Silicon research of the Webergroup: Transition-Metal Physics

Transition metals, especially 3d transition metals such as Fe, Ni and Cu are ubiquitous in IC production lines. It is well known that 3d transition metals dissolved in silicon introduce deep energy levels in the band gap and act as generation-recombination centers, which reduce minority carrier lifetime, degrade the microchip devices, and give severe reliability problems. The knowledge of fundamental properties such as diffusivity and solubility is critical to design the gettering treatment. Recently, our group is working on the following projects:

1. Intrinsic diffusion coefficient of interstitial copper in silicon

Probably the most surprising recent discovery associated with the physics of Cu in Si was the new determination of its diffusion coefficient [1] by our group. The diffusion coefficient of Cu in Si was thought to be well established since the work of Hall and Racette [2] published in 1964. Their expression for Cu diffusivity, D = 4.7×10³×exp(–0.43 eV/k_BT) cm² s^-1, has been widely used for modeling diffusion of Cu in Si and was included in all major textbooks (e.g., Ref. [3]). Starting from approximately 1990, a discussion started in the literature [4-6] that Hall and Racette, who used p⁺ -Si ([B] = 5×10²⁰cm^-3) for their diffusion studies, did not take into account the effect of pairing of positively charged interstitial Cu, Cu, with negatively charged substitutional boron, B. The consequence of this pairing is that only a fraction of the total Cu concentration is mobile at any given moment, while the rest is temporarily trapped. Following the diffusion theory of Frank and Turbull [7] and Reiss et al.,[8] it was suggested that Hall and Racette measured the effective, i.e., decreased by the effect of trapping by shallow acceptors, diffusion coefficient of Cu in p⁺-Si, and that their data should be revised to extract the intrinsic diffusion coefficients, i.e., the diffusion coefficient in Si without trapping sites[4-6]. Although in most real-life situations for p-type Si an effective diffusion coefficient is to be used, the intrinsic diffusion coefficient is important to know in order to calculate the effective Cu diffusivity for any p-type doping level of the substrate. Therefore, the practical significance of the intrinsic diffusion coefficient is paramount.

Several attempts to calculate the intrinsic Cu diffusivity by using various assumptions for the interaction potential between Cu and B from either the data of Hall and Racette [4] or from data points obtained by the transient ion drift (TID) technique at room temperature [5][6] were reported. However, none of these results were reliable since there was no evidence that the simple electrostatic models used in Ref. [4-6] to account for the interaction potential between Cu and B were sufficiently good approximations of the true potential. Indeed, theoretical calculations indicated that the bonding in Cu-B pairs has a significant covalent component [9], which cannot be quantitatively described by a simple model. In 1998, our group designed an experiment which allowed us to determine the intrinsic diffusion coefficient of Cu directly from the experimental data. This was achieved by minimizing Cu-B interactions to a negligible level by (i) using Si samples with low boron doping level (1.5×10¹⁴ cm ^-3) and (ii) performing transient ion drift measurements at elevated temperatures (up to 110°C). Further details of the experiment can be found in Ref. [1]. In particular, we found that the intrinsic diffusion coefficient of interstitial Cu in Si is given by Ref. [1]

whereas the effective diffusion coefficient (i.e., the diffusion coefficient which takes into account trapping of Cu by acceptors) is given by a system of equations, which for the moderately boron-doped (Na=10¹⁷cm^-3) Si can be reduced to the following explicit formula [1]

In this equation, temperature, T, is measured in kelvin and the boron doping level, Na, in cm^-3. Note that in the case of heavily doped samples (Na>10¹⁷ cm^-3) or in the case of Al or Ga-doped wafers one should solve a system of equations given in Ref. [1] rather than use Eq. 2

The intrinsic diffusion coefficient was defined in Ref. [1] as the diffusion coefficient of Cu in intrinsic float zone with low levels of oxygen and carbon. The impact of oxygen and carbon on Cu diffusivity is unclear, but there are indications that it is very small [6]. Since there is no experimental data on the pairing of Cu with positively charged shallow donors such as phosphorus, we think that the intrinsic diffusion coefficient may also be applied to moderately doped n-type Si at high temperatures. At low temperatures, the diffusivity of Cu in n-type Si may be impaired by the high likelihood of the formation of clusters and precipitates of Cu in n-Si (see the section on Defect reactions of Cu). The diffusivity of Cu in n⁺-Si requires a separate investigation since it was suggested [2][10] that a significant fraction of Cu becomes substitutional in n⁺ -Si, thus changing its diffusion mechanism and making feasible a pairing of negatively charged substitutional Cu with shallow donors [11].

The fact that the intrinsic diffusion coefficient of Cu in Si at room temperature, 2.8×10^-7 cm²/s (Eq. 1), is three orders of magnitude greater than extrapolated from the data of Hall and Racette [2], implies that Cu diffusivity is sufficiently high to enable Cu to diffuse significant distances in a wafer even at room temperature. For instance, Cu can diffuse at room temperature through a standard 4 in. p-type boron-doped 10 cm Si wafer in about 15 h.

It is important to point out that despite a difference of three orders of magnitude between our data for the intrinsic diffusion coefficient of Cu at room temperature and the expression suggested for Cu diffusivity by Hall and Racette, our results do not contradict the old Cu diffusivity data. This is illustrated in Fig. 1, which summarizes all published data on the Cu diffusivity in boron-doped Si with different boron concentrations (symbols), the intrinsic Cu diffusivity (curve 1), and the calculated diffusivities for different doping levels (curves 2-5), including that used by Hall and Racette (curve 5). Besides four data points of Hall and Racette [2], a data point obtained by Struthers for intrinsic Si²² is also shown. The data point of Struthers lies indeed on the intrinsic diffusivity line (curve 1). It is seen from Fig. 1 that the effective diffusion coefficient of Cu calculated for the boron doping level of 5×10²⁰ cm^-3 is in perfect agreement with the data of Hall and Racette [2], see curve 5 in Fig. 1. This indicates that their data were correct, but unfortunately applicable only to p⁺-Si with a doping level of 5×10²⁰ cm^-3, and only in the temperature range where their data points were taken.

Fig. 1. Effective diffusion coefficient of Cu in Si calculated for different boron doping levels (lines) and experimental data obtained by Istratov et al.[1] (circles) Na = 1.5×10¹⁴ cm^-3 and (diamonds) Na = 2×10¹⁵ cm^-3, by Hall and Racette; [2] (triangles) Na = 5×10²⁰cm^-3, by Struthers [12] (gray triangle, intrinsic silicon). Curve 1, intrinsic silicon (corresponds to the intrinsic diffusivity). Curve 2, Na = 1.5×10¹⁴ cm^-3. Curve 3, Na = 2×10¹⁵ cm^-3. Curve 4, Na = 1×10¹⁷ cm^-3. Curve 5, Na = 5×10²⁰ cm^-3.

The diffusion barrier of 0.18 eV is by far lower than that of any other impurity in Si. This low value is due primarily to the small ionic radius of Cu in Si and the weakness of covalent interactions of Cu with the crystal lattice. It is known that the diffusion barrier of any impurity consists of two major components, determined by the elastic and electronic interactions with the lattice atoms [13]. Utzig [14] estimated the elastic component of the diffusion coefficient of 3d metals in Si and obtained results surprisingly close to the experimental data for the majority of transition metals, with the exception of the ionized copper Cu, whose ionic radius was so small that Utzig's model predicted a zero diffusion barrier for it. Woon et al. [15] predicted the electronic component of the Cu diffusion coefficient at 0.24 eV, in good agreement with our experimental data.

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