Conduction mechanisms of LRS and HRS

In the previous part, much work has been done on the studies of the resistive switching behaviors and mechanisms of the HfOx-based RRAM device. To better understand the physics behind the resistive switching phenomenon, the current conductions of both LRS and HRS are examined with the temperature dependent I-V measurements in this part.

Fig. 3.6(a) shows the I-V characteristics of the LRS under different temperatures. A linear I-V relationship with the slope of ~1 is observed for all the temperatures, showing the ohmic

conduction of LRS for the oxygen vacancy based conductive filament. The overlap of these I-V curves indicates that the temperature has little effect on the LRS. This temperature

independent behavior is also confirmed in Fig. 3.6(b), in which no obvious change for current (read at 0.1V) is observed. In general, the current transport for LRS can be attributed to electron hopping effect or ohmic conduction mechanism. For the electron hopping effect, there is no continuous filament formed between the top and bottom electrodes, and the electrons will hopping among the discrete oxygen vacancies [111]. In this situation, the thermal excitation process will be enhanced at higher temperature, so the resistance should decrease with the increase of the temperature.In contrast, when there is a strong enough filament connecting the top and bottom electrodes, ohmic conduction can be observed. And the conductive filament here is usually metallic with the resistance increasing with the temperature [112]. For the device in this work, the ohmic conduction with weak temperature dependence could be attributed to the very small activation energies of the carrier conduction in the oxygen vacancy based conductive filament.

Unlike the LRS, the current transport mechanism has electric field dependence for HRS.

A linear relationship between the current and voltage is observed at low electric filed for HRS, as shown in Fig. 3.7(a). Fig. 3.7(b) shows the ohmic conduction behavior of the HRS with the voltage ranging from 0 V to 0.2 V under different temperatures. In contrast to the temperature independent behavior of the LRS, the current here increases with the increase of the temperature, which is quite similar to the semiconductor’s current-temperature property.

For this ohmic conduction, the current can be written as:

_c V exp ^-E^a

Fig. 3.6. (a) I-V characteristics of the LRS under various temperatures. (b) The current read at 0.1 V versus temperature. The trend line is for guiding eyes only.

where I is the current, q is the electron charge, A is the device size, Nc is the effective density states in the conduction band, μ is the electronic mobility in insulator, V is the applied voltage, d is the film thickness, Ea is the activation energy, k is the Boltzmann constant, and T is the absolute temperature [113]. Fig. 3.7(c) shows the Arrhenius plot (ln(I) versus 1/kT) of the HRS at the voltage of 0.1 V. The activation energy Ea, yielded from the slope of the Arrhenius plot, is about 0.286 eV. Based on the above discussion, the current conduction of the HRS at low electric field can be attributed to the electron hopping from one defect to

another by thermal excitation. This excitation process will be enhanced at higher temperature, which leads to a higher current level, as shown in Fig. 3.7(b).

Fig. 3.7. (a) I-V characteristic of the HRS under room temperatures. (b) I-V characteristics of the HRS at low electric field under the temperature ranging from 313 K to 413 K. (c) Arrhenius plot of the HRS current at a low electric field. The current was measured at 0.1 V.

When the applied voltage is high, the I-V curve departs from the ohmic conduction, as shown in Fig. 3.7(a). The current transport of HRS at high electric filed can be explained by Poole-Frenkel emission model, which is a mechanism of bulk effect. For the HfOx-based RRAM here, the Coulombic traps in Poole-Frenkel emission model should be oxygen vacancies, which are neutral when filled with electrons and positive charged when empty.

The Poole-Frenkel emission I-V relationship can be described as [114]:

where A is the device area, C is a constant, d is the film thickness, q is the electron charge, qΦPF is the depth of potential well, ε0 is the vacuum permittivity and εi is the dynamic permittivity [114]. According to this equation, there should be a linear relationship between the ln(I/V) and V^1/2 for Poole-Frenkel emission model. And this relationship is confirmed for the HRS at high electric field under the temperatures ranging from 313 K to 413 K, as shown in Fig. 3.8(a). As shown in Fig. 3.8(a), the current increases with the temperature, and this is also due to the enhanced thermal excitation effect, which is the same as the situation in low

electric field. The activation energy of Poole-Frenkel emission,

0

obtained from the Arrhenius plots (ln(I/V) versus 1000/T), as shown in Fig. 3.8(b). The slope of every fitting line in Fig. 3.8(b) corresponds to the activation energy of HRS under different voltages. As can be seen in Fig. 3.8(c), the activation energy has a linear dependence on the square root of voltage and it has a decreasing trend with the applied voltage. In the typical Poole-Frenkel emission model, higher voltage results in more serious barrier lowering effect.

Thus, less thermal activation energy is needed for the electrons to escape from the Coulombic traps, so the activation energy will decrease with the applied voltages. In addition, the depth of the potential well (qϕPF) that is extracted from the intercept of the fitting line in Fig. 3.8(c)

is about 0.328 eV. Based on the above discussion, the current transport of the HRS at high electric field can be described as Poole-Frenkel emission model. The oxygen vacancies act as Coulombic traps inside the HfOx layer. When temperature increases, the probability for the trapped electrons to escape from the traps will increase, so the conductivity of the material will be increased. Meanwhile, when there is a larger voltage applied to the device, a smaller resistance can be expected due to the barrier lowering effect.

Fig. 3.8. Current conduction of the HRS at high electric field. (a) The Poole-Frenkel emission plots of ln(I/V) vs V^1/2for the HRS under various temperatures. (b) The Arrhenius plots of ln(I/V) vs 1000/T for HRS under different voltages. (c) The activation energy as a function of the square of the voltage.