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Sains Malaysiana
40(1)(2011): 55–58
Finite Difference
Calculation of Electron States in CdTe-CdS Core-Shell Quantum Dots
(Pengiraan
Perbezaan Terhingga bagi Keadaan Elektron dalam Titik Kuantum Teras-Petala CdTe-Cds)
C.Y. Woon1*, G. Gopir1,2 & A.P. Othman1
1School of Applied Physics, Faculty of Science and Technology
Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
2Institute of Space Science, Universiti Kebangsaan Malaysia
43600 Bangi, Selangor, Malaysia
Diserahkan: 7 Disember 2009 / Diterima: 16 Julai 2010
ABSTRACT
We determined
theoretically the confined electron states in a colloidal core-shell CdTe-CdS
quantum dot system with CdTe as the core material with electron effective mass
0.095 me, CdS as barrier material of electron effective mass
0.25 me and having conduction band offset of 0.265 eV. Based on
the one band effective mass approximation, the Schrödinger equation of this
system with BenDaniel-Duke Hamiltonian is numerically solved using the finite
difference method to obtain the energy level and wave function of the electron
confined states. These electronic parameters are obtained by diagonalising the
resultant N×N Hamiltonian matrix for principal quantum number n=l – 3, orbital
quantum number l=0 – 3 and dot size r=10 – 100 Å. For comparison, we also
analytically solve the Schrödinger equation with classical Hamiltonian and
similar input parameters to determine the electronic properties. There is good
agreement in the results of these two computational methods, where specifically
their energy levels differ by less than 15%.
Keywords: BenDaniel-Duke
Hamiltonian; core-shell; electron state; quantum dot; Schrödinger equation
ABSTRAK
Kami menentukan secara
teori keadaan elektron terkurung dalam sistem titik kuantum teras-petala
CdTe-CdS berkoloid dengan CdTe sebagai bahan teras dengan jisim berkesan
elektron 0.095 me, CdS sebagai bahan sawar dengan
jisim berkesan elektron 0.25 me dan mempunyai ofset jalur
konduksi 0.265 eV. Berdasarkan penghampiran jisim berkesan satu jalur,
persamaan Schrödinger bagi sistem ini dengan Hamiltonan BenDaniel-Duke telah
diselesaikan secara berangka dengan menggunakan kaedah perbezaan terhingga
untuk mendapatkan aras tenaga dan fungsi gelombang bagi elektron yang
terkurung. Parameter-parameter elektronik ini telah diperoleh dengan
memenjurukan matriks Hamiltonan N × N bagi nombor kuantum prinsipal n=l – 3,
nombor kuantum orbit l=0 – 3 dan saiz titik r=10 – 100 Å. Sebagai perbandingan,
kami juga menyelesaikan persamaan Schrödinger secara analitik dengan Hamiltonan
klasik dan parameter input serupa untuk menentukan sifat-sifat elektronik itu.
Terdapat persetujuan yang baik antara dua kaedah komputasi ini dan secara
khusus aras tenaga berbeza dengan kurang daripada 15%.
Kata kunci:
Hamilton BenDaniel-Duke; keadaan elektron; persamaan Schrödinger; teras-petala;
titik kuantum
RUJUKAN
Alivisatos,
A.P. 1996. Semiconductor clusters, nanocrystals, and quantum dots. Science 271:
933-937.
Banyai,
L. & Koch, S.W. 1993. Semiconductor quantum dots, Singapore: World
Scientific.
BenDaniel,
D.J. & Duke, C.B. 1966. Space-charge effects on electron tunneling. Phys.
Rev. 152: 683-692.
Conley,
J.W., Duke, C.B., Mahan, G.D. & Tiemann, J.J. 1966. Electron Tunneling
in Metal-Semiconductor Barriers. Phys. Rev. 150: 466-469.
Klimov,
V.I., Mikhailovsky, A.A., Xu, S., Malko, A., Hollingsworth, J.A., Leatherdale,
C.A., Eisler, H.J. & Bawendi, M.G. 2000. Optical gain and stimulated
emission in nanocrystal quantum dots. Science 290: 314-317.
Kuhaimi,
S.A.A. 2000. Conduction and valence band offsets of CdS/CdTe solar cells. Energy 25: 731-739.
Madelung,
O. 2004. Semiconductor: Data handbook. New York: Springer 3.17:1-26
& 3.19: 1-19.
Schaller,
R.D. & Klimov, V.I. 2004. High efficiency carrier multiplication in PbSe
nanocrystals: Implications for solar energy conversion. Phys. Rev. Lett.
92: 1-4.
Schiff,
L.I. 1968. Quantum Mechanics. 3rd Ed. New York:
McGraw-Hill, p. 76-87.
Schwabl,
F. 1992. Quantum Mechanics. New York: Springer p. 313-324.
*Pengarang untuk surat-menyurat; email: jackwoon@gmail.com
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