Temperature effect on phase states of quartz nano-crystals in silicon single crystal

Full text: Oxygen penetrates into the silicon lattice up to the concentration of 2·1018 cm-3 in the course of growing [1]. By the author's opinion at a low oxygen content the formation of solid solution is possible in the local defect places of the silicon single crystal lattice due to the difference in effective ion radius of oxygen and silicon (rO 0.176 and rSi = 0.065 nm). Upon reaching some critical content (∼ 1017 cm-3), it becomes favorable energetically for oxygen ions to form precipitates (SiOx) and finally a dielectric layer (stoichiometric inclusions of SiO2). It was shown later that depending on the growth conditions, indeed the quartz crystal inclusions are formed in the silicon single crystals at an amount of 0.3 /0.5 wt. % [2]. However the authors did not study a phase state of the quartz inclusions. Therefore the aim of this work was to study a phase state of the quartz inclusions in silicon crystal at various temperatures. We examined the silicon single crystals grown by Czochralski technique, which were cut in (111) plane in the form of disk of 20 mm diameter and 1.5 thickness and had hole conductivity with the specific resistance ρo ≅ 1/10 Ohm cm. The dislocation density was ND ≅ 101/103 cm-2, the concentrations of oxygen and boron were N0 ≅ 2/ 4·1017 cm-3 and NB ≅ 3*1015 cm-3. Structure was analyzed at the set-up DRON-UM1 with high temperature supply UVD-2000 ( CuK = 0.1542 nm) at the temperatures of 300, 1173 and 1573 K measured with platinum-platinum-rhodium thermocouple. The high temperature diffraction spectrum measured at 1573 K in the angle range (2Θ≅10/70degree) there is only one main structure reflection (111) with a high intensity and d/n ≅ 0.3136 nm (2 Θ≅ 28.5degree) from the matrix lattice of silicon single crystal. The weak line at 2 Θ≅ 25.5degree(d/n≅0.3136 nm) is β component of the main reflection (111), and the weak structure peak at 2Θ≅59degree(d/n≅ 0.1568 nm) is its second order (222). But the reference peak (111) is a singlet with no splitting over α1 and α2 radiation that should occur in the equilibrium state of the sample. It is indicative of a statistic oxygen distribution over the energy equivalent interstitials in the silicon lattice at the high temperature (1573 K), yet a bit lower than the melting point (Tm ≅ 1685 K). The intensity ratio of the 'forbidden' reflection (222) to the allowed peak (111) came to I(222)/I(111) ≅ 10-4. Such a small value also points to a statistic oxygen distribution in the lattice and practical absence of micro-strains having the component normal to the reflecting silicon surface. Thus the diffraction pattern at 1573 K corresponds to the silicon matrix crystal with oxygen ions distributed evenly over interstitials. Diffraction pictures of the silicon crystal at 300 and 1173 K were practically the same, but differed essentially from the high temperature spectrum. Low temperature diffraction spectra included weak additional selective reflections with d/n ≅ 0.3345 nm (2Θ≅ 26.6degree) and 0.2468 nm (2Θ≅ 36.6degree), which correspond to the diffraction reflections (101) and (110) of quartz crystals SiO2. The characteristic size of the quartz inclusions was determined ∼ 4 nm from the width of the singlet reflection (110). Besides, the main reflection (111) was observed to split over α1 and α2 radiation, and also 6-times increase in the forbidden (222)-reflection intensity I(222)/I(111) ≅6*10-4 of the silicon matrix. These facts evident of non-even oxygen distribution over the lattice interstitials and increase in local area with micro-strains. Possible reason of changing the diffraction pattern depending on the temperature is the change of oxygen phase state in the silicon lattice. According to the silicon-oxygen phase diagram solid solution is form ed at temperatures close to the melting point. In this case oxygen behaves like a point defect and does not influence on the structure reflection intensities of silicon lattice. At lowering temperature the isotropic oxygen distribution in silicon, which is characteristic of high temperatures, violates and there appears anisotropy. The last results in exceeding the solubility limit for oxygen concentration at this temperature especially in several defect places like {111} since they are the densest layers. Such a state of the solid solution is unstable thermodynamically and decomposes into two phases enriched and depleted with oxygen [1]. The perfect fragments of silicon lattice release the average statistic strain caused by difference in ionic radius of silicon and oxygen by means of oxygen ion replacement into the defective regions. In this way the extra oxygen bounds chemically with silicon forming SiO2 inclusions responsible for the additional structure reflections in the silicon diffraction pattern. It explains the splitting of the main reflection (111) of the silicon lattice over 1 and 2 radiation. The ratio of elementary units of quartz and silicon V(SiO2)/V(Si) ≅ 2, meaning that quartz inclusions distort the silicon lattice and hence the intensity of the 'forbidden' silicon reflection with d/n 0.1568 nm increases. The obtained results agree with those of [3], where beginning from the oxygen concentration ∼ 1017 sm-3 and higher, the value of the upper limit of silicon crystal plastic fluidity decreases presumably due to sedimentation of dispersed particles. The work is supported by contract F2.1.2 with the Center for Science and Technology of Uzbekistan. (author)