4.2.1. Background
Prior to works summarized in this chapter, none information concerning the bulk Ge crystals uniformly doped with Na can be found in literature and many parameters of this impurity, such as the diffusion parameters, solubility, electrical activity of Na in germanium crystals remained authentically unknown. Moreover, one could even find statements that a mutual solubility of Ge and alkaline metals in solid state is absent [1].
As to possible donor behavior of alkali metal impurities in germanium, it was predicted
G. S. Pekar
V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine
[2] that those impurities (except lithium) have no energy levels close to the edges of c- and v- bands. The undoping effect of diffused sodium in Ge has been experimentally confirmed in some works [3, 4].
The latter study of Na incorporation into Ge wafers showed that, under heating conditions, radioactive sodium 24Na diffuses into surface layer of p-Ge and n-Ge wafers but no n-type regions resulted from Na diffusion, were detected in Ge by thermoelectric type of testing [5]. It was attributed to formation of neutral pairs of interstitial sodium ions Nai+ with oppositely charged vacancies V¯ or acceptor impurities A¯.
However, the proof of donor properties of sodium implanted in p-Ge, was obtained recently by means of thermoelectric measurements, although only some tenths of percent of the incorporated Na ions exhibited donor behavior [6]. A similar quantitative effect had been previously observed in Si where the active donor density in Na diffused region was three orders of magnitude lower than the total density of this impurity [7].
At the same time, doping of germanium with sodium remained an attractive task primarily since sodium could become an alternative to unstable lithium in detectors of ionizing radiation, and, in addition, it seemed promising to investigate the properties of optical germanium doped with this supposed interstitial donor impurity.
4.2.2. Growth of Ge:Na Crystals Intended for Optical Applications
Due to the facts that bulk germanium crystals may have a high optical transparency in the infrared (IR) region, are characterized by the highest refractive index of any of the infrared transmitting materials, low dispersion properties across a wide range of temperatures, high surface hardness, robust mechanical strength, good thermal conductivity, absence of hygroscopicity and toxicity, crystalline germanium is gaining a key position among the materials employed for fabrication of passive optical elements, such as windows, lenses and protecting screens, used for the 1.8-18 µm region at 300 K and 1.5-18 µm at 50 K.
To provide a high transparency of Ge crystals, doping with donor-type impurities at definite range of their concentrations has to be used. Such a doping has to ensure n-type conductivity of germanium which makes it possible to avoid direct transitions of carriers between the sub-bands of the valence band resulting in high absorption of IR radiation.
However, the doping level must be not too high to avoid increased absorption by free electrons. It is commonly considered that Ge crystals doped with donors at a density that provides the crystal resistivity from 5 to 40 Оhmꞏcm (the respective values of free electron concentrations lies approximately between 4ꞏ1014 and 5ꞏ1013 сm-3 [8]) may serve as an optical material for IR technique (note that the indicated limits concentration are not strict). However, the best optical parameters were observed experimentally in somewhat narrower resistivity ranges, and the borders of those ranges vary in the works of different authors. According to our experiments, this region lies between 10 and 25 Оhmꞏcm at room temperature which roughly coincides with some previously published data [9, 10].
As a donor impurity, the V group elements whose atoms substitute Ge in the crystalline lattice sites, are mostly used. Among those elements, antimony has been used most frequently since, basing on some physical considerations and according to many experimental data (see, for example, [11]) germanium single crystals doped with antimony (Ge:Sb crystals) have a maximum transmittance which corresponds to the absorption coefficient of 0.02 cm-1 for single crystals and 0.035 cm-1 for polycrystalline germanium at the wavelength 10.6 µm at 300 K [9]).
The technology for growing Ge:Sb crystals had been rather good developed long ago [12].
Over more than four decades, Ge:Sb crystals met all main technical requirements of the IR technique, especially for manufacturing discrete optical elements for IR systems, such as lenses, windows, etc. However, creation of multicomponent optical elements or systems (for example, multiple-lens objectives) and especially of modern thermal-imaging systems puts forward additional strict requirements to optical parameters of Ge, and it presents often some difficulties to satisfy them by using commercially available Ge:Sb crystals. The enquiry is that for higher visibility (i.e., for decreasing signal-to-noise ratio or increasing resolution) as well as for higher brightness of the image, Ge optical elements have to be characterized by a low dispersion and high regular transmission of IR radiation that passes through those elements. To provide such characteristics, Ge crystals should contain the minimum density of inclusions and other crystal lattice inhomogeneities whose dimensions are comparable with the wavelength of passing IR radiation. Among those lattice inhomogeneities are the following:
thermoelastic tensions of the lattice, dislocations and dislocation loops decorated with impurities, and, finally, the clouds of impurities (i.e., the regions with increased density of free carriers) [13]. Hopefully, the content of the first and second types of inhomogeneities may be diminished by improving the technological conditions of crystal growing (for example, by reducing the fluctuations of the melt temperature and of the instantaneous rates of crystal formation [13]). As to clouds of impurities, it was shown that such clouds may be formed by some types of impurities, among them Sb atoms when concentrating at isolated dislocations or at dislocations forming the low-angle boundaries [14]. The fact that Sb has a rather high solubility in Ge (up to 1.2∙1019 cm-3 at 800 ºС [15]), should promote existence of such impurity clouds. Formation of Sb clouds may be one of the principal limitations of this impurity as to reproducible obtaining Ge crystals with low dispersion and high directional transmission of IR radiation. In addition, substitution of Ge atoms with Sb atoms in the Ge lattice sites should lead to the local lattice strain since Ge and Sb covalent radii differ rather essentially (1,22 Å и 1,38 Å, respectively [16] ).
Studies of a large number of optical Ge crystals doped with a substitutional impurity have shown that dispersion of IR radiation may randomly vary within very wide limits, beginning from the very rare value 0.6 % and up to 23 % [13].
To avoid all the negative consequences of doping with antimony, which are set out above, we decided to replace Sb (or other substitutional donor-type impurity) with an impurity whose introduction into Ge lattice doesn’t result in formation of foregoing inhomogeneities inherent to Ge:Sb crystals as well as in respective quality losses of optical germanium. For this purpose we decided to dope Ge crystals by an interstitial impurity whose atoms can be easily introduced into Ge interstitial space but whose dimensions are
not too small to promote fast diffusion in the Ge lattice. From this point of view Na, whose ionic radius equals 0.95 Å [16], seems to be the best candidate. However, we have not managed to find any information on growing Ge bulk crystals uniformly doped with Na.
Some years ago we have succeeded to develop a technology that makes it possible to grow Ge crystals uniformly doped with Na in the course of their growing. The distinct feature of the technology developed is that none volatile Na-containing chemical compounds are formed during the doping process. It may be supposed that, in particular, just such a formation put obstacles in Na incorporation into grown Ge crystals.
By means of the technology developed, single crystals and coarse-grain boules of Na-doped germanium were grown from the melt [17, 18]. Different growth methods were used, among them Czochralski and Stepanov techniques, the method of immersed form-builder as well as the modified method of horizontal directional crystallization. The following types of crystals were grown and studied: (1) cylindrical crystals with a diameter from 10 to 300 mm; (2) coarse-grain bars up to 160×160×60 mm in size;
(3) coarse-grain plates up to 230×180×20 mm in size with rectangular or rounded edges.
The weight of the largest crystals reached 10 kg.
Fig. 4.1 presents, as examples, the grown Ge:Na crystals of different shape and dimensions.
Fig. 4.1. Some Ge:Na crystals of different shape and dimensions. Two upper photos show three cylindrical single crystals with diameters 75 mm (left photo), 12 mm and 45 mm (right photo), as well as a coarse-grain rectangular ingot 42×47×88 mm in size (right photo). All crystals were pulled from the melt. The lower photo shows a coarse-grain Ge:Na plate, 310×130×20 mm in size, grown by horizontal directional crystallization.
4.2.3. Optical Properties of Ge:Na Crystals
Optical transmission of Ge:Na crystals in comparison with Ge:Sb crystals is given in Table 4.1. Lines 1 and 2 in Table 4.1 show the values of Ge theoretical maximum transmission and the minimum transmission of the crystals recommended for practically use [19]. The lines 3-5 show the experimental values of transmission of Ge:Sb and Ge:Na single crystals grown by us from the same raw material under the same technological conditions [20].