Rapid phase transition of a phase-change metamaterial perfect absorber

Tun Cao; Chenwei Wei; Robert E. Simpson; Lei Zhang; Martin J. Cryan

doi:10.1364/OME.3.001101

1. Introduction

Phase-change material (PCM) technology represents one of the best candidates for future electronic FLASH memories and is already in commonly used as the active layer in rewritable optical data storage media [1, 2]. PCMs have provided clearly commercial and technological advances for a universal memory by virtue of many advantages such as their nonvolatile nature, high read/write speeds, high scalability and long read/write endurance [3–5]. PCM memory operation, based on the reversible switching between amorphous and crystalline states is generally achieved by heating: photothermal heating in optical memory and electrical Joule heating in phase-change-random-access memory (PC-RAM) [3]. However, the application of PCMs requires fast crystallization. Crystallization times on the order of 10-100ns and ideally of less than 1ns are necessary for non-volatile PC-RAM to compete with the speed of volatile dynamic random access memory [6–8]. This has restricted the selection of PCMs and raises the question of how the crystallization speed be increased. Some works have addressed this issue and shown the possibility of achieving a speed faster than 100ns [9–12]. In particular, an optical method has been presented where the crystallization time of Ge₂Sb₂Te₅ under a focused laser irradiation is as short as 10ns [12], however this requires a high total optical power (~8mW) limiting its applications in the field of nanoscale device. Recently, Makino et al. experimentally showed that ultrafast phase change from amorphous into crystalline phases in Ge₂Sb₂Te₅ can be achieved using femtosecond pump-pulse pairs with a low energy of 1.46eV [13]. Here for the first time, we present that it is possible to increase the speed that energy is delivered to the Ge₂Sb₂Te₅ with a small optical injection power of 0.6mW focused into a spot of radius 10 μm corresponding to an intensity of 150 W/m², using a Metamaterial Perfect Absorber (MMPA). Our approach is based on the idea of utilizing the strong plasmon resonance of the MMPA to concentrate optical energy within the Ge₂Sb₂Te₅ layer.

It is well known that Metamaterials (MM) are capable of manipulating electromagnetic fields at an artificially engineered surface, producing effects such as left handed refraction [14] and focusing of emitted, reflected, or transmitted radiation in the thermal infrared band [15]. Metamaterial absorbers show a strong absorption of light, owing to strong localized plasmon resonances [16] and impedance matching to free space [17, 18]. For such a system the energy of absorbed light is converted into heat [19]. Therefore, the dielectric layer in a metamaterial absorber can reach a high temperature very rapidly at low incident optical powers. In particular, with the rapid development of nanotechnology, laser heated plasmonic systems have already shown potential applications in photothermal therapy [20], drug delivery [21], optical data storage [22] and reshaping of metal nanoparticles [23]. Thus, with such strong credentials in photothermal applications, it is more than reasonable to assume that metamaterial absorbers have much to offer in the area of PCMs.

In this work, to increase the rate of power delivery to the Ge₂Sb₂Te₅, we integrate Ge₂Sb₂Te₅ within the metamaterial absorber. The absorber is composed of an array of thin squares of Au separated from a continuous Au film by a Ge₂Sb₂Te₅ layer [24]. A heat model is constructed to investigate the temporal variation of the temperature of the Ge₂Sb₂Te₅ layer in the absorber. The model shows that the temperature of Ge₂Sb₂Te₅ can be raised from room temperature to > 900K in just 3.4ns with a low light power of 0.6mW in the metamaterial absorber. Such structures could be used to lower the power requirements for photonic devices based on a thermal phase change. Furthermore, our results also show that an absorber with a widely tunable spectrum can be obtained by switching between the amorphous and crystalline states of Ge₂Sb₂Te₅.

2. Structure and design

Our metamaterial absorber consists of two Au layers separated by a PCM layer. The physical origin of near perfect absorbance is the localization of electric and magnetic dipole resonances in the metal-dielectric-metal structure. Here the PCM is selected as Ge₂Sb₂Te₅ [25]_. Figs. 1(a)-1(c) show a schematic drawing of the tri-layer metamaterial absorber, where the lattice constant is L = 1000 nm, the side length of the Au square is d_x = d_y = 900nm, the thickness of the top Au layer is 40 nm, the Ge₂Sb₂Te₅ layer is 40 nm and the bottom Au layer is 80 nm in order to prevent any transmission through the structure [26]. A single unit can be treated as an optical resonator. The unit cells are periodically arranged to form a two-dimensional square lattice in both the x and y directions. Furthermore, the thick Au bottom layer also interacts with the upper Au squares to give rise to a close loop of displacement current (J_D) and localize an electromagnetic (EM) field within the Ge₂Sb₂Te₅ dielectric layer. The whole structure resides on a 200μm thick BK7 glass. Au is selected as the metal due to its stability and low ohmic loss. The geometry of the Au pattern and the thickness of the sandwich layers have been chosen to allow for both impedance matching and strong absorbance [27]. For comparison, a 40nm thick Ge₂Sb₂Te₅ dielectric layer is also shown in Figs. 1(d)-1(e). The simulation is performed by commercial software COMSOL, which is based on the Finite Element Method (FEM). The dielectric properties of Au are described by a drude-type dielectric function,

Fig. 1 (a) Schematic of the metamaterial absorber and the incident light polarization configuration. The thicknesses of Au squares, Ge₂Sb₂Te₅ spacer and Au mirror are 40nm, 40nm and 80nm respectively. The lattice constant in both x and y-directions is L = 1000nm and square dimension is dx = dy = 900nm. The whole structure resides on a BK7 silica glass with 200μm thickness. β is a cross-section plane of the structure. (b) Side view of the absorber. (c) Top view of the absorber. (d) Schematic of the single Ge₂Sb₂Te₅ dielectric layer of 1000nm x 1000nm x 40nm deposited on a BK7 silica glass and the incident light polarization configuration. The thicknesses of Ge₂Sb₂Te₅ and BK7 substrate is 40nm and 200μm respectively. β is a cross-section plane of the structure. (e) Side view of the Ge₂Sb₂Te₅ dielectric layer.

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ε (ω) = 1 - \frac{ω_{p}^{2}}{[ω (ω + i ω_{c})]}

where ω_p = 1.37x10¹⁶ Hz is the plasma frequency and ω_c = 4.08x10¹³ Hz is the collision frequency for bulk Au [28]. Both of the structures are excited by a super continuum light source with a wavelength range from 2000 to 3000 nm, propagating along the negative z direction with the E field polarized in the x direction as shown in Fig. 1(a). The light source has a repetition rate f_r = 25kHz and pulse duration of 2.6ns.The intensity of the incident light beam on the structure has a Gaussian profile expressed as [23],

F_{l} (r) = \frac{2 P_{0}}{π w^{2} f_{r}} \exp (- \frac{2 r^{2}}{w^{2}})

where P₀ = 0.6mW is the total power of the injection light, f_r = 25kHz is the pulse repetition rate, r is the distance from the beam center, w = 10μm is Gaussian beam waist. Perfectly match layer (PML) absorbing boundaries are applied in the z direction and periodic boundaries are used for a unit cell in the x-y plane. The frequency dependent Absorbance, A(ω) can be calculated from [18],

A (ω) = 1 - R (ω) - T (ω)

R (ω) = {| r_{1} |}^{2}

T (ω) = {| t_{1} |}^{2}

where R(ω) is reflectance, T(ω) is transmittance, r₁is the complex reflection coefficient and t₁ is the complex transmission coefficient

The real, ɛ₁(ω) and imaginary, ɛ₂(ω) parts of the dielectric function of Ge₂Sb₂Te₅ at different phases are obtained from the experimental data in [25] and for the mid-infrared (M-IR) spectral range the dielectric function is shown in Fig. 2; as can be seen there is a very large change in the dielectric function’s real component. The dielectric constant of Ge₂Sb₂Te₅ is very dispersive and has a non-negligible imaginary part. It also changes considerably during the reversible structural transformation from amorphous to crystalline. Different PCMs can display similar behavior in other parts of the spectrum.

Fig. 2 Dielectric constant (a) ɛ₁(ω) vs wavelength, (b) ɛ₂(ω) vs wavelength for both amorphous and crystalline phases of Ge₂Sb₂Te₅.

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3. Results and Discussions

Figure 3(a) presents the reflectance R(ω) and Fig. 3(b) presents the absorbance A(ω) of the structures shown in Figs. 1(a) and 1(d) respectively for normal incidence in the amorphous state. It clearly shows a strong resonance peak at 2300nm with near unity absorbance owing to the impedance matching and nearly zero transmittance. Whilst a single Ge₂Sb₂Te₅ layer has a much lower absorbance due to the absence of the plasmon resonance, its absorbance curve is nearly flat across the whole spectrum. The result shows that the design of the Au square array on the Ge₂Sb₂Te₅-Au film is a highly efficient device at harvesting optical energy in the M-IR.

Fig. 3 3D-FEM simulation of spectrum of (a) reflectance, (b) absorbance of both a metamaterial absorber and a single Ge₂Sb₂Te₅ layer for the amorphous state at normal incidence.

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In order to observe the underlying mechanism of the absorbance, it is instructive to examine the distribution of the electromagnetic field and the displacement current (J_D) for the resonant mode for the different structures along a cross-section plane, β shown in Fig. 1. For example, Figs. 4(a)-4(c) show the field distributions and J_D of the metamaterial absorber at the absorbance peak wavelength of 2300nm for the amorphous phase. Here, the arrows represent J_D whereas the color represents the magnitude of the EM field intensities. The total electric field intensity distribution,

Fig. 4 3D-FEM simulation of (a) total electric field intensity distribution, (b) total magnetic field intensity distribution, (c) displacement current (JD) distribution for metamaterial absorber with amorphous phase at normal incident angle where λ = 2300nm; Simulation of (d) total electric field intensity distribution, (e) total magnetic field intensity distribution, (f) displacement current (J_D) distribution for single Ge₂Sb₂Te₅ layer with amorphous phase at normal incident angle where λ = 2300nm

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E = \sqrt{E_{x}^{2} + E_{y}^{2} + E_{z}^{2}}

associated with A(ω) = 0.91 at λ = 2300nm is shown in Fig. 4(a). It clearly shows that the electric field is concentrated in both the Ge₂Sb₂Te₅ layer and the area between the Au squares. The total magnetic field intensity distribution,

H = \sqrt{H_{x}^{2} + H_{y}^{2} + H_{z}^{2}}

shown in Fig. 4(b) indicates that the significant magnetic response can be generated in the Ge₂Sb₂Te₅ layer since J_D in both top Au squares and the bottom Au layer are opposite to each other as presented in Fig. 4(c) [27]. Therefore, the high absorbance effect in the metamaterial is due to the excitation of localized magnetic and electric dipole resonances [25, 29].

The patterns of EM field and J_D associated with A(ω) = 0.44 at λ = 2300nm for the amorphous phase of a monolithic Ge₂Sb₂Te₅ layer are shown in Figs. 4(d)-4(f) respectively. Figures 4 (d) and 4(e) show that both E and H fields are weakly trapped in the Ge₂Sb₂Te₅ layer, and the loop of J_D no longer exists as presented in Fig. 4(f). It indicates that the monolithic Ge₂Sb₂Te₅ layer cannot efficiently localize the light without the electric and magnetic resonance dipoles induced by the plasmon resonance. The high absorbance in the metamaterial absorber suggests that it would allow rapid heating of the PCM thus permitting efficient tuning of the Ge₂Sb₂Te₅-Metamaterial absorber properties. To show this, a heat transfer model is used to investigate the temporal variation of temperature of Ge₂Sb₂Te₅ layer for different structures using the Finite Element Method (FEM) solver within COMSOL. The material thermal properties used for the simulation are summarized in Table 1. The thermal conductivity of Ge₂Sb₂Te₅ changes with the temperature and this is presented elsewhere [30]. In this simulation, the thermal energy absorbed by one unit cell is defined as [23],

Table 1. Material thermal properties used in the Heat transfer model

View Table

E_{t h} (r) = R_{a} \times L^{2} \times F_{l} (r)

where L = 1000nm is the lattice constant of the metamaterials, R_a is 0.78 for the metamaterials absorber and 0.38 for the single Ge₂Sb₂Te₅ dielectric layer respectively, derived from the product between the light source power density spectrum and the absorbance spectrum, shown in Fig. 3(b), at the resonant wavelength of 2300nm .The heat source power for different structures is then described by,

Q_{s} (r, t) = E_{t h} (r) \frac{1}{\sqrt{π} τ} \exp (- \frac{{(t - t_{0})}^{2}}{τ^{2}})

where τ = 1.5ns is the time constant of the light pulse, t₀ = 3ns is the time delay of the pulse peak. Figure 5(a) shows the heat source power: Q_s(r,t) at the wavelength of 2300nm for the two structures, where the structures are located at the center of a Gaussian light beam, and Fig. 5(b) shows the comparison of temperatures in Ge₂Sb₂Te₅ layer for the two structures.

Fig. 5 (a) 3D-FEM simulation of heat power irradiating on metamaterials absorber and single Ge2Sb2Te5 layer with amorphous phase located at the beam center, where the solid line presents the heat power irradiating on the metamaterial absorber, the dash line presents the heat power irradiating on the single Ge₂Sb₂Te₅ layer. (b)The solid line stands for the temperature of Ge₂Sb₂Te₅ layer in metamaterials absorber during one pulse and the dash line presents temperature of the single Ge₂Sb₂Te₅ dielectric layer during one pulse. (c)The cross section view of the unit cell of metamaterials absorber, where the color image indicates the temperature distribution and the arrows indicate the heat flux at 3.4ns. (d)The cross section view of the single Ge₂Sb₂Te₅ layer, where the color image indicates the temperature distribution and the arrows indicate the heat flux at 3.4ns.

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Figure 5(b) shows that the temperature of Ge₂Sb₂Te₅ in the metamaterial absorber can reach 900 K (the melting point of Ge₂Sb₂Te₅) after 3.4 ns and a maximum of 981K after 4.2 ns under a small incident power of 0.6mW. Due to heat dissipation and radiation to the surroundings, the temperature starts dropping after 4.2ns before the next pulse arrives. The highest temperature of the monolithic Ge₂Sb₂Te₅ layer is nearly 100 K lower at 812K under the same incident power of 0.6mW. A large temperature difference of 169K at 4.2ns between the two structures is clearly shown in Fig. 5(b); thus showing the usefulness of a metamaterial absorber for increasing the rate at which heat is delivered to Ge₂Sb₂Te₅. The temperature distribution of the two structures at 3.4ns is shown in Figs. 5(c) and 5(d) respectively. One can observe that the temperature within Ge₂Sb₂Te₅ in the MMPA is much higher than the single Ge₂Sb₂Te₅ dielectric layer. In both of the structures, the dominant temperature gradient is along the same direction of incident light, indicating that BK7 silica substrate is an effective heat sink [23].

A study of the tunable effects of the metamaterial absorber incorporating a PCMs is shown in Fig. 6, the stimulated reflectance R(ω) and absorbance A(ω) of the structure for normal incidence at different states of Ge₂Sb₂Te₅ is presented. In Fig. 6(b), it can be seen that the absorbance peak shifts towards longer wavelength (from 2300nm to 2680nm) when the phase of Ge₂Sb₂Te₅ switches from amorphous to crystalline which is a 16% tuning range. The absorbance A(ω) exceeds 0.5 in the wavelength ranging from 2270nm to 2340nm for amorphous Ge₂Sb₂Te_5. In particular, a nearly perfect absorbance (A(ω) = 0.91) is achieved around 2300nm. In contrast, a maximum absorbance of 0.3 is obtained at 2680nm for crystalline Ge₂Sb₂Te₅ in addition to a shift, owing to a reduction in the impedance matching of the structure to vacuum at λ = 2680nm [32]. Moreover, we also find that the resonant peak broadens which we believe is due to increased damping of the plasmon resonance [33]_. Therefore an absorber with a widely tunable spectrum can be obtained by switching between the amorphous and crystalline states of Ge₂Sb₂Te₅. Furthermore by partially crystallizing the PCM it will be possible to control the wavelength of the absorbance between 2300 nm and 2680 nm. However, the narrow absorbance bandwidth of the proposed MMPA still makes it challenging to become a high quality metamaterial absorber. To solve this problem, the possibility of a tunable multi-band or broadband metamaterial perfect absorber based on the Ge-Sb-Te system will be investigated in the future [34].

Fig. 6 3D-FEM simulation of spectrum of (a) reflectance, (b) absorbance for different phases of Ge₂Sb₂Te₅ at normal incidence

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To further understand the absorption mechanism in the MMPA it is useful to study the dispersion of the SPP modes within the multilayer structure. Both the internal and external SPP modes in the MMPA are similar to those of the same structure without resonant elements i.e. metal-dielectric-metal (MDM) films [35, 36]. In the MDM film case the internal SPP mode resonates on the inner surfaces of the metal layers and the external SPP mode resonates on the outer surfaces of the metal layers. Therefore, the SPP dispersion relation of the MMPA can be approximately approached by that of the MDM sheets. In order to study the influence on the dispersion relations of the surface plasmon polaritons (SPPs) caused by the phase transition between the amorphous and crystalline, in Fig. 7 we have calculated the SPP modes dispersion relation of the Au- Ge₂Sb₂Te₅-Au trilayer with the top Au film thickness d₁ = 40nm, middle Ge₂Sb₂Te₅ film thickness d₂ = 40nm and bottom Au film thickness d₃ = 80nm, using the commercial software Lumerical FDTD Solution based on Finite Different Time Domain (FDTD) method. The transmission spectrum of the MMPA calculated by COMSOL is depicted together with the dispersion relation of the Au-Ge₂Sb₂Te₅-Au film.

Fig. 7 Representation of the dispersion relation of the Au-Ge2Sb2Te5-Au trilayers (left) and the absorbance of the MMPA (right) for both (a) amorphous Ge₂Sb₂Te₅ and (b) crystalline Ge₂Sb₂Te₅

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Recalling the coupling condition from light to SPP modes [36], it can be seen that the (2, 0) internal resonance of the Au-Ge₂Sb₂Te₅-Au trilayer is excited at 2080nm associated with the amorphous Ge₂Sb₂Te₅ in Fig. 7(a).This internal SPP resonance can then red shift to 2980nm when the amorphous state changes to the crystalline state shown in Fig. 7(b). We also observe that the two internal (2, 0) modes appear at 2080nm and 2980nm in the simple MDM structure don’t perfectly match the two absorbance peaks at the resonance wavelength of 2300nm and 2680nm in the MMPA for both the amorphous and crystalline phases, respectively. This difference is because the dispersion relation of the SPP modes used as matching condition doesn’t include the resonant squares, which cause a resonance shift [36].

4. Conclusion

In summary, we have theoretically shown that the rate that energy can be delivered to the prototypical data storage material, Ge₂Sb₂Te₅ can be increased by using a metamaterial absorber constructed from a two-dimensional periodic array of Au squares on a Ge₂Sb₂Te₅/Au glass substrate in the mid-infrared wavelength region. The EM field can be trapped efficiently inside the proposed absorber at the resonant modes. Furthermore, by virtue of the perfectly absorbing PCM-Metamaterial structure, our model predicts that Ge₂Sb₂Te₅ can reach 900K in just 3.4 ns with a low optical power of 0.6mW focused into a spot of radius 10 μm. In contrast, the monolithic Ge₂Sb₂Te₅ layer cannot obtain its melting temperature, which is required for switching its optical properties, under the same conditions of optical illumination. The absorbance spectra of metamaterial’s perfect absorber show a large wavelength shift of 16% by switching between the amorphous and crystalline states of Ge₂Sb₂Te₅.This work presents a new mean to achieve fast and energy efficient optical devices based on PCMs, and can find numerous applications in energy harvesting, biology and optical storage.

Acknowledgments

We acknowledge the financial support from National Natural Science Foundation of China (Grant No. 61172059), Ph.D Programs Foundation of Ministry of Education of China (Grant No. 20110041120015), Postdoctoral Gathering Project of Liaoning Province (Grant No. 2011921008), and The Fundamental Research for the Central University (Grant No. DUT12JB01).

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	Special heat capacity Cs(J/(kg·K))	Density ρ(kg/m³)	thermal conductivity k(W/(m·k))
gold	129 [31]	19300 [31]	317(bulk) [31], 165(thickness = 80nm) [31], 110(thickness = 40nm) [31]
GST	220 [30]	6150 [30]	Temperature dependence [30]
silica	741 [23]	2200 [23]	1 [23]
air	1 [23]	$\frac{353 [K]}{T}$ [23]	0.03 [23]

Rapid phase transition of a phase-change metamaterial perfect absorber

Abstract

1. Introduction

2. Structure and design

3. Results and Discussions

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (9)

Optical Materials Express