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Abstract
The optical constants of germanium antimony telluride (GST), measured by spectroscopic ellipsometry (SE), for the spectral range of 350-30,000 nm are presented. Thin films of GST with composition Ge2Sb2Te5 are prepared by sputtering. As-deposited samples are amorphous, and when heated above the phase transition temperature near 150 °C, films undergo an amorphous to face-centered cubic crystalline phase transition. The optical constants and thicknesses of amorphous and crystalline GST films are determined from multi-angle SE measurements, applying a general oscillator model in both cases. Then, in order to evaluate the optical constants at intermediate states throughout the phase transition, GST films are heated in situ on a temperature stage, and single-angle SE measurements are carried out at discrete temperature steps in a range from 120–158 °C. It is shown that ellipsometric data for partially crystallized states can be fit by treating the GST as an effective medium consisting of its amorphous and crystalline states. Its optical constants, fractional crystallinity, and thickness can be determined at intermediate crystallization states throughout the phase transition. As a practical demonstration of the usefulness of this method, samples are held at fixed temperatures near the transition temperature, and SE is performed periodically. The fraction of crystallinity is determined as a function of time, and an activation energy for the amorphous to crystalline phase transition is determined.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Since they were first reported in 1968, a class of chalcogenide materials, sometimes known as ovonic materials after their discoverer, S.R. Ovshinsky [1], have attracted a great deal of interest due to their phase change properties [2–7]. These phase change materials (PCMs) can be switched from amorphous semiconductors to their crystalline phases with the introduction of energy, supplied either thermally, by heating directly or with a pulsed laser, or with an electric field. The phase change is typically reversible; when heated above its melting temperature and quenched, the PCM returns to its amorphous state [7]. Analysis indicates that some PCMs may be capable of undergoing as many as ∼1015 phase transitions before failure [8]. These materials exhibit dramatically different properties between their amorphous and crystalline states including changes in their electrical conductivity [1], optical constants [9–12], and volume [13].
Interest in PCMs increased through the 1980’s after sub-nanosecond switching times were demonstrated and their potential application in phase change memory became clear [6]. PCMs found widespread use in rewritable CDs and DVDs. More recently, a wider range of uses for PCMs has been developed including applications in integrated optic components such as switches [14–16] and tunable microring resonators [17], neuromorphic computing [7,18–20], and switchable metasurfaces [21–24].
A variety of compositions for PCMs has been explored, with different compositions leading to a range in parameters such as switching time, magnitude of change in the refractive index, and electrical resistivity [3]. Germanium antimony telluride (GST) with a composition of Ge2Sb2Te5 was one of the earliest PCMs with sub-nanosecond switching time and probably remains the most commonly used composition.
Recently, there has been increasing interest in continuously tuning the optical properties of PCMs—rather than using them only in their amorphous and crystalline states—for photonic applications [25]. In order to accurately model optical devices based on these materials, it is critical to have reliable values for the optical constants for not only the amorphous and crystalline states but also for intermediate, i.e. partially crystallized, states. Previous work has provided optical constants for only the totally amorphous and totally crystalline states of Ge2Sb2Te5 by spectroscopic ellipsometry (SE) [9–11] and by emittance measurements [12].
In this work spectroscopic ellipsometry SE is applied to determine the refractive index and absorption coefficient as a function of wavelength, n(λ) and k(λ) respectively, for the spectral range of 350-30,000 nm, a larger range than has been previously reported, for amorphous and crystalline Ge2Sb2Te5 films. Both states are modelled using an oscillator model, and best fit parameters for these models are provided. It is then shown that intermediate states, achieved by controlled heating, can be treated as effective media consisting of a combination of these states, and that it is possible to determine the percent crystallinity and thickness of films in these intermediate states. Finally, by holding GST samples at fixed temperatures and periodically repeating SE measurements, the reaction rate for crystallization is determined at several temperatures, and an activation energy for crystallization is determined.
2. Experiment
Films of GST are deposited by radio frequency magnetron sputtering from a 7.6 cm diameter commercial sputtering target onto soda lime glass (SLG) substrates. Samples are held at room temperature and films are deposited in a pure argon atmosphere with a pressure of 3 mT and at a power of 50 W. Samples are removed from the chamber and coated with a 12 nm thick alumina (Al2O3) passivation layer by atomic layer deposition to prevent surface oxidation. The back surface of each sample is roughened via bead blasting to eliminate specular reflection.
SE is first carried out at incident angles of 55°, 65°, and 75° on soda lime glass (SLG) substrates and alumina films at room temperature using two different ellipsometers, one covering a spectral range from 190-1690 nm (Woollam, M-2000) and the other from 1,700-30,000 nm (Woollam, IR-VASE). These measurements are repeated on as-deposited (amorphous) GST films on SLG substrates with alumina passivation layers.
Next, SE was performed in situ on GST samples in intermediate states. A heat cell (Linkam, THMS600) with infrared transmitting zinc selenide windows was installed and calibrated. With this cell installed, only a single incident angle of 70° can be used, and the spectral range of the instrument is reduced to approximately 1,900-17,000 nm. The following ramp schedule was used: After stabilizing at a temperature of 120 °C, the stage is programmed to ramp to each set temperature over 10 minutes, hold the set temperature for 10 minutes and then perform a measurement which takes approximately 30 minutes. Increasing the temperature ensures that a full range of crystallization states are accessed. In general, percent crystallinity is not directly correlated with a particular annealing temperature but instead depends on the annealing history of the sample. Note that crystallization is a dynamic process and continues during each measurement, so some error is introduced by performing the scan while the sample is heated. However, cooling the sample between measurements would result in additional annealing during temperature ramps, causing additional uncertainty, so it is not viable here.
Fully crystallized samples are removed from the heat cell, the heat cell is removed, and multi-angle SE measurements are performed on this sample on both ellipsometers, as described above, in order to obtain data for crystallized GST for the full spectral range.
Finally, with the heat cell present, fresh samples are held at fixed temperatures of 140 °C, 144 °C, or 148 °C, and SE is performed repeatedly at fixed time intervals.
3. Model
To carry out SE measurements, the polarization state of the incident beam is varied, and the ratio of the reflection coefficients for p- and s-polarized light, Rp and Rs respectively, is measured. Their ratio can be expressed as
where Ψ is related to the magnitude of the p- and s-polarized components, and Δ is the phase difference between them.The GST film is modeled with a Kramers-Kronig consistent general oscillator model—a model that treats the dielectric function as a summation of complex terms with defined functional forms [26]. Once the dielectric function is defined, theoretical values of Ψ and Δ can be calculated, and parameters in each oscillator term can be adjusted to provide a best-fit between the model and experimental data for Ψ and Δ.
The complex dielectric constant as a whole may be written
It is determined that the optimal model for the dielectric function for GST also contains a Tauc-Lorentz function to describe the absorption due to the electronic transitions, described by
4. Results
Data for the alumina film and SLG substrate were fit with general oscillator models, and parameters for these models were kept fixed for further data analysis. Temperature dependence for these layers is neglected; the thermo-optic coefficient of SLG has been shown to be approximately 5 × 10−6 K−1 [27], too small to impact the fit for the GST film in the temperature range of interest, while that of alumina is larger, approximately 5 × 10−4 K−1 [28], but still too small to have an observable impact given that the alumina layer is only 12 nm thick. Next, SE data for GST films in their amorphous and crystalline states as well as partially crystallized states were obtained, and Ψ and Δ were fit based on the model described in Sec. 3. Best-fit parameters for amorphous and crystalline films and the resulting optical constants are provided. Then, it is shown how optical constants for intermediate states can be determined. Finally, an estimation for the activation energy for crystallization is obtained.
4.1 Optical constants of amorphous and crystalline GST
SE was performed on a single GST film, both an amorphous state before heating and a crystalline state resulting from a thermally-induced phase change, and a fit was determined based on the model for complex permittivity described by Eq’s (2)–(7). For the crystalline state, the presence of the rho-tau oscillator indicates the importance of free carrier effects.
While data was collected for the range of 190-30,000 nm, when fitting Ψ and Δ, the inclusion of data for wavelengths less 350 nm resulted in a poor fit, indicating that the model does not accurately capture GST’s properties in this range. Therefore, for the purpose of accurately fitting data over the maximum range, these shorter wavelengths were neglected, and optical constants were determined for the wavelength range of 350-30,000 nm
For the sample analyzed here, the best fit for the film’s thickness in its amorphous state, ta, was 97.1 nm and in its crystalline, tc, state was 87.7 nm, representing a 9.7% reduction in thickness, consistent with previous observations that indicated that GST’s volume decreases by approximately 10% when crystallized [13]. The best-fit parameters determined from this sample are shown in Table 1. Measured values and fits to Ψ and Δ are included in supplemental document Supplement 1, Figs S1-S4.
Table 1. Fit Parameters for Amorphous and Crystalline GST
Calculated values for n and k are shown in Fig. 1. The main plot shows data for a range in λ of 350-5,000 nm, while the inset shows data for the full range, up to 30,000 nm. The underlying data for n and k as a function of wavelength, λ, is available in CSV format in document Data File 1. The amorphous film exhibits a peak in n of 4.463 at λ≈950 nm, and the crystalline film exhibits a peak in n of 6.491 at λ≈1,430 nm. Beyond a wavelength of 5,000 nm both the amorphous and crystalline films exhibit relatively constant values for n, 3.7 and 5.3 respectively, representing a Δn of 1.6. For the amorphous film, k is approximately zero beyond λ=1630 nm, while for the crystalline film, k has a minimum near 2,300 nm and increases nearly linearly with λ beyond this point.
Fig. 1. Calculated n and k. Values for the amorphous film are shown as solid lines and for the crystalline film as dashed lines. The inset shows data for the full λ range, up to 30,000 nm.
4.2 Optical constants of intermediate crystallization states
In addition to determining the optical constants of GST films in their amorphous and crystalline states, it is useful to determine their properties in intermediate crystallization states where some fraction of the material’s volume, fc, has been crystallized and the remaining part is amorphous. In order to do so, a linear effective medium approximation (EMA), is assumed. The results are not sensitive to the choice of EMA model. Thus, while a more sophisticated model such as the Bruggeman EMA could be applied, we use the linear EMA as a fast and adequate method to interpolate between crystal states’ dielectric functions to determine the optical constants of partially crystallized films. Given the assumption of an EMA, the thickness of a partially crystallized film is taken to decrease linearly with respect to fc. If ta and tc are the measured values of a film’s thickness in its amorphous and crystalline phase respectively, then a partially crystallized film’s thickness, t, can be expressed as t = ta-fc × (ta-tc). This relationship between thickness and fc is assumed when fitting the data.
Ideally, an SE measurement is repeated at multiple incident angles to provide data near the pseudo-Brewster angle, i.e. the angle at which reflection from a material with a complex index of refraction is minimized for p-polarized light [29], maximizing the difference between Rp and Rs. However, introducing a rotating compensator in front of the analyzer for both ellipsometers enables accurate SE measurement at various angles by altering the output polarization state. In this work, multiple angles are used for room temperature measurements, but for measurements at elevated temperatures, the heat cell geometry permits only single-angle measurements. However, in this case, models for amorphous and crystalline films’ properties have already been established based on room temperature measurements, and these models may be used as a starting point for the elevated temperature samples, making the single-angle measurements sufficient. Furthermore, adding more angles typically provides repeated information for isotropic samples. Thus, the good seed values of the fit parameters and the isotropic nature of the GST films ensure accurate determination of the optical constants at elevated temperatures.
For these measurements, note that a particular temperature should not be taken to be correlated in all cases with a given value of fc. The value of fc will depend on the film’s thermal history, i.e. its time and temperature, at elevated temperature sufficiently close to the phase transition temperature. Instead the temperatures shown here, given by the heating schedule shown in Sec. 2, are used to access intermediate crystallization states and demonstrate the utility of applying a linear EMA to model these films.
Data for fc and t/ta as a function of T are shown in Fig. 2. fc and t/ta were also measured at T = 25 °C prior to heating to higher temperatures and found to be 0% and 1.0 respectively. At temperatures beyond T = 120 °C, fc increases and t/ta decreases, both in a sigmoidal manner to values of 100% and 0.903 respectively, with a transitioned centered near T = 145 °C. As a check, SE was performed again after T was ramped back down to 25 °C, and fc and t/ta were measured to have the values of a fully crystallized film, 100% and 0.903 respectively.
Fig. 2. fc (left vertical axis, black symbols and lines) and t/ta (right vertical axis, green symbols and lines) as a function of T. Note that these trends depend on the particular heating process adopted in this paper.
Next, the linear EMA is applied to partially crystallized films in order to determine their optical constants. Figures 3 and 4 show plots for n and k respectively as a function of λ for films at various values of T throughout the transition.
Fig. 3. Values for n versus λ for various values of T throughout the transition. The lowermost and uppermost curves show values for T = 120 °C and 158 °C respectively, and the other plots show results for T = 138-152 °C in 2 °C increments.
Fig. 4. Values for k versus λ for various values of T throughout the transition. The lowermost and uppermost curves show values for T = 120 °C and 158 °C respectively, and the other plots show results for T = 138-152 °C in 2 °C increments.
These results indicate that intermediate states are readily accessible with carefully controlled heating. It is therefore possible to anneal a GST film to a state where, for example, a desired value for n for a given value of λ is reached.
5. Activation energy
Finally, the analysis described above—treating the GST with an EMA and extracting fc—is applied to obtain an estimate of the activation energy for crystallization of GST—a measure of the minimum energy per molecule required to cause the phase transition. To do so, samples are held in the heat cell at one of several fixed temperatures, SE is performed repeatedly at fixed time intervals, and the EMA model is applied to determine fc at each step. Figure 5 shows fc as a function of t.
Fig. 5. fc as a function of elapsed t where the time is taken to be the midpoint of a given measurement.
For the sample held at 140 °C, fc increases nearly linearly whereas for the 144 °C and 148 °C, a roll off is observed as the amorphous phase is depleted. It is unclear why fc does not approach unity, but this may be the result of small compositional variations within the film that cause spatial variation in transition temperature, or it may indicate a change in crystallization dynamics as the phase change progresses. This data may be understood by applying the Avrami equation, a relation that is applied to model phase transitions [30]. The equation is derived from a sigmoidal function,
where kc is the reaction rate of crystallization. The equation may be rewritten asFig. 6. The Avrami relation showing ln(-ln[1-fc(t)]) as a function of ln(t). The dashed lines indicate linear fits. The inset shows an Arrhenius plot based on their slopes.
From the intercepts, values of ln(kc) of −12.54, −12.37, and −10.49 are obtained for T = 140 °C, 144 °C, and 148 °C respectively. When ln(kc) is plotted as a function of 1/T, this is the well-known Arrhenius relation, with slope -Ea/kB where Ea is the activation energy and kB is the Boltzmann constant. In this case, we obtain a value of Ea = 3.8 ± 1.9 eV, with uncertainty reported for one standard deviation. As discussed in detail by Choi et al., most reported values of Ea for GST with slow heating rates (under 40 °C/min) or isothermal conditions lie in the range of 2.2-3.0 eV [31]. The value reported in this work is somewhat larger, but the uncertainty in the measurement is large; further work is required to obtain an accurate value of Ea by the ellipsometric method used here. In principle, additional measurements at other values of T could be carried out and should reduce the uncertainty. However, in this work, the authors were limited by the number of samples deposited under identical conditions. Nevertheless, these results serve as a demonstration that the proposed method can have practical applications and, with more data points, could be applied to measure Ea with lower uncertainty.
6. Conclusions
In this paper, SE was performed on GST in its amorphous and crystalline states in a spectral range of 350-30,000 nm. Both states were modeled with a general oscillator model, and n(λ) and k(λ) were obtained. Samples of GST were heated in situ in a heat cell and measurements were carried out at intermediate states throughout the amorphous to crystalline phase transition, and it was shown that a linear EMA model can be applied to determine film thickness, fractional crystallinity, and the film’s optical constants in intermediate states. This method was then applied to measure the activation energy for the amorphous to crystalline phase transition in GST, obtaining a value of Ea = 3.8 ± 1.9 eV. As the use of phase change materials in photonics continues to increase, the authors hope the methods demonstrated in this work can be applied to model a variety of phase change materials.
Funding
U.S. Naval Research Laboratory (6.2 base funding); FESR o FSE, PON Ricerca e Innovazione 2014-2020 (DM 1062/2021).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Data File 1.
Supplemental document
See Supplement 1 for supporting content.
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