Modeling the Charge State of Monatomic Hydrogen and Other Defects with Arbitrary Concentrations in Crystalline Silicon

Abstract

A rigorous physical‐mathematical model for predicting the charge states of both mono‐ and multivalent defects with arbitrary concentrations in Si in both thermal equilibrium and non‐equilibrium steady‐state conditions is presented. The model avoids the assumption that the defect concentration is much lower than the doping level, which is common in previous approaches. It is shown that the general occupancy ratio given by α = (kn1 + p)/(kn + p1) is still valid under these more general conditions. However, more caution needs to be taken when calculating the equilibrium and excess carrier densities in the presence of larger defect concentrations, because of: a) the non‐negligible contribution to n0 and p0 from defect ionisation, and b) unequal Δn and Δp caused by the change in the occupied states at the defect level from equilibrium to non‐equilibrium. Modeled examples of monatomic H and interstitial Fe in Si are shown and the effects of defect concentration, temperature, and carrier injection are discussed.

The Impact of Different Hydrogen Configurations on Light- and Elevated-Temperature- Induced Degradation

“…In its atomic form, hydrogen can have different charge states (H + , H 0 , H -) depending on the position of the Fermi level, which is impacted mainly by the doping concentration, the temperature, and the excess charge carrier density. Being a negative-U impurity defect, H + is dominant in p-type and Hin n-type Si, whereas H 0 exists in relevant quantities only under certain conditions [38], [39].…”

“…This implies that the specific kinetics of the hydrogen inand out-diffusion might differ between p-and n-type wafers. Possible causes could, for example, be the charge state of atomic hydrogen and related diffusivities, or the trapping-kinetics of atomic hydrogen with the dopants, which all differ between Band P-doped silicon [38], [51], [70], [71].…”

Dynamics of Hydrogen in Silicon at Finite Temperatures from First Principles

“…They involve processes driven by kinetics and excitations (quenching, illumination, annealing), all of which cannot be understood if we leave vibrational and electronic excitations out of the physical picture. The recent work by Sun and co-workers [47,48] revised the second (electronic) type of excitations, with an evaluation of the relative concentrations of different charge states of H under nonequilibrium steady-state carrier injection. In this article, we consider the effect of vibrational degrees of freedom on several hydrogenrelated properties and processes.…”

Hydrogen Reactions with Dopants and Impurities in Solar Silicon from First Principles

“…Recent studies indicate that in n‐type Si (doping level 10 15 cm −3 ), H + becomes the dominant species in thermal equilibrium at . [ 42,43 ] This is also an approximate upper limit for the thermal stability of PH. The graph is therefore limited to that temperature.…”

“…However, it can show up transiently upon changes of thermodynamic or excitation conditions (e.g., release of H from H-related complexes upon capture of photogenerated carriers). The fractional populations of charge states of free H as a function of temperature has been described by Sun et al [42,43] using a general occupancy ratio model, which incorporates not only information regarding the transition levels of the defects, but also their capture cross sections for free carriers.…”