Investigation of ferromagnetism in Al-doped 4H–SiC by density functional theory

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Abstract

Ferromagnetism of Al-doped 4H–SiC is investigated by means of first-principles calculations. Our results show that Al dopant alone does not introduce any spin-polarization in the doped 4H–SiC, whereas the complex of substitution Al for Si together with a silicon vacancy can induce spin-polarization and local magnetic moment in Al-doped 4H–SiC. The interaction between the local moments results in the ferromagnetism order. The substitutional Al for Si atom introduces hole and mediates spin-polarizations resulting from silicon vacancy to form ferromagnetism in 4H–SiC.

Graphical abstract

The carbons around the silicon vacancy and the nearby Al dopant may be responsible for the ferromagnetism in Al-doped 4H–SiC.

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Research highlights

► We find out the possible theoretical origin of ferromagnetism in Al-doped 4H–SiC using first-principles methods and verify the experiments’ data. ► There is no any d electron in Al-doped 4H–SiC and p electrons dominion the ferromagnetism in this system. ► Silicon vacancy has high formation energy but it is one of the important factors of the ferromagnetism in Al-doped 4H–SiC.

Introduction

Dilute magnetic semiconductors (DMSs) have become one of the hottest topics for their promising applications [1]. Silicon carbide (SiC) is one of the most promising wide band-gap semiconductors due to its outstanding electrical and mechanical properties, which makes it an excellent candidate for high-power and high-frequency device applications. SiC has more than 200 different polytype structures according to the stacking sequence of the atomic double layers in the crystal. 4H–SiC is one of the most important polytype structures because it has large energy gap (3.26 eV), high breakdown electric field (2.3 MV/cm for a 600 V device blocking rating), high carrier mobility [2], and high thermal conductivity (about three times than silicon’s), which makes 4H–SiC devices can be used at higher blocking voltage and higher temperature than silicon devices. Recently, Song’s group firstly reported the observation of glassy ferromagnetism (FM) in Al-doped 4H–SiC [3]. Their experiment raised some basic questions toward understanding the origin of spin order in non-transition metal (non-TM) doped wide-gap semiconductor. Ferromagnetism of non-TM element-doped DMS, such as C-doped ZnO [4], C-doped TiO2[5], really arouses great attention for its breaking the primary magnetism theory in DMSs. However, there are still d electrons in most of the studied system, such as Zn in C-doped ZnO, Ti in C-doped TiO2 whereas there is no any d electron in Al-doped 4H–SiC. Thus Al-doped 4H–SiC may be an ideal system to know well about the non-TM DMSs’ ferromagnetism.

Electron paramagnetic resonance revealed that vacancies (VC and VSi), carbon vacancy–antisite pairs and divacancy, are common defects in high-purity semi-insulating 4H–SiC [6]. Zhao et al. [7] predicted that stable ferromagnetic ordering of the VSi-induced local magnetic moments (2μB per vacancy) may be obtained if N:VSi ratio is near 2:1 in 3C–SiC. Troffer et al. [8] speculated that Al acts as a shallow acceptor in SiC. However, these previous investigations did not concern the ferromagnetic property of Al-doped 4H–SiC.

Since the conventional theory fails to explain the origin of the observed magnetic behavior in Al-doped 4H–SiC system, several issues appear and are necessary to be investigated. For example, can Al atom induce local magnetic moment in 4H–SiC? Can the vacancy contribute to the FM coupling? Does Al-doping facilitate the vacancy’s formation? And how is the interaction between Al and the vacancy? What is the origin of the FM ordering in Al-doped 4H–SiC? In order to know these issues, we performed first-principles calculations to examine the geometric structure, the electronic structures and the spin density distribution of several possible Al-doped and vacancy related models of 4H–SiC. Furthermore, we explore the mechanism of the FM in Al-doped 4H–SiC.

Section snippets

Computational details

Spin-polarized density functional theory (DFT) calculations are carried out in the framework of the generalized gradient approximation (GGA) [9] by using the Vienna ab initio simulation package (VASP) [10], [11]. The Perdew–Wang 91 exchange–correlation functional [12] and the ultrasoft pseudopotential [13] are employed in our calculations. We use a plane-wave basis set with cutoff energy of 400 eV and a 2 × 2 × 2 Monkhorst–Pack k-points mesh for the Brillouin-zone sampling [14]. A 72-atom 3 × 3 × 1

Defect formation energy of Al and vacancy in doped 4H–SiC

The formation energy of a single vacancy as well as substitution Al in 4H–SiC (EfX) can be calculated as follows:EfAl_X=EdopedAl_X-Eundoped-μAl+μXEfV_X=EdopedV_X-Eundoped+μXμSiCbulk=μSi+μCwhere EdopedAl_X is the total energy for the supercell with substitution Al for X (Si or C), and EdopedV_X is the total energy for the supercell with the vacancy at site of X (Si or C), Eundoped is the total energy for the supercell of undoped 4H–SiC, μAl and μX are the chemical potential of Al and X (Si or

Effect of Al and Vacancy on the magnetic properties of doped 4H–SiC

The valence shell of Al atom is 3s23p1 and Si atom is 3s23p2. Thus, Si atom has one more electron than Al atom. Which means that when Al replaces for Si, each Al atom releases one less electron to the 4H–SiC lattice site than each Si atom does. So that, the introduction of one substitution Al for Si removes one electron from the lattice and the system has an unpaired electron. Generally, the unpaired electron may induce spin-polarization and therefore a corresponding magnetic moment. The

The origin of ferromagnetic ordering in Al-doped 4H–SiC

To understand the origin of FM coupling in Al-doped 4H–SiC, the distributions of spin density of model 4 and model 19 are shown in Fig. 3. The results display that the spin density mainly comes from C atoms around the VSi. There is no spin density around the Al atom. In the calculated DOS of model 19 under FM setting (see Fig. 4(a)), that the Fermi level (EF) lies in the related gap states near and up the Valence Band (VB) shows p-type semiconductor character whose majority carriers are holes.

Concluding remarks

In summary, we have investigated the electronic structure and magnetic properties of Al-doped 4H–SiC by first-principles DFT calculations for several possible configurations. The results indicate that FM order can appear in Al-doped 4H–SiC, and it is confirmed that the FM may result from the substitution Al for Si with a silicon vacancy (VSi + Al@Si) in 4H–SiC. Single Al dopant cannot introduce spin-polarization, while the spin-polarization appears when additional VSi existing in the Al-doped

Acknowledgement

This work is supported by the National Basic Research Program of China 973 program (Grant No. 2007CB613302), National Natural Science Foundation of China under Grant Nos. 10774091 and 20973102, and Natural Science Foundation of Shandong Province under Grant No. Y2007A18.

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