^{1}, M. M. Aziz

^{2}, A. Shalini

^{1}, C. D. Wright

^{2}and R. J. Hicken

^{1}

### Abstract

The phase transition between the amorphous and crystalline states of Ge_{2}Sb_{2}Te_{5} has been studied by exposure of thin films to series of 60 femtosecond (fs) amplified laser pulses. The analysis of microscope images of marks of tens of microns in size provide an opportunity to examine the effect of a continuous range of optical fluence. For a fixed number of pulses, the dependence of the area of the crystalline mark upon the fluence is well described by simple algebraic results that provide strong evidence that thermal transport within the sample is one-dimensional (vertical). The crystalline mark area was thus defined by the incident fs laser beam profile rather than by lateral heat diffusion, with a sharp transition between the crystalline and amorphous materials as confirmed from line scans of the microscope images. A simplified, one-dimensional model that accounts for optical absorption, thermal transport and thermally activated crystallization provides values of the optical reflectivity and mark area that are in very good quantitative agreement with the experimental data, further justifying the one-dimensional heat flow assumption. Typically, for fluences below the damage threshold, the crystalline mark has annular shape, with the fluence at the centre of the irradiated mark being sufficient to induce melting. The fluence at the centre of the mark was correlated with the melt depth from the thermal model to correctly predict the observed melt fluence thresholds and to explain the closure and persistence of the annular crystalline marks as functions of laser fluence and pulse number. A solid elliptical mark may be obtained for smaller fluences. The analysis of marks made by amplified fs pulses present a new and effective means of observing the crystallization dynamics of phase-change material at elevated temperatures near the melting point, which provided estimates of the growth velocity in the range 7-9 m/s. Furthermore, finer control over the crystallization process in phase-change media can be obtained by controlling the number of pulses which, along with the laser fluence, can be tailored to any medium stack with relaxed restrictions on the thermal properties of the layers in the stack.

We gratefully acknowledge the financial support of the UK Engineering and Physical Sciences Research Council (EPSRC) via Grant No. EP/F015046/1. We would also like to thank Dr. Andrew Pauza of formerly Plarion Ltd. for supplying the phase-change disk samples.

I. INTRODUCTION

II. EXPERIMENTAL DETAILS

III. EXPERIMENTAL RESULTS

A. Mark area and laser fluence

IV. HEAT FLOW AND CRYSTALLIZATIONMODELS

A. Simulation results

V. DISCUSSION

VI. CONCLUSIONS

### Key Topics

- Crystallization
- 66.0
- Reflectivity
- 49.0
- Amorphous state
- 30.0
- Mode locking
- 24.0
- Crystal growth
- 20.0

## Figures

Optical microscope image of the marks obtained after excitation by single pulses of 60 fs duration. The value of the spatially averaged pulse fluence *F _{avg} * (mJ/cm

^{2}) is shown.

Optical microscope image of the marks obtained after excitation by single pulses of 60 fs duration. The value of the spatially averaged pulse fluence *F _{avg} * (mJ/cm

^{2}) is shown.

Optical microscope images of the marks obtained after excitation by a series of 2000 pulses of 60 fs duration. The value of the spatially averaged pulse fluence *F _{avg} * (mJ/cm

^{2}) is shown.

Optical microscope images of the marks obtained after excitation by a series of 2000 pulses of 60 fs duration. The value of the spatially averaged pulse fluence *F _{avg} * (mJ/cm

^{2}) is shown.

The change in reflectance of Ge_{2}Sb_{2}Te_{5} films *ΔR*/*R _{am} * (defined as

*ΔR*=

*R−R*where

_{am}*R*is the measured reflectance and

*R*is the reflectance of the as-deposited amorphous material) after exposure to 2000 pulses of 60 fs pulse width is shown for different values of

_{am}*F*(the spatially averaged fluence). Spatial profiles of marks recorded for

_{avg}*F*values of 3.50 and 5.83 mJ/cm

_{avg}^{2}are shown in panels (a) and (b) respectively. Panel (c) shows the measured variation of the maximum reflectance within the area of the mark (squares), the reflectance at the centre of the mark (circles), and relative change of reflectivity measured by the probe beam (triangles) compared with the theoretical reflectance change at the centre of the mark (solid and dashed lines). The dependence of the area of thehigh reflectance region upon

*F*is shown in (d), where the black squares are experimental data, the red solid curve is from the geometrical fit and the dashed lines are calculated from the crystallization model.

_{avg}The change in reflectance of Ge_{2}Sb_{2}Te_{5} films *ΔR*/*R _{am} * (defined as

*ΔR*=

*R−R*where

_{am}*R*is the measured reflectance and

*R*is the reflectance of the as-deposited amorphous material) after exposure to 2000 pulses of 60 fs pulse width is shown for different values of

_{am}*F*(the spatially averaged fluence). Spatial profiles of marks recorded for

_{avg}*F*values of 3.50 and 5.83 mJ/cm

_{avg}^{2}are shown in panels (a) and (b) respectively. Panel (c) shows the measured variation of the maximum reflectance within the area of the mark (squares), the reflectance at the centre of the mark (circles), and relative change of reflectivity measured by the probe beam (triangles) compared with the theoretical reflectance change at the centre of the mark (solid and dashed lines). The dependence of the area of thehigh reflectance region upon

*F*is shown in (d), where the black squares are experimental data, the red solid curve is from the geometrical fit and the dashed lines are calculated from the crystallization model.

_{avg}The dependence of crystallisation upon the number of 60 fs pulses and *F _{avg} *. (a) microscope images of marks where the values of

*F*have been labelled and the number of pulses varies from 200 at the far left to 600 at the far right with increment of 50. In (b), (c) the dependence of the area of the crystallised region, and the relative change of reflectivity, at the high reflectivity crystalline region, respectively upon the number of pulses is shown for different

_{avg}*F*values. The dashed lines in (b) are the calculated mark areas using the thermal and crystallization models. (d) Calculated optical reflectance curves as a function of pulse number corresponding to the experimental curves in (c) from the crystallization model for two reaction orders,

_{avg}*n*= 1, 3.

The dependence of crystallisation upon the number of 60 fs pulses and *F _{avg} *. (a) microscope images of marks where the values of

*F*have been labelled and the number of pulses varies from 200 at the far left to 600 at the far right with increment of 50. In (b), (c) the dependence of the area of the crystallised region, and the relative change of reflectivity, at the high reflectivity crystalline region, respectively upon the number of pulses is shown for different

_{avg}*F*values. The dashed lines in (b) are the calculated mark areas using the thermal and crystallization models. (d) Calculated optical reflectance curves as a function of pulse number corresponding to the experimental curves in (c) from the crystallization model for two reaction orders,

_{avg}*n*= 1, 3.

(a) Microscope image of crystallised mark obtained using 2000 pulses of 60 fs duration with *F _{avg} * = 3.50 mJ/cm

^{2}. (b) Microscope image after re-amorphization using a single 60 fs pulse with

*F*= 9.33 mJ/cm

_{avg}^{2}.

(a) Microscope image of crystallised mark obtained using 2000 pulses of 60 fs duration with *F _{avg} * = 3.50 mJ/cm

^{2}. (b) Microscope image after re-amorphization using a single 60 fs pulse with

*F*= 9.33 mJ/cm

_{avg}^{2}.

Calculated transient temperature distributions using the analytical model derived in this work for applied pump fluence of *F _{avg} * = 2.33 mJ/cm

^{2}over 60 fs. Plots (a) and (b) show the temperature distribution through the GST layer as a function of normalised thickness at different times when fully amorphous and fully crystalline respectively. Plots (c) and (d) are the calculated the transient temperatures at different points through the 20 nm thick, fully amorphous and fully crystalline GST layer respectively.

Calculated transient temperature distributions using the analytical model derived in this work for applied pump fluence of *F _{avg} * = 2.33 mJ/cm

^{2}over 60 fs. Plots (a) and (b) show the temperature distribution through the GST layer as a function of normalised thickness at different times when fully amorphous and fully crystalline respectively. Plots (c) and (d) are the calculated the transient temperatures at different points through the 20 nm thick, fully amorphous and fully crystalline GST layer respectively.

Calculated average fluence *F _{avg} * (for a single laser pulse) required to induce melting at the centre of the irradiated region at increasing depths into the GST layer for different crystalline volume fractions. The melting threshold fluence

*F*is indicated at the average fluence of 4.66 mJ/cm

_{melt}^{2}observed from measurements and calculations in Figs. 3(c) and 3(d).

*z*= 0 nm corresponds to the surface of the GST layer. The required fluence for melting was calculated using the theoretical heat flow model which does not account for melting and movement of the melting front. This leads to the exaggerated large values of

*F*near the capping and under-layers (

_{avg}*z*= 0 and 20 nm respectively). In practice, the melting front would reach and make contact with these interfaces.

Calculated average fluence *F _{avg} * (for a single laser pulse) required to induce melting at the centre of the irradiated region at increasing depths into the GST layer for different crystalline volume fractions. The melting threshold fluence

*F*is indicated at the average fluence of 4.66 mJ/cm

_{melt}^{2}observed from measurements and calculations in Figs. 3(c) and 3(d).

*z*= 0 nm corresponds to the surface of the GST layer. The required fluence for melting was calculated using the theoretical heat flow model which does not account for melting and movement of the melting front. This leads to the exaggerated large values of

*F*near the capping and under-layers (

_{avg}*z*= 0 and 20 nm respectively). In practice, the melting front would reach and make contact with these interfaces.

Reflectance line scans along the semi-major axis of the marks shown in Fig. 4(a) produced using different number of 85 femtosecond pulses at *F _{avg} * = 4.20 mJ/cm

^{2}showing the growth of the crystalline material from the inner perimeter and central region of the annular rings with increasing pulse number.

Reflectance line scans along the semi-major axis of the marks shown in Fig. 4(a) produced using different number of 85 femtosecond pulses at *F _{avg} * = 4.20 mJ/cm

^{2}showing the growth of the crystalline material from the inner perimeter and central region of the annular rings with increasing pulse number.

Measurements of the inner diameters of the annuli in Fig. 4(a) for two fluences as functions of increasing laser pulse number. The straight lines fits reveal an estimate of the elevated temperature growth velocity assuming that the growth occurs over a 2 ns period from the application of a laser pulse, during which the maximum temperature reduces to the glass-transition temperature and the amorphous-to-crystalline interface displacements is at its steady-state value.

Measurements of the inner diameters of the annuli in Fig. 4(a) for two fluences as functions of increasing laser pulse number. The straight lines fits reveal an estimate of the elevated temperature growth velocity assuming that the growth occurs over a 2 ns period from the application of a laser pulse, during which the maximum temperature reduces to the glass-transition temperature and the amorphous-to-crystalline interface displacements is at its steady-state value.

Diagram illustrating the two-layer, semi-infinite model of the experimental stack used for evaluating the temperature distribution *T* _{1} in the GST layer. The laser beam energy absorption, identified by the power density term *g*, is limited to the thickness of the GST layer *d*.

Diagram illustrating the two-layer, semi-infinite model of the experimental stack used for evaluating the temperature distribution *T* _{1} in the GST layer. The laser beam energy absorption, identified by the power density term *g*, is limited to the thickness of the GST layer *d*.

## Tables

List of thermal and kinetic parameters for the Ge_{2}Sb_{2}Te_{5} and ZnS:SiO_{2} layers used in the calculations.

List of thermal and kinetic parameters for the Ge_{2}Sb_{2}Te_{5} and ZnS:SiO_{2} layers used in the calculations.

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