Physics / 2. Solid state physics
Postgraduate student Golovko O.K.
Zaporizhzhia State Engineering Academy, Ukraine
Oxygen atoms in an optically non-active state 
in silicon single crystals
 
Condition of the problem. Silicon single crystals, grown by the Czochralski process (Cz-silicon), are widely used for the manufacture of microelectronic devices [1]. The study of atomic processes occurring in silicon single crystal during its growth is an actual problem at the present stage of improving the parameters of Cz-silicon.
Formulation of the problem. Atoms of oxygen impurities are placed in a crystal lattice of silicon in the interstitial positions, forming a solid solution. Such atoms absorb infrared light with a wavelength ≈ 9.1 μm, which allows us to control their concentration by the standard method of infrared absorption [2]. However, some of the oxygen atoms in a single crystal of silicon fall out of a solid solution. Such atoms are involved in oxygen precipitation and in the formation of chemical complexes and structural microdefects. Due to the formation of chemical bonds with silicon atoms or other impurities, oxygen atoms lose their optical activity. The concentration of optically non-active oxygen atoms can not be measured by the method of infrared absorption, so it is not controlled neither by manufacturers nor consumers of silicon single crystals. Oxygen complexes reduce the important parameter of monocrystalline silicon – the lifetime of nonequilibrium charge carriers, and also can cause deterioration of the parameters of devices and decrease the yield of suitable silicon chips.
The purpose of this work is to estimate the concentration of optically non-active atoms of an impurity of oxygen in Cz-silicon based on experimental data of the concentration of optically active oxygen atoms.
Mathematical modeling and evaluation of the concentration of optically non-active oxygen atoms in Cz-silicon. The methodological approach to modeling is based on experimental observation of a decrease in the effective segregation coefficient of oxygen in silicon during the growth of a single crystal [3]. According to the kinetic theory [4], due to a certain change in the parameters of the technological process during the growth of a silicon single crystal, the change in the effective segregation coefficient of oxygen in silicon k may be less than 1%. Calculation using the experimental data of the concentration of optically active oxygen atoms shows a decrease of k by 19% [5]. On the basis of such contradiction, we assume that the observed changes are only related to the optically active oxygen atoms of the kact and associated with the transition of a number of oxygen atoms into various complexes.
According to the theory of directional crystallization [6], the effective segregation coefficient of the impurity k taking into account the uneven density of the liquid and solid phases:
 , (1)
where γm – silicon melting density, g · cm-3; γc – density of the crystal, g · cm-3; g – fraction of crystallized melt; Nc – concentration of impurity in a crystal, cm-3;  Nm – concentration of impurity in the melt, cm-3; N0 – initial concentration of oxygen atoms in the melt, cm-3.
We consider (1) in silicon monocrystal the presence of concentration of oxygen atoms in two different states – optically active Nc(act) and non-active Nc(non-act): 

.

We denote the segregation coefficient of optically active oxygen atoms:

.

Determine the concentration of optically non-active oxygen atoms in a silicon single crystal: 
.
We determine the ratio of the concentrations of optically non-active and active oxygen atoms in a silicon single crystal:
 . (2)
We use the developed model (2) to estimate the ratio of the concentrations of optically inactive and active oxygen atoms in four silicon single crystals with a diameter of 135 mm with a crystallographic orientation {100} which were grown in a single Czochralski plant from identical raw materials. Single crystals doped with boron, specific electrical resistance ρ = 0,5 ... 1,7 Ω · cm. Measurement of the concentration of optically active oxygen atoms was carried out with an infrared spectrometer with a Fourier transform. To determine the kact(g) of oxygen atoms at different stages of growing a single crystal of silicon, use the previously developed mathematical model [7]. The results of the evaluation on the model (2) of the concentrations ratio of optically non-active and active oxygen atoms along the length of a single crystal are shown in Fig. 1. The first intersection of the cylindrical part of the single crystal is selected as the beginning of the reference x = 0.

Fig. 1 - Distribution of the concentrations ratio of optically non-active and active oxygen atoms along the length of a silicon single crystal 
 
It can be seen from the figure that the concentration of optically non-active oxygen atoms in the lower parts of it increases with respect to the upper part of the single crystal. From this fact it follows that complexes and microdefects with the participation of oxygen atoms are formed at high temperatures near the crystallization front. During the growth of a silicon single crystal its temperature decreases in a accordance to the distance growth between this single crystal's cross section from it's crystallization front. There is a restructuring of oxygen complexes, some of the oxygen atoms return to interstitial positions and become optically active.
Conclusions. Using the developed mathematical model for the first time, the concentration of optically non-active oxygen atoms in Cz-silicon is estimated. It is shown that oxygen atoms move to complexes and microdefects, preferably at high temperatures near the crystallization front. With a decrease in temperature in those parts of a single crystal of silicon, which during the growth are removed from the crystallization front, there is a partial annealing of some oxygen complexes.
 
References:

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2. F 1188-00. Standard test method for interstitial atomic oxygen content of silicon by infrared absorption; 2000.01.07. – Philadelphia: Annual book of ASTM Standards. Vol. 10.05, 2000. – 7 Р.

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4. Burton J.A. The distribution of solute in crystals grown from the melt / J.A. Burton, R.S. Prim, W.P. Slichter // Journal chemical physics. – 1953. - Vol. 21, № 11. - P. 1987 – 1991.

5. Швець Є.Я., Головко Ю.В. Залежність коефіцієнта розподілу домішок у монокристалі кремнію від швидкості його вирощування / Металургія. Збірник наукових праць ЗДІА. - Запоріжжя: ЗДІА, 2011. – Вип. 24. – С. 113 -116.

6. Пфанн В. Зонная плавка / B. Пфанн / Пер. с англ. под ред. Вигдоровича В.Н. – М.: Мир, 1970. – 366 с.

7. Швец Е.Я. Исследование массообмена кислорода в процессе выращивания монокристаллов кремния по методу Чохральского / Е.Я. Швец, Ю.В. Головко // Теория и практика металлургии, 2008. - №4-5 (65). – С.3-7.