Set of equations for transient enhanced diffusion in shallow ion-implanted layers

Abstract

Abstract. To simulate the transient enhanced diffusion near the surface or interface, a set of equations describing the impurity diffusion and quasichemical reactions of dopant atoms and point defects in shallow ion-implanted layers is proposed and analyzed. The diffusion equations obtained take into account different charge states of mobile or immobile species and drift the mobile species in the built-in electric field and field of elastic stresses. The absorption of self-interstitials on the surface and drift of the defects due to elastic stresses result in the nonuniform distributions of point defects. It was shown analytically and by means of numerical calculations that consideration of the nonuniform defect distributions enables one to explain the phenomenon of "uphill" impurity diffusion near the surface during annealing of ion-implanted layers. The performed calculations of the boron concentration profile after annealing of a shallow implanted layer agree well with the experimental data confirming the efficiency of the proposed equations.

Change in the microscopic diffusion mechanisms of boron implanted into silicon with increase in the annealing temperature

“…It means that a significant transient enhanced diffusion occurs. The extracted value of the empirical coefficient β F 1 which describes the contribu-tion of singly charged self-interstitials [10] is equal to 0.27 a.u. The average migration length of boron interstitials is equal to 12 nm.…”

“…Here C and C AI are the concentrations of substitutionally dissolved impurity atoms and nonequilibrium dopant interstitials, respectively; C AC and C AD are the concentrations of impurity atoms incorporated into clusters and bound to the extended defects, respectively; S ACS and S ACI are respectively the rates of absorption of substitutionally dissolved impurity atoms and impurity interstitials due to the cluster formation; S ADS and S ADI are respectively the rates of absorption of substitutionally dissolved impurity atoms and impurity interstitials by extended defects; G ACS and G ACI are respectively the rates of generation of separate substitutionally dissolved impurity atoms and impurity interstitials during cluster transformation or dissolution; G ADS and G ADI are respectively the rates of generation of separate substitutionally dissolved impurity atoms and impurity interstitials during extended defect annealing; CV × and CI× are the concentrations of vacancies and self-interstitials in the neutral charge state normalized to the equilibrium concentrations C V × eq and C I× eq , respectively; D E (χ) is the effective diffusivity of impurity atoms due to the vacancy-impurity pair mechanism; D F (χ) is the effective diffusivity of impurity atoms due to migration of the "impurity atom-self-interstitials" pairs; χ is the concentration of charge carriers normalized to the intrinsic carrier concentration n i ; C B is the concentration of impurity with the opposite-type conductivity; d AI is the diffusivity of nonequilibrium impurity interstitials; τ AI is the average lifetime of impurity interstitials mediated by recombination with vacancies and kickout of silicon atoms from the lattice sites. We note that the concentration dependencies D E (χ) and D F (χ) are described in [10].…”

Analytical solution of the equations describing interstitial migration of impurity atoms

“…Let us consider a possible mechanism of the formation of such "tails". In recent years the mechanism of dopant diffusion in silicon crystals due to the formation, migration, and dissociation of the "impurity atom -vacancy" or "impurity atom -self-interstitial" pairs (the pair diffusion mechanism) has become commonly accepted (see, for example [1,16,17,18]). It is supposed within the framework of the pair diffusion mechanism that a local thermodynamic equilibrium prevails between substitutionally dissolved dopant atoms, intrinsic point defects, and the pairs.…”

Modeling of Thermal Processing at the Formation of Shallow Doped IC Active Regions

“…To calculate the distributions of nonequilibrium vacancies and self-interstitials, the diusion equations such as equations for point defects described in [14] are used. For solution of these equations, the process of defect trapping in silicon crystals is characterized by the average lifetimes of vacancies and self-interstitials.…”