Excitation of GeII in collisions of slow electrons with germanium atoms

Inelastic collisions of slow electrons with germanium atoms leading to the population of excited levels of a singly charged germanium ion have been studied experimentally. One hundred GeII excitation cross sections have been measured at an exciting electron energy of 30 eV. Nine optical excitation functions (OEFs) have been recorded in the electron energy range of 0–200 eV. The behavior of excitation cross-sections is discussed for six GeII spectral series.


Introduction
Germanium, predicted as ekasilicon by Dmitri Mendeleyev in 1871 and discovered in one of the silver minerals by Clemens Winkler in 1886, shared the fate of many other elements in finding no practical application for several decades. Its true value for science and technology only became clear after 1940, when germanium, along with silicon, was recognized as one of the primary elements for electronic components and, somewhat later, for IR optics.
Naturally, the majority of germanium researchers were concerned with studying its properties in the solid phase. Yet, the gas-phase behavior of germanium atoms and ions was not completely devoid of researchers' attention. As we turn to the singly charged germanium ion in particular, it should be noted that early publications (Lang 1928(Lang , 1929 recorded and partially interpreted the GeII spectrum within the wavelength range of 100-715 nm obtained in an electrical spark discharge. A new comprehensive study of the GeII spectrum was undertaken using a hollow cathode (Shenstone 1963) within the spectral range of 60-1000 nm; almost simultaneously it was added to by a number of other papers.
The lowest-lying GeII energy levels have been identified by Lang (1929). Considerable progress was made in the interpretation of the singly charged germanium ion spectrum in the 1960 s: levels of the displaced term 4s4p 2 2 D have been located, together with the normally excited levels 4s 2 5p, 6p, 4d, 5d, 4f, 5f, 5g, 6g, 7g (Kaufman and Andrew 1962) and, later, the levels 4s 2 5s, 6d, 7d (Kaufman and Ward 1966). Many high-lying GeII levels were discovered in an extensive analysis (Shenstone 1963). A compilation published three decades later (Sugar and Musgrove 1993) included all available data on energy levels of a singly-charged germanium ion.
Researchers studying GeII atomic constants mostly focused on radiation constants (transition probabilities, oscillator strengths) as well as radiative lifetimes and branching factors. It should be noted that a monograph by Corliss and Bozman (1962) provides no data whatsoever on the singly charged germanium ion. Later papers, both experimental and theoretical (e.g. Miller andRoig 1973, Marcinek andMigdalek 1993) present rather limited data on the values of A ki and f ik with regard to transitions between low-lying GeII levels. Only Ganas (1995) provided a theoretical definition of oscillator strengths for 4s 2 4p 2 P 1/2 → 4s 2 ns 2 S 1/2 and 4s 2 4p 2 P 1/2 → 4s 2 nd 2 D 3/2 transitions up to n = 10. The same paper references the discovery of GeII in a photospheric spectrum of a chemically peculiar B-star, χ Lupi, in experiments with the Hubble Space Telescope. Finally, a recent work by Charro et al (2008) provides a theoretical treatment of forbidden spontaneous transitions of E2 and M1 types in Ga-like ions including GeII.
GeII collision properties (excitation cross-sections) are studied in a single experimental paper (Kolosov and Smirnov 1990) published long ago when the experience with extended crossing beams was still scant, and conditions for experiments with germanium were far from optimal. All of these circumstances have been taken into account during the work described herein.
Even though germanium does not hold the spotlight of researcher's and application expert's attention right now, research into atomic constants of germanium may be of some interest due to a number of problems. While, in the past, germanium-containing plasma appeared in germanium rod refinement installations utilizing the zone melting method, as well as durning vacuum-deposition of germanium films using electron-beam vaporization, recent years have seen the rise of more complicated technologies and processes. For example, Chen Hu and Wang Jia-xian (2012) used RF magnetronic sputtering in conjunction with thermal annealing to obtain a Ge/Al-SiO 2 film. Yang Ru-Yuan et al (2012) have synthesized YInGe 2 O 7 : Eu 3+ powder by sintering in a microwave furnace at T = 1200°C. In both cases low-temperature multicomponent plasma containing germanium atoms and ions was formed.

The experiment
The excitation of a singly charged germanium ion in collisions of slow electrons with germanium atoms is studied using the method of extended crossing beams. Considering that this method has already been discussed several times , Kuchenev and Smirnov 1993, Smirnov 1994, it is unnecessary to repeat this information in the present paper. We will only note the basic conditions concerning the germanium experiment.
In order to obtain an atomic beam, germanium was placed into an open-top graphite crucible and vaporized by heating its surface with an electron beam to 1650 K. As a result, the germanium atom concentration in the crossing area of the electronic and atomic beams reached 2.5 × 10 10 cm −3 . The concentration of atoms decreased to 3 × 10 9 cm −3 during the study of germanium atom resonance lines to minimize reabsorption. However, this factor was unimportant to the study of GeII resonance lines as the ion concentration in the beam was several orders of magnitude smaller than the atom concentration.
Like in the original paper (Kolosov and Smirnov 1990), this study was concerned with the excitation process and simultaneous single ionization as described by the reaction where e and e′ are the incident and scattered electrons, respectively, and e″ is the electron ejected from the germanium atom in its ionization. The asterisk denotes the excited particle. Naturally, in this case the excitation of some germanium atoms also takes place (without them being ionized). Optical spectroscopy methods are used to distinguish between GeI and GeII excitation processes. The spectrogram has been recorded on a chart recorder tape. The registered GeI and GeII spectral lines have been identified using the reference data from Meissner 1958, Shenstone 1963, with small additions from the later papers. The ground term of the germanium atom is an even triplet, 4s 2 4p 2 3 P J , with energy levels E = 0, 557, 1410 cm −1 for J = 0, 1, 2, respectively. Assuming that atoms are distributed through these levels in the beam according to the Boltzmann law, at the evaporation temperature of T = 1650 K the resulting concentration ratio for the above-mentioned levels would be 1.00: 1.85: 1.46, i.e. 23.2%, 42.8% and 33.8% of the total concentration of atoms in the beam. The population of the nearest excited level, 4s 2 4p 2 1 D 2 , with an energy E = 7125 cm −1 , is negligibly small at 0.23%. The distribution of atoms in the beam over the ground term levels must be taken into consideration when comparing the experimental cross-section data with the theoretical results (as soon as they are published). However, this circumstance is of no great relevance for practical applications, as any real devices vaporizing germanium would have atoms similarly distributed over the ground term levels.
Atoms were excited using a controlled-energy monoenergetic electron beam produced by a special-purpose lowvoltage electron gun. Electrons were emitted by a flat and long (13 × 200 mm) oxide thermocathode. The electronic and atomic beams crossed to form a right-angled parallelepiped sized 13 × 30 × 200 mm. The atoms' and ions' optical radiation directed toward the greater dimension of the crossing zone was detected and arranged into a spectrum by a diffraction-grating monochromator. Photomultiplier tubes with antimony-cesium or multialkali photocathodes were used as radiation receivers.
The electron beam current density in the whole electron energy operating range of 0-200 eV stood below 1.0 mA cm −2 . The setup had an effective spectral resolution of about 0.1 nm in the short-wave part of the spectrum, at λ < 600 nm. It could have been improved to 0.05 nm for medium-intensity lines if necessary. The spectral resolution degraded to ∼0.2 nm at longer wavelengths, λ > 600 nm, as the diffraction grating of the monochromator had to be replaced.
Absolute cross-section values were obtained using spectral line intensities emitted by helium atom flows through a vacuum chamber in a series of special calibration experiments. Excitation cross-sections for the four HeI lines have Table 1. Excitation cross-sections of even levels of one-charged germanium ion (with OEF). The concentration of germanium atoms was determined by measuring the mass of germanium film deposited over a fixed time on titanium-foil calibration plates. Eight such plates were placed beyond the crossing zone of electronic and atomic beams on a cooled wall of the vacuum chamber at a right angle to the atomic beam. The mass of the condensed film (∼ 1 mg) was measured to a precision of 0.01 mg. Relative cross-section values were measured within the spectral range of 250-600 nm with an error of 5-15%, depending on the intensity of a particular line and its position in the spectrum. The error rose to 10-20% at λ < 250 nm as a result of a decrease in the setup sensitivity. An increase of error to 12-30% in the red was caused by decreasing signalto-noise ratios, brought about by greater background illumination of the photodetector with continuous-spectrum radiation from the molten germanium surface. Absolute crosssection values were determined with errors of 17-27%, 22-32% and 24-42%, respectively.

Results and discussion
Data on the process being studied were obtained by examining the optical emission spectrum produced by germanium atoms colliding with a beam of monoenergetic electrons with fixed energies. 100 excitation cross-sections of spectral lines of a singly charged germanium ion, all located within a wavelength range of 193-732 nm, were measured at an exciting electron energy of 30 eV. These lines include 12 blends that mostly arise as a consequence of transitions from 4s 2 ng 2 G 7/2,9/2 levels featuring rather low J-splitting values. Excitation cross-sections as functions of exciting electron energy (optical excitation functions, OEFs) were studied in another series of experiments. Nine OEFs were recorded in the exciting electron energy range of 0-200 eV. The nine cross-sections measured by us belong to unclassified lines, which are arbitrarily included in a common table with transitions from odd levels. It was not possible to record OEFs for either of the unclassified lines, as their cross-sections were all smaller than 0.54 × 10 −18 cm 2 .
Tables 1 to 3 summarize the results obtained, with reference data added as needed. Tables 1 and 2 contain transitions from even levels (with and without OEF, respectively) while table 3 contains transitions from odd levels. Listed in the tables are wavelengths (table 1-in a vacuum, tables 2 and 3-in air), transitions, quantum numbers of total electron shell moment for lower J low and upper J up levels, energies of lower E low and upper E up levels (counted from the ground level of a germanium ion), excitation cross sections at exciting electron energy of 30 eV, Q 30 , and at the OEF maximum, Q max , as well as the position of the maximum E (Q max ). The numbers in the OEF column correspond to the curve numbers in figures 1 and 2 for tables 1 and 3, respectively. Reference data on wavelengths, transitions, J and energy levels have been derived from papers (Shenstone 1963, Sugar and Musgrove 1993). It should be noted here that Sugar and Musgrove (1993) present the levels 4s4p ( 3 P°)4f 2 F, 4 F, 4 D as odd. However, levels of this configuration can only be even, and this is exactly how they are stated in the original paper by Shenstone (1963).
Some of the lines discovered in the present paper in the yellow-red are not found in publications available to the author concerning the spectra of GeI and GeII (it would be irrelevant to consider spectra of GeIII, GeIV etc at an electron      (Sugar and Musgrove 1993). However, several lines have also been classified as GeII transitions. Precise wavelength values for these lines have been calculated using energy levels from (Sugar and Musgrove 1993). The results obtained this way are indicated in tables 2 and 3 in brackets. Attention should be paid to the line with λ = 523.72 nm, described by Shenstone (1963) as the transition 5s 4 P°1 /2 -5p 4 P 3/2 ; this transition is spelt out completely as 4s4p( 3 P°)5s 4 P°1 /2 -4s4p( 3 P°)5p 4 P 3/2 with level energies E = 122 694.3 cm −1 and 141 787 cm −1 , respectively. However, such energy levels result in a wavelength λ = 523.614 nm, differing from the observed value by Δλ = 0.1 nm. Within the present paper, a transition 4s 2 10p 2 P°1 /2 -4s4p( 3 P°)5p 2 P 3/2 has been proposed for the line λ = 523.72 nm. This transition corresponds to an exact calculated wavelength of λ = 523.713 nm. In the case of the transition proposed by Shenstone (1963), the discrepancy between the observed and theoretical transition energies is Δσ obscalc = −3.7 cm −1 . A similar value of Δσ o-c is found for another transition from a multiplet proposed by Shenstone (1963), where a transition 4s4p( 3 P°)5 s 4 P°1 /2 -4s4p( 3 P°)5p 4 P 1/2 is proposed for the particular line λ = 533.07 nm with the same lower level as the line λ = 523.72 nm. For another line from this multiplet with λ = 524.95 nm, Δσ o-c = +1.3 cm −1 , whereas the remaining three lines described by Shenstone (1963) exhibit a coincidence between calculated transition energy values and observed values within the error margin. Therefore, the level energies 4s4p( 3 P°) 5s 4 P°and 4s4p( 3 P°)5p 4 P found by Shenstone (1963), together with the level energies of other high-lying displaced terms of GeII, call for repeated measurement with state-of-the-art attainable accuracy standards. Figure 3 shows an energy-state diagram for a singly charged germanium ion with the transitions under study. Considering that J-splitting is negligible enough for the majority of states being studied, all terms have been indicated without regard to J-splitting. Whenever possible, level labels have been placed below the abscissa axis. Values of the quantum number n are indicated as numbers near to levels on the left side of the diagram. On the right side of the chart, designations of terms belonging to the same configuration are indicated in the figure area.
Q 30 = f(n) plotted as straight lines, corresponding to a power law i 30 i where A i and α i are constants with fixed values within every series. Table 4 summarizes these values for four series of GeII behaving in accordance with (2).

Summary
Optical spectroscopy with the extended crossing beam method has been used to study the excitation of a singly charged germanium ion in electron-atom collisions (excitation with simultaneous single ionization). The levels studied are populated after an electron collision both during excitation of an outer 4p electron as well as excitation of any of equivalent 4s electrons (or even both 4s electrons as in the case with the 4p 3 2 P°3 /2 level). The serial dependence Q = f(n) behaves as a power function for four out of the six series considered here.