Oxygen Content and Annealing

A great amount of experimental effort has been devoted to the development of reliable means for the control and measurement of oxygen content (8+$\delta$), and to its use as an effective variable for investigating transport properties. The current understanding relating to the results of annealing experiments upon the stoichiometric Bi-2212 phase is briefly reviewed here. A substantial body of literature also exists regarding the use of cation substitution as a means to similar ends. The dopant concentration is an extra variable which may be more easily determined than $\delta$, and dopants can also be used to extend the range of variability $\Delta\delta$. The potential additional structural effects of cation ordering and phase separation, however, add to the complexity, and discussion of cation doping experiments will therefore be confined to appropriate points where they offer additional enlightenment not available through annealing alone.

The earliest literature on annealing experiments, effectively that prior to 1990, went only as far as to demonstrate that oxygen content was an important variable. The details, however, often relayed apparently conflicting results. For instance, the influence on T$_c$ of oxygen treatment of samples was reported to have little effect by Sunshine [45], while a decrease in T$_c$ was reported by Morris [135], and conversely increases in T$_c$ by Niu [136] and Forro [114]. The maximum attainable T$_c$ was also widely inconsistent, and Bi-2212 was frequently categorised as an 80K superconductor [137]. These initial contradictions evaporate when considered relative to the starting oxygen contents of the samples, and the later understanding of the T$_c$-$n_s$ relationship; as already mentioned, under-doped and over-doped regimes both exist. Some mindfulness for the influence of the various experimental parameters (such as anneal temperature, oxygen partial pressure, and anneal period) is also essential to understanding the changes brought about in a particular experiment.

An important later experiment in determining the evolution of oxygen loss with annealing temperature was that of Nagoshi [111]. In this, the unusual application of a mass spectrometer was made to analysing the evaporating atmosphere from a single crystal annealed in vacuum at temperatures between 200-600$^o$C. Oxygen loss from the crystal commenced as low as 220$^o$C, albeit slightly. Two regions of significance were identified, between 300$^o$C and 500$^o$C, and above 500$^o$C where the evaporation increased strongly. A similar two-stage process can be seen in the results of Deshimaru [112] using a different technique, the oxygen loss commenced at 260$^o$C and initially peaked around 400$^o$C. The results suggest that two distinct sites participate in the oxygen loss, and that the two are activated at the different temperatures. This fact is reflected in the results of numerous experiments where annealing above about 450$^o$C appears to induce different changes to annealing below this threshold [122,113]. In particular, this may have its most striking demonstration in measurements made by Dimesso [121] who annealed textured Bi-2212 thick films under flowing nitrogen for various periods at three different temperatures. The T$_c$ varied in an almost identical manner for the two temperatures of 300$^oC$ and 400$^o$C; rising from its as-grown value of 74K up to a maximum of 80K for a few hours annealing, and falling again for longer periods. But it was only by annealing at 500$^o$C that it was possible to achieve a maximum T$_c$ of 85K. So although the carrier concentration had been varied through the optimum value by the lower temperature oxygen changes, it appears necessary to also make alteration to the higher activation energy site before T$_c$ can be maximised. It can be concluded then, that to facilitate the most complete change in $\delta$, temperatures in excess of 500$^o$C are required.

However, annealing at too high a temperature for too long is also to be avoided with sample decomposition shown to accompany annealing as low as 450$^o$C [113]. The nature of the decomposition is highly dependent upon the annealing atmosphere as shown in a study by Forro [114] where annealing at 745$^o$C in various oxygen partial pressures produced entirely reversible changes except for oxygen partial pressures below 0.04mbar when permanent decomposition resulted. The TEM observations by Gao [109] found the majority of decomposition occurs as Bi-2201 inter-growths, the samples remaining crystalline. A systematic investigation of the problem using x-rays by Wu [115] also found inter-growths, and an additional unidentified phase with a ${\bf c}$ axis of 9.6${\rm\AA}$. After 120 hours annealing at 650$^o$C in air Wu [115] also characterised the additional problem of Bi evaporation in an oxygen rich atmosphere due to the evaporation of Bi$_2$O$_3$. Re-cleaving of the crystal surface and SEM views of the cross section showed this decomposition to be principally confined to a depth of $\approx$10$\mu$m, and that the decomposition did not progress further below the surface if the annealing was extended.

The actual parameters of oxygen diffusion as a function of temperature have been investigated by Runde [138]. Using tracer diffusion of $^{18}$O in single crystals annealed in one atmosphere of oxygen it was established that the diffusion is highly anisotropic, and is relatively slow below 550$^o$C. The a-b plane diffusion was found to have a far larger diffusion coefficient than that of the much slower c axis diffusion. The activation energies were also considerably different, suggesting an interstitial mechanism within the Bi$_2$O$_2$ layers with a low activation energy to be responsible for a-b diffusion: in the c axis no such convenient interstitial mechanism exists linking the Bi$_2$O$_2$ layers, and so diffusion is limited by the higher activation energy required for oxygen vacancy creation, presumably in the CuO$_2$ planes. The in situ measurement of the weight change of single crystal samples as a function of time and temperature, and of crystal dimensions, by Li and Kes [125] showed further anisotropy within the a-b plane itself with $\frac{D_a}{D_b}>5$. The anisotropic diffusion results overall are very similar to those for Y-123 [139], even down to similar values of activation energies for the a-b diffusion. In Y-123 the a-b anisotropy is explained by invoking the influence of the oxygen chains, an oxygen atom jumps from an oxygen chain into a neighbouring empty row along which it can then move rapidly until next encountering a chain fragment. The a-b anisotropy in Bi-2212 is almost certainly the result of the modulation, the rows of Bi concentrated bands playing a similar role to the chain fragments in Y-123.

In practical terms, then, the change in $\delta$ can be highly dependent upon the period of annealing at lower temperatures. In the results of Li [125], for example, periods in excess of 10 hours, extending to over 90 hours, are necessary to reach an equilibrium at 500$^o$C. And this is of course strongly dependent upon crystal dimensions. Above 600$^o$C, however, the diffusion process is so rapid that annealing for periods longer than one or two hours will be of little consequence to the equilibrium content. A study by Emmen [122] in which crystals were annealed in an oxygen atmosphere for 60 hours at temperatures between 400$^o$C and 800$^o$C, found this anneal period to be more than sufficient except at the lowest of temperatures below 450$^o$C; the crystal platelets had dimensions 10x3x0.3mm.

The controllable diffusion of oxygen in the Bi-2212 structure is well facilitated by the annealing methods described: quantifying the magnitude of the resultant change in oxygen, though, remains unreliable. The classical thermogravimetric method (TGA) has been commonly applied, and once contributions from contaminants such as water vapour and CO$_2$ are eliminated, authors show strong faith in the ability of the technique to measure relative changes in $\delta$ to $\pm$0.001[125] for single crystals (the problems associated with polycrystalline samples are far more unpredictable, however). The biggest hurdle comes in determining an absolute value for $\delta$. For this a reference point is required against which the variations may be marked, and this results in large uncertainties which are typically $\pm$0.1 [140]. Potential solutions to this have included iodometric titration, hydrogen reduction, and carbon reduction methods, but the results show that no two techniques, even when applied to the same sample, are able to produce the same answer. This is to be held in mind when comparing the contrary results of different authors. In addition, it must be remembered that the absolute value of $\delta$ is also dependent upon the cation stoichiometry of a crystal, and so will inevitably be different to some degree for crystals from different growths. To side step such issues, many experiments have instead simply reported results as a function of the oxygen partial pressure during annealing, or as a function of the anneal temperature instead.

Common agreement upon the form of the T$_c$-$\delta$ relationship established by the different means does exist. The first part of the curve in the overdoped region was measured by Nagoshi [111], where T$_c$ increased with oxygen loss to a plateau. Groen [141] established the underdoped region, where increasing the oxygen partial pressure resulted in T$_c$ decreasing, and the same relationship was shown by Mitzi [140]. An important measurement was the variation of T$_c$ across the complete plateau region of the curve, going from overdoped to underdoped as the oxygen loss increased, as studied by Li [125]. The variation in $\delta$, as measured by TGA for this plateau region, was 0.12: the range of T$_c$ was for about 85K to T$_c^{max}$ to 80K on the underdoped side (the maximised T$_c$ varying between particular crystals). Similar magnitudes for $\delta$ were measured by Mitzi [140], and Morris [135], also using TGA. Using iodometric titration, Schweizer [142] measured a range of 0.10 for $\delta$ going from the plateau down to 65K in the underdoped regime. An anomalously small change in $\delta$ of only 0.04 for a range of T$_c$ of 40K, measured using TGA on powdered samples, caused Groen [141] to invoke a charge re-distribution process rather than oxygen loss to be responsible for the T$_c$ changes. The inaccuracy of TGA when applied to powdered samples would seem a more reasonable explanation for this inconsistency however. A similar charge redistribution argument was used by Nagoshi [111] who measured a tiny change of only 0.006 for a T$_c$ increase of 27K. Again this seems implausible; it can only be speculated that a flaw in the analysis of the unusual mass spectrometer method is responsible.

The c axis lattice parameter also varies with $\delta$, and an unequivocal linear relationship exists between c and T$_c$, for which very good agreement is found amongst authors. The magnitude of this variation, in which c increases with increasing T$_c$, is typically of the order of $\Delta c =0.10{\rm\AA}$ for $\Delta$T$_c$ of 10K, from a survey of the published values [125,140,122,141]. Modifications in the other lattice parameters are less well characterised, a few reporting no observable changes in a or b, but with more accurate measurement a small degree of change is apparent. Making no distinction between the two, Nagoshi [111] measured an expansion for $a$ and $b$ over a range of 0.005${\rm\AA}$ accompanying oxygen loss, and Mitzi [140] observed a contraction of 0.005${\rm\AA}$ with oxygen incorporation. Where measured, no change in the modulation period has ever been discerned to accompany changes in $\delta$ [111,140,143]. The observations of Section 4.3.4 are also in accord with this result. Because of the linear correspondence between c and T$_c$, explanations have been sought to explain how, ultimately, the c axis may govern hole concentration. Certainly, removal of oxygen from the Bi$_2$O$_2$ layers could be reasonably expected to lead to an increase in the separation of neighbouring BiO bi-layers, and an expansion of c [81]. It was similarly reported by Xue [144] that incorporation of excess oxygen between the BiO layers causes the repulsion between the bi-layers to decrease, and hence the SrO-BiO-BiO-SrO slab to contract. For the c axis expansion to be involved directly in the control of $n_s$, however, an expansion of the interlayer CuO$_2$ to BiO distance would seem a more necessary component for it to effect charge transfer directly. A discussion of the effects upon hole concentration, and whether these alterations actually act in consort with charge transfer will require more detailed observations.

Within the phase range of Bi-2212 a wide variation in cation stoichiometry is possible, which can mean samples used in the different experiments and only nominally identified as Bi-2212 can have in reality very different cation compositions. Unfortunately, unless some extrinsic doping has been specifically introduced as a variable in an experiment, then cation composition is rarely investigated. The difference in T$_c^{max}$ already mentioned [125], is attributed to just these differences. The work by Deshimaru [112] has addressed this question by examining the effects of annealing upon samples with various Sr/Ca ratios, Bi$_2$Sr$_{2-x}$Ca$_x$Cu$_2$O$_y$ ($x$=0.0 to 1.0). The clearest indication of the Sr/Ca ratio was found to be the ${\bf c}$ axis, which ranged from 30.6${\rm\AA}$ for x=0.8 to 30.9${\rm\AA}$ for x=0.0. Upon annealing, the $c$ lattice parameter appeared to show a linear relationship with oxygen content for all values of $x$, and all varied over similar ranges but within different absolute limits depending upon $x$. The simple T$_c$ vs. $c$ relationship just mentioned was not found to hold, however, with an almost parabolic relationship for x=0.8, and even when more linear the slope of the curve changed dramatically, becoming much steeper for x=0.0. The T$_c^{max}$ which can be inferred from their results showed a value of $\approx$95K for x=0.0 but was limited to values less than 85K for higher values. In annealing studies of lead doped epitaxial films, Balestrino [145] found a similar dependence to that of Deshimaru [112] in the relationship between T$_c$ and annealing; but this time with the lead content. It was also found that the $c$ lattice parameter underwent a smaller change with the annealing, the greater the lead content.

Direct determination of the carrier concentration in the CuO$_2$ planes can be made by Hall measurements. Assuming the oxygen changes do take place in the Bi$_2$O$_2$ layers, then the variation of $n_s$ with $\delta$ is an indication of the degree of charge transfer which actually occurs between the layers. Hall measurements have been carried out by, amongst others, Rateau [146], Mitzi [140], and Nagoshi [111]. All provide only limited data, but there is reasonable agreement upon the magnitude of the changes. With oxygen loss, Nagoshi measured $n_s$ decreasing from 4x$10^{21}$ to 2x$10^{21}$ carriers per cm$^2$, and with oxygen incorporation Mitzi measured an increase from 3.1x$10^{21}$ to 4.6x$10^{21}$. A calculation can be made of the expected adjustment in hole content based upon the accompanying measurement of the change in $\delta$. As measured by Mitzi, $\Delta\delta$=0.29 and would be expected to contribute 0.58 holes p.f.u., compared to the actual change measured from $n_s$ of only 0.32 extra holes p.f.u.. This is an indication that a proportion of the holes do not contribute to the mobile carrier concentration but are rather localised and responsible for partially oxidising the BiO layer. A similar localisation of holes is known to occur in the CuO chain layer of Y-123. Strong support for this picture of charge transfer was provided by a study of the bismuth valence by Schweizer [142] using a chemical method. It was found that the bismuth valence varied linearly with oxygen content, confirming that oxidation of the BiO layers occurs.

Scanning tunnelling spectroscopy (STS) and microscopy (STM) techniques have been used in conjunction to probe changes in the electronic state of the BiO layer (the methods are described in detail by Zhang [147]). This is facilitated by the ease with which Bi-2212 single crystals may be cleanly and reliably cleaved, however, the studies are confined to the state of the single surface BiO layer. Awana [148] was able to directly observe excess oxygen atoms on this surface layer, and even observed the changes due to oxygen annealing with additional oxygen being incorporated in a disordered fashion in the STM image. It was found that nitrogen annealing produced instead well ordered BiO images. Whether the BiO layers may ever be entirely metallic is disputable, but certainly the increased oxygen content was found to augment the non-metallic nature of layers [148,149]. Their interpretation of the effects of this upon the superconductivity are unfortunately wildly astray, suggesting that the decreasing metallicity of the Bi$_2$O$_2$ layers is wholly responsible for the decrease in T$_c$ [148,150] but takes no account of the overdoping of the CuO$_2$ layers by the increasing oxygen content. A zero density of states and non-metallic behaviour has also been reported by Shih [70] using STS. A study by Wu [143] of samples vacuum annealed for varying periods at 400$^o$C, which altered T$_c$ from 85K to non-superconducting, unlike Awana [148] failed to observe any change in the STM images. This led Wu (and has been taken up by others) to speculate that the suppression of T$_c$ may not be due to oxygen loss from the BiO layer. However, unlike the images of the Awana study, it is not clear whether the images are of the bismuth or oxygen sub-lattices, and as is admitted in the paper, if bismuth alone were being resolved this would more simply explain the failing. A change was found in the local electronic states near the Fermi level, with non-periodic variations over a length scale of 20-30${\rm\AA}$ observed in the non-superconducting samples, and which were entirely absent from the as-grown samples. Wu suggested these to be significant as they occur on the same scale as the coherence length, and they may well be the result of oxygen loss accommodated by the BiO layer by changes in the bismuth coordination.

The behaviour of the normal state properties are also, of course, strongly affected by the annealing related changes. Because of the highly anisotropic nature of the transport properties they must be considered separately within the ${\bf a-b}$ plane and perpendicular to it. As T$_c$ decreases so the ${\bf a-b}$ plane resistivity $\rho_{ab}$ increases systematically, as does the slope $d\rho/dT$ [114]. The resistivity is linear and metallic-like down to temperatures close to T$_c$, but this can change for samples rendered oxygen deficient by annealing where a semiconductor like increase in $\rho_{ab}$ is observed above T$_c$ [151]. The $\bf c$ axis resistivity $\rho_c$ is upwards of several orders of magnitude larger than $\rho_{ab}$ due, it is believed, to the localisation of the carriers within the CuO$_2$ planes and the large separation of these by the insulating charge reservoir layers. The behaviour of the normal state properties are qualitatively the same amongst all high-T$_c$ superconductors. In an experiment by Yoo [133] $\rho_c$ was found to range from semiconductor-like to more metallic behaviour with increasing annealing temperature. This, and the strong sample dependence of the behaviour, is explained by some form of structural distortion between the CuO$_2$ layers which leads to a reduction in the interlayer coupling, and which is relieved by the annealing. The overall behaviour can then be explained in the context of thermally activated hopping between the CuO$_2$ layers.

The picture which emerges from this survey of the literature is one in which the changes associated with oxygen diffusion are complex, and are either contrary to, or are far from adequately described by, the currently accepted assumptions of oxygen behaviour in Bi-2212. The control of oxygen stoichiometry by annealing can be used to range over a substantial range of $n_s$ and hence T$_c$. There is evidence that the full range of $\Delta\delta$ is greater than the $\Delta \delta \leq 0.2$ which can be accounted for by the single excess oxygen model. Although absolute values are difficult to determine reliably, relative changes in oxygen content of $\Delta \delta \geq 0.3$ have been commonly reported amongst annealing experiments [135,140,152]; Mitzi [140], for example, observed a fully reversible variation in $\delta$ of 0.29(5) which corresponded with the alteration of T$_c$ by 13K (the full range by which T$_c$ can be varied is substantially larger). The variation of oxygen in excess of $\Delta\delta$=0.2 must, therefore, involve the variation of oxygen at additional crystallographic sites. This is supported by the wide range of values summarised in Table 3.1 of Chapter 3. A further commonly cited assumption is that the modulation period is a function of $\delta$. But this runs contrary to the actual observations of structure studies, and the results presented in Chapter 4 confirm this to be a false picture. Clear evidence for two distinct sites comes also from the evolution of the annealing process with temperature (this is further supported by the results presented in Chapter 4). Most importantly, there is some suggestion that alteration of the lower activation energy site alone is not sufficient to achieve the highest values of T$_c$ [121]. There is also much evidence that substantial structural adjustments accompany the variation of oxygen stoichiometry [142,140,143,148]. That some form of structural adjustments have additional influence beyond controlling $n_s$ alone, and effecting T$_c^{max}$, is a distinct possibility, and would also explain the change in nature of $\rho_c$ [133]. The oxygen content question therefore remains controversial, but there is much to suggest that the commonly assumed picture is at best a naive one, and that subtle oxygen related structural adjustments have yet to be identified.