1. Introduction

Twenty six years ago, my colleague at the Naval Research Laboratory Joe Friebele and I respectively performed optical absorption and electron-spin-resonance (ESR) isochronal annealing experiments from ~100 K to ~900 K following x-irradiation at 77 K of separate sub-samples of a GeO₂-SiO₂ glass cut from the core of an experimental fiber-optic preform. To my knowledge, such a concurrent pair of ESR and optical experiments carried out over such an extended temperature range has never again been repeated. Therefore, the data that we obtained back then remain relevant to a still-highly-active field of research. Unfortunately, however, Joe and I failed to completely describe our experimental details – or our methods of data analysis – in our sole publication on the subject, a short review article for a conference proceedings [1]. Even worse, it turns out that we have both lost our respective spectra, calculations, and other records pertaining to this experiment. Thus, the present paper begins by describing our experiments and methods of analysis as best as we have been able to recall them following a recent exchange of e-mails between the two of us.

In this communication I will present a replotted version of Joe’s and my original isochronal-anneal figure with certain changes reflecting my deduced reconstruction of some important but heretofore unrevealed details of our experiments 26 years ago. I will explain why this new graph appears to be the key to resolving decades-old disagreements regarding the natures of the paramagnetic Ge(1) and Ge(2) centers, as well as the hole-trapping properties of twofold-coordinated germaniums (commonly termed “germanium lone pair centers” or GLPCs). Crucial to this objective is the previously noted [2] high degree of correspondence between the ESR spin Hamiltonian parameters of the Ge(1) and Ge(2) centers in GeO₂-SiO₂ glasses and those of their far better characterized doppelgangers in Ge-doped crystalline α quartz [3], the Ge(II) and Ge(I) centers, respectively. Here I will elaborate for the first time the similarity of the temperature dependencies of the relative number densities of the Ge(1) and Ge(2) centers in the glasses to those rigorously determined [3] for the Ge(II) and Ge(I) centers, respectively, in α quartz. And because of this similarity I will argue that the former pair of defects, like the latter, represents two energetically inequivalent configurations of an electron trapped on a GeO₄ tetrahedron that are typical of both of these polymorphs of silicon dioxide. This means that the GeO₄ tetrahedra that trap electrons in Ge-doped silica glasses must possess a degree of quartz-like local structure, a revelation bound to lead to adjustments in our current understanding of silica glass structure.

2. Experimental Details Finally Revealed, Partially

The sample material was a GeO₂-SiO₂ fiber-optic preform provided by U.S. industry (probably Corning, Bell Laboratories, or 3M); the deposition method and fraction of GeO₂ have both been forgotten. Only the core of this sample was used for the experiments. Both samples were subjected to a 5 kGy dose of 100 keV x rays at 77 K. The optical sample consisted of a disk ~0.75 cm in diameter and 0.69 mm thick optically polished on both sides. Another piece (or pieces) of the same sample was (were) used for the ESR studies. If a single piece, it would have been sawed into parallelepiped fitting into a 3-mm-inside diameter fused silica sample tube, which would have been evacuated and sealed. Otherwise, the ESR sample might have been powdered before loading it into the sample tube. In either case, x-ray-induced defects in the sample tube itself would have been annealed out prior to any ESR measurements by exposure to the flame of an H₂-O₂ torch while the sample itself was maintained 77 K in the opposite end of the tube.

The ESR isochronal anneals were accomplished in situ in the microwave cavity of either a Varian E-9 spectrometer operating at 9.1 GHz or a Bruker ER 200 operating at 9.35 GHz, likely for 5 min at each temperature, up to 473 K by use of a Varian V4540 N₂ flow-through temperature controller. Anneals at higher temperatures were carried out ex situ in a laboratory furnace. In all likelihood, this experiment was accomplished in the same manner as isochronal annealing experiments on an x-irradiated pure silica sample that I performed ~6 months later [4], wherein the measurement temperature for all spectra was 105 K, the anneal temperature increments were + 20 K below 300 K, + 25 K between 300 and 525 K, and + 50 K at higher temperatures.

The optical sample was irradiated at 77 K in situ in an Air Products Heli-Tran variable temperature cryostat designed to mate with the Cary Model 14 or 17 spectrophotometer used to acquire the spectra. All optical spectra pertaining to isochronal anneals up to 300 K were recorded at 100 K [5], whereas for anneals to still higher temperatures the sample was removed to a laboratory furnace and the corresponding spectra were recorded at room temperature using a standard Cary sample mount.

3. Original Results and Data Analyses

Fig. 1 (identical with Fig. 3A of [1]) represents the only surviving spectrum of any sort from the experiment described in [1]. None of the original ESR spectra have been found. This figure illustrates Joe Friebele’s Gaussian resolutions of the optical spectrum recorded at 100 K immediately following x-irradiation at 77 K.

 

Fig. 1 Optical absorption spectrum of the GeO₂-SiO₂ glass of this study after x-irradiation to a dose of 5 kGy at 77 K and measurement at 100 K. Fitted curves are Gaussians. Figure taken directly from [1].

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Fig. 2 is a scanned, digitized, and replotted version of Fig. 3B of [1], which preserves all of the original curves and data points in their original interrelationships. Joe Friebele and I are in agreement that the oscillator strengths reported in Table 2 of [1] – reproduced in Table 1 of the present paper – were determined from the Gaussian decomposition of optical spectra illustrated in Fig. 1 in combination with ESR spin counts derived from spectra also recorded at or near 100 K immediately after irradiation.

 

Fig. 2 Isochronal annealing behavior of the ESR spin concentrations of various paramagnetic defects (continuous and broken lines) and optical intensities of optical bands (symbols) recorded for separate sub-samples of the same GeO₂-SiO₂ glass following identical x-irradiations at 77 K. The y-axis scale is calibrated to the optical intensities only. As discussed in the text, the interrelationships of the various ESR data are not entirely correct as relative number densities. This figure is replotted from the original [1] without any changes of the plotted data points or curves.

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Table 1. Parameters of the ESR and optical measurements at 77 K partially reported in [1] and used to develop Fig. 2 (same as in [1]) and Fig. 3 (original to the present work).

View Table

In consonance with the way that I carried out the ESR isochronal anneal studies reported in [4] (published contemporaneously with [1]) it is virtually certain that I obtained absolute ESR spin counts (number densities) by double numerical integration of the first-derivative curves recorded at 100 K or 105 K and comparison of these results with the similarly obtained double integral of the spectrum of a Varian standard sample containing a known number of spins [6]. Indeed, obtaining ESR-determined number densities N_i corresponding to each optical absorption band is the only way that oscillator strengths f_i could have been calculated by means of Smakula’s relation for Gaussian bands [7]:

In this context, it should also be mentioned that in practically all ESR isochronal annealing experiments that I have ever performed, I have calibrated by double-numerical integration only the initial spectral components (after irradiation but before annealing above the measurement temperature of 100 or 105 K). I compared these areas with that of an ESR standard sample to obtain absolute number densities N_i immediately following irradiation. I have customarily taken all data at higher anneal temperatures as spectral amplitudes, which I then normalized to the respective numerical integrations of corresponding spectra recorded at the low-temperature starting point. So, with the exception of the Ge E′ center (which wasn’t detected until late in the isochronal annealing process) this was very likely what I did to produce the ESR data of Fig. 2 (shown as curves that had been fitted to my now lost data points).

Normally I would have made the y axis represent the values of N_i in spins/cm³ or spins/gram, e.g., as I did in [4]. However, Joe Friebele plotted his optical data as absolute optical intensities OI (α_i⋅W_i in units of eV/cm), and this y-axis scale was retained in Fig. 3B of [1] despite the superposition of ESR number-density data. In its present digital resurrection as Fig. 2, I have retained Joe’s y-axis scale in units of eV/cm. Joe remembers initially moving my calibrated ESR number-density curves vertically as a rigorously interlocked group to achieve the best possible agreements with his rigidly fixed OI data. However, to better match the OI data points, he thinks he may have moved one of my ESR curves away from its original calibration with respect to all the others in terms of N_i values.

 

Fig. 3 Isochronal annealing behavior of the ESR-determined number densities of various paramagnetic defects (continuous and dash-dot bold lines) and optical band intensities (squares, triangles, and circles) recorded for separate pieces of the same GeO₂-SiO₂ glass following 100-keV equal-dose x-irradiations at 77 K. The y-axis scale is calibrated in optical-intensity units (eV/cm), but as described in the text this scale is also used here to represent the relative number densities of the paramagnetic species corresponding to the three bold unbroken lines and the dash-dot one; (the bold short-dash line is added for comparison purposes and is not a true number density). “Ge(2) true” is corrected from “Ge(2)” in Fig. 2 as described in the text. The thin unbroken curve in the temperature range 200 to 375 K represents one half of the sum of the decreases of Ge(1) and “Ge(2) true” in the same temperature range, expressed as positive numbers (added to the mean value of the diamonds in the range 150 – 175 K); thus this curve represents a sequence of number densities comparable to any other number density tied the present y-axis scale. The diamonds comprise the optical intensities shown in Fig. 2 moved upward to discover their coincidence with the thin unbroken curve in the range ~250 – 375 K. Therefore, in this presentation, the units of the diamonds are no longer optical intensity but instead become relative number densities of the GLPC (see text). The dotted TSL curve is taken from [20] and has been added for comparison purposes as described in the text. This figure is replotted from the original [1] (reproduced here as Fig. 2) in order to elucidate the important corrections and correlations mentioned above and further described in the text.

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But this does not mean that my original calibration was lost forever...

4. Archeology

The fact that oscillator strengths were given in [1] is de facto proof that I had determined the spin densities of all three of the ESR-active defects putatively associated with an optical band by double-numerical integration of the ESR spectra recorded immediately following x-irradiation to the same dose and measured within 5 K of the same temperature as were the optical spectra for anneal temperatures ≤300 K.

More crucially, the fact that the oscillator strengths of Ge(1) and Ge(2) were obtained separately means that I must have separated their overlapping ESR spectra [8] by computer line-shape simulations and double integrated these component simulations in order to obtain before-annealing N _Ge(1) and N _Ge(2) values separately. Indeed, inspection of a contemporaneous publication [4] proves that in those days I routinely decomposed overlapping ESR spectra by means of multi-component computer simulations ...each of which could easily have been double integrated to determine the relative intensities of the individual spectral components.

Fortuitously, two of the oscillator strengths originally reported in [1] were identical (Table 1), i.e., those pertaining to the ESR-recorded Ge(1) centers and certain then-unspecified “oxygen hole centers” (OHCs). Although the original spectra are lost, the OHC spectrum very likely had the same zero-crossing g value and spectral shape as those of the OHC spectrum that I recorded shortly afterwards for an x-irradiated sol-gel silica glass containing Ge impurities ...a spectrum that still exists by virtue of its having been published [9]. About 3 years later (by 1989 [10]) I identified this particular type of spectrum in irradiated pure silica glasses as being due to self-trapped holes (STHs, which I subsequently characterized in great detail [11,12]). In fact, the “2.4 eV” band of Fig. 1 is now firmly linked to STHs, having been determined by polarized optical bleaching to comprise a linear combination Gaussian bands peaking at 2.16 and 2.60 eV, respectively assigned to STH₂ and STH₁ in bulk silica [13]. (Several lower-energy STH bands are found to dominate in optical fibers [12,14,15].)

The fact of having determined two oscillator strengths to be identical means that it must have been possible to simultaneously match the initial ESR number densities N _Ge(1) and N _STH that I originally determined for these two defects at 105 K (starting points of curves in Fig. 2) to the optical intensities OI _{4.4 eV} and OI _{2.4 eV} recorded by Joe Friebele prior to further annealing (triangles and squares, respectively) and plotted at 100 K in Fig. 2. In this situation, Eq. (1) can be simplified as follows:

This outcome proves that we must have previously achieved the fits of the Ge(1) curve to the 4.4 eV data (triangles) and the OHC-cum-STH curve to the 2.4 eV data (squares) in Fig. 2 by preserving the ESR-determined number densities N _Ge(1) and N _STH in the same ratio as I had originally determined them.

However, when I tried to employ the very same value of C to calculate the position of the ESR spin count for Ge(2) on the y-axis of Fig. 2 according to the relation

This misleading situation is rectified in the modified graph of Fig. 3, where I exhibit the true N _Ge(2) curve as recovered via Eq. (3) by use of the same constant C archeologically determined above in combination with the archeological-relic oscillator strength f _Ge(2) = 0.77 from Table 2 of [1]. The short-dashed curve added to Fig. 3 is a replica of the “Ge(2) true” curve displaced upward to show its excellent relationship to the data points of the 5.8 eV band (solid circles) below 300 K. For reasons yet to be determined, the 5.8 eV data points for temperatures above 300 K all fall between the ad hoc-positioned short dashed curve and the true N _Ge(2) curve.

Presumably the dash-dot ESR intensity curve for Ge E′ center (for which no optical absorption spectrum was recorded) is correctly represented in Figs. 2 and 3 in relation to the other ESR number-density curves because there would have been no reason to have moved it. Apropos, the optical absorption band of the Ge E′ center has been found to peak near 6.3 eV [16,17], likely accounting for the high-energy band tail completing the curve fit of Fig. 1.

5. The Ge(1) and Ge(2) Centers

The natures of the Ge(1) and Ge(2) centers and their respective relationships to the 4.4 and 5.8 eV optical bands have remained controversial in the literature for more than two decades, e.g [18–22]. However, in a recent publication [2] I have stressed the fact that the spin Hamiltonian parameters for Ge(1) and Ge(2) in x-irradiated GeO₂-SiO₂ glasses are so close to those of the Ge(II) and Ge(I) centers, respectively, in x-irradiated α quartz [3] that they are almost certainly the same defects (differing mainly in the statistical broadening of the ⁷³Ge hyperfine lines, which unsurprisingly characterizes the glasses but not the crystal; see [2]). Moreover, I noted in [2] that Ge(I) in the crystal has a glass-like quality in that the orbitals of the unpaired spins do not reflect any quartz-crystal symmetry; whereas based on their nearly identical g values the Ge(1) center in glasses must have the same crystal-like twofold local symmetry as the Ge(II) center in quartz! The reader is commended to ref [2]. for a more detailed account of these arguments.

In the present paper I raise a separate issue that had escaped my attention during the writing of [2]. Quoting from the introduction of [3]:

Moreover, Isoya et al. [3] conclude their abstract with this sentence:

In the case of the present irradiated GeO₂-SiO₂ glass sample, the signal intensity ratios of N _Ge(1) to N _Ge(2) can be determined from the data of Table 1(2.9:1 at 105 K) and from the Ge(1) and Ge(2)-true curves of Fig. 3 (2.3:1 at ≈220 K and 1.8:1 at ≈300 K). Thus it is apparent that the ratio of N _Ge(1) to N _Ge(2) in the glass decreases with increasing temperature in the range 100 to 300 K according to numbers similar to, but smaller than, the corresponding N _Ge(I)-to-N _Ge(II) ratios in quartz. This is strong evidence that Ge(1) and Ge(2) are also “energetically inequivalent configurations of the same Ge³⁺ center [3].”

Less evident, but certain to be significant in “the grand scheme of things,” is the fact that the “glass-like” Ge(I) center is the ground state in α quartz [3], whereas the crystal-like Ge(1) center appears to be the ground state in the glass! If, as I believe, this proposition turns out to be true, it will be of profound interest to glass scientists – particularly to theoreticians engaged in first-principles calculations of silica glass structures.

In summary, it is known for certain from the work of Isoya, Weil, and Claridge [3] that there are two crystallographically and inequivalent Ge(I) configurations jointly comprising the ground state and a single Ge(II) configuration making up the closely lying (Δ~0.008 eV at 300 K [3]) excited state of a class of defects resulting from electron trapping on Ge⁴⁺ ions substituted for Si⁴⁺ ions in crystalline α quartz. And based on the data of Fig. 3, I have inferred above that the ground and excited states of their respective doppelgangers in GeO₂-SiO₂ glasses, Ge(2) and Ge(1), are reversed. In Fig. 4 , I sketch my musings regarding the configuration coordinates representing these two situations.

 

Fig. 4 The author’s visualization of (a) the configuration coordinates of the Ge(II) and Ge(I) trapped-electron centers in x-irradiated Ge-doped α quartz based on the work of Isoya, Weil, and Claridge [3] and (b) the analogous Ge(1) and Ge(2) centers, respectively [2], in an x-irradiated GeO₂-SiO₂ glass based on Fig. 3 of the present work. The potential wells represent the directionalities of the orbitals of the unpaired spins, as well as the directions of any spontaneous movements of the Ge⁴⁺ ion away from the origin of coordinates in response to having captured an electron. There is a crystallographic difference between positive and negative distortions along the twofold a axis of α quartz, which evidently favors distortions in the positive direction [3], thus the deeper well in this direction shown in (a). Isoya et al. [3] reported the energetic separation Δ between the Ge(II) excited state and the Ge(I) ground state in α quartz to be temperature dependent and equal to ~0.0025, ~0.0055, ~0.0077, and ~0.0078 eV at ~15, ~80, ~220, and ~300 K, respectively. No comparable numbers exist for Ge(1) and Ge(2) in glasses. However, from Fig. 3 it is inferred that in the glasses Ge(1) is the ground state at ~100 K, as illustrated in (b).

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6. The GLPC

Germanium lone pair center (GLPC) is the descriptive term assigned to a diamagnetic, charge-neutral twofold-coordinated germanium, which can be a native and/or a radiation-induced oxygen-deficiency center (ODC) in pure GeO₂ or GeO₂-SiO₂ glasses (e.g., [22]). Its structure is commonly cartooned as = Ge••, where “=” represents a pair of bonds to oxygens bridging to the rest of the glass network and “••”stands for a pair of electrons in a dangling sp ² orbital at the apex of, and in the plane of, the triangular O‒Ge²⁺‒O structure.

In the event that such a structure traps a hole “h⁺” it would become a paramagnetic defect center (GLPC⁺) according to

It has been widely suggested (e.g., [19–21]) that Ge(2) is identical with the defect on the right-hand side of Eq. (4). The general rational for this popular belief has been the fact that Ge(1) and Ge(2) tend to grow linearly with dose in a nearly 1:1 ratio (when the irradiation is carried out at room temperature) and Ge(1) is universally accepted as being a trapped electron center. Therefore, according to this argument, if no universally recognized trapped-hole centers (generally, OHCs) are detected matching the combined number densities of Ge(1) and Ge(2), then by process of elimination Ge(2) must be the trapped-hole center.

This argument has been regarded as consistent with the radiation-induced attrition of the GLPC⁰ optical absorption band peaking at 5.2 eV (more commonly reported as the 5.1 eV band, (e.g.,[16,20]) and/or of its photoluminescence bands at 3.2 and 4.3 eV (e.g., [16,23]) concomitant with creation of equal numbers of Ge(1)s (surely electrons trapped on substitutional Ge⁴⁺s) and Ge(2)s (putatively holes trapped in GLPC⁰s). This effect is particularly apparent when the irradiation source is a 5.0 eV KrF laser, which destroys the GLPC⁰ 5.2 eV absorption band while simultaneously creating strong optical absorption bands at 4.4 and 5.8 eV associated with Ge(1) and Ge(2), respectively (e.g., [1,16,19–21]).

However, if the [ = Ge•]⁺ model for Ge(2) should be true, then all of the remarkable correspondences between the Ge(I) and Ge(II) centers in crystalline α quartz and their respective doppelgangers Ge(2) and Ge(1) in GeO₂-SiO₂ glasses described in Sect. 5 would have to be regarded as one of the most remarkable non-causal coincidences of all time. Fortunately, however, this dilemma can be avoided by virtue of some additional archeology that I’ve performed on the data of [1].

7. More Archeology

There may be universal agreement that the increases in the GLPC⁰ optical intensity of the 5.2 eV band upon annealing an irradiated Ge-doped silica glass in the range ~220 to 375 K (diamonds in Fig. 2) result from GLPC⁰s that had trapped holes during irradiation at 77 K now recapturing the electrons released by Ge(1) in this warming phase. However, there is a divergence of opinion regarding the nature of Ge(2). Specifically, there is a popular belief mentioned in Sect. 6 that Ge(2) is synonymous with GLPC⁺ ...completely at variance with the thesis that I have developed, which states instead that Ge(2) and Ge(1) are two energetically inequivalent configurations governing the trapping of electrons on Ge⁴⁺ ions substitutional for Si⁴⁺ in the glass network.

How can we decide which story is right?

It occurred to me that the answer might lie in Joe Friebele’s and my data as replotted in Fig. 3 ...where the Ge(1) and Ge(2) number densities are displayed in their true relative proportions. I decided that the most germane annealing action was taking place in the temperature range ~220 to 375 K. And to begin my analysis of this temperature range, I decided to subtract each of those two isochronal anneal curves from horizontal lines respectively intersecting their values at 200 K. The results of doing so comprise a pair of curves (not plotted here), −ΔN _Ge(1) and − ΔN _Ge(2) which increase monotonically with increasing temperature in the range ~200 K to 375 K and signify the temperature dependencies of the cumulative numbers of electrons (or electrons and holes, respectively, in the popular model) that are released at temperatures above 200 K by Ge(1) and Ge(2), respectively. Together, these two curves comprise the total number of electrons available for recombination with GLPC⁺s (in my view) or else the numbers of electrons, Ge(1), and holes, Ge(2), available for recombination with each other (if one believes the GLPC⁺ = Ge(2) model).

Next I assessed how well various linear combinations of these two curves might fit the increase in the optical intensity data of GLPC⁰s (diamonds in Fig. 2) in this same temperature range. First I tried fitting the GLPC⁰ recovery data using the sum −ΔN _Ge(1) − ΔN _Ge(2) but it was much too steep. Then I tried the decay of Ge(1) alone, −ΔN _Ge(1), which corresponds to the first part of popular model discussed in Sect. 6. However, this curve was still too steep to match the observed increase in the 5.2 eV absorption band (diamonds of Fig. 2). Moreover, the second part of the popular model, which specifies that [ = Ge•]⁺ is synonymous with Ge(2), fails even worse ...because Ge(2) is seen to decrease at a much slower rate than the rate at which Ge(1) sheds electrons in the range 220 to 375 K. Therefore, the [ = Ge•]⁺ model for Ge(2) does not fit these isochronal anneal data at all. (N.B. This same conclusion was reached on the basis of a very different experiment carried out by Nishi et al. [24].)

Finally, I tried summing the two curves and dividing this sum by different trial numbers. A good fit to the diamonds began to materialize when I divided this sum by 2.0 (expressed as [−ΔN _Ge(1) − ΔN _Ge(2)]/2). This fit became excellent when I added a constant term of 5.85 to extrapolate the quasi constant behavior of the diamonds between 150 and 200 K and thus refine my model curve fit in the restricted range 200 – 230 K. The result of doing this is shown as the thin continuous curve in the range 200 to 375 K in Fig. 3. The diamonds in Fig. 3 are positioned by multiplying the diamonds of Fig. 2 by a factor of 2.56, determined by a cut-and-try process to provide the best fit to the self-positioned thin continuous curve.

It is crucial to recognize that the curve that I have created here is a hypothetical number density based on a pair of actual number densities. Thus, whereas the diamonds in Fig. 2 represent optical intensities (OI _{5.2 eV}) associated with GLPC⁰, the shifted diamonds of Fig. 3 transmogrify into the number density of GLPC⁰s (N _GLPC) on the present dual-purpose y-axis scale. Accordingly, following the same rational as developed for Eqs. (2) and (3), one can write

Thus, according to my reanalysis of Joe Friebele’s and my ancient data, two released electrons appear to be required to recover the optical spectrum of a single GLPC⁰. Ergo, the GLPC must selectively trap holes in pairs!

8. A Striking Richness of Defect Kinetic Processes Revealed in a Single Graph

Most of the observations, conclusions, and hypotheses elicited below are based on inspection of Fig. 3, which I believe accurately exhibits the relative number densities of the Ge(1), Ge(2), and STH paramagnetic defects in an x-irradiated GeO₂-SiO₂ glass plotted as functions of isochronal anneal temperature on the dual-purpose y-axis scale developed in Sect. 4 (bold unbroken and dash-dot curves) ...as well as the relative number density of the GLPC⁰s (diamonds) as determined in Sect. 7.

8.1 Between 100 and 200 K

Here the decay of the STHs is mimicked by a corresponding drop in the GLPC⁰ number density. However, this GLPC drop is about equal to twice the number of disappearing STHs. Moreover, as inferred from the results of Sect. 7, the disappearance of the GLPC⁰s must be the result of trapping holes in pairs. Therefore, the ESR-determined number of STHs at 100 K represents far too few released holes to account for the thermal depletion of GLPC⁰s in this anneal temperature range. Accordingly, I suggest that about ¾ of the STHs initially present at 100 K were likely in the form of ESR-silent self-trapped-hole pairs! (More work for theorists.)

N.B. Any STHs that trap holes in pairs very likely comprise solely STH₂s, because I have shown that STH₂s result from hole trapping at the quartz-like precursor sites that support delocalization of even single trapped holes over two bridging oxygens [11,12].

8.2 Between 100 and ~225 K

Here there appears to be a small-scale one-for-one conversion of Ge(1)s to Ge(2)s (best observed in the optical spectra) that preserves the sum N _Ge(1) + N _Ge(2) at a constant value. This observation provides strong support for the notion that Ge(1) and Ge(2) are “energetically inequivalent configurations of the same Ge³⁺ center” – as has been proven to be the case for Ge(I) and Ge(II) centers in α quartz [3].

8.3 Between 225 and 375 K

In this range Ge(1) decays much faster than Ge(2). However, the combined decays of N _Ge(1) + N _Ge(2) is precisely equal to twice the number of GLPC⁰s restored in this range (see Sect. 7). So, if it should be accepted that Ge(1) and Ge(2) are both trapped-electron centers, then it follows that GLPC⁰ must exclusively trap holes in pairs. This could be explained if the energy level of the unpaired electron of a GLPC⁰ that has trapped a single hole ([ = Ge•]⁺) lies near the mobility edge of holes in the valence band ...in which case capture of a second hole would be virtually instantaneous during x or γ irradiation. (This notion should be tested by first principles calculations.)

8.4 Between 375 and 575 K

Using the 4.4 eV optical data in Fig. 3 as a proxy for the number density of Ge(1)s, it can be inferred that N _Ge(1) is ~25% lower than N _Ge(2) in the range 375 – 425 K. This result for a GeO₂-SiO₂ glass subjected to 100-kV x rays at 77 K and measured following a 5-minute anneals at 375 and 425 K compares favorably with the results of a recent ESR study of a series of samples of a similar glass stored for ~1 month at room temperature after 10-keV x-irradiations: N _Ge(2) ≈1.25 N _Ge(1), irrespective of dose in the range ~0.05 to 1kGy [22].

In Fig. 3, Ge(1) and Ge(2) are seen to decay in parallel with increasing temperature in the 375 to 475 K temperature range, but at a much lower rate per unit temperature increment than did Ge(1) in the range ~250 to 375 K. Concomitantly, N _GLPC (diamonds) decreases slightly, rather than increasing as would be expected for double-hole-trap GLPC²⁺s capturing the electrons released from Ge(1) and Ge(2). I could not have guessed the reason for this without the thermally-stimulated luminescence (TSL) data reported by Fujimaki et al. [20], which I have reproduced on an arbitrary scale as the dotted curve in Fig. 3.

Now my best hypothesis is that in this temperature range GLPC⁰s, [ = Ge••]⁰, must metastably trap electrons in the non-bonding orbital perpendicular to the plane of the O–Ge²⁺–O triangle, becoming [ = Ge•••]^-. If this GLPC structure were to subsequently capture a hole in the non-bonding orbital in-plane with the O–Ge–O triangle, it would find itself in the T₁ state, which would immediately decay to the S₀ state with the emission of a 3.1 eV photon [25]...exactly as recorded by Fujimaki et al. [20]. Therefore, in analogy with the experimentally-supported explanation of the TSL of twofold-coordinated silicons in pure silica glass [26] (also reviewed in [2]), I envision that (i) any GLPC that traps an electron must become a GLPC^- that no longer contributes to the GLPC⁰ 5.2 eV optical absorption signal (thus accounting for the diamonds in Fig. 3 initially decreasing in this temperature range) and (ii) by 490 K (the center of the TSL intensity curve [20]) single holes are being steadily released from GLPCs that had trapped two holes, and each time that one of these free holes arrives at a GLPC^- trapped-electron site, the T₁→S₀ TSL transition is triggered, thereby recreating a GLPC⁰. Referring to the diamonds in Fig. 3 as the measure of N _GLPC, the foregoing process restores N _GLPC to its interim high value at 375 K by the time the 525 K anneal is completed and finally hikes it to a higher value upon the 575 K anneal.

8.5 Temperatures higher than 575 K

Some of the Ge E′ centers indicated in Fig. 3 by the dash-dot curve appear to have been present even below this temperature, but they seem to have briefly increased in number in the range 575 to ~640 K by amounts similar to the number of Ge(2) centers decaying in this range. These things can be understood in the following context:

It has been widely noted that as a function of ≥10 kev x-irradiation at room temperature, the Ge(1) and Ge(2) centers both grow linearly with dose until saturating at ~5 kGy (e.g., [21,22,24]). Evidently Ge E′ centers begin replace Ge(1) and Ge(2) at still higher doses [24]. Since the dose administered in the experiments of Figs. 1-3 was 5 kGy, the presence of E′ centers in numbers equivalent to ~5% of initially induced G(1) and Ge(2) centers is not surprising, even after anneals to ~800 K (Fig. 3). Indeed, Nishi et al. [24] showed that by subjecting a 10GeO₂-90SiO₂ glass sample to a 960 Joule dose (~10 kGy) of 5.0 eV KrF laser pulses at 77 K, cross-band-gap two-photon excitations resulted. And the part of the induced ESR spectrum that was annealed out after 5 min at room temperature was found [24] to consist of equal numbers STHs and Ge(1) + Ge(2) + Ge E′ centers, with the Ge E′ centers seeming to dominate. From this result, the latter authors argued that at such high doses the Ge(1) and Ge(2) centers must be converted to metastable trapped-electron-type Ge E′ centers by breakage of one of the four Ge-O bonds at the Ge(1) and Ge(2) sites, with the unpaired spin residing in an sp ³ orbital of a resulting threefold-coordinated Ge while the negative charge is found on the neighboring non-bridging oxygen.

9. Conclusions

I conclude that the paramagnetic defect centers labeled Ge(1) and Ge(2) in irradiated GeO₂-SiO₂ glasses, like their respective doppelgangers in irradiated α quartz, Ge(II) and Ge(I) [3], are two energetically inequivalent configurations of the same center, i.e., an electron trapped on a GeO₄ tetrahedron substituted for an SiO₄ tetrahedron in the glass network or quartz-crystal lattice, respectively. I further conclude that charge-neutral twofold-coordinated Ge²⁺ ions (denoted GLPC⁰s) in such glasses tend to trap holes exclusively in ESR-silent pairs ...yet they also seem to be capable of metastably trapping single electrons in the temperature range ~350 to 580 K. Clearly, additional experimental and theoretical investigations will be necessary to solidify, or perchance refute, these conclusions.