Таble 4.1. Optical transmission of different optical germanium crystals
4.5. Diffusion Parameters, Solubility, and Electrical Activity of Na in Bulk Ge Crystals Ge Crystals
4.5.3. Discussion of Results
According to scientific literature, all impurities in Ge can be divided into 3 types according to the values of their diffusion coefficients D (Table 4.6) [53, 56].
As seen from Table 4.6, the values of D for the 1st-type impurities correspond to slow diffusion and equal from 2×10–14 tо 10–11 cm2/s, while the values of D for the 2nd-type impurities correspond to fast diffusion and equal from 4×10−9 tо 3×10−5 сm2/s. The 3rd-type impurities that includes gaseous elements H, He and Xe, we are not going to consider here. It should be noted [53] that many of values given in Table 4.6, could be considered valid only within an order of magnitude due to the low penetration depth of impurities in the crystals during the measurements.
Table 4.6. Diffusion parameters of impurities in Ge [18, 20].
As seen from Table 4.6, the values of D for the 1st-type impurities correspond to slow diffusion and equal from 2×10-14 tо 10-11 cm2/s, while the values of D for the 2nd-type impurities correspond to fast diffusion and equal from 4×10−9 tо 3×10−5 сm2/s. The 3rd-type impurities that includes gaseous elements H, He and Xe. It should be noted [53]
that many of values given in Table 4.6, could be considered valid only within an order of magnitude due to the low penetration depth of impurities in the crystals during the measurements.
On the basis of results shown in Table 4.6, it has been naturally assumed that the impurities of the 1st-type, including Na, form substitutional solid solutions with Ge, are of acceptor nature and diffuse through vacancies in the Ge lattice. The 2nd-type impurities include Li as well as transition and noble metals. Of these, Li (which is most thoroughly studied) is a shallow donor which diffuses through interstitials in the Ge crystal lattice. This is promoted by a small ionic radius of Li+ ion which is 0.68 Å (for Pauling), 1.56 Å (the effective value obtained taking into account the influence of the crystalline surroundings) and 0.94 Å (actual value calculated from experimental data) [66]. All these values are significantly lower than the nearest distance between Ge atoms in the crystal lattice (2.45 Å) [67].
Other 2nd-type impurities substitute the Ge atoms in the crystal lattice and have mainly an acceptor nature, although, at least as to some of them, the situation is not yet completely understood.
The diffusion parameters of Na in Ge obtained in this study, namely: D = 3.6×10−7 сm2/s, D0 = 0.13 сm2/s and Q = 0.33 еV at temperatures from -2 °C to 23 °C give grounds to exclude Na from the 1st-type impurities and include it to the 2nd-type of the above classification. Indeed, the value of the Na diffusion coefficient obtained is by some orders of magnitude higher as compared with those of substitutional impurities (1st-type), despite
the fact that we conducted measurements at much lower temperatures than those given in Table 4.6. Thus, we can suppose that Na diffuses in Ge crystals via interstitials, like Li, but Na diffusion is likely to be slower than Li diffusion. This should be promoted, in particular, by the value of Na ionic radius, that is 0.95 Å (for Pauling), 1.89 Å (the effective value obtained taking into account the influence of the crystalline surroundings) and 1.17 Å (actual value calculated from experimental data), which are also lower than the size of interstitials in the Ge lattice but are larger than the respective values for Li ions.
However, it is necessary to remember that, although the size of the diffusing atom is important for the activation process, a great influence on these processes have the electrostatic interactions, including interactions between the impurity and the vacancies, and polarization or deformation of valence bonds of the crystal lattice [50].
A conclusion about the interstitial nature of Na diffusion in Ge is consistent with the very recently published results of theoretical calculations [48] which shows that (1) the formation energy of interstitial Na atoms in Ge lattice is more than twice smaller than the formation energy of substitutional Na atoms and, hence, the interstitial site is a most stable site for Na atoms in Ge, and (2) the calculated diffusion barrier energy for Na atoms with the interstitial mechanism is about 0.9 eV. This value is rather close to the activation energy for Na diffusion in Ge obtained in the present study.
A sufficiently high rate of Na diffusion in Ge crystal lattice correlates with the above results of our evaluations of maximum solubility of Na in Ge, which at room temperature is not greater than 1015 сm−3 and is much less than the values given previously [56]. This correlation consists in the fact that we have obtained a quite low value of Na solubility in Ge and, as known, low solubility in the host crystals is peculiar to fast diffusing impurities [62].
The obtained value of the Na diffusion coefficient in Ge is consistent with our experimental results that indicate a sufficiently fast diffusion of Na ions in an electric field, but, on the other hand, an absence of perceptible diffusion of Na ions during long-term storage of Ge:Na crystals at room temperature. As a result, the electrical and optical parameters of Ge:Na crystals remain stable, regardless on the resistivity distribution over the crystal volume. The fact that the observed drift of Na ions is rather fast in Ge:Na crystals, while under the same electric field the drift of the substitutional Sb impurity whose diffusion coefficient D = 1.1×10–11 сm2/s, cannot be even recorded, indicates that the value of Na diffusion coefficient D = 1.2×10-11 сm2/s [2] which had been included in reference literature [56], is likely to require revision, at least for the bulk Ge crystals uniformly doped with Na.
4.6. Conclusions
The Na-doped germanium bulk single crystals, coarse-grain boules and large coarse-grain plates were first obtained by the authors of this review, then studied and implemented for practical applications.
The donor behavior of Na in Ge crystals was demonstrated and an interstitial location of Na impurity was verified. Although the doping was made from an unlimited Na source, Na contamination in the grown crystals is usually in the range 5×1013 to 4×1014 сm-3 which (perhaps, accidently) is optimal for optical-grade germanium. The Ge:Na crystals are shown to have a number of advantages over Ge:Sb crystals (conventional optical germanium) grown similarly and from the same raw material, among them the higher transparency in the IR region, smaller radiation scattering and higher regular optical transmission, smaller dislocation density, more uniform distribution of electrical and optical characteristics over the crystal volume, the identity in the transparency of the single and coarse-grain crystals. The most of above-listed features are explained by the determined small maximum solubility of Na in Ge, which, in particular, causes the absence of impurity clouds in Ge:Na.
On the base of the experiments made, the following values of some parameters of Na impurity in Ge crystals are obtained: diffusion coefficient D=3.6×10-7 сm2/s, pre-exponential factor D0 = 0.13 сm2/s, activation energy for diffusion Q = 0.33 eV, the maximum solubility of Na in Ge crystals at room temperature Сsmах = (0.3–1)×1015 сm-3 and the distribution coefficient of Na in Ge k0 = (0.7–2.3)×10−7. Most of these values significantly differ from those previously reported in literature and determined at Na diffusion in Ge thin surface layer. Using the values obtained, it is possible to explain many features peculiar to Ge:Na.
The observed effective drift of interstitial sodium donors under a direct electric field application in combination with a high stability of sodium ions in Ge at room temperature is shown to open prospects of replacing lithium with sodium in semiconductor detectors of ionizing radiations.
Experimentally established that the large Ge:Na coarse-grain optical germanium plates grown in the inert ambient, contain uncontrolled hydrogen at a concentration above 1017 cm-3 which may result in the porosity of plates as well as in formation of microcracks and surface micropores, cracking of plates and the release of toxic gaseous products at the plate machining. The ultrasonic processing technique for significant removing dissolved hydrogen from Ge:Na plates is developed which results in strengthening of the plates, the increase of their density, the decrease of the porosity and the decrease of the crystal lattice parameter. This, in particular, eliminates all above-listed troubles in machining of plates when manufacturing the protective Ge:Na screens for thermal imaging systems.
Acknowledgements
The studies reported in Sections 4.3 and 4.4 were carried out with the financial support of the Ministry of Education and Science of Ukraine under the Projects DZ/39-2015 and DZ/39-2017, respectively. The authors are grateful to their colleagues at various laboratories in Ukraine, the United States and Russia, in which some measurements were made. We had expressed our gratitude to all of them in the previous publications used in this review. We want to thank Prof. Yu.V. Milman of the Institute for Problems of Materials Science for recent fruitful discussions concerning the fracture toughness
measurements and Dr. I. Goncharova of the same Institute for conducting these measurements. Prof. G.S. Pekar would like to express sincere thanks to Prof. S.Y. Yurish for his kind invitation to submit this chapter.
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