Phase-change memory technology is based on the high speed reversible amorphous-to-crystalline transformation of a thin film material. The limiting process in rewritable media is the slow crystallization process. For that reason, in recent years many experimental and theoretical studies to investigate the amorphous-to-crystalline phase transformation have appeared in the literature.

Studies of crystallization kinetics of phase change films, are often analyzed using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model for isothermal annealing (see the following reference [1-5]), which allow to determine the activation energy for the crystallization process. According to the JMAK model the transformed volume fraction x can be determined by the following expression.

where K = γexp(–E/kT) and γ, E, t and n are the frequency factor, effective activation energy, time of annealing and Avrami exponent, respectively. In materials with random nucleation and isotropic growth the plot vs should be a straight line with a slope corresponding to the Avrami exponent, which provides information about the mechanisms of crystallization.

The kinetic parameters in the literature for Ge₂Sb₂Te₅, Ge₁Sb₂Te₄, Ge₁Sb₄Te₇ and Ge₄Sb₁Te₅ (the most common material used in phase change technology) show a large discrepancy. Values from 1.2 to 4.4 for the Avrami exponent and from 0.81 to 4.3 eV for the effective activation energy have been reported [1-7].

The aim of this work is to compare the isothermal crystallization kinetic in the films along GeTe-Sb₂Te₃ line.

The amorphous Ge₂Sb₂Te₅, Ge₁Sb₂Te₄, Ge₁Sb₄Te₇ and Ge₄Sb₁Te₅ films, with thickness about of 200 nm, were produced using thermal evaporation from bulk alloys. The composition of films was evaluated by energy dispersive spectroscopy (EDS) and it did not differ more than 2% from the composition of the bulk materials.

In situ optical reflection (using a laser diode emitting at 650 nm) and X-ray measurements were carried out using a resistance heater. The temperature was controlled with a device which was programmed to heat the sample to a predetermined temperature for isothermal measurements. X-ray diffraction measurements were carried out using a Rigaku X-ray diffractometer with a Cu tube.

In the reflectance measurements the volume fraction of crystalline phase was calculated using the generally employed assumption that the signals are linearly related to the transformed crystalline volume fractions x using the next expression.

where Ra and Rc are the reflectance of amorphous and crystalline phase, respectively.

The next Figure 1 and Figure 2, show the evolution in the volume fraction of the transformed crystalline phase obtained from reflectance measurements during isothermal annealing at the indicated temperatures in films with the following compositions: Ge₂Sb₂Te₅, Figure 1(a), and Ge₄Sb₁Te₅, Figure 2(a). All films show long incubation time for crystallization, or time required to reach a critical nuclei size which lead to an abrupt increasing in the crystalline volume fraction. However there are two well defined crystallizations behaviors; in films with the

Ge₂Sb₂Te₅ and Ge₁Sb₂Te₄ (not shown) compositions, the results show a relative large amounts of crystallized phase (about 20%) during the incubation time, whereas in those with the other two compositions (Ge₁Sb₄Te₇ and Ge₄Sb₁Te₅) the crystallized material during this time is much smaller (less than 2%).

X-ray measurements indicate that during incubation time, a metastable phase with the fcc Ge₁Sb₄Te₇ composition is formed in the Ge₂Sb₂Te₅ and Ge₁Sb₂Te₄ films. This metastable phase has a lower crystallization temperature and it probably appears in the two ternary alloys due to local fluctuations in the composition of the amorphous films [8,9]. Thus, the process of isothermal crystallization in Ge₂Sb₂Te₅ and Ge₁Sb₂Te₄ takes place in two stages: in the first stage, nuclei of a metastable phase with composition Ge₁Sb₄Te₇ precede the formation of the stable fcc phases; in the second stage, the nuclei transform into the equilibrium fcc stoichiometric structures with a composition correspondent to the parent amorphous material.

In materials where phase transformation starts with the formation of metastable phases, the isothermal crystallization process cannot be simply described by the JMAK theory and the Avrami plots are not linear which implies that Avrami exponent n does not remain constant during the crystallization process (Figure 1(b)). The kinetics of two-stage crystallization can be described by a modified JMAK model which assumes that the metastable phase grows up to a certain fraction and then stops growing. The second stage consists of simultaneous nucleation and growth of the stable phase into the metastable (until the grain limit is reached) and within the amorphous phases [8,9].

In films with compositions Ge₄Sb₁Te₅ and Ge₁Sb₄Te₇, the X-ray diffraction data shows crystallization into the same and final phase during the whole annealing time. In this case it is possible to neglect the amount of crystallized material during the incubation time τ and define τ as the beginning of the transformation [1], the JMAK equation is now expressed:

According to Equation (3) the plot vs must be a straight line with the slope n (Figure 2(b)). This means that crystallization process in Ge₄Sb₁Te₅ and Ge₁Sb₄Te₇ material display random nucleation and isotropic growth.

The values of Avrami exponent n (n = 1.8 for Ge₄Sb₁Te₅ and n = 1.94 for Ge₁Sb₄Te₇) and effective activation energy E_a (E_a = 3.46 eV for Ge₄Sb₁Te₅ and E_a = 1.7 eV for Ge₁Sb₄Te₇) have been calculated from reflection measurements. According to J. W. Christian [10], the values of n in the range 1.5 < n < 2.5 correspond to a crystallization process dominated by all shapes growing from small dimensions with decreasing nucleation rate.

Relative low effective activation energy obtained for Ge₁Sb₄Te₇, low crystallization temperature, and the possibility to growth from small dimension allow suggesting that the appearance of nanocrystalline nuclei with the Ge₁Sb₄Te₇ phase in the process of crystallization of the Ge₂Sb₂Te₅ and Ge₁Sb₂Te₄ materials could be related to local fluctuations in composition of the amorphous matrix.

In this work the crystallization mechanism in phasechange materials along GeTe-Sb₂Te₃ line is compared. The traditional JMAK model did not explain the isothermal crystallization kinetics results in all samples. In Ge₂Sb₂Te₅ and Ge₁Sb₂Te₄ films crystallization starts with formation of a metastable phase with Ge₁Sb₄Te₇ composition. In contrast in Ge₁Sb₄Te₇ and Ge₄Sb₁Te₅ crystallization kinetics can be described by a JMAK model which take into account incubation times