With the discovery of ferroelectricity in hafnium oxide first in 20111, it has gained significant attention owing to its application in many novel microelectronic memory devices like ferroelectric tunnel junctions2,3, nonvolatile ferroelectric field effect transistors4, as well as ferroelectric capacitors5. Since its great Complementary Metal Oxide Semiconductor process compatibility, thickness scalability, and other outstanding properties, HfO2-based ferroelectric devices have been shown as the primary material for a diverse range of cutting-edge and high-demand applications.

Under atmospheric temperature and pressure conditions, bulk HfO2 adopts a monoclinic structure with space group P21/c6. This structure is centrosymmetric, meaning it lacks the necessary conditions for spontaneous polarization, which is essential for a genuine ferroelectric response. The discovery of ferroelectric properties in a fluorite-structured oxide initially came as a surprise, and this ferroelectric response has been attributed to the presence of a non-centrosymmetric, metastable orthorhombic phase characterized by space group Pca211. In previous research, various factors have been explored to enhance the stability of ferroelectric performance in hafnia. These include reducing the film thickness7, applying in-plane stress or strain8, leveraging oxygen vacancies9, and doping with other elements10,11, which has been demonstrated to be one of the most important study subjects.

As many HfO2-based devices can be integrated into back-end-of-line (BEoL), recent research focused on hafnium zirconium oxide (HZO), for the feature facilitates low-temperature crystallization, aligning with the BEoL thermal budget prerequisites12. However, the decrease of crystallization temperature is very important, especially for BEoL integration, recent research has discovered an innovative approach for crystallization within the hafnium oxide system, specifically known as electric-field-induced crystallization. In this way, hafnium oxide is allowed to nucleate only at a very low temperature, ~400 °C, and then crystalize under the application of an electric field13. Throughout the electric-field-induced transition process from the amorphous to the crystalline phase, experimental observations have revealed that both crystallinity and polarization exhibit continuous variations with the application of a periodic electric-field pulse14. This phenomenon is particularly noteworthy as it aligns with the desirable characteristics sought after in ferroelectric memory devices15,16

Theoretical study on HfO2-based ferroelectric material generally revolves around the impact of elemental doping and different crystal grain orientations on ferroelectric performance17,18, Research involving electric-field-induced crystallization is still limited as of now. Most of the works are modeling the process of field-induced crystallization for phase-change material19,20, However, the current phase-field models lack consideration for the influence of crystallinity on polarization. This has resulted in significant challenges in research endeavors spanning both experiment and simulation. So, there is a pressing need to expand the scope of simulation studies dedicated to electric-field-induced crystallization which can hold great promise in offering invaluable insights and guidance for experimental endeavors in this domain.

In this work, we extend our previous phase-field model21,22,23, into electric-field-induced crystallization to investigate the electric properties and domain evolution during electric-induced HZO film crystallization. We assume that the crystallization of HZO film is under the application of an electric field pulse. As depicted in Fig. 1a, our analysis focuses on HZO-based Metal-Ferroelectric-Metal stacks, which are commonly employed to characterize ferroelectric behavior. This approach directly paves the way for the integration of ferroelectric memory devices. The HZO thin films are currently undergoing pre-nucleation annealing at lower temperatures, as illustrated in Fig. 1b, followed by growth under the influence of an applied electric field. Our studies indicate that we can finely control the degree of crystallization and in consequence polarization in a highly precise manner. This capability allows us to achieve common ferroelectric operations with a selected maximum remnant polarization. This work has practical significance, especially for ferroelectric artificial synapses, where precise control of ferroelectric properties is crucial.

Fig. 1: Schematic diagram of HZO thin film for simulation research.
figure 1

a Metal-ferroelectric-metal structure. b Schematic of electric-field-induced crystallization in ferroelectric layer.

Results and discussion

Characterization of electric-field-induced crystallization

This work utilizes a 10 nm HZO film as the model system for simulation to investigate the phenomena and properties during the process of electric-field-induced crystallization. The simulated results of crystallization are depicted in Fig. 2. We initially simulate the pre-nucleation sites by generating random numbers, considering the spherical region with the nucleation size as radius as \(\eta \left(i,j,k\right)=1\), corresponding to the ferroelectric phase. And the other region indicates the amorphous phase, where \(\eta \left(i,j,k\right)=0\). Then, an electric field pulse of 2 MV cm−1 is applied to crystallization. Figure 2a displays the initial pre-nucleation stage and the process of crystallization under 1000, 2000, and 4000 electric field pulses, respectively. During the process of crystallization, the P–E hysteresis of HZO film shows a wake-up effect as shown in Fig. 2b, which means that the hysteresis opens as the electric field is progressively cycled up and down. Moreover, the remnant polarization values increasing from nearly zero to 24 µC cm−2 and the saturation polarization reaching 32 µC cm−2 will be found for a 10 nm thin film from simulation.

Fig. 2: The process of electric-field-induced crystallization.
figure 2

a The growth of crystalline phase under electric field cycling at 2 MV cm−1, where η = 1 represents crystalline phase, and η = 0 represents amorphous phase. b P–E loop at different numbers of electric field cycles. c Simulated and JMA equation of crystalline volume fraction.

Additionally, in thermally-induced crystallization, the Johnson–Mehl–Avrami (JMA) equation can be applied to the crystallization process in a variety of amorphous solids24. So, we can also utilize this method in our system aiming to validate the rationality of our crystallization model by fitting our results with the JMA equation. The JMA equation is the fractional amount of crystallization as a function of time, which is given by

$$\varphi (t)=1-\exp \left[-k{\left(\tau -t\right)}^{n}\right]$$

where φ is the degree of crystallinity, t is time, τ is incubation time, k is the reaction rate constant, and n is Avrami exponent which is related to the behaviors of nucleation and growth25,26,27, As previously mentioned, there is a pre-nucleation at a low temperature, so we consider the τ = 0 in our model. Figure 2c shows the JMA equation fitting to our simulation data. The fitting result in a value of n = 1.7, which is considered close to 1.5, implies a diffusion-controlled spherical growth28. The crystallization behavior at varying electric field magnitudes is also simulated which is depicted in Supplementary Fig. 1. As the electric field magnitude increases, the crystallization rate significantly accelerates. However, when the electric field is below the critical threshold, electric-field-induced crystallization will not occur.

To gain a profound understanding of electric-field-induced crystallization, we will analyze the evolution of domain structure during this process. Figure 3 shows the simulated domain structure at different degrees of crystallinity of HZO film. The film size is 128 × 128 × 16 nm³, and the number of cells is 128 × 128 × 16. Specifically, we established a grid comprising 17 layers, where the bottom 3 layers represent the substrate, the middle 10 layers describe the ferroelectric film and the top 3 layers for the space above the film. The crystalline phase is consisted of four types of orthorhombic domains, labeled as \({O}_{1}^{+}\) phase, \({O}_{1}^{-}\) phase, \({O}_{2}^{+}\) phase and \({O}_{2}^{-}\) phase. The blank areas indicate the absence of ferroelectric polarization, representing the amorphous phase. In the initial stage of crystallization, where the pre-nucleation is considered to occupy 0.1 volume, most of the crystalline nuclei are single nano-domains because of their small size. Then, as the crystalline phase grows, nano-domains come into contact with each other, forming stripe domains. During this process, most of these single domains are more inclined to form 60° and 120° domain walls. Eventually, all the amorphous phases transform into ferroelectric phases, resulting in a checkerboard-like domain structure and the emergence of topological vortex domains composed of four different orthorhombic domains. The final domain structure closely resembles the observed domain structure of HZO thin films in experiments1,18,29, referred to as the orthorhombic phase. To further verify the accuracy and reliability of our model, we also conducted simulations of the crystallization process using the coefficient from another ref. 30 in which the content of hafnium oxide is 0.45 (see Supplementary Figs. 35). The results exhibit similar crystallization behavior. The difference between the two simulated results is considered that mainly caused by the component of hafnium oxide. And we also observed the wake-up effect in the P–E curves, and the domain structure is to be of the orthorhombic phase.

Fig. 3
figure 3

The simulated domain structure in HZO thin films at different degrees of crystallinity, which is shown to be orthorhombic.

The artificial ferroelectrics synapse based on crystallization

Further, building upon a comprehensive understanding of the structural and electrical properties of HZO thin films, more synapse functions have been investigated. In artificial ferroelectrics synapse, the operating principle demands that the relevant electrical performance responses will continuously change with consecutive input signals and can stabilize at a long-lived state, which we consider as long-term potentiation (LTP) in neuromorphic engineering31. In the human brain, as a biological spike, the presynaptic membrane releases neurotransmitters, leading to the generation of an action potential in the postsynaptic membrane. The artificial synapse shows similar behavior to biological synapses while most studies are focused on ferroelectric tunnel junction devices, in which the reversal of polarization can induce a continuous variation of tunnel electroresistance32,33, Based on reference studies, a structure with multiple HZO ferroelectric nano-islands on the substrate is fabricated. Each island can independently apply electric-field-induced crystallization, which is considered an artificial spike, as shown in Fig. 4a. When applying an external electric field, the amorphous HZO begins to crystallize. And we can store different information by controlling crystallinity in each island.

Fig. 4: Design of the HZO artificial synapse based on electric-field-induced crystallization.
figure 4

a Schematic of HZO artificial synapse. b The polarization versus applying electric field cycles. And the electric field is 2 MV cm−1. c The polarization response of state 1 under readout signals and training signals as electric field pulse respectively. d The schematic of crystallinity in different states.

As the gradual crystallization of HZO film under the influence of an external electric field, the polarization performs a continuous increase with applying electric field cycling at 2 MV cm−1, which is shown in Fig. 4b. The trend of increasing polarization is similar to the trend of increasing crystallinity, further indicating that polarization magnitude is correlated with crystallinity. We have selected four points on the graph, denoted as state 0, state 1, state 2, and state 3, which represent four distinct states for information storage, aiming to simulate the performance of artificial neural synapses. Here we consider a training pulse as 2 MV cm−1 and a readout pulse as 1 MV cm−1. Taking state 1 as an example, we examine the changes in polarization response under 100 cycles of applying training and readout pulses. As is demonstrated in Fig. 4c, the result shows that the training pulse will cause an increase of polarization, while the readout pulse stabilizes the polarization. The stability of other states is also simulated, which is shown in Fig. S2. In this manner, we have proposed a training approach within ferroelectric HZO thin films to simulate neural synapses leveraging its property of continuous variation of crystallinity and polarization of HZO under prolonged excitation by an external electric field. The entire training process is illustrated in Fig. 4d as shown below.

In summary, we have successfully extended the phase-field model based on the time-dependent Ginzburg-Landau (TDGL) equation by coupling the crystallization model, which can analyze the evolution of dynamic polarization during the process of electric-field-induced crystallization. An order parameter \(\eta \left(i,j,k\right)\) is introduced in our phase-field model, which is used to describe the transformation from an amorphous phase to a crystalline phase. We validate the electric-field-induced crystallization process by analyzing the variation of \(\eta \left(i,j,k\right)\) and observing the wake-up effect of polarization hysteresis by applying a 2 MV cm−1 electric field pulse for more than 4000 cycles. This result is close to the JMA equation as well. It was found that the remanent polarization can increase to 24 µC cm−2 and maximum polarization reach 32 µC cm−2 during the wake-up process. The evolution of polarization from a single nano-domain to a stripe domain is also demonstrated in our simulation. The crystalline phase mainly consists of four types of orthorhombic phase which aligns with the observation of HZO film in experiments. Finally, we proposed an artificial neural synapse device leveraging the property that allows for continuous polarization variation under electric field pulses. Through our simulation, we have verified the LTP properties under training signals and the stability under multiple readout signals. This demonstrates that electric-field-induced crystalline HZO holds promise as a candidate for electric artificial synapses.


Phase-field modeling of electric-field-induced crystallization

Our method couples the crystallization model and the TDGL equation. In the crystallization model, we introduce an order parameter denoted as \(\eta (i,j,k)\) to differentiate between the crystal phase and the amorphous phase. The evolution equation for the order parameter is \(\eta \left(i,j,k\right)\) given as follows:

$$\frac{\partial \eta \left(i,j,k\right)}{\partial t}=-L\frac{\delta F}{\delta \eta (i,j,k)}$$

where L is the kinetic coefficient. And F is the total energy of two systems, which can be written as,

$$F={\int }_{\!V}\left[{\varepsilon }^{2}{\nabla }_{\eta(i,j,k)}^{2}+f\left[\right.\eta (i,j,k)\right]dV$$

where ε is the gradient energy coefficient, and η is the gradient distribution of η(i, j, k). As the hafnium oxide system has many complex crystalline phases, for simplicity, we assume that all the grains in the simulated microstructure are ferroelectric. As a result, we only need to consider the transformation process from the amorphous phase to the ferroelectric phase. In this way, the η(i, j, k) can be described by a double-well function:

$$f\left[{\rm{\eta }}\left({\rm{i}},{\rm{j}},{\rm{k}}\right)\right]={\rm{H}}{{\rm{\eta }}}^{2}\left({\rm{i}},{\rm{j}},{\rm{k}}\right)\left[1-{\rm{\eta }}\left({\rm{i}},{\rm{j}},{\rm{k}}\right)\right][1-{\rm{\eta }}\left({\rm{i}},{\rm{j}},{\rm{k}}\right)+\Delta{\rm{\mu }}]\left\}\right.$$

where H is potential well depth, ∆μ is related to the driving force in the electric-field-induced crystallization system. If η(i, j, k) equals 0, it means that the unit is amorphous. While η(i, j, k) equals 1, it corresponds to the crystalline (ferroelectric) phase.

Since electric-field-induced crystallization is a complicated transformation process, we assumed that the driving force in this system could be analogously compared to thermally-induced crystallization. In the process of thermally induced crystallization, increasing the temperature enhances the thermal motion of atoms or molecules, leading them to rearrange and form a crystalline structure34. Similarly, in the context of electric-field-induced crystallization, the application of an electric field can alter the arrangement of atoms or molecules within the material, facilitating the transition to a crystalline state. So, the driving force ∆μ in Eq. (3) can be considered depending on the applied electric field and the stability of crystallization, which can be given as

$$\Delta \mu ={\rm{\beta }}\left({\varphi }_{{\rm{stable}}}-\varphi \right)\left\{\exp [E(i,j,k)-{{\rm{E}}}_{{\rm{crit}}}]-1\right\}$$

where β is a defined coefficient related to the driving force, \({\rm{\varphi }}=\frac{\sum {\rm{\eta }}\left({\rm{i}},{\rm{j}},{\rm{k}}\right)}{{nx}\times {ny}\times {nz}}\) which represent the current degree of crystallinity. And \({{\rm{\varphi }}}_{{\rm{stable}}}\) is the stable degree of crystallinity, E(i, j, k) is the local electric field, and Ecri is the critical electric field to crystallization.

For phase transition analysis in ferroelectric materials, we typically choose polarization Pi(r,t) as the order parameter. Based on the principle of energy minimization, the temporal evolution of spatially inhomogeneous polarization behavior in the ferroelectric layer can be described by the TDGL equation35,36:

$$\frac{\partial {P}_{i}\left(r,t\right)}{\partial t}=-L\frac{\delta F}{\delta {P}_{i}\left(r,t\right)},\left(i=1,2,3\right)$$

where L is the kinetic coefficient components relating to the domain switching, t is the time, and F is the total free energy of the system, which can be given as:

$$F=\int \left({f}_{{\rm{bulk}}}+{f}_{{\rm{grad}}}+{f}_{{\rm{ela}}}+{f}_{{\rm{dep}}}+{f}_{{\rm{appl}}}\right){dV}$$

where fbulk, fgrad, fela, and fappl are the contributions from bulk free energy, gradient energy, elastic strain energy, depolarization energy, and applied electric field, respectively.

The bulk free energy can be expressed as a function of various parameters such as temperature, pressure, and composition. It plays a crucial role in determining the equilibrium state of a system and can be used to predict phase changes, chemical reactions, and other thermodynamic behaviors. So, the order parameters P(r,t) and η(i, j, k) are coupled by bulk free energy:

$$\begin{array}{ll}{f}_{{\rm{bulk}}}=\eta (i,j,k)\left[{a}_{1-{\rm{FE}}}({P}_{1}^{2}+{P}_{2}^{2}+{P}_{3}^{2})\right]+\left[1-\eta (i,j,k)\right]\left[{a}_{1-{\rm{amor}}}({P}_{1}^{2}+{P}_{2}^{2}+{P}_{3}^{2})\right]\\\qquad\quad +\,\eta (i,j,k)\left[{a}_{11-{\rm{FE}}}({P}_{1}^{4}+{P}_{2}^{4}+{P}_{3}^{4})\right]+\left[1-\eta (i,j,k)\right]\left[{a}_{11-{\rm{amor}}}({P}_{1}^{4}+{P}_{2}^{4}+{P}_{3}^{4})\right]\\\qquad\quad +\,\eta (i,j,k)\left[{a}_{111-{\rm{FE}}}({P}_{1}^{6}+{P}_{2}^{6}+{P}_{3}^{6})\right]+\left[1-\eta (i,j,k)\right]\left[{a}_{111-{\rm{amor}}}({P}_{1}^{6}+{P}_{2}^{6}+{P}_{3}^{6})\right]\end{array}$$

where \({a}_{1-{\rm{FE}}}\), \({a}_{11-{\rm{FE}}}\), \({a}_{111-{\rm{FE}}}\), \({a}_{1-{\rm{amor}}}\), \({a}_{11-{\rm{amor}}}\), \({a}_{111-{\rm{amor}}}\) are the Landau coefficient of the ferroelectric phase and amorphous phase respectively. It should be noted that the Landau energy does not include the coupling coefficient of the ferroelectric phase and amorphous phase, like \({a}_{12-{\rm{FE}}},{a}_{12-{\rm{amor}}}\). This is because not considering it will not affect the main result29. The Landau coefficients are listed as follows18,37, \({a}_{1-{\rm{FE}}}=-1.1\times {10}^{9}{C}^{-2}{m}^{2}N,{a}_{11-{\rm{FE}}}=-1.98\times {10}^{10}{C}^{-4}{m}^{6}N,{a}_{111-{\rm{FE}}}=-1.6\times {10}^{11}{C}^{-6}{m}^{10}N,{a}_{1-{\rm{amor}}}=1.6\times {10}^{8}{C}^{-2}{m}^{2}N,{a}_{11-{\rm{amor}}}=1.8\times {10}^{13}{C}^{-4}{m}^{6}N,{a}_{111-{\rm{amor}}}=0\).

The gradient energy in the ferroelectric system is also regarded as the domain-wall energy, which originates from the inhomogeneous distribution of polarization in the film. The expression of gradient energy is as follows


where \({P}_{i,j}=\partial {P}_{i}/\partial {x}_{j}\), and Gijkl is the gradient energy coefficient.

The elastic strain energy is based on elasticity theory, which can be described as

$${f}_{{\rm{elas}}}=\frac{1}{2}{C}_{{ijkl}}\left({\varepsilon }_{{ij}}-{\varepsilon }_{{ij}}^{0}\right)\left({\varepsilon }_{{kl}}-{\varepsilon }_{{kl}}^{0}\right)$$

where Cijkl is the elastic stiffness tensor, εij is the total strain of the system, and \({\varepsilon }_{{ij}}^{0}\) is intrinsic strain, which means the strain produced by the materials without external stress.

The electrostatic free energy density consists of the depolarization field and the external electric field, which are given by

$${f}_{{\rm{dep}}}=-\frac{1}{2}{{\varepsilon }_{0}{\varepsilon }_{{\rm{r}}}E}_{i}{E}_{j}$$

where ε0 is vacuum permittivity, εr is the dielectric constant, and Ei is the local electric field.