict is about 65% of that calculated by the plane wave expansion method. We also study the omnidirectional light propagation in 2D photonic crystals and find an efficient way to identify a complete band gap.
For ab initio calculations of QM, the density-functional theory is used to calculate the work function and surface energy of the cathode surfaces with adsorbed atoms. In general, work function is reduced and increased by electropositive and electronegative adsorbates, respectively. The material we study is tungsten as the cathodes can operate at higher temperatures, above 1000℃. However, its work function is too high to achieve high current densities. With adsorbed atoms of alkali metal and alkaline earth metal on the surface, the work functions can be dramatically reduced, except beryllium. In our calculations, the reduction of work function due to the adsorbed atoms, with variant coverage and structural arrangement has been investigated. Finally, we calculate the surface charge density and dipole moment density to explain and understand how and why the work function changes.

[1] E. M. Purcell, “Spontaneous emission probabilities at
radio frequencies”, Phys. Rev.69, 681 (1946).
[2] A. Lamouri, W. Mller, and I. L. Krainsky, “Geometry
and unoccupied electronic states of Ba and BaO on W
(001)”, Phys. Rev. B 50, 4764 (1994).
[3] M. C. Lin and R. F. Jao, “Quantitative analysis of
photon density of states for a realistic superlattice
with omnidirectional light propagation”, Phys. Rev. E
74,046613, (2006).
[4] I. Alvarado-Rodrguez, P. Halevi, and J. J. Snchez-
Mondragn, “Density of states for a dielectric
superlattice: TE polarization”, Phys. Rev. E 59, 3624
(1999).
[5] J. R. Zurita-Snchez and P. Halevi, “Density of
states for a dielectric superlattice. II. TM
polarization”, Phys. Rev. E 61, 5802 (2000).
[6] M. C. Lin and R. F. Jao, “Finite element analysis of
photon density of states for two-dimensional photonic
crystals with in-plane light propagation”, Opt.
Express 15,207 (2007).
[7] C. T. Chan and Steven G. Louie, “Theoretical study of
the surface energy and surface relaxation of the W
(001) surface”, Phys. Rev. B 33, 2861 (1986).
[8] M. C. Lin, R. F. Jao, and W. C. Lin, “Work functions
of cathode surfaces with adsorbed atoms based on ab
initio calculations”, J. Vac. Sci. Technol. B 26, 821
(2008).
[9] J. D. Joannopoulos, R. D. Meade, and J. N. Winn,
Photonic Crystals: Molding the Flow of Light (Princeton
University Press, Princeton, New Jersey 1995).
[10] F. L. Pedrotti and L. S. Pedrotti, Introduction to
Optics, 2nd ed. (Prentice-Hall,Englewood Cliffs, NJ,
1993).
[11] K. Sakoda, Optical Properties of Photonic Crystals
(Springer, Berlin, 2001).
[12] C. Kittel, Introduction to Solid State Physics (Wiley,
New York, 1976).
[13] R. J. Glauber and M. Lewenstein, “Quantum optics of
dielectric media”, Phys. Rev. A 43, 467 (1991).
[14] M. Scalora, J. P. Dowling, A. S. Manka, C. M. Bowden,
and J. W. Haus, “Pulse propagation near highly
reflective surfaces: Applications to photonic band-gap
structures and the question of superluminal tunneling
times”, Haus, Phys. Rev. A 52,726 (1995).
[15] M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork,
M. J. Bloemer, M. D. Tocci, C.M. Bowden, H. S.
Ledbetter, J. M. Bendickson, J. P. Dowling, and R. P.
Leavitt,“Ultrashort pulse propagation at the photonic
band edge: Large tunable group delay with minimal
distortion and loss”, Phys. Rev. E 54, R1078 (1996).
[16] M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling,
C. M. Bowden, R.Viswanathan, and J. W. Haus, “Pulsed
second-harmonic generation in nonlinear,one-
dimensional, periodic structures”, Phys. Rev. A 56,
3166 (1997).
[17] M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling,
and C. M. Bowden,“Measurement of spontaneous-emission
enhancement near the one-dimensionalphotonic band edge
of semiconductor heterostructures”, Phys. Rev. A 53,
2799 (1996).
[18] F. Ramos-Mendieta and P. Halevi, “Propagation
constant-limited of surface modes in dielectric
superlattice”, Opt. Commun. 129, 1 (1996).
[19] D. Kleppner, “Inhibited Spontaneous Emission”, Phys.
Rev. Lett. 47, 233 (1981).
[20] A. O. Barut and J. P. Dowling, “Quantum
electrodynamics based on self-energy:Spontaneous
emission in cavities”, Phys. Rev. A 36, 649 (1987).
[21] H. Rigneault and S. Monneret, “Modal analysis of
spontaneous emission in a planar microcavity”, Phys.
Rev. A 54, 2356 (1996).
[22] J. P. Dowling and C. M. Bowden, “Atomic emission
rates in inhomogeneous media with applications to
photonic band structures”, Phys. Rev. A 46, 612
(1992).
[23] T. Suzuki and P. K. L. Yu, “Emission power of an
electric dipole in the photonic band structure of the
fcc lattice”, J. Opt. Soc. Am. B 12, 570 (1995).
[24] A. Kamli, M. Babiker, A. Al-Hajry, and N. Enfati,
“Dipole relaxation in dispersive photonic band-gap
structures”, Phys. Rev. A 55, 1454 (1997).
[25] A. S. Snchez and P. Halevi, “Spontaneous emission
in one-dimensional photonic crystals”, Phys. Rev. E
72, 056609 (2005).
[26] P. Halevi and A. S. Snchez, “Spontaneous emission
in a high-contrast one-dimensional photonic crystal”,
Opt. Commun. 251, 109 (2005).
[27] J. M. Bendickson, J. P. Dowling, and M. Scalora,
“Analytic expressions for the electromagnetic mode
density in finite, one-dimensional, photonic band-gap
structures”, Phys. Rev. E 53, 4107 (1996).
[28] A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley,
New York, 1984).
[29] M. M. Sigalas, R. Biswas, K. M. Ho, and C. M.
Soukoulis, “Theoretical investigation of off-plane
propagation of electromagnetic waves in two-
dimensional photonic crystals”, Phys. Rev. B 58, 6791
(1998).
[30] Z. Y. Li and Y. Xia, “Omnidirectional absolute band
gaps in two-dimensionalphotonic crystals”, Phys. Rev.
B 64, 153108 (2001).
[31] T. Haas and A. Hesse, T. Doll, “Omnidirectional two-
dimensional photonic crystal band gap structures,”
Phys. Rev. B, 73, 045130 (2006).
[32] J. D. Joannopoulos, P. R. Villeneuve, and S. Fan,
“Photonic crystals: putting a new twist on light,”
Nature (London) 386, 143 (1997).
[33] K. Sakoda, “Optical transmittance of a two-
dimensional triangular photonic lattice”,Phys. Rev. B
51, 4672 (1995).
[34] K. Busch and S. John, “Photonic band gap formation in
certain self-organizing systems,” Phys. Rev. E 58,
3896 (1998).
[35] H. S. Szer, J. W. Haus and R. Inguva, “Photonic
bands: Convergence problems with the plane-wave
method”, Phys. Rev. B 45, 13962 (1992).
[36] A. J. Ward and J. B. Pendry, “Calculating photonic
Green’s functions using a nonorthogonal finite-
difference time-domain method”, Phys. Rev. B 58, 7252
(1998).
[37] H. Y. D. Yang, “Finite difference analysis of 2-D
photonic crystals”, IEEE Trans.Microwave Theory Tech.
44, 2688 (1996).
[38] G. Tayeb and D. Maystre, “Rigorous theoretical study
of finite-size two-dimensionalphotonic crystals doped
by microcavities”, J. Opt. Soc. Am. A 14, 3323 (1997).
[39] W. Zhang, C. T. Chan, and P. Sheng, “Multiple
scattering theory and its application to photonic band
gap systems consisting of coated spheres”, Opt.
Express 8, 203 (2001).
[40] J. K. Hwang, S. B. Hyun, H. Y. Ryu, and Y. H. Lee,
“Resonant modes of two-dimensional photonic bandgap
cavities determined by the finite-element method
and by use of the anisotropic perfectly matched layer
boundary condition”, Opt. Soc.Am. B 15, 2316 (1998).
[41] W. Axmann and P. Kuchment, “An efficient finite
element method for computing spectra of photonic and
acoustic band-gap materials”, J. Comput. Phys. 150,
468 (1999).
[42] M. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain
beam propagation method and its application to
photonic crystal circuits”, J. Lightwave Tech. 18,
102 (2000).
[43] A. Figotin and Y. A. Godin, “The computation of
spectra of some 2D photonic crystals”, J. Comput.
Phys. 136, 585 (1997).
[44] R. C. McPhedran, L. C. Botten, J. McOrist, A. A.
Asatryan, C. M. de Sterke, and N. A.Nicorovici,
“Density of states functions for photonic crystals”,
Phys. Rev. E 69,016609 (2004).
[45] E. Moreno, D. Erni and C. Hafner, “Band structure
computations of metallic photonic crystals with the
multiple multipole method”, Phys. Rev. B 65, 155120
(2002).
[46] J. M. Elson and P. Tran, “Coupled-mode calculation
with the R-matrix propagator for the dispersion of
surface waves on a truncated photonic crystal”, Phys.
Rev. B 54,1711 (1996).
[47] L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C.
Martijn de Sterke, and A. A.Asatryan, “Photonic band
structure calculations using scattering matrices”,
Phys. Rev.E 64, 046603 (2001).
[48] D. Hermann, M. Frank, K. Busch, and P. wlfle,
“Photonic band structure computations”, Opt. Express
8, 167 (2001).
[49] J. B. Pendry and A. MacKinnon, “Calculation of photon
dispersion relations”, Phys.Rev. Lett. 69, 2772
(1992).
[50] A. Taflove, Computational Electrodynamics: The Finite-
Difference Time-Domain Method, (Artech, Boston, Mass.,
1995).
[51] J. Jin, The Finite Element Method in Electromagnetics,
2nd ed. (Wiley-Interscience,New York 2002).
[52] D. P. Fussell, R. C. McPhedran, C. Martijn de Sterke,
and A. A. Asatryan,“Three-dimensional local density
of states in a finite two-dimensional photonic crystal
composed of cylinders”, Phys. Rev. E 67, 045601(R)
(2003).
[53] M. M. Sigalas, R. Biswas, K. M. Ho, and C. M.
Soukoulis, “Theoretical investigation of off-plane
propagation of electromagnetic waves in two-
dimensional photonic crystals”, Phys. Rev. B 58, 6791
(1998).
[54] S. Foteinopoulou, A. Rosenberg, M. M. Sigalas, and C.
M. Soukoulis, “In- and out-of-plane propagation of
electromagnetic waves in low index contrast two
dimensional photonic crystals”, J. Appl. Phys. 89,
824 (2001).
[55] A. Rosenberg, R. J. Tonucci, and E. L. Shirley, “Out-
of-plane two-dimensional photonic band structure
effects observed in the visible spectrum”, J. Appl.
Phys. 82,6354 (1997).
[56] R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D.
Joannopoulos, “Existence of a photonic band gap in
two dimensions”, Appl. Phys. Lett. 61, 495 (1992).
[57] R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl,
“All-angle left-handed negative refraction in Kagom
and honeycomb lattice photonic crystals”, Phys. Rev.
B 73,165310 (2006).
[58] X. H.Wang, R.Wang, B. Y. Gu, and G. Z. Yang, “Decay
distribution of spontaneous emission from an assembly
of atoms in photonic crystals with psudogaps”, Phys.
Rev. Lett. 88, 093902 (2002).
[59] P. Hohenberg and W. Kohn, “Inhomogeneous electron
gas”, Phys. Rev. 136, B864 (1964).
[60] W. Kohn and L. J. Sham, “Self-consistent equations
including exchange and correlation effects”, Phys.
Rev. 140, A1133 (1965).
[61] M. Born and R. Oppenheimer, “Zur Quantentheorie der
Molekeln”, Ann. Phys.(Leipzig) 84(20), 457 (1927).
[62] R. G. Parr and W. Yang, DENSITY-FUNCTIONAL THEORY OF
ATOMS AND MOLECULES (Oxford University Press, New York
1989).
[63] D. J. Singh, “Plane waves, pseudopotential and the
LAPW method”, Kluwer Academic Publisher, Boston,
Dortrecht, London (1994).
[64] G. Kresse, and J. Furthmuiller, Vasp Manual. 2005
http://cms.mpi.univie.ac.at/vasp/vasp/vasp.html
[65] J. B. Taylor and I. Langmuir, “The evaporation of
atoms, ions and electrons from
caesium films on tungsten”, Phys. Rev. 44, 423 (1933).
[66] G. A. Haas, A. Shih, C. R. K. Marrian,. “Interatomic
Auger Analysis of the Oxidation of. Thin Ba Films”,
Appl. Surf. Sci. 16, 139 (1983).
[67] E. Wimmer, A. J. Freeman, J. R. Hiskes, and A. M.
Karo, “All-electron local-density theory of alkali-
metal bonding on transition-metal surfaces: Cs on W
(001)”, Phys.Rev. B 28, 3074 (1983).
[68] L. A. Hemstreet, S. R. Chubb, and W. E. Pickett,
“Electronic properties of stoichiometric Ba and O
overlayers adsorbed on W(001)”, Phys. Rev. B 40, 3592
(1989).
[69] L. A. Hemstreet and S. R. Chubb, “Electronic
structure of c(2×2) Ba adsorbed on W(001)”, Phys.
Rev. B 47, 10748 (1993).
[70] A. Lamouri, W. Mller, and I. L. Krainsky, “Geometry
and unoccupied electronic states of Ba and BaO on W
(001)”, Phys. Rev. B 50, 4764 (1994).
[71] K. L. Man, R. Zdyb, S. F. Huang, T. C. Leung, C. T.
Chan, E. Bauer, and M. S. Altmanl, “Growth
morphology, structure, and magnetism of ultrathin Co
films on W(111)”, Phys. Rev. B 67, 184402 (2003).
[72] S. F. Huang, R. S. Chang, T. C. Leung, and C. T. Chan,
“Cohesive and magnetic properties of Ni, Co, and Fe on
W(100), (110), and (111) surfaces: A first-principles
study”, Phys. Rev. B 72,075433 (2005).
[73] T. C. Leung, C. L. Kao, W. S. Su, Y. J. Feng, and C.
T. Chan, “Relationship between surface dipole, work
function and charge transfer: some exceptions to an
established rule”, Phys. Rev. B 68, 195408 (2003).
[74] S. F. Huang, T. C. Leung, B. Li, and C. T. Chan,
“First-principles study of field-emission properties
of nanoscale graphite ribbon arrays”, Phys. Rev. B 72,
035449 (2005).
[75] B. Li, T. C. Leung, and C. T. Chan, “Highly spin-
polarized field emissions induced by quantum size
effects in ultrathin films of Fe on W(001)”, Phys.
Rev. Lett. 97, 087201 (2006).
[76] A. U. MacRae, K. Mller, J. J. Lander, J. Morrison,
and J. C. Phillips, “Electronic andlattice structure
of cesium films adsorbed on tungsten”, Phys. Rev.
Lett. 22, 1048 (1969).
[77] T. W. Pi, I. H. Hong, and C. P. Cheng, “Synchrotron-
radiation photoemission study of Ba on W(110)”, Phys.
Rev. B 58, 4149 (1998)
[78] Y. Yamamoto and T. Miyokawa, “Emission
characteristics of a conical field emission gun”, J.
Vac. Sci. Technol. B 16, 2871 (1998).
[79] P. E. Blchl, “Projector augmented-wave method”,
Phys. Rev. B 50, 17953 (1994).
[80] G. Kresse and J. Joubert, “From ultrasoft
pseudopotentials to the projector augmented-wave
method”, Phys. Rev. B 59, 1758 (1999).
[81] E. Wimmer, A. J. Freeman, M. Weinert, H. Krakauer, J.
R. Hiskes, and A. M. Karo,“Cesiation of W (001): work
function lowing by multiple dipole formation”, Phys.
Rev. Lett. 48, 1128 (1982).
[82] P. A. Serena, J. M. Soler, and N. Garca, and I. P.
Batra, “Work function of metals upon alkali-metal
adsorption: overlayer relaxation”, Phys. Rev. B 36,
3452 (1987).
[83] H. Ishida and K. Terakura, “Coverge dependence of the
work function and charge transfer on the alkali-metal-
jellium surface”, Phys. Rev. B 36, 4510 (1987).
[84] J. P. Muscat and I.P. Batra, “Coverage dependence of
the work function of metals upon alkali-metal
adsorption”, Phys. Rev. B 34, 2889 (1986).
[85] W. Ning, C. Kailai, and W. Dingsheng, “Work function
of transition-metal surface with submonolayer alkali-
metal coverage”, Phys. Rev. Lett. 56, 2759 (1986).