Research Article |
Corresponding author: Oleg A. Ruban ( myx.05@mail.ru ) © 2023 Andrey N. Aleshin, Oleg A. Ruban.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Aleshin AN, Ruban OA (2023) Estimation of the activation energy in the Ag/SnSe/Ge2Se3/W self-directed channel memristor. Modern Electronic Materials 9(3): 115-122. https://doi.org/10.3897/j.moem.9.3.113245
|
In this study, we conducted an investigation into the Ag/SnSe/Ge2Se3/W ionic memristor, focusing on the determination of activation energies associated with its two primary operational processes: the formation of conductive filaments and memristor degradation. To ascertain the electrical conductivity of the memristor in both its basic electronic states, a low resistance state and a high resistance state, we constructed current-voltage characteristics. The estimation of activation energy values was carried out employing the Arrhenius law and the provisions of irreversible thermodynamics, with specific reference to Onsager's second postulate. This fundamental concept posits that the growth rate of irreversible component of entropy can be expressed as the summation of products involving fluxes and thermodynamic forces when a system tends towards its equilibrium state. In the context of this study, the equilibrium state of the memristor is defined as the condition at which the memristor can no longer function as a resistive memory cell. Our experimentation involved the application of a flux of Ag+ ions (electromigration). The calculated activation energy values were found to be 0.24 eV for the initial process and 1.16 eV for the latter. These divergent activation energy values indicate the differentiation between the agglomerative mechanism that governs the formation of conductive channels, prevalent in the Ag/SnSe/Ge2Se3/W memristor, and the "conventional" substance transfer mechanism based on a group of point defects that manifests itself during the memristor's degradation.
electrical conductivity, solid electrolyte, amorphous matrix, activation energy, agglomeration
Memristors are dynamic electronic components whose electrical conductivity changes its value depending on the applied voltage. These devices exhibit a transition between their high resistance state (HRS) and low resistance state (LRS), accomplished through a resistive switching mechanism. Specifically, conductive filaments (CFs) are formed and disrupted within their solid body structure. These CFs can take the form of conductive phases, such as the TinO2n-1 Magnelli phases [
Karpov V. et al. [
The investigation of these processes in the ionic memristor, which utilizes a Ge2Se3 solid electrolyte in its amorphous state with a glass transition temperature of 340 °C (it was documented by Feltz A. [
The study focused on SDC memristors produced by Knowm Inc. (USA). These memristors are bipolar devices housed within ceramic packages. Detailed information about their design can be found in references [
Figure
We employed an automated measuring setup consising of a Tertroniks TDS 2042C oscilloscope, a Digilent Analog Discovery 2 oscilloscope and analyzer, and a PC for instrument control and data processing. This configuration proved well-suited for the continuous and repeated recording of I-V curves of the memristor, conducted at various switching frequencies and temperatures. In order to investigate the influence of temperature on memristor performance, we utilized an SM-60/150 80 TX climatic chamber. For I-V curve recording, a time-variable bipolar triangular voltage was applied to the top electrode of the memristor, while the bottom electrode remained grounded. Our I-V curve recordings were conducted to determine the activation energy associated with CF formation at switching frequencies of 10, 100, and 1000 Hz, representing three distinct frequency values, across temperatures of 22 (room temperature), 50, and 75 °C. To determine the effects of degradation on the SDC memristor performance, we tested the device at 22, 35, 50, and 65 °C and a 100 Hz switching frequency. For generating I-V curves, we continuously recorded the applied electric potential at the top electrode and the resulting current. To determine the conductivity values of the SDC memristor, we aggregated a series of the I-V curves representing ten consecutive cycles.
Sequence of layers in an Ag/SnSe/Ge2Se3/WSDC memristor and their functional purposes: (1) active silver electrode, (2) spacer, (3) Sn2+ ion source, (4) Ge2Se3 solid electrolyte (active layer), (5) inert tungsten electrode. Interelectrode space is 15 nm
Initial stages of Ag+ ion agglomeration within the Ge2Se3 amorphous matrix: (a) unperturbed short-range order of the amorphous matrix; (b) formation of a microcavity when an Au atom substitutes a Ge atom in one of the Ge–Ge dimers; (c) accumulation of Ag+ ions around the microcavity. Arrows indicate the directions of movement of Ag+ ions near the microcavity from neighboring (parallel) regions of the amorphous matrix. The figure was generated by the authors using data sourced from [
Aleshin A. et al. [
, (1)
where σ represents the specific electrical conductivity of silver, S denotes the cross-sectional area of the CF, dS/dt is the kinetic constant representing the rate of change in the CF’s cross-section area, t stands for time, and l represents the length of CF. The kinetic constant dS/dt can be determined as follow:
, (2)
to achieve this, it is essential to have I-V curves registered at a minimum of three different switching frequencies. The kinetic constant dS/dt quantifies changes in the cross-sectional area of the CF over time, and consequently we can utilize the Arrhenius law (as it is described by Bokshtein B. et al. [
, (3)
where Q denotes the activation energy of the CF formation process, T represents the thermodynamic temperature,and k stands for the Boltzmann constant.
As mentioned previously, measurements of the kinetic constant dS/dt were conducted at switching frequencies of 10, 100, and 1000 Hz and temperatures of 22, 50, and 75 °C. Figure
The application of the Arrhenius law to the kinetic constant dS/dt, as estimated from Eq. (2) while considering the temperature correction for the specific conductivity of silver σ, is depicted in Fig.
I-V curves changes induced by alterations in the switching frequency within the SDC memristor at (a) 22 °C, (b) 50 °C, and (c) 75 °C
In our investigation of SDC memristor degradation, we subjected the device to continuous I-V curves registration at 100 Hz and temperatures of 22, 35, 50, and 65 °C. The I-V curves were recorded for durations of 30, 7, 1, and 0.142 h, respectively. Registration of the I-V curves was terminated when the curves exhibited significant degeneration, with I-V curves either strongly converging or, in some cases, completely merging. At this point, denoted as ξ, the I-V curve registration was halted. The transition of the I-V curve from its conventional shape (Fig.
In order to determine the activation energy of degradation, we employed the principles of thermodynamics of irreversible processes, specifically, Onsager's second postulate, expressed as follows [
, (4)
where j represents the particle flux, X is the generalized thermodynamic force, and s denotes the entropy of the system per unit volume. In the stationary state, the flux of positively charged silver ions jAg is cv (where c is the concentration of silver ions; v is the drift velocity). The generalized thermodynamic force in this context is the electric force qE (where q is the charge of the Ag+ ion; E is the electric field). As per the Nernst equation [
, (5)
where DAg stands for the diffusion coefficient of Ag+ ions in the Ge2Se3 amorphous electrolyte. If we assume that electromigration is the dominant process governing structural changes during the operation of the SDC memristor, we can establish a relationship between the growth rate of the irreversible component of entropy (∂/∂t)irrev of the system in which the electromigration occurs, and the activation energy of electromigration:
, (6)
where W represents the activation energy of electromigration. Consequently, during electromigration in isothermal conditions, the growth rate of the irreversible component of the entropy (∂s/∂t)irrev increases with temperature. This (∂s/∂t)irrev value reflects the rate at which the system approaches its equilibrium state, which for the memristor signifies the loss of its functionality as a resistive memory cell. The memristor enters a degenerate state. The inverse of the time taken for the memristor to transition into its degenerate state ξ-1 behaves similarly to (∂s/∂t)irrev: it increases with temperature. Given that the degenerate state of the SDC memristor remains consistent across all temperatures, we can deduce that (∂s/∂t)irrev ∝ ξ-1. By substituting (∂s/∂t)irrev for ξ-1, in equation (6), we derive:
, (7)
where U represents the activation energy of degradation. Figure
The fact that the activation energy U is nearly an order of magnitude higher than the activation energy of CF formation in the SDC memristor suggests the existence of an alternative mechanism for Ag+ ion transport within the Ge2Se3 solid electrolyte, apart from migration along the structural block boundaries of the amorphous matrix. One possibility of the implementation of such a mechanism is the involvement of a group of point defects, which is typical in crystalline substances. This type of electromigration may occur spontaneously from time to time due to local spontaneous crystallization of the amorphous matrix, induced by factors such as thermal fluctuations, elastic stresses, electric field gradients, etc.According to a simplified model of heterophase fluctuations presented by Klinger L. [
Degradation curves for the LRS and HRS states at 100 Hz for various temperatures and test durations: (a) 22 °C, 30 h; (b) 35 °C, 7 h; (c) 50 °C, 1 h; (d) 65 °C, 0.142 h
In our study, we conducted a comprehensive analysis and estimation of the activation energy associated with both the CF formation and degradation processes in Ag/SnSe/Ge2Se3/W SDC memristors. This investigation involved the registration of I-V curves and measurements of the conductivity of the SDC memristor in both its basic electronic states: the LRS and the HRS. To estimate the activation energy for these processes, we employed the Arrhenius law and applied principles of thermodynamics of irreversible processes. The results reveal that the activation energy for CF formation is 0.24 eV, indicating that the SDC memristor can effectively maintain its resistive memory function even at high switching frequencies, extending up to 105 Hz. This finding aligns with the agglomeration mechanism of CF formation, which is associated with the migrarion of Ag+ ions along the boundaries of structured within the first coordination sphere blocks of the amorphous matrix of the Ge2Se3 solid electrolyte. In contrast, the elevated activation energy associated with memristor degradation aligns with the notion of Ag+ ion migration occurring directly within the bulk of the amorphous matrix, potentially through mechanisms like local crystallization. This occurrence signifies a breakdown in the agglomeration process crucial for CF formation. Such a failure is the underlying cause of SDC memristor degradation, serving as an indicator that the behavior of the Ag/SnSe/Ge2Se3/W system deviates from its ideal state when subjected to a prolonged passage of direct electric current.
This research received support from the Russian Foundation for Basic Research, project No. 19-29-03003 MK.
Ethics declarations
The authors declare that they do not have any conflicts of interest.