Redefining the Speed Limit of Phase Change Memory Revealed by Time-resolved Steep Threshold-Switching Dynamics of AgInSbTe Devices

Although phase-change memory (PCM) offers promising features for a ‘universal memory’ owing to high-speed and non-volatility, achieving fast electrical switching remains a key challenge. In this work, a correlation between the rate of applied voltage and the dynamics of threshold-switching is investigated at picosecond-timescale. A distinct characteristic feature of enabling a rapid threshold-switching at a critical voltage known as the threshold voltage as validated by an instantaneous response of steep current rise from an amorphous off to on state is achieved within 250 picoseconds and this is followed by a slower current rise leading to crystallization. Also, we demonstrate that the extraordinary nature of threshold-switching dynamics in AgInSbTe cells is independent to the rate of applied voltage unlike other chalcogenide-based phase change materials exhibiting the voltage dependent transient switching characteristics. Furthermore, numerical solutions of time-dependent conduction process validate the experimental results, which reveal the electronic nature of threshold-switching. These findings of steep threshold-switching of ‘sub-50 ps delay time’, opens up a new way for achieving high-speed non-volatile memory for mainstream computing.

Therefore, understanding their electrical switching dynamics and programming of nanoscale PCM device using picosecond (ps) electrical pulses require an advanced experimental setup with exceptional measurement capabilities at gigahertz (GHz) frequencies in order to address several challenges involved in PCM programming. These include a rapid change in resistances about more than three orders of magnitude during switching, which can cause loading/unloading of parasitic capacitance/inductance involved in the measurement line. Due to this, the response of switching dynamics of PCM device is restricted in the order of at least 1-50 ns 9 . Hence a high frequency compatible impedance matching circuit (IMC) is required in order to match the source and load resistances with the resistance of PCM along with overall electronics involved in the path 4,10 .Therefore, an in-house advanced programmable electrical tester (PET) setup was designed to handle such numerous challenges during testing of PCM cells 11 .

Calibration and performance analysis of PET:
At high frequency, several crucial factors such as noise, parasitic capacitance/inductance may affect electrical signals. This setup has been made with complete care to minimize these adverse effects. The performance of the setup is checked using the standard test pulse (STP) that is available with DSO having rise/fall time of 100 ps and pulse width of 100 ns with amplitude of 0.5 V. A systematic performance analysis was made on PET components such as high frequency cables and the contact-boards. All the high frequency cables were tested with STP and shown to have the rise/fall time of 100 ± 50 ps, which is almost same as that of STP within minimum (50 ps) variation as displayed in Fig. S1. Hence all the cables are capable to show step-response at least ≥ 100 ps. Furthermore, the contact-boards were tested with STP and the rise time of contact board found to be 250 ± 50 ps as shown in Fig. S2 and hence, the contact-boards can reveal the step response of PCM cells at least ≥ 250 ps.

Figure S1.
Step-response of high frequency cable for STP having rise/fall time of 100 ps and pulse width of 100 ns. The rise/fall time of cable is found to be 100 ± 50 ps.

Figure S2.
Step-response of high frequency PCB for STP having rise/fall time of 100 ps and pulse width of 100 ns. The rise/fall time of PCB connected using cables is found to be 250 ± 50 ps.

Temperature dependent resistivity measurement of AIST cells:
AIST phase-change material is known to have fast crystal growth velocities 1,3 . The temperature-dependent sheet resistance measurement of AIST is shown in Fig. S3. The measurement was performed in Ar environment with four-point probe configuration using "Temperature dependent Van-der-Pauw resistivity measurement setup". The as-deposited thin films are heated at the heating rate of 5 K min -1 and the resistivity decreases smoothly with increasing temperature, reflecting the semiconducting nature of the sample. For further increased temperature, a drastic drop occurs in their resistivity (nearly four orders of magnitude), owing to the phase change from the amorphous to the onset of crystallization.
Crystallization temperature is found to be 175 ºC and is well matched with literature 14,15 .

Time-resolved electrical switching measurements of AIST cells:
To identify a steady-state threshold voltage (V T ) Table S1. Furthermore, threshold switching behavior is observed at V T of 1.6 V, where a steep current-rise is seen for all the applied voltages such as 1.8 V, 2.1 V and 2.6 V. This clearly demonstrates that the threshold-switching behavior at V T is independent of applied voltage and hence a steep threshold-switching is demonstrated at V T within 250 ps for all the applied voltages. Figure S4 shows a switching response of AIST cells including instantaneous threshold switching at V T followed by a rapid crystallization process for electrical pulse having rise/fall time of 1ns and pulse width of 1.5 ns. The low resistance crystalline state was confirmed by read pulse (0.3 V, 100 ns pulse width).    Table S1. Transient parameters of AIST device for pulses of different amplitudes

Matching experimental I-V curve with subthreshold conduction model:
The subthreshold conduction model proposed for amorphous chalcogenides is based on trap limited conduction mechanism 18 . The conduction mechanism in the low current subthreshold regime (V<V Th ) is described as the thermally assisted hopping of carriers due to the significant concentration of localised states 18 . The subthreshold I-V curve shows a linear behaviour for smaller applied voltages and an exponential behaviour for larger voltages. The parameters used in the model are given in Table S2 and the equation used to calculate device current is given below: where I is the current, q is the carrier charge, A is the contact area, N T is the total trap density, ∆z is the inter-trap distance, τ 0 is the carrier escape time, E C -E F is the activation energy, k is the Boltzmann constant, T is the temperature, V A is the applied voltage and u a is the thickness of amorphous region.

Parameters
Values Activation energy (E C -E F ) 0.315 eV Inter-trap distance (∆z) 7 nm Amorphous chalcogenide thickness (u a ) 80 nm Total trap density (N T ) 2.5 x 10 20 cm -3 Escape time (τ 0 ) 1 x 10 -15 s Boltzmann constant (k) 8.629 x 10 -5 eV/K Temperature (T) 300 K Carrier charge (q) 1.6 x 10 -19 C Table S2. Parameters used for analytical solution in sub-threshold regime as shown in Fig. 1c (green). Δz and N T are the fitted parameters and K B , T and q are the constants.

Matching experimental I-V curve with numerical solution based threshold switching model:
The numerical solution for threshold switching 19 is used to match an experimental I-V curve.
In this model, bi-stability is described as trap limited conduction assisted by hot electron effects. At lower currents, most of the carriers occupy the trap states and giving a negligible contribution to the conduction. When increasing the current, the heated charge carriers occupy the band states for a significant conductivity. The simulated curve is obtained numerically by solving the below two supplementary equations as given in Ref. 19.
where J is the current density, F is the electric field, n is the total carrier concentration, k is the Boltzmann constant, T e is the electron temperature, µ is the mobility of the band carriers, τR is carrier relaxation time, gT/gB is the ratio of density of trap to band states, ∆E is the activation energy and T 0 is the temperature.   Fig. 1c (blue). µ, τ R and g T /g B are the fitted parameters and K B , T o and q are the constants.

Parameters of interest at Threshold event:
The electron temperature (T e T ), current (I T ) and electric field (E T ) at threshold event is calculated using analytical solution 19 . The equations 10 and 11 of an analytical solution mentioned in Ref. 19 are used to calculate the above parameters. Table S4 shows the calculated parameters at threshold event. T e T value obtained from analytical solution is in agreement with numerical solution.

Parameters at threshold Values
Electron Temperature (T e T ) 324.65 K Current (I T ) 24.85 µA Electric Field (E T ) 17.71 V.µm -1 Voltage (V T ) 1.417 V Table S4. Calculated numerical values of the parameters at threshold switching event using analytical solution 19 .