Charged species in the thermal oxidation of silicon: the surviving open cores of Mott's 1981 questions — the mobile charged species under electron-available oxidation conditions and the charged centres in as-grown thermal SiO2

In 1981 N. F. Mott analyzed the thermal oxidation of silicon within the Deal-Grove framework and enumerated four unresolved issues about the charged and mobile species involved: (1) the parabolic rate constant fixes only a combination of the activation energy $U$ for $O_2$ diffusion and the free energy $W$ for introducing $O_2$ into a normal interstitial site of the oxide, with no experiment able to separate the two; (2) the identity of the mobile charged species implied by Jorgensen's electric-field oxidation experiments, tentatively proposed to be a highly charged silicon vacancy; (3) the identification of the charged defects $C_1^-$ and $T_3^+$ as 'Pepper's centres' — the oxide charges whose random potential localizes carriers in Si inversion layers — an identification resting on unconfirmed energy-level assumptions and contradicted for the oxide bulk by DiMaria's trap spectroscopy; and (4) the existence and concentration of $T_3^+$ centres in thermal oxide, their relation to the $E'$ centre, and the Lucovsky-Galeener disagreement over the origin of the Raman D1/D2 defect lines of vitreous silica. Later literature resolves much of this cluster: photoluminescence of interstitial $O_2$ now separates solubility from diffusivity, the Raman lines are conclusively assigned to three- and four-membered rings, and the valence-alternation picture was superseded by the modern $E'$/$P_b$/fixed-charge defect taxonomy. What survives without a definitive literature answer is the atomic identification of the mobile charged species when electrons are available during growth, and the identity, charge state, and concentration of the charged centres in as-grown thermal $SiO_2$.

Background

Thermal oxidation — heating a silicon wafer in $O_2$ (dry) or $H_2O$ (wet) — grows the thin $SiO_2$ film whose interface with silicon underlies the metal-oxide-semiconductor (MOS) transistor. The Deal-Grove model (Deal and Grove 1965) describes film thickness versus time by a linear-parabolic law whose parabolic rate constant $B$ is proportional to the product of the oxidant's diffusion coefficient $D$ and its equilibrium concentration $C^*$ in the oxide; kinetics alone fix only the product $D C^*$, not the two factors separately. In dry oxidation the oxidant is the $O_2$ molecule occupying interstitial sites, i.e. positions between the atoms of the amorphous $SiO_2$ network. Mott (1981) distinguished two energies for interstitial $O_2$: the activation energy $U$ for hopping between ordinary interstitial sites, which controls diffusion, and the free energy $W$ for introducing an $O_2$ molecule into a normal interstitial site. He further distinguished 'special low-energy sites', deeper traps which in his model determine the measured solubility but are not relevant to the rate of oxidation; consequently oxidation kinetics fix only a combination of the two energies, and he argued that no existing experiment could separate them. Heavy-oxygen isotope tracing — introducing the isotope $^{18}O$ and detecting it, for example by nuclear reaction analysis — identifies which oxygen atoms move during growth and whether $O_2$ exchanges atoms with the network. Jorgensen (1962) oxidized silicon under an applied electric field and found growth rates that depended on field polarity — oxidation is enhanced when the silicon is made positive and retarded, up to complete cessation, when it is negative — implying that the mobile species inside the oxide is charged (ionic) rather than the neutral $O_2$ molecule. Electron spin resonance (ESR, equivalently EPR) detects paramagnetic defects, those with unpaired electrons: the $E'$ centre family is associated with oxygen vacancies, in the standard model a hole trapped at an oxygen vacancy leaving an unpaired electron on a threefold-coordinated silicon neighbour of the vacancy, and the $P_b$ centre is a trivalent-silicon dangling bond at the $Si/SiO_2$ interface. In a MOS device the gate field induces an inversion layer, a two-dimensional electron gas at the silicon surface; Anderson localization is disorder-induced localization of carriers, which in Si inversion layers is produced by the random electrostatic potential of charged centres in or near the oxide — 'Pepper's centres' (Pepper 1977). Valence-alternation pairs, a concept introduced for amorphous chalcogenide semiconductors, are defects whose coordination number and electric charge change together; in the standard notation $C$ denotes a chalcogen (here oxygen) and $T$ a tetrahedral atom (here silicon), with the subscript the coordination number and the superscript the charge. Lucovsky (1979) argued from spectroscopic evidence that defect bands of vitreous (amorphous) $SiO_2$ originate in such valence-alternation-pair defect states, and developed the intimate-pair variant of the picture in Lucovsky (1980). Mott's source text writes $T_3^+$ for a positively charged threefold-coordinated silicon, a defect naturally related to the $E'$ family, and discusses $C_1^-$ (a negatively charged onefold-coordinated oxygen) and $T_3^+$ as candidate Pepper's centres. Vitreous silica exhibits two narrow Raman 'defect' lines, D1 near 495 $cm^{-1}$ and D2 near 606 $cm^{-1}$, whose origin was disputed between defect-based readings (Lucovsky) and small-ring readings (Galeener). The fixed oxide charge $Q_f$ is the immobile positive charge present in as-grown thermal $SiO_2$ near the $Si/SiO_2$ interface. Mott's companion papers (Mott 1977, Advances in Physics; Mott 1980, Journal of Non-Crystalline Solids) develop the charged-defect framework on which the 1981 paper rests.

Problem Statement

The problem is the atomistic identification of the charged and mobile species involved in the thermal oxidation of silicon, as posed by Mott (1981) and narrowed by four decades of subsequent work. The source question had four parts. Part 1 — find an experiment that separates the free energy $W$ for introducing $O_2$ into a normal interstitial site of the oxide from the activation energy $U$ for diffusion between such sites — is settled: species-selective photoluminescence of interstitial $O_2$ now measures the dissolution rate, solubility, and diffusivity independently. Part 4's Raman component — the Lucovsky-Galeener disagreement over whether the D1/D2 lines of vitreous silica betray defect centres — is settled in favour of small-ring structures, and the $E'$-centre structure is established. Part 3 — the identification of $C_1^-$ (a negatively charged onefold-coordinated oxygen) and $T_3^+$ (a positively charged threefold-coordinated silicon) as Pepper's centres, the oxide charges whose random potential localizes carriers in silicon inversion layers — was superseded by the modern $P_b$/$E'$/fixed-charge defect taxonomy rather than definitively answered. What remains open, precisely stated, is: (i) the atomic identity and charge state of the mobile charged species that transports oxygen through $SiO_2$ when electronic current is available during growth (Jorgensen's electrode configuration) — Jorgensen's oxygen-ion reading and Mott's charged-silicon-vacancy proposal have never been discriminated by a direct experiment; and (ii) the nature of the stationary charged centres present in as-grown thermal $SiO_2$ and at the $Si/SiO_2$ interface — their atomistic identity, charge states, and concentration, including whether they are related to $E'$-family paramagnetic centres and what microscopic structure carries the fixed positive oxide charge $Q_f$. The four parts of the source question are only loosely coupled, and the source poses the two surviving cores as two distinct questions; the problem comprises both cores, so a definitive identification of either core resolves that core and leaves the other open.

References

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