Aggregation Kinetics of Thermal Double Donors in Silicon

Abstract

A general kinetic model based on accurate density-functional-theoretic total-energy calculations is introduced to describe the aggregation kinetics of oxygen-related thermal double donors (TDD's) in silicon. The calculated kinetics, which incorporates the reactions of associations, dissociations, and isomerizations of all relevant oxygen complexes, is in agreement with experimental annealing studies. The aggregation of TDD's takes place through parallel-consecutive reactions where both mobile oxygen dimers and fast migrating chainlike TDD's capture interstitial oxygen atoms.

Interstitial oxygen loss and the formation of thermal double donors in Si

“…11 The aim of the present letter is to extend the previous calculations and to report the long-time annealing behavior for the whole relevant temperature range of 300-650°C. Of specific interest is the role of O i loss in the growth of the TDD series.…”

“…11,18 -20 We find that the chain-like oxygen complexes are energetically most favorable and have the lowest migration energies. 11,18,20 The oxygen chains are ring-type and systematically assigned to TDDn with increasing number of oxygen atoms up to O 14 as follows: 11,20 In the kinetic model, the association of two migrating oxygen chains O j ͑containing j O atoms͒ and O k into an O jϩk complex occurs with the reaction rate (1 The restructuring of the complexes O k into the other structures occurs with the rate exp(Ϫ⌬E/kT)͓O k ͔ where is a frequency factor and ⌬E is the activation energy for the restructuring process. The longest O chains considered consist of 14 O atoms.…”

“…The longest O chains considered consist of 14 O atoms. 11 The calculated early formation rate of TDDs, d( ͚ n ͓TDDn͔)/dt, and the corresponding loss rate of O i , Ϫd͓O i ͔/dt, are shown as functions of annealing temperature in Fig. 1.…”

Local vibrations of thermal double donors in silicon

“…29 Both TDD1 and TDD2 are found experimentally to be bistable with the same electrically inactive X state, 30 showing that these structures are closely related and are probably different configurations of the same complex. These experimental findings are difficult to explain if TDD1 and TDD2 have a different number of O atoms as is the case in the model by Coutinho et al, 13,15,16 At low temperatures the electrons donated to the conduction band return to the TDD's making them electrically neutral ͑the TDD's change from the doubly positive state to the 0 state͒. It may be expected that the LVM frequencies of the TDD's undergo a positive shift when T becomes low because two more localized electrons strengthen the interatomic bonding.…”

“…14 13 We have shown that a rate-equation model for the O chains is able to produce the experimentally observed annealing kinetics of the TDD's. 15,16 However, the agreement may depend on the parameters we use in the kinetic model. It is therefore of paramount importance to compare the calculated LVM frequencies and modes of the O chains directly with the corresponding experimental quantities for the TDD's.…”