RU2813061C1 - Method for express analysis of objective identification of isotopically pure germanium single crystal - Google Patents

Abstract

FIELD: electronics.

SUBSTANCE: invention relates to electronics, photonics, semiconductor technology, the production of high-purity substances, as well as isotopically enriched germanium, and can be used in the manufacture of highly sensitive low-background infrared radiation detectors, matrix elements of quantum computers, photodetectors, highly sensitive detectors of ionizing radiation, in particular, for research processes double beta decay. First, phonon absorption of samples of isotopically pure germanium single crystals from the series ⁷⁰Ge, ⁷²Ge, ⁷³Ge, ⁷⁴Ge, ⁷⁶Ge is recorded using the IR spectroscopy method. Phonon absorption peaks of germanium samples are recorded in the wavelength range of 11.8-33.3 mcm, corresponding to wave numbers of 300-850 cm^-1. From the wave number of any of the phonon absorption peaks in the specified wavelength region, the value of M is calculated using the formula M = -(1/k)(lnϑ_n/ln(1.6ϑ₀), where ϑ_n is the wave number of the n-th phonon absorption peak of the identified isotopically pure germanium single crystal in the region of 11.8 - 33.3 mcm, n is the serial number of the absorption peak; ϑ₀ is the wave number of the corresponding n-th peak of phonon absorption for natural germanium ^natGe; k is a coefficient in the range of 0.0062-0.0072. The calculated M value for ⁷⁰Ge is 70; for ⁷²Ge - 72; for ⁷³Ge - 73, for ⁷⁴Ge - 74, for ⁷⁶Ge - 76.

EFFECT: invention allows for express analysis of objective identification of isotopically pure germanium single crystal for the entire range of isotopic varieties of germanium.

1 cl, 3 dwg, 2 tbl

Description

The present invention relates to the field of electronics, photonics and semiconductor technology, namely: to the field of obtaining high-purity substances used in microelectronics, IR optics, nanophotonics, namely: to methods for objective identification of isotopically enriched germanium, which can be used, for example, in as highly sensitive low-background infrared radiation detectors, arrays of elements of quantum computers, photodetectors, highly sensitive detectors of ionizing radiation, in particular, for studying double beta decay processes, and other semiconductor devices and materials.

Monocrystalline germanium is the most studied semiconductor material [1]. Germanium is widely used in IR optics, mainly for working in the atmospheric transparency window of 8 - 14 μm, however, the phonon absorption peaks present in the IR region (corresponding to wavelengths 11.8-33.3 μm) significantly limit its use. The position of phonon absorption peaks in the spectra of germanium crystals is practically a constant of the material. The use of germanium is growing as the technology for purifying single crystals from impurities and other structural defects improves. Germanium with a concentration of electrically active impurities in the material at the level of 10 ⁹ -10 ¹⁰ cm ^-3 is used as detectors of ionizing radiation and highly sensitive low-background receivers of infrared radiation. The problem of purifying germanium from electrically neutral impurities, for example, oxygen, which also affects the properties of germanium, is also at the stage of being solved [2]. A technology for producing dislocation-free crystals has also been developed.

With the improvement of the technology for producing germanium, the influence of isotopic purity on the properties and use of the material became clear. Germanium in nature ^nat Ge (atomic number 32, atomic mass 72.59) is a mixture of stable isotopes with approximate mass numbers 70, 72, 73, 74, 76: ⁷⁰ Ge - 20.57%, ⁷² Ge - 27.45%, ⁷³ Ge - 7.75%, ⁷⁴ Ge - 36.50%, ⁷⁶ Ge - 7.73% [3]. Even-numbered isotopes of germanium have zero nuclear spin, which allows them to be used as a matrix of elements for quantum computers. Single crystals of the ⁷⁶ Ge isotope are used as detector material for studying double beta decay processes and other fundamental physical processes. As technologies for obtaining isotopically pure germanium single crystals develop, other areas of their application appear, and therefore there is a need for a relatively simple method for identifying the isotope used, which is a difficult task due to the significant similarity of the physicochemical properties of the isotopes.

The crystal lattice of germanium perceives another isotope as a kind of structural defect that affects the phonon spectrum of the crystal. In this case, the phonon structure of the crystal turned out to be very sensitive to these defects. This was previously demonstrated using the example of thermal conductivity and heat capacity [3-7]. In particular, in the temperature dependences of thermal conductivity for isotopically pure and structurally perfect germanium single crystals, I.Ya. Pomeranchuk theoretically predicted [4, 5] and subsequently discovered [6, 7] a significant anomaly. Thus, isotopically pure germanium can have a thermal conductivity 8.5 times higher than that of a germanium crystal of natural composition, which is directly related to the nature of the phonon spectrum.

For both optical, detector and other applications of germanium in electronics, temperature stability is important, which is directly related to the thermal conductivity of the material (it is known that the operating temperature of germanium is limited to 70°C, and it is important to ensure good heat removal from the crystal during operation).

Therefore, it is extremely relevant to develop a technology for express analysis of objective identification of the corresponding germanium isotopes, in particular, in the study of isotopically pure varieties of elemental germanium.

There is a known method for identifying isotopic varieties of elemental germanium with a high degree of isotopic purity using the method of “extended” spectroscopy of the fine structure of X-ray absorption (Extended X-ray Absorption Fine Structure - EXAFS) with femtometer accuracy by the amplitude of relative atomic vibrations, by the temperature dependence of the difference in the Debye-Waller factors [ 8].

The disadvantage of this method is that it uses x-ray radiation, which requires special protective equipment, a special room, and provision of the necessary safety precautions. The method does not provide the determination of the entire series of germanium isotopes, but only determines isotopes that differ significantly in mass - Ge ⁷⁰ and Ge ⁷⁶ - due to the similarity of the physicochemical properties of other germanium isotopes.

The closest to the claimed method in its technical essence (prototype) is a method for determining the atomic mass of single crystals of isotopic varieties of germanium ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge, including registration of phonon absorption of germanium samples using the IR spectroscopy method, recording the shift of phonon absorption peaks germanium samples in the wavelength range 11.8 - 33.3 μm (which corresponds to the range of wave numbers - 300-850 cm ^-1 ), while the phonon absorption peaks in the spectrum of the ⁷² Ge isotope shift to short wavelengths, and in the spectra of the ⁷³ Ge isotopes , ⁷⁴ Ge, ⁷⁶ Ge - to the long wavelength, relative to the phonon absorption peaks of a germanium single crystal of natural isotopic composition ^nat Ge, and identification by the shift of the phonon absorption peak of the corresponding germanium sample of its isotopic variety [9].

The disadvantage of this method is that it does not take into account the phonon absorption peaks of the germanium isotope ⁷⁰ Ge to enable rapid express analysis of this isotope, which is very important for a number of practical applications, for the purpose of express analysis of objective identification of isotopically pure germanium single crystals.

The new technical result achieved by the proposed invention is an express analysis of the objective identification of an isotopically pure germanium single crystal for the entire range of isotopic varieties of germanium.

A new technical result is achieved by the fact that in the method of express analysis of the objective identification of an isotopically pure germanium single crystal of the isotopic varieties of germanium ⁷⁰ Ge, ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge, including recording IR spectra of phonon absorption of germanium samples, fixing the position of the phonon absorption peaks absorption of radiation from germanium samples in the region of 11.8-33.3 microns and objective identification of isotopically pure germanium single crystals from the series ⁷⁰ Ge, ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge by calculating the value of M using equation 1 from the wave number of any of the phonon peaks absorption of an identifiable sample of isotopically pure germanium single crystal in the region of 11.8-33.3 microns,

, (1)

where ϑ _n is the wave number of the nth phonon absorption peak of the identified isotopically pure germanium single crystal in the region 11.8 - 33.3 μm, where n is the serial number of the absorption peak; ϑ ₀ - wave number of the corresponding n-th peak of phonon absorption for natural germanium ^nat Ge; k is a coefficient in the range 0.0062-0.0072.

so M = 70 for ⁷⁰ Ge, 72 for ⁷² Ge, 73 for ⁷³ Ge, 74 for ⁷⁴ Ge, 76 for ⁷⁶ Ge.

As the wave number of the nth peak of photon absorption of the studied germanium single crystal, the wave number of the maximum peak can preferably be chosen, which is most suitable in terms of the value of the recorded absorption for the thickness of the studied single crystal of the isotopic variety of germanium.

So. a sample thickness of 12-22 mm ensures that the actual transmittance value in the region of maximum transparency is not less than 0.4 and allows one to reliably identify the position of the studied phonon absorption peaks in the region of 12-17 μm.

For thinner samples (for example, 2-3 mm thick), due to the higher absorption coefficient, it is preferable to use photon absorption peaks in the region of 23-24 μm.

The absorption coefficients in each of the 16 bands differ markedly. This makes it possible to select for objective identification of the studied isotopically pure germanium single crystal exactly the band that is most suitable for the thickness of the sample under study.

The position of the phonon absorption peaks in the region of 11.8-33.3 μm of the IR spectrum of germanium is determined by phonon effects in the germanium crystal and corresponds to the isotopic variety of germanium in accordance with equation 1, obtained experimentally, and the position of the peaks is clearly identified, including at room temperature .

The experiments performed showed a clear correspondence between the position of any of the phonon absorption peaks in the IR spectrum and the isotopic variety of germanium.

The experimental data obtained are fully consistent with the existing theoretical concepts of light absorption by the crystal lattice in monatomic semiconductors such as germanium. They exhibit multiphonon light absorption associated with both optical (longitudinal (TO) and transverse (LO)) and acoustic (by analogy - TO and LO) modes [11]. In total, 16 lattice absorption bands are recorded in the region of 11.8-33.3 μm (Table 17 in [9]).

As reference samples, we use optically processed plates of germanium single crystals of natural isotopic composition, grown at the Zaporozhye Titanium-Magnesium Plant and at Tver State University from obviously different batches of raw materials and obtained by different methods: Czochralski and Stepanov [12].

It is experimentally shown in Table 1 that 16 bands of lattice absorption peaks are recorded, observed both in the transmission spectrum of germanium single crystals of natural isotopic composition, and in samples of isotopically pure germanium single crystals ⁷⁰ Ge, ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge, which are consistent with equation 1.

In fig. Figure 1 shows an example of the difference in the transmission spectrum of experimentally obtained phonon absorption bands in the IR spectra of samples of natural ^nat Ge ( ^72.59 Ge) - a and isotopically pure germanium single crystals ( ⁷⁰ Ge - b, ⁷² Ge - c, ⁷³ Ge - d, ⁷⁴ Ge - d, ⁷⁶ Ge - f) in the region of wave numbers 407-438 cm ^-1 (corresponding to wavelengths of 23-24 μm) on samples with a thickness of 2-3 mm. The error in transmittance measurement is 0.5%.

In fig. Figure 2 shows examples for samples ⁷⁰ Ge - a, ⁷² Ge - b, ⁷³ Ge - c, ⁷⁴ Ge - d, ⁷⁶ Ge - d, isotopically pure germanium single crystals, for the first three absorption bands. Compared to an isotopically pure ⁷⁰ Ge single crystal, the additional shift in the wave number Δϑ of the optical phonon is 0.34 ± 0.04 cm ^-1 [13]. In fig. Figures 1 and 2 show some of the phonon absorption bands recorded in the transmission spectrum measured using a spectrophotometer. Absorption losses are recorded during transmission.

At the same time, in ⁷⁰ Ge and ⁷² Ge single crystals there is an increase in the wave number ϑ of the phonon absorption peaks compared to single crystals of natural isotopic composition, and in ⁷³ Ge, ⁷⁴ Ge and ⁷⁶ Ge single crystals the wave number ϑ of the phonon absorption peak decreases compared to single crystals of natural germanium isotopic composition ^{of nat} Ge.

In general, the dependence of the M - number characterizing the isotopic variety of isotopically pure germanium single crystals on the wave number ϑ of phonon absorption peaks in isotopically pure germanium single crystals ⁷⁰ Ge, ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge in the region of 11.8-33.3 μm can be approximated by the experimentally obtained equation 1.

The method for objective identification of isotopically pure single crystals of isotopic varieties of germanium from the series ⁷⁰ Ge, ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge is implemented as follows: fix the position of any of the phonon absorption peaks in the IR spectrum, determine the value of M using formula 1; carry out the process of objective identification of an isotopically pure germanium single crystal in compliance with: M = 70 for ⁷⁰ Ge, 72 for ⁷² Ge, 73 for ⁷³ Ge, 74 for 74Ge, 76 for 76Ge, using known (tabular) values of ϑ ₀ .

Since the absorption coefficient of germanium in the region of 11.8-33.3 μm differs markedly, preference when choosing a phonon absorption peak for identification should be given to the peak that is better resolved for the sample thickness used. For example, as the wave number of the nth peak of phonon absorption of germanium samples, the wave number of the maximum peak is chosen, which is usually better resolved for the sample thickness used. The wave number ϑ values for each maximum phonon absorption peak in each germanium isotope are given in Table 1.

Table 1 - Differences in the transmission spectrum of the experimentally obtained positions of the maxima of phonon absorption bands for samples of natural and monoisotopic germanium crystals

^{Composition of germanium} Maxima of phonon absorption bands in the transmission spectrum of germanium ϑ ₁ , cm ^–1 ϑ ₂ , cm ^–1 ϑ ₃ , cm ^–1 ϑ ₄ , cm ^–1 ϑ ₅ , cm ^–1 ϑ ₆ , cm ^–1 ϑ ₇ , cm ^–1 ϑ ₈ , cm ^–1
(the bar corresponds
fig. 1) ϑ ₉ ,
cm ^–1 ϑ ₁₀ , cm ^–1 ϑ ₁₁ , cm ^–1 ϑ ₁₂ , cm ^–1 ϑ ₁₃ , cm ^–1 ϑ ₁₄ , cm ^–1 ϑ ₁₅ , cm ^–1 ϑ _16, cm ^{–1 72 .59} Ge (nat) 839.6 750.3 641.9 560.2 522.2 502.5 469.2 423.2 389.2 360.4 350.8 351.5 342.5 318.5 287.4 273.2 ⁷⁰ Ge 856.9 763.2 655.6 571.4 532.2 506.6 471.0 429.2 390.3 367.0 354.4 352.0 347.2 324.7 292.8 278.9 ⁷² Ge 844.9 751.8 643.5 563.4 526.0 504.3 470.2 424.4 389.6 361.7 353.7 344.8 342.4 321.5 289.0 276.6 ⁷³ Ge 839.5 750.2 641.5 558.7 521.6 502.4 469.0 421.0 388.8 360.2 351.4 346.2 341.3 319.5 287.4 272.9 ⁷⁴ Ge 833.7 743.6 638.1 554.0 519.4 498.0 466.7 418.4 385.2 356.5 344.8 344.8 338.4 315.5 284.1 270.6 ⁷⁶ Ge 822.9 736.2 629.5 548.9 512.6 492.3 466.2 414.1 380.8 352.7 344.2 342 335.6 313.5 278.6 266.7

Note 1: ϑ ₁ – first phonon absorption band; ϑ ₂ - second phonon absorption band; ϑ ₃ – third phonon absorption band; ϑ _n – nth phonon absorption band (n = 1, 2, 3, …, 16).

The range of coefficient k = 0.0062-0.0072 was selected on the basis of an experimental study of the phonon absorption peaks of isotopically pure single crystals of isotopic varieties of germanium from the series ⁷⁰ Ge, ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge in the IR spectrum region 11.8 -33.3 µm.

The selection of the best approximation dependence M = f(ϑ) was carried out using the computer program “Maple” according to the data on the measured quantities. The dependence of the value M, which characterizes the isotopic variety of germanium, on the wave number of the phonon absorption peak M = f(ϑ) is approximated by an exponential dependence.

Table 2 – Position of the maximum of absorption bands: experiment and calculation using formula (1)

Composition of germanium Maximums of phonon absorption bands in samples of monoisotopic germanium crystals ϑ ₁ , cm ^–1 ϑ ₂ , cm ^–1 ϑ ₃ , cm ^–1 ϑ ₄ , cm ^–1 ϑ ₅ , cm ^–1 ϑ ₆ , cm ^–1 Expert Formula (1) k = 0.00645 Expert Formula (1) k = 0.00645 Expert Formula 1)
k = 0.00645 Expert Formula 1)
k = 0.00645 Expert Formula 1)
k = 0.00645 Expert Formula 1)
k = 0.0065 ⁷⁰ Ge 856.9 856.0 763.2 762.9 655.6 653.9 571.4 570.7 532.2 532.0 506.6 510.0 ⁷² Ge 844.9 845.0 751.8 753.2 643.5 645.5 563.4 563.4 526.0 525.1 504.3 503.5 ^72.59 Ge (nat) 839.6 841.8 750.3 750.3 641.9 643.1 560.2 561.2 522.2 523.1 502.5 501.6 ⁷³ Ge 839.5 839.6 750.2 748.4 641.5 641.4 558.7 559.7 521.6 521.7 502.4 500.3 ⁷⁴ Ge 833.7 834.2 744.6 743.5 638.1 637.2 554.0 556.1 519.4 518.4 498.0 497.0 ⁷⁶ Ge 822.9 823.5 736.2 734.0 629.5 629.1 548.9 549.0 512.6 511.8 492.3 490.6

A comparison of the experimental data presented in Table 2 for the first six maxima of phonon absorption bands for samples of monoisotopic germanium crystals shows that the lattice phonon absorption peaks observed in germanium single crystals of natural isotopic composition, in samples of isotopically pure germanium single crystals ⁷⁰ Ge, ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge are in good agreement with those calculated by formula 1.

The influence of the isotopic composition on the properties of germanium crystals is correlated with the fact that isotopic disorder violates the translational invariance of the lattice and leads to phonon scattering, hence the difference in the position of phonon absorption peaks with changes in the isotopic varieties of germanium.

In fig. Figure 3 shows an example that shows the wave numbers ϑ of phonon absorption peaks, measured experimentally and calculated from the approximation dependence - equation 1, for the first six characteristic peaks of phonon absorption of isotopic varieties of germanium in the studied samples - correspond to Table 2. Wave numbers of phonon absorption peaks, observed in the transmission spectrum of germanium, for monoisotopic and natural germanium: ϑ1 - the first peak of phonon absorption; ϑ2 - second phonon absorption peak; ϑ3 - third peak of phonon absorption; ϑ4 - fourth phonon absorption peak; ϑ5 - fifth peak of phonon absorption; ϑ6 is the sixth phonon absorption peak.

Measurements are carried out using an IR spectrophotometer, for example, using a Bruker Vertex 70 Fourier IR spectrometer - spectral range 1.3-670.0 μm. The instrument is calibrated using reference spectra (normals), wave numbers, and absorption band maxima, which are precisely known, for example, for polystyrene. To improve the quality of registration of the absorption spectrum by germanium, the background signal associated with absorption by atmospheric gases, the influence of thermal radiation from the cell space, etc. is eliminated.

The measurement technique and accuracy assessment depending on the transmission measurement methods and the quality of sample processing are given in [10].

To confirm the agreement of the experimental data with those calculated using formula 1, according to the methods and analysis of the conditions for obtaining the most accurate values of transmittance coefficients using spectrophotometric methods with an error in measuring the wave number ϑ of the order of 1 cm- ¹ , samples of isotopically pure stable isotopic varieties of germanium ⁷⁰ single crystals are prepared and studied. Ge, ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge with the same chemical purity of at least 99.9% in the form of plane-parallel plates with crystallographic orientation <111> and <100> (with the same crystalline perfection) and a diameter of 30-45 mm. The working surfaces of the samples are polished according to class IV GOST 11141-76, the roughness of the polished surfaces corresponds to Rz 0.05 μm at a base length of 0.08 mm according to GOST 2789-73. Germanium single crystals are polished using a single specially developed technology of chemical-mechanical optical processing.

Since it is believed that isotopic enrichment of more than 99.99% in one of the isotopes [14] does not lead to a noticeable change in thermal conductivity at room temperature, it can be assumed that for these maxima of phonon absorption bands, the shift value in germanium is a finite fixed value.

Based on the above, the new achieved technical result of the proposed invention is provided with the following technical advantages compared to the prototype.

1. The proposed method for identifying isotopic varieties of elemental germanium with a high degree of isotopic purity can be used for rapid assessment of the isotopic composition of germanium single crystals based on the position of phonon absorption bands.

2. A simplification of the isotope identification method for the entire series of germanium isotopes by at least 10% is achieved by reducing the labor intensity of operations for performing experimental operations for express analysis of samples.

Currently, Tver State University and Tydex LLC (St. Petersburg) have tested the proposed method for determining the isotope identification of isotopic varieties of elemental germanium with a high degree of isotopic purity, and on their basis, technological documentation for the implementation of the method has been issued.

Sources used

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2. Podkopaev O.I., Shimansky A.F. Growing germanium single crystals with a low content of dislocations and impurities. Krasnoyarsk: Sib. federal univ. 2013. 104 p.

3. Gusev A.V., Gibin A.M., Andryushchenko I.A., Gavva V.A., Kozyrev E.A. Heat capacity of high-purity isotope-enriched germanium-76 in the range 2-15K // Solid State Physics. 2015. T. 57. Issue. 9. S. 1868-1870.

4. Pomeranchuk I.Ya. On the thermal conductivity of dielectrics at temperatures lower than the Debye temperature // JETP. 1942. T. 12. pp. 245-254.

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7. Ozhogin V.I., Inyushin A.V., Taldenkov A.N., Tikhomirov A.V., Popov G.E., Haller Yu., Ito K. Isotopic effect in the thermal conductivity of germanium single crystals // JETP Letters . 1996. T. 63. V. 6. pp. 463-467.

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9. Lipsky V.A., Preparation and optical properties of high-purity isotope-enriched germanium: dissertation for the degree of candidate of chemical sciences. Nizhny Novgorod. 2021. 119 p.

10. GOST 3520-92. Optical materials. Methods for determining attenuation rates. Enter. 1993-07-01. M.: Publishing house of standards. 1992. 20 p.

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Claims (4)

A method for express analysis of objective identification of isotopically pure germanium single crystal, including registration of phonon absorption of germanium samples using the IR spectroscopy method, recording of phonon absorption peaks of germanium samples in the wavelength range 11.8-33.3 μm, corresponding to wave numbers - 300-850 cm ^-1 , characterized in that the objective identification of isotopically pure germanium single crystals from the series ⁷⁰ Ge, ⁷² Ge, ⁷³ Ge, ⁷⁴ Ge, ⁷⁶ Ge is carried out by calculating the value of M from the wave number of any of the phonon absorption peaks in the region 11.8-33.3 µm: , where ϑ _n is the wave number of the nth phonon absorption peak of the identified isotopically pure germanium single crystal in the region 11.8 - 33.3 μm, n is the serial number of the absorption peak; ϑ ₀ - wave number of the corresponding n-th peak of phonon absorption for natural germanium ^nat Ge; k is a coefficient in the range 0.0062-0.0072; so M = 70 for ⁷⁰ Ge, 72 for ⁷² Ge, 73 for ⁷³ Ge, 74 for ⁷⁴ Ge, 76 for ⁷⁶ Ge.