Dielectric properties of amorphous phase-change materials

The dielectric function of several amorphous phase-change materials has been determined by employing a combination of impedance spectroscopy (9 kHz–3 GHz) and optical spectroscopy from the far- $(20\mathrm{c}{\mathrm{m}}^{-1}$, 0.6 THz) to the near- $(12000\mathrm{c}{\mathrm{m}}^{-1}$, 360 THz) infrared, i.e., from the DC limit to the first interband transition. While phase-change materials undergo a change from covalent bonding to resonant bonding on crystallization, the amorphous and crystalline phases of ordinary chalcogenide semiconductors are both governed by virtually the same covalent bonds. Here, we study the dielectric properties of amorphous phase-change materials on the pseudobinary line between GeTe and $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$. These data provide important insights into the charge transport and the nature of bonding in amorphous phase-change materials. No frequency dependence of permittivity and conductivity is discernible in the impedance spectroscopy measurements. Consequently, there are no dielectric relaxations. The frequency-independent conductivity is in line with charge transport via extended states. The static dielectric constant significantly exceeds the optical dielectric constant. This observation is corroborated by transmittance measurements in the far infrared, which show optical phonons. From the intensity of these phonon modes, a large Born effective charge is derived. Nevertheless, it is known that crystalline phase-change materials such as GeTe possess even significantly larger Born effective charges. Crystallization is hence accompanied by a huge increase in the Born effective charge, which reveals a significant change of bonding upon crystallization. In addition, a clear stoichiometry trend in the static dielectric constant along the pseudobinary line between GeTe and $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ has been identified.

Figure 1

Electric field distribution in in-plane structures (a) and in sandwich structures (b). Equivalent circuit for sandwich structures (c). $C_1$ and $R_1$ refer to the capacitance and the resistance of the PCM layer shown in (d), whereas $R_0$ denotes the contact resistance. (d) Cross-sectional structure of the impedance spectroscopy samples.

Figure 2

Temperature dependence of the DC conductivity ${\sigma }_{\mathrm{DC}}$ derived from an amorphous $\mathrm{G}{\mathrm{e}}_3\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_6$ sandwich structure. The activation energy $E_A$ and the preexponential factor ${\sigma }_0$ according to Eq. (7) are 0.38 eV and $\sim 1236\mathrm{S}/\mathrm{cm}$, respectively.

Figure 3

Dielectric permittivity ${\varepsilon }_1$ as a function of frequency $f$ for amorphous $\mathrm{G}{\mathrm{e}}_2\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_5$ obtained from different device geometries. Neither doubling the layer thickness $d$ nor doubling the capacitor area $A$ has a significant impact on the obtained permittivity. The inset graph displays $C/{\varepsilon }_0$ vs $A/d$. As expected, the data points obtained from different geometries are located on a straight line through the origin, where the slope of 33.4 corresponds to ${\varepsilon }_1$.

Figure 4

The Nyquist plot displays the impedance spectroscopy data on 5 GeTe-$\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ PCMs. The solid lines correspond to fits according to the one-RC model defined by Fig. 1 and Eq. (4).

Figure 5

AC conductivity ${\sigma }_{\mathrm{AC}}$ of amorphous PCMs. In the entire frequency range, no frequency dependence is observed. This finding is in line with transport by extended states at the mobility edge.

Figure 6

Dielectric permittivity ${\varepsilon }_1$ of five amorphous GeTe-$\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ alloys. Section 3b explains the origin of the noise at low frequencies and the upturn at high frequencies. In the intermediate range, where reliable data could be acquired, no frequency dependence is discernible.

Figure 7

Static $\left({\varepsilon }_{\mathrm{st}}\right)$ and optical $\left({\varepsilon }_{\infty }\right)$ dielectric constants of amorphous ${(\mathrm{GeTe})}_{\left(1\text{−}x\right)}\text{−}{\left(\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3\right)}_x$ alloys from impedance spectroscopy and FTIR. While ${\varepsilon }_{\infty }$ depends only weakly on the stoichiometry, there is a marked surge in ${\varepsilon }_{\mathrm{st}}$ on increasing the $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ content.

Figure 8

Real and imaginary parts of the dielectric function obtained from the transmission spectra depicted in the Supplemental Material [40]. Pronounced phonon absorption is discernible below $9\mathrm{THz}\left(300\mathrm{c}{\mathrm{m}}^{-1}\right)$. Adding $\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ in the GeTe-$\mathrm{S}{\mathrm{b}}_2\mathrm{T}{\mathrm{e}}_3$ system induces a reduction of the phonon frequencies, probably a consequence of the Ge vs Sb mass difference. The extrapolation of the real part down to zero frequency reproduces the stoichiometry trend in ${\varepsilon }_{\mathrm{st}}$, which has already been observed by impedance spectroscopy in Fig. 6.