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

REFERENCES

 

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.

 

*Corresponding author; email: jackwoon@gmail.com

 

 

previous