Hybrid-Functional Calculations of the Copper Impurity in Silicon

Abstract

We calculate formation energies and transition levels for copper-related defects in silicon using the screened hybrid functional of Heyd, Scuseria, and Enzernhof HSE06. We considered Cu siting on interstitial sites (Cu i), substitutional site (Cu Si), Cu Si-Cu i pair, a complex formed of substitutional Cu and intersititial hydrogen (Cu Si-H i) and a complex formed of a substitutional Cu and three interstitial Cu (Cu Si-3Cu i). We find that Cu i is a fast diffuser, with migration barrier of only 0.19 eV, in good agreement with experimental values. Cu i is a shallow donor and its formation energy is lower than that of Cu Si for all Fermi level positions in the band gap. Cu Si , on the other hand, induce levels in the gap, which are related to the occupation of antibonding states originated from the coupling between the Cu 3d states (t (d) 2), resonant in the valence band, and the vacancy-induced gap states (t (p) 2). The stable charge states of Cu Si in the gap are +1, 0,-1, and-2. The transition levels of Cu Si-Cu i and Cu Si-H i are closely related to the levels of isolated Cu Si : a donor level (+/0) near the valence band, an acceptor level near mid gap, and a double acceptor level in the upper part of the gap. The calculated transition levels are in good agreement with experimental results, and the formation energies explain the observed solubility.

Point defect engineering in thin-film solar cells

“…The solubility and diffusivity of transition metals measured by several techniques shows an increasing trend from Ti to Cu 27,28,36,37 . Defect levels of metal impurities have been investigated by both spectroscopic methods 26,28,36,[38][39][40][41][42] and quantum mechanical simulations 43,44 . The most detrimental impurities can be removed from the material using various processing techniques (e.g.…”

Challenges facing copper‐plated metallisation for silicon photovoltaics: Insights from integrated circuit technology development

“…One of the concerns raised about using Cu to form the metal electrodes to Si solar cells is that the Cu may penetrate into the Si where it can form deep‐level traps that are detrimental to cell performance . The introduction of Cu interconnects into ICs also faced that concern .…”

“…Copper contamination can reduce the minority carrier lifetime in p‐type Si and n‐type Si with the impact on carrier lifetime being more significant in n‐type . The effect of Cu impurities on the carrier lifetime in Si and attribution of the associated recombination to energy levels within the Si bandgap has been widely reported over the years.…”

“…The effect of Cu impurities on the carrier lifetime in Si and attribution of the associated recombination to energy levels within the Si bandgap has been widely reported over the years. Copper can exist in interstitial (Cu i ) forms, substitutional (Cu s ) forms, in complexes with Si (eg, Cu 3 Si), other Cu atoms (Cu s Cu 3i ) and other Cu impurities including hydrogen (eg, Cu s ‐H i ) (see Figure ) . The Cu i state does not induce any defect levels in the gap and is stable only in the singly positive charge state (Cu i + ) for all Fermi‐level positions in the Si band gap.…”

“…In p‐type Si, Cu 3 Si has been shown to reach the neutrality level, only when the Cu concentration exceeds the acceptor density by 1 × 10 16 cm −3 . Consequently, n‐type Si is more sensitive to Cu contamination than p‐type Si due to the ease at which Cu precipitates can grow and, in p‐type Si, the more benign Cu s ‐Cu 3i complex predominantly forms (see Figure ) …”