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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
Received: 7 December 2009 / Accepted: 16 July 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
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*Corresponding author;
email: jackwoon@gmail.com
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