三、 Principle
3.2 Electron transportation mechanism
3.2.4 The electron hopping transportation mechanism
The electron hopping transportation[20] is another common electrical transportation of RRAM and it shows a non-linear I-V curve. The early researches indicated that this mechanism has low temperature conduction behavior in strongly disordered systems with localized states. Several researches reported the Mott variable range hopping (VRH) characteristics of RRAM materials. Figure 3-12 shows the band diagram of VRH. These gradation localized states is formed by the strongly disordered systems.
Figure 3-12. The band diagram of variable range hopping20.
The VRH[62] transport mechanism is depicted by Eq. (3-4). Here, R is the hopping distance, N(Ef) is the density of state, k is the Boltzman’s constant, E is the electric field, α is the decay parameter of wave function, and νph is dependent on the frequency of
However, if eRF is much smaller than kT in a weak electric field, we can approximate the relation as simplification equation. This simplification Mott VRH equation as shown by Eq. (3-5).
20 http://people.math.gatech.edu/~jeanbel/TalksE/mott09.pdf
38
) exp(
' 1/4
A BT
J …..(3-5)
Moreover, with the calculation of Origin software, we can obtain the value of (eRE/kt) with the hyperbolic sine fitting curve. Also, the hopping distance is calculated by the fitting value, and the relationship between this value and hopping distance is shown by Eq. (3-6).
kTd CV eRV kT
eRF ……(3-6)
The typical VRH electrical curve is shown in figure 3-13. The VRH electric characteristic appears both in LRS and HRS of RRAM electrical transportation mechanism. In several researches[20,29] of gradation oxidation systems, for example of WOx-based RRAM, the week metal oxide film shows gradation WOx system and the electron transportation characteristic follows the Mott VRH mechanism.
Figure 3-13. The electrical curve of Mott variable range hopping (VRH).
3.2.5 SCLC mechanism
Another electron transportation mechanism of RRAM is the SCLC[46]. This mechanism occurs before the charge injection when the charges accumulate at the interface and form a space charge cloud near the injecting electrode. The concentration of space charges rapidly dies out away from the electrode. The band diagram of the SCLC is shown in figure 3-14.
39
Figure 3-14. The band diagram of SCLC mechanism21.
The SCLC transportation mechanism shows that the current proportionally increase with the square of the electric field relationship in electrical characteristic, which can be described by equation (3-7). Here, μ is mobility, and d is the thickness.
3 2
8 9
d J iV
…..(3-7)
Figure 3-15. The electrical curve of SCLCxxiv.
21 http://ceot.ualg.pt/OptoEl/theory/2terminal/
40
Figure 3-15 shows the electrical characteristic of SCLC. This figure shows the linear I-V curve with metal ohm contact behavior when the applied electric field is below 1000 V/cm. Also, the electric characteristic displays the SCLC behavior when the applied electric field is between 1000 and 10000 V/cm. When the electric field applied is above 10000 V/cm, the electron transportation mechanism exchanges to another transportation mechanism, which is not discussed in this section. Similar to the band diagram of Schottky emission mechanism, the SCLC transportation mechanism of RRAM is attributed to the charge concentration near the injecting electrode with the transportation characteristic is also shown in previous report[50] of RRAM researches.
Figure 3-16 shows the band diagram of TAT. This figure also shows the direct tunneling (DT) characteristic. It is obvious to see the difference between DT and TAT in this band diagram. The TAT phenomenon in insulator is attributed to the tunneling characteristic with charge trap influence, and it is divided into elastic and inelastic TAT phenomena (not discussed here).
Figure 3-16. The band diagram of TAT mechanism22.
Figure 3-17 shows the TAT electric characteristic in MOS device. The TAT mechanism also appears in the RRAM transportation characteristic. Figure 3-18 shows the TAT characteristic of RRAM[63]. The electric characteristic of metal-insulator-metal
22 J. Wu, L. F. Register, and E. Rosenbaum, Annual International Reliability Physics Symposium, 389, (1999)
41
(MIM) structure combines with both TAT and DT curves, and it shows the similar SILC electric characteristic in the electric analysis. Moreover, the TAT mechanism always appears in the HRS.
Figure 3-17. The electrical curve of TAT in MOS device23.
Figure 3-18. The electrical curve of TAT in RRAM.
In summary, most electron transportation mechanisms such as Poole-Frenkel emission, electron hopping transportation, and TAT mechanisms show the charge trapping phenomenon in the oxidation layer. This result indicates the oxide film of RRAM with imperfect insulator performance, and it could be attributed to the presence of defects. Most references correlated these defects with the oxygen vacancies, which provide the charge trapping. Also, these oxygen vacancies play an important role in the resistance switching characteristic.
23 http://www.diegm.uniud.it/driussi/biografia/dottorato/node47.html
42
3.3 Resistance Switching Mechanisms
In recent years, there are many studies[64-74] proposed the resistive switching mechanism. Although the resistance switching theories in these reports show several different resistance switching mechanisms, most researches[51,54,55,75]
reported that the oxygen vacancy in the oxidate film plays an important role in the resistance switching phenomenon. The electric characteristic exhibits the filament characteristic while the electrons pass through these oxygen vacancies. In this section, we discuss the conducting filament (CF) characteristic and the oxygen vacancy phenomenon for the explanation of resistance switching phenomenon in RRAM.
3.3.1 The Conducting Filament Characteristic
In the early research of RRAM, the resistance switching phenomenon of RRAM is attributed to the CF characteristic. Ryoo and Oh et al. [51] proposed that the filament mechanism of resistive switching characteristics. The electric characteristic exhibits a CF formed and ruptured behavior in the resistance switching process. Figure 3-19 shows the sketch of both set and reset processes. As shown in figure 3-19 (a), the CF was ruptured near the top-electrode region and the resistance state changes from LRS to HRS in the reset process. Also shown in figure 3-19(b), the CF formed and the resistance state recovered from HRS to LRS in set process. The CF model can be used to explain the resistive switching characteristic.
Figure 3-19. Sketch of (a) reset process (from LRS to HRS) and (b) set process (from HRS to LRS)
43
Another study[52] also indicates the CF characteristic in their research. By means of the electron-beam-induced current (EBIC) image, we can clearly observe the CF image on the surface of oxide film and it shows the real CF image of the oxidation film. Figure 3-20 shows both EBIC image and I-V characteristic. Moreover, it also indicates the relation between these two factors. At the “initial” state, the resistance state is located at HRS, which is shown in figure 3-20 (a). When a negative voltage is applied, the resistance state switches from HRS to LRS, and the EBIC image observes several additional spots in figure 3-20 (b). Also, figure 3-20 (c) shows that several spots disappear in EBIC image when the resistance state switches back to HRS with a positive applied voltage. Figure 3-20 (d) shows more spots appear when the resistance state switches to LRS with another negative applied voltage. These spots of EBIC images indicate the existence of CF, and it also can be used to explain the resistance switching characteristics.
Figure 3-20. Sequence of EBIC image[52] and I-V characteristic (a) Initial state (b) Switch to LRS (c) Back to HRS (d) sweep to LRS.
44
Another image of CF can be observed with the conducting atom force microscopy (CAFM) system[53]. Figure 3-21 shows the CAFM image of ON and OFF state. It is clear to see the difference in both resistance states. Figure 3-21 (a) shows the CAFM image on HRS, and there are a few spots on the surface of oxidation film. It indicates that there are a few conducting channels in this oxide film. Also, the CAFM image of LRS shows many spots on the surface of oxidation film, which is shown in figure 3-21 (b). It indicates that there are many conducting channels in the oxide film.
Figure 3-21. The conducting atom force microscopy (CAFM) of ON and OFF states[53].
3.3.2 The Oxygen Vacancy Phenomenon
In previous section, we discuss the CF theory for the resistance switching characteristic of RRAM. However, this theory can’t explain the root cause of the resistance switching characteristics. It just depicts the phenomenon of resistance switching characteristics. In this section, we discuss delineate another theory to explain the resistance switching characteristic. This theory also illustrates the influence of resistance switching due to physical factors.
Gao proposed a unified physical theory for bipolar oxide-based resistive switching memory[54]. His study indicates that the oxygen vacancies can be generated by ionizing the oxygen atoms in lattice under a voltage bias. Xu et al.[55] also proposed that the oxygen vacancies and non-lattice oxygen ions play a critical role in the resistive switching device. Figure 3-22 shows the sketch of the carrier transport in both HRS and LRS.
In the set process, the oxygen ions are moved out from the lattice, and the oxygen vacancies appear at the same time. Also, the resistance state is switched from HRS to LRS because these oxygen vacancies appear in this resistance switching process. Figure 3-22 (a) shows the electron transportation in LRS. In this figure, the CF is formed by localized Vo and the conduction transportation is mainly due to electron hopping
45
transport among these Vo. Moreover, the charge-free of localized Vo+ exhibits longer hopping distance than Vo.
In the reset process, the oxygen ions are recombined with electrons and the oxygen vacancies disappear. At the same time, resistance state is switched back to HRS. Figure 3-22 (b) shows the electron transportation in HRS. In this figure, the CF is ruptured by recombination of oxygen ions and the diminish of oxygen vacancies at the moment. The electrons can’t conduct with hopping transportation due to the recombined oxygen ions.
Since the hopping channel is destroyed, the electric characteristic switched to HRS.
By means of the theory of oxygen vacancy, we can explain the mechanism of resistive switching character. Combined with the CF theory, it can give readers much clear pictures in the RRAM film.
In summary, these theories can explain the bipolar operation resistance switching mechanism. But the unipolar operation resistance switching mechanism is still missing.
Most references attribute the root cause of unipolar RRAM to the Joule heating effect.
The research of unipolar operation resistance switching mechanism is still required.
Figure 3-22. Schematic illustration of conduction transport in (a) LRS (b) HRS.
3.4 Resistance Switching Model
In recent years, many resistance switching models for RRAM has been proposed.
These models are as follows: The stochastic model[56], two-variable resistor model[46,57], compact model[58], rupture ball model[38], thermal dissolution model[48,59], filament anodization model[76], numerical model[77] etc. In below, these models and discussed briefly.
46
3.4.1 The “Rupture Ball” Model
This model[38] is a blend of CF theory and oxygen vacancy theory. The electron transportation depends on the oxygen vacancy and the electric characteristic displays a CF phenomenon. Based on the results of previous researches, this model explains the relationship among “forming”, “set”, “reset”, and “degradation” process. Figure 3-23 illustrates the schematic diagram of RRAM in above processes.
During the “forming” step, voltage is applied to the whole dielectrics as illustrated by figure 3-23 (b). After this process, the CFs can be formed by sufficient voltage.
When further stress is applied to induce the “reset” process, CFs are ruptured by thermal effect depending on the applied power as illustrates by figure 3-23 (c). This “set”
process resulting in the growth of Cfs as shown in figure 3-23 (d). However, with a continuous increase of the “reset” current, most of CFs can be destroyed due to the increased “reset” current, resulting in lowered current level as shown in figure 3-23 (e).
These phenomena might cause irreversible degradation of dielectric films in the “over reset” process.
In this “rupture ball” model, it is shown that CFs are formed by the aggregation of oxygen vacancies through the “set” process. Also, the CFs are ruptured by deaggregation of oxygen vacancies through the “reset” process. In other words, the
“rupture ball” might be formed by thermal diffusion of oxygen vacancies through the
“reset” process, and the “rupture ball” might be destroyed with the diffusion of oxygen vacancies through the “set” process.
Figure 3-23. Schematic diagram[38] of dielectric status of RRAM at (a) fresh (b) after
“forming” process, and (c) after “reset” process (d) after “set” process, and (e) after “over reset” process, respectively.
47
3.4.2 The Stochastic Model
In the stochastic model[56], the modeling of set/reset transitions is addressed by a statistical framework. The stochastic model for set and reset processes is developed by defining the probabilities for the cell to be in a set or reset state as Pset and Preset, respectively. Assuming a Poisson statistics for set/reset, the time variation of Pset can be expressed by Eq. (3-8) where the average transition times are τset and τreset for set and rate β= dVcell/dt, where Vcell is the voltage across the RRAM cell, the stochastic model calculates the set/reset time as shown in figure 3-24.
Figure 3-24 (a) shows the relationship betweenβand set/reset voltage. The “reset”
voltage is smaller than the “set” one for small β.On the other hand, the set voltage is smaller than the reset one when the sweep rate is above 107 Vs-1. In this case, the reset voltage increases quickly and it is ease to destroy the memory cell in the transition process. Figure 3-24 (b) shows the relationship between set/reset transition time and voltages. The crossover ofτset and τreset is about 200 ns and Vcell is about 2.2 V. In this figure, the reset voltage shows sudden change when the transition time is below 200 ns.
Also, the set voltage shows the characteristic of slow increasing characteristic when both β and transition times increased.
Figure 3-24. Measured and calculated relationships[56] of NiO film between the set/reset voltage and (a) the sweep rate or (b) the set/reset transition times.
48
To clarify the conditions for stable set/reset transitions, figure 3-25 shows the calculated I-V curves in set and reset states. Here, the reference assumes ohmic conduction with resistances from 1 to 50 kΩ for set and reset states, respectively. This curve shows the correspondence to the transition time according to the simulation results in figure 3-24. The dashing lines indicate the transition process at the same transition time. For example, at 100 ns transition time (open triangles), the reset voltage is smaller than the set voltage. It indicates that the probability of reset process is smaller than set process at 100 ns. On the other hand, at 10 us transition time (open squares), the set voltage is smaller than the reset voltage. It indicates that the probability of set process is smaller than reset process at 10 us.
In summary, it is shown that stable reset and set processes can take place above and below 200 ns, respectively.
Figure 3-25. Calculated I-V curves for set and reset states[56]. The dashed lines connect transition point at equal transition times on two curves.
3.4.3 The Thermal Dissolution Model
The thermal dissolution model[48,59] is based on the CF theory and it can be used to explain resistance switching characteristic in the “reset” process. Figure 3-26 (a) shows the I-V curve of the CF based RRAM. It shows the characteristics of resistance increase when the applied voltage is increased. This result indicates the heating effect of the CFs.
As shown in the inset in the figure, the temperature dependent relationship with resistance indicates the metals or doped semiconductors behavior. Moreover, Eq. (3-10) can be developed by this electric character. In this equation, the value of α is about 1.7x10-3.
49
)]
( 1 [ )
(T R0 T T0
R ……(3-10)
According to this equation, the resistance can be used as a thermometer for CF and can also be used to calculate the maximum temperature. Figure 3-26 (b) shows the relation between the temperature and the applied voltage. From this figure, the temperature increases with the increasing applied voltage. The critical temperature Tcrit
is about 550 K when reset process occurs.
Figure 3-26. (a) The reset switching I-V curve and the temperature dependence relationship with resistance (inner) (b) Temperature has been evaluated from I-V curve[48].
Figure 3-27 shows the measured and calculated I-V curve during the reset process.
Points A, B, C, and D correspond to the simulation results in figure 3-28, which is in the left region of CF. When the voltage is applied to the cell, a current flow will go through it, causing the CF temperature to increase as a consequence of Joule-heating. For a symmetric CF system, the temperature will be equal to room temperature at cell
50
electrodes, and it will reach a maximum temperature in the middle of the filament. In figure 3-27, points A and B show the I-V curve of cell without resistance switching phenomenon. Also, the first two pictures of figure 3-28 show the temperature relationship of these two points. Besides, point C shows the resistance switching phenomenon, and the third picture of figure 3-28 shows the simulation result of thermal dissolution. Finally, point D shows the HRS after the reset process, and the fourth picture of figure 3-28 shows the simulation result. It shows the CF is destroyed with the thermal dissolution and the temperature of this rupture CF is near the room temperature.
The right picture of figure 3-28 shows the temperature profile along the symmetry axis in the cylindrical CF, representing the four bias points A-D in figure 3-27.
Figure 3-27. Measured and calculated I-V curve during reset process.
Figure 3-28. Simulation results for thermal dissolution of the CF[59]. The left four images show the four bias points A-D in figure 3-27 and the right image shows the temperature profile of A-D.
The thermal dissolution model indicates that the physical mechanisms underneath CF dissolution are diffusion of conductive particles or defects, resulting from the CF outward and their annealing or the reaction with other elements. This model can be used to explain the reset process of RRAM.
51
3.4.4 The Two-variable-resistor Model
The two-variable-resistor model[46,57] is based on the oxygen vacancy mechanism and can be used to explain the bipolar resistance switching. Figure 3-29 is the schematic illustration of this model. The structure of Al/TiOx/Al is shown in the left part of figure 3-29 and this initial TiOx film is in HRS (Roff). In this bipolar operation, the electrode β is ground, and the bias is applied to electrode α. The appearance of both positive and negative polarities of bias in this device can be understood if we use tow-variable-resistor model. The assumptions of this model are as follows. First, oxygen vacancies in TiOx layer act as trap for electrons, and they are uniformly distributed in TiOx layer. Second, the TiOx layer is divided into two parts: a well conductive part (Ron) of thickness ω(t) and a less conductive part (Roff) of thickness D-ω(t). Third, the filled-trap region of TiOx shows good conductivity (Ron). Finally, the unfilled-trap region of TiOx shows poor conductivity (Roff). After applying bias, the total resistance of the TiOx layer is determined by the two variable resistors in series, which consist of a low resistance resistor (Ron) and a high resistance resistor (Roff). Thus, the total resistance can be described by the following Eq. (3-11):
))
Figure 3-29. Schematics[57] to explain the resistive switching in the Al/TiOx/Al structure considering the variation of the filled-trap region (Ron) of TiOx by injected carrier.
52
In addition, D is the total thickness of TiOx film. Moreover, the calculated I-V curve and the measured data of this device are shown in figure 3-30. It indicates that the result of calculated I-V curve is similar to the measured electric character.
Figure 3-30. Calculated I-V curve of the Al/TiOx/Al device and the measured data[57]. In summary, the applying bias controls the filled-trap region of TiOx film, and the
Figure 3-30. Calculated I-V curve of the Al/TiOx/Al device and the measured data[57]. In summary, the applying bias controls the filled-trap region of TiOx film, and the