Once we increase the width of the programming pulse in the fastest compounds (44 and 53 at. % of Ge content), we observe a decreasing of the current needed to amorphize the phase-change material. We highlight that this happens when we try to RESET again a cell, already in the RESET state (Fig. 3.7a). Taking into account that in the range of pulse durations explored in the experiment, we reach a stationary regime for the temperature, largely before the end program pulse, we would rather expect the RESET current not to depend on the pulse duration. Once reached the stationary regime in the cell in fact, the melted volume is stable, and the melt quenching and the final resistance state of the cell, are affected only by the fall time of the pulse. To explain why the result is not matching this hypothesis, we analyzed in detail what is happening during the pulse application in our cells.
3.1 GexTe100−x 101
Fig. 3.7. In the left graph, experimental points are interpolated, to evidence the differences in the RESET-SET characteristics of Ge53Te47 samples, obtained with different pulse widths (in red 50 ns, in green 500 ns). In blue are reported the data relative to the SET-RESET characteristic (not affected by the pulse width). Applying more than 20 mA on a SET cell, the melted material is quenched in an amorphous dome that covers the plug interface (inseta). The same amount of current, applied on a RESET cell for 50 ns, takes the device to a SET state (inset b). Only increasing the duration of the programming pulse (insetc) the residual amorphous regions generated far from the plug interface (after the current spike caused by the electronic switch) are recrystallized, recovering the same thermal stationary conditions observed in inset a. If we increase the current in the case of the 500 ns pulse (insetd), the melted volume is even higher, and the longer will be the pulse width necessary to recover the stationary condition.
Our analytical device is not able to perform a self-limitation of the current during the electronic switch event (namely the change from RESET state to the high conduc-tive state, called ON-state). The discharge of the parasitic capacitance during the SET operation, gives rise to a spike of current and a related increase of the temperature in the cell [129]. The temperature reached during this spike enables the melting of a large volume of phase-change material. Then the current decreases in time range in the order of the characteristic time constant of the discharge (∼ 1 ns). The fast decrease of the temperature in the regions far from the plug interface provides residual amorphous domains that are preserved also once the stationary thermal conditions are restored during the pulse applied (after the spike transient). Since the thermal resistiv-ity of amorphous GeTe is higher than the crystalline [16], the thermal barrier created by these amorphous domains, enhances the recrystallization of the volume of material closer to the plug interface, at the end of the pulse applied. This can be possible only if the growth speed of the material is sufficiently high (since the fall time of the pulse is 10 ns). This situation is described in Fig. 3.7b, and confirmed by the TEM image reported in Fig. 3.8.
If now we increase the duration of the pulse, we can achieve the recrystallization of these residual amorphous regions far from the plug center (in fact far from the plug, the temperature is lower and so the growth speed), and then restore a situation in which the melted region is not surrounded by any amorphous domains. In this case, at the
Fig. 3.8. TEM image representative of the inset b of Fig. 3.7. Is evident the presence of a polycrystalline region (A) and of the lateral residual amorphous regions (B).
Fig. 3.9. Simulations of the R-I characteristics obtained for a lance-type device, increasing and decreasing the standard growth speed of the GST (multiplied by 1.2 and 0.4), in order to study the effects of the growth speed on the programming curves.
end of the pulse, the high thermal conductivity of the crystalline GeTe surrounding the melted volume, fast quenches the material in an amorphous phase (Fig. 3.7c). It is why we observe an apparent reduction of the RESET current for Ge44Te56 samples at higher pulse widths. This effect can be highlighted really well only if the crystallization speed of the material is fast enough to provide crystallization in ns range of time (as the fall time of the pulse applied).
Increasing now the voltage applied on the cell (Fig. 3.7d) we increase also the melted volume generated by the current spike. It provides residual amorphous domains that are even more distant from the plug interface, making necessary even longer pulses to recrystallize them. In Fig. 3.6 Ge53Te47 shows this effect, strongly dependent on the high growth speed of this material. This leads also to a higher randomness in the programming curve that is in agreement with the optical results reported in Fig. 3.4.
3.1.5 Simulation of the growth speed effects on the R-I char-acteristic
Thanks to the simulations performed, we were able to justify the changed electrical behavior of the cell, observed when the growth speed of the phase-change material is considerably high (like in the case of GeTe). In particular, we were interested in the effects of the crystallization speed, on the final programming characteristics. In Fig. 3.9 we show the results obtained for a lance-type device. The material parameters used, are the same of the GST, but we increased and decreased the growth speed, just multiplying eq. 2.31 by a constant parameter. The cell is programmed in the RESET state, before each pulse applied. We see that the minimum SET resistance achieved (we used the same pulse width of 50 ns for both the simulations), increases when we
3.1 GexTe100−x 103
Fig. 3.10. I-V characteristics. Each point is the average value on 3 cells. In the inset is reported the trend of the threshold voltage (VT H) as function of the Ge content.
decrease the growth speed, as expected. Furthermore, the RESET current is lowered by the decrease of the crystallization speed, showing that even if the current amplitude is already able to form an amorphous dome to cover the plug surface, if the growth speed is sufficiently high, during the falling edge of the pulse a partial growth of the surrounding crystalline phase can be activated, programming finally the device in a partial SET state.
3.1.6 Threshold voltage investigation
The investigation of the trend of the threshold voltage (VT H) varying the Ge content was performed on the current-voltage curves (I-V) for the different stoichiometries pro-grammed in the RESET state. The procedure applied to extract the I-V curves is the same than the one used in section 3.1.3. The SET pulse used for the I-V measurements had a width of 100 ns. In Fig. 3.10 we report the extracted cell current during the programming pulse versus the voltage drop on the cell for four stoichiometries. In the inset we report the value for VT H obtained for each composition as function of the Ge at. %. If we compare the trend of VT H with the trend of the activation energy reported in Fig. 3.2b, this two seem to support the relation reported in [100], in which the threshold voltage is correlated with the nucleation energy barrier (VT H ∝W0, as we can derive from eq. 2.18, whereW0 is the zero-field activation energy of the nucleation).
At the same time in Fig. 3.1 we see a decrease of the activation energy of the conduction (EC) of the amorphous phase, increasing the Ge content (0.50 eV in Ge36Te64 down to 0.28 eV in Ge69Te31) that is a sign of the reduction of the energy band gap. Probably both the reduction of the activation energy of the nucleation and the reduction of the energy gap of the material contribute to the decrease of the threshold voltage when we increase the Ge content in the compounds.
10
Fig. 3.11. Endurance test for Ge36Te64, Ge44Te56 and Ge53Te47 devices. The RESET pulse width is 50 ns; the SET pulse width is 500 ns.