Phase field modeling of domain dynamics and polarization accumulation in ferroelectric HZO

Abstract

In this work, we investigate the accumulative polarization (P) switching characteristics of ferroelectric (FE) thin films under the influence of sequential electric-field pulses. By developing a dynamic phase-field simulation framework based on time-dependent Landau-Ginzburg model, we analyze P excitation and relaxation characteristics in FE. In particular, we show that the domain-wall instability can cause different spontaneous P-excitation/relaxation behaviors that, in turn, can influence Pswitching dynamics for different pulse sequences. By assuming a local and global distribution of coercive field among the grains of an FE sample, we model the P-accumulation process in Hf 0.4 Zr 0.6 O 2 (HZO) and its dependency on applied electric field and excitation/relaxation time. According to our analysis, domain-wall motion along with its instability under certain conditions plays a pivotal role in accumulative P-switching and the corresponding excitation and relaxation characteristics.Ferroelectric (FE) materials, particularly Zr doped HfO 2 (Hf 1-x Zr x O 2 :HZO 1 ) have drawn significant research interest in recent times due to CMOS process compatibility 2 , thickness scalability 3,4 as well as many promising attributes of ferroelectric field effect transistors 2,5 (FEFETs) for low-power logic 5-8 and non-volatile memories 9,10 applications. In addition, FEFETs can provide multiple non-volatile resistive states that harness the multi-domain FE characteristics, leading to the possibilities for multi-bit synapses 11,12 in a neuromorphic hardware 13 . Further, newly reported accumulative polarization (P)-switching process 14 in ultra-thin FE leads to many appealing opportunities for novel applications like correlation detection 15 and other non-Boolean computing paradigms 16 . For such emerging applications of FEFETs, the P-switching dynamics in response to sub/super-coercive voltage pulse trains play an important role and are, therefore, critical to understand.To that effect, this letter analyzes spatially local Pswitching dynamics and its participation in globally observable P-accumulation characteristics in response to a pulse train. Our analysis is based on a dynamic phase field model 17,18 coupled with measured accumulation characteristics of HZO. By providing the spatial distribution of P (Pmap) in different electric field (E-field) excitation and relaxation steps, we discuss different types of P excitation and relaxation processes and their corresponding dependency on Efield (E) amplitude (E app max ), ON time (or excitation time T on ) and OFF time of the pulse (or relaxation time T o f f ). Finally, considering a coercive-field distribution among different FE grains, we analyze the experimental P-accumulation characteristics by utilizing our simulation framework.Let us start by describing the experimentally observed Pswitching characteristics in HZO. Fig. 1(a) shows the measured charge vs. E-field (Q-E) characteristics of a 10nm HZO film (x=0.6, grown by ALD with TiN capping layer as top and bottom contact). He...

Multi-Domain Negative Capacitance Effects in Metal-Ferroelectric-Insulator-Semiconductor/Metal Stacks: A Phase-field Simulation Based Study

“…7 can be derived, where the Landau coefficients incorporates both of the strain and polarization contribution of the free energy density (see Supplementary Section of ref. 14 ). Now, for the considered system, the Poisson's equation can be written as, in TDGL equation (Eq.…”

“…For the gradient energy coefficient (g ), a range of values are considered (see Methods section) as the actual value is still unknown for www.nature.com/scientificreports www.nature.com/scientificreports/ HZO. We assume that the spontaneous P direction in FE is along the thickness of the film (z-axis), which is parallel to the c-axis of the orthorhombic crystal phase of HZO 13,14 . For DE, we consider SiO 2 , Al 2 O 3 and HfO 2 , and for the semiconductor, we consider undoped silicon.…”

Supervised Learning in All FeFET-Based Spiking Neural Network: Opportunities and Challenges

“…Figure 1E shows the transient polarization switching dynamics highlighting the temporal integration of applied voltage pulses and relaxation during the absence of input pulse. The neuronal dynamics is emulated by utilizing the ferroelectric polarization accumulation property (Ni et al, 2018;Saha et al, 2019) that allows temporal integration of PSP. Such ferroelectric polarization switching dynamics bear close resemblance to that of a LIF spiking neuron.…”

“…This is contrary to that of a standard LIF neuron built using linear dielectric capacitor, where the discharge rate of the capacitor increases with the pulse number. Such a deviation in polarization relaxation dynamics can be understood by considering the interaction among the ferroelectric domains within the thin film and has been recently studied using phase-field modeling approach (Dutta et al, 2019b;Saha et al, 2019).…”

“…All experiments reported here have been performed on FeFETs with channel length of 34 nm and width of 80 nm. On application of successive sub-coercive voltage pulses to the gate of FeFET, the ferroelectric polarization within the Si:HfO 2 layer switches due to an accumulative effect (Mulaosmanovic et al, 2018a;Ni et al, 2018;Saha et al, 2019), resulting in the modulation of the threshold voltage (V T ) of the FeFET. As seen in Figure 2B, the V T gets modulated abruptly from a high-V T to low-V T state.…”