H.-C. Chang1, T.-H. Shieh2, H.-W. Ting1, K.-M. Hung1,a), J.-L. Li1 and Y.-H. Hsu1
1Dept. of Electronics Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan
2Dept. of Electronics Engineering, Kun Shan University, Tainan Hsien, Taiwan
Introduction
The Si-base ferromagnetic semiconductors (FS) are of great interest as a spin-reservoir material in spintronic metal-oxide-semiconductor field-effect transistor (SMOS) and non-volatile magnetic memory (NMM) due to the convenience of the processing compatibility with modern Si fabrication technology. Even though, many diluted magnetic semiconductors, such as Co/GaAs [1], Mn/GaAs [2] and Si vacancies in SiC [3], have been proposed and widely studied, the main difficulty in realizing Si-base SMOS and NMM is still short of a suitable FS that is compatible with Si matrix. In this paper, we report a phenomenon of field-induced ferromagnetism in bulk Si with diluted two-carbon clusters (SDTC). This property not only makes the realization of Si-base SMOS possible, but also available in the applications where the field-controllable ferromagnetism is important.
Theory and Structure Model
In this work, the density functional theory (DFT) as implemented in the CASTEP and DMOL3 codes is applied to study the band structures and magnetic properties of SDTC. The DMOL3 code uses atomic-orbital basis to fully treat the interaction between core and valence electrons, while the CASTEP uses plane wave to expand the system wave functions and applies pseudo-potential approximation instead of the core states to reduce the basis and, thus, to decrease the computation. Since the DMOL3 package is more accurate in lattice constant estimation than CASTEP code, but is worse in band-gap estimation than the latter, the DOML3 code is first applied to calculate the fully relaxed structure of SDTC. This relaxed structure, then, is used to estimate the band structure and density of states using the CASTEP package with a 64-atom supercell, as shown in Fig. 1. The k-point sampling is 2x2x2 and the cutoff energy is 600eV. The interaction between core and valence electrons is included by an effective (Norm-conserving) pseudo-potential in the CASTEP package, and the generalized gradient approximation of Perdew and Wang is used for the exchange-correlation functional [4].
Fig. 1 A 64-atom supercell with a two-carbon cluster.
Results and Discussions
The fully-relaxed structures with (a) one electron charge (q=-1), (b) neutral charge (q=0) and (c) one hole charge (q=1) are shown in Fig. 2. The calculated results show two main features: (i) the C-C bond lengths for three different charging conditions are
the high electro-negativity of carbon atom attracts the electron from its neighbor Si atoms to the carbon site, as shown in Table-I.
The additional electrons at C sites increase the Coulomb repulsive force between C atoms.
Table-I The number of electrons at C sites, 1NN Si sites and 2NN Si sites.
Charge C sites (# of atoms)
1NN (# of atoms)
2NN (# of atoms) 0 9.805 (2) 21.862 (6) 224.332 (56) -1 9.920 (2) 21.845 (6) 225.209 (56) 1 9.783 (2) 21.766 (6) 223.398 (56)
The repulsive force weakens the bond strength and pushes the carbons away from each other to elongate the bond length. For the case of q=+1, the additional hole charge mainly populates the second nearest-neighbor (2NN) Si sites that surround the C cluster.
The surrounding positive charge associated with the electron charge at C sites forms an attractive force to further stretch the C-C bond length. For q=-1, a small part of the additional electron charge populates C sites and the most part populates 2NN Si sites.
The increase of electron charge at C sites increases the repulsive force between C atoms, however, this force is somewhat balanced by the repulsive force according to the increased charge at 2NN Si sites. Hence, the C-C bond-length is slightly contracted in comparison with the case of q=+1.
Fig. 2 The relaxed structures of (a) q=-1, (b) q=0, and (c) q=+1, where the blue area is the net spin equi-surfaces.
In order to understand the ferromagnetic properties of SDTC under different conditions, we calculate the band structures for bulk Si, q=0, q=-1, and q=+1 as shown in Fig. 3. The band structure of q=0 in comparison with bulk Si clearly shows an impurity band that is slightly above the valence-band maximum. A non-magnetic property is observed because the total net spin is zero as shown in Fig. 4 (black line). For q=-1, the impurity spin-up (thick-blue lines) states are occupied by additional electron charge but leaves the spin-down (thin-red lines) states empty. For q=+1, the impurity spin-up states are partially filled by the additional hole charge and the spin-down states are empty. Moreover, the spin-down heavy-hole band is lifted above the Fermi level for q=+1. The net-spin density of states as plotted in Fig. 4 exhibits a non-zero total spin in the cases of q=-1 and q=+1. The estimated total net spin is 1.297 and 1.145 for the conditions of q=+1 and q=-1, respectively. These results clearly indicate a ferromagnetic property for the cases of q=-1 and q=+1.
Conclusion
The structure of two-carbon clusters in bulk Si is studied using density functional theory. The band structure and net-spin density of states indicate that SDTC system with q=0 is non-magnetic but is ferromagnetic as the system is charging with one electron or one hole. This phenomenon can be applied to design and fabricate Si-base SMOS, NMM, and other Si-base spintronic devices where the field-controllable ferromagnetism is important.
-1 0 1 2
L X
L X
Energy (eV)
bulk Si q=0 q=-1 q=+1
L X L X
Fig. 3 The band structures of bulk Si and SDTC with the charges q=0, q=-1 and q=+1.
-15 -10 -5 0 5
-3 -2 -1 0 1 2 3
Density of States (electrons/eV)
Energy (eV)
Fig. 4 The net-spin density of states for the conditions of q=0 (black line), q=-1 (red line) and q=+1 (blue line).
Acknowledgement
This work is supported by the Science Council of the Republic of China, Taiwan, under Contract No.
NSC97-2112-M-151-001-MY3.
References
a) To whom all correspondence to be sent: kmhung@cc.kuas.edu.tw.
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