Mechanisms of boron diffusion in silicon and germanium

Abstract

B migration in Si and Ge matrices raised a vast attention because of its influence on the production of confined, highly p-doped regions, as required by the miniaturization trend. In this scenario, the diffusion of B atoms can take place under severe conditions, often concomitant, such as very large concentration gradients, non-equilibrium point defect density, amorphous-crystalline transition, extrinsic doping level, co-doping, B clusters formation and dissolution, ultra-short high-temperature annealing. In this paper, we review a large amount of experimental work and present our current understanding of the B diffusion mechanism, disentangling concomitant effects and describing the underlying physics. Whatever the matrix, B migration in amorphous (a-) or crystalline (c-) Si, or c-Ge is revealed to be an indirect process, activated by point defects of the hosting medium. In a-Si in the 450-650 C range, B diffusivity is 5 orders of magnitude higher than in c-Si, with a transient longer than the typical amorphous relaxation time. A quick B precipitation is also evidenced for concentrations larger than 2 x10^20 B/cm3. B migration in a-Si occurs with the creation of a metastable mobile B, jumping between adjacent sites, stimulated by dangling bonds of a-Si whose density is enhanced by B itself (larger B density causes higher B diffusivity). Similar activation energies for migration of B atoms (3.0 eV) and of dangling bonds (2.6 eV) have been extracted. In c-Si, B diffusion is largely affected by the Fermi level position, occurring through the interaction between the negatively charged substitutional B and a self-interstitial (I) in the neutral or doubly positively charged state, if under intrinsic or extrinsic (p-type doping) conditions, respectively. After charge exchanges, the migrating, uncharged BI pair is formed. Under high n-type doping conditions, B diffusion occurs also through the negatively charged BI pair, even if the migration is depressed by Coulomb pairing with n-type dopants. The interplay between B clustering and migration is also modeled, since B diffusion is greatly affected by precipitation. Small (below 1 nm) and relatively large (5-10 nm in size) BI clusters have been identified with different energy barriers for thermal dissolution (3.6 or 4.8 eV, respectively). In c-Ge, B motion is by far less evident than in c-Si, even if the migration mechanism is revealed to be similarly assisted by Is. If Is density is increased well above the equilibrium (as during ion irradiation), B diffusion occurs up to quite large extents and also at relatively low temperatures, disclosing the underlying mechanism. The lower B diffusivity and the larger activation barrier (4.65 eV, rather than 3.45 eV in c-Si) can be explained by the intrinsic shortage of Is in Ge and by their large formation energy. B diffusion can be strongly enhanced with a proper point defect engineering, as achieved with embedded GeO2 nanoclusters, causing at 650 °C a large Is supersaturation. These aspects of B diffusion are presented and discus...

Response to “Comment on ‘Diffusion of n-type dopants in germanium’ ” [Appl. Phys. Rev. 2, 036101 (2015)]

“…This equation yields D I ¼ 4.8 Â 10 À12 cm 2 s À1 for 550 C. Provided that the kick-out reaction solely controls B diffusion in Ge under irradiation as stated by Cowern et al 3 and other previous studies, 4,11,12 the data deduced for D I from the B profile at 550 C must be consistent to the data deduced from self-diffusion under irradiation. However, the simulation of radiation enhanced B diffusion at 550 C yields…”

“…The corresponding g and k parameters slightly deviate from those deduced from the g/k analysis. These simulations on the basis of the full differential equation system describing dopant diffusion via the kick-out mechanism demonstrate that the experimental B profiles reported in the literature 3,4,11,12 can be well reproduced with the kick-out model. The simulations based on the full model reveal similar g and k parameters as those determined from the approximated g/k approach (see main text).…”

“…The approach is applicable when this specific mode of dopant diffusion prevails under the particular experimental conditions. Cowern and coworkers 3,4,11,12 were stimulated by the exponential shape of the B profiles in Ge established under proton irradiation to assume that the radiation enhanced diffusion of B in Ge is controlled by selfinterstitials. Accordingly, the transport capacity C BI D BI is concluded to be similar or even exceeds C I D I under radiation.…”

Diffusion ofn-type dopants in germanium

“…72,87 Recently, Cowern et al 59 used B diffusion measurements to probe the nature of I in Ge. They report on two distinct selfinterstitial forms, i.e., one form with a low and another with high activation entropy.…”

Doping strategies to control A-centres in silicon: insights from hybrid density functional theory

“…[1][2][3] However, detailed understanding of defect-dopant interactions that can affect the host material properties is not well established. [4][5][6][7] The interactions are important given that the characteristic dimensions of devices are in the nanometer scale. Oxygen (O) is introduced in Czochralski-Si during crystal growth with significant concentrations.…”