Experimental Relaxation Volume of Al Impurity in Si(Al) Thermomigrated Structures

Abstract

Temperature gradient zone melting, employing local dissolution on metal dopants, is a versatile technology capable of producing heavily doped regions (through narrow p-channels, silicon matrices of 3D architectures, etc.) in semiconductors utilized in power high-voltage electronic devices. This approach was applied to fabricate a model Si(Al) structure with uniform distribution of both Al impurity and strains, which is suitable for studies of Al solubility. Using a combination of X-ray Bragg’s diffraction and secondary ion mass spectroscopy, we established that with temperature gradient zone melting at T = 1350 K, the solubility of Al in solid silicon was 0.95 × 10¹⁹ at/cm³ that differs from the value of 1.95 × 10¹⁹ at/cm³ expected from the previously published data, which is used in the physical chemistry of semiconductors. A reason for this may be the high level of intrinsic stresses, increasing the Gibbs energy of the solid Al–Si phase, or some additional factors, which were not taken into account in the previous electrical measurements. Here, we performed a precise experimental determination of the microscopic parameters (strain coefficient, relaxation volume, and dipole tensor) of Al impurity in Si, which describe the effect of the intrinsic stress on the Gibbs energy of the solid Al–Si phase. In addition, these parameters allow the determination of the value of the impurity content from the X-ray diffraction data. It was found that Al in a substitutional position gives rise to the lattice strain coefficient β of 1.54 × 10^–24 cm³. First-principles density functional calculations were performed for the Al atom in the substitutional position in Si. The results clarify the effect of the defect size and electronic strain on the lattice strain coefficient. The practical impact of this study is the development of the technique of nondestructive diagnostics of heavily doped semiconductor structures with intrinsic stresses.