Ferroelectric Tunnel Junction (FTJ)

1. Theory

• Definition: A ferroelectric tunnel junction (FTJ) is a two-terminal device in which a ferroelectric layer a few nanometres thick is the tunnel barrier between two electrodes; the polarization direction sets the tunnelling resistance.
• Tunnelling electroresistance (TER): The ratio $R_{OFF}/R_{ON}$ between the two polarization states.
• Barrier modulation: Unequal screening in two different electrodes makes a polarization-dependent potential step $\Delta U$ across the barrier; piezoelectric strain and interface bonding add smaller effects.
• Asymmetric electrodes needed: Identical electrodes and interfaces give no first-order TER.
• Thickness trade-off: Current falls as $\exp (-2\kappa t)$; a thicker barrier raises TER but lowers read current, while too thin a film loses ferroelectricity to the depolarizing field.
• Materials: Perovskites ($\mathrm{BaTi}{\mathrm{O}}_3$, PZT) with oxide electrodes in early work; CMOS-compatible doped $\mathrm{Hf}{\mathrm{O}}_2$ (e.g. HZO) more recently.

2. Working Principle

• Write: A voltage above the coercive voltage sets the polarization, and so the barrier profile, to the high- or low-resistance state.
• Non-destructive read: A read voltage well below $V_c$ measures the tunnelling current without disturbing the polarization.
• Tunnelling regime: Reads are in direct tunnelling; at higher bias the barrier becomes triangular (Fowler-Nordheim), so TER must be quoted at a stated read voltage.
• Composite barrier: Adding a thin dielectric (MFIM) raises TER through asymmetric voltage division but increases the write voltage.
• Analog states: Partial domain switching gives intermediate conductance $G=x{G}_{ON}+(1-x)G_{OFF}$.
• No transistor channel: The cell is a simple crosspoint element, but its read current is much smaller than a FeFET’s of the same area.

3. Applications

• Current status: Research devices; not yet in commercial products.
• Crosspoint non-volatile memory (target): Dense two-terminal arrays with non-destructive reads.
• Neuromorphic synapses (research): Analog conductance states for in-memory computing.

Name	Formula	Related Formulae	Variables/Constants
Tunnelling electroresistance (TER) ratio	$TER=\frac{R_{OFF}}{R_{ON}}=\frac{J_{ON}}{J_{OFF}}$	$TE{R}_{\%}=\frac{R_{OFF}-R_{ON}}{R_{ON}}\times 100\%$	$\begin{array}{r}TER:ratiooftheresistance(orcurrent\\ density)ofthetwopolarizationstatesat\\ thesamereadvoltage\end{array}$ $\begin{array}{r}{R}_{ON},J_{ON}:resistanceandcurrentdensityof\\ thelow-resistancestate\end{array}$ $\begin{array}{r}{R}_{OFF},J_{OFF}:resistanceandcurrentdensity\\ ofthehigh-resistancestate\end{array}$ $\begin{array}{r}TE{R}_{\%}:thesamequantityinthepercentage\\ formusedinsomepapers(thetwo\\ definitionsdifferbyoneandthe\\ percentageformmustnotbecompared\\ directlywiththeratioform)\end{array}$
Direct tunnelling through a thin barrier (WKB)	$T\approx \exp \left(-2{\int }_0^t\kappa (x)dx\right)$ $\kappa (x)=\frac{\sqrt{2m^{\ast }\left[U(x)-E\right]}}{\hslash }$	$J\approx J_0\exp \left(-\frac{2t\sqrt{2m^{\ast }\bar{\phi }}}{\hslash }\right)$ $J_{low}=\frac{3\sqrt{2m\bar{\phi }}}{2t}{\left(\frac{q}{h}\right)}^{2}V\exp \left(-\frac{4\pi t}{h}\sqrt{2m\bar{\phi }}\right)$	$\begin{array}{r}T:transmissionprobabilityofanelectron\\ throughthebarrier\end{array}$ $\begin{array}{r}\kappa (x):decayconstantofthewavefunction\\ atpositionxinsidethebarrier\end{array}$ $\begin{array}{r}t:barrierthickness(theferroelectric\\ layerthicknessforasingle-layer\\ junction)\end{array}$ $\begin{array}{r}U(x),E:potentialenergyprofileofthe\\ barrierandenergyoftheelectron\end{array}$ $m^{\ast }:effectivetunnellingmassinthebarrier$ $\bar{\phi }:averagebarrierheightabovetheFermilevel$ $\begin{array}{r}{J}_0:prefactorthatdependsonthe\\ electrodestatesandthebias\end{array}$ $\begin{array}{r}{J}_{low}:low-biascurrentdensityfromthe\\ Simmonsmodelforarectangularbarrier,\\ withVtheappliedvoltageandmthefree\\ electronmass(validforqVmuchlessthan\\ \bar{\phi })\end{array}$ $\begin{array}{r}q,h,\hslash :elementarycharge,Planck\\ constantandreducedPlanckconstant\end{array}$
Polarization-dependent screening and barrier step	$\Delta U=\frac{qP}{{\epsilon }_0}\left(\frac{{\delta }_1}{{\epsilon }_1}-\frac{{\delta }_2}{{\epsilon }_2}\right)$	${\phi }_{ON,OFF}={\phi }_0\mp \frac{\Delta U}{2}$ ${\delta }_{TF}=\sqrt{\frac{{\epsilon }_0{\epsilon }_e}{q^{2}g(E_F)}}$ ${\sigma }_s=\frac{Pt}{t+{\epsilon }_b\left({\delta }_1/{\epsilon }_1+{\delta }_2/{\epsilon }_2\right)}$	$\begin{array}{r}\Delta U:differenceintheelectrostatic\\ potentialenergystepacrossthebarrier\\ betweenthetwopolarizationstates\end{array}$ $P:polarizationoftheferroelectricbarrier$ $\begin{array}{r}{\delta }_1,{\delta }_2:screeninglengthsoftheleftand\\ rightelectrodes\end{array}$ $\begin{array}{r}{\epsilon }_1,{\epsilon }_2:relativepermittivitiesofthe\\ screeningregionsofthetwoelectrodes\end{array}$ $\begin{array}{r}{\phi }_0:averagebarrierheightwithzero\\ polarization\end{array}$ $\begin{array}{r}{\phi }_{ON},{\phi }_{OFF}:averagebarrierheightsofthe\\ low-resistanceandhigh-resistancestates\end{array}$ $\begin{array}{r}{\delta }_{TF}:Thomas-Fermiscreeninglengthofan\\ electrode\end{array}$ $\begin{array}{r}{\epsilon }_e:backgroundrelativepermittivityof\\ theelectrode(1forasimplemetal;a\\ latticevalueforanoxideor\\ semiconductorelectrode)\end{array}$ $\begin{array}{r}{\sigma }_s:screeningchargeperunitareain\\ eachelectrode(Zhuravlevetal.);the\\ mainformulauses{\sigma }_s\approx P,andP\\ shouldbereplacedby{\sigma }_{s}whenthe\\ barrierisverythin\end{array}$ $\begin{array}{r}g(E_F):densityofstatesperunitvolume\\ attheFermileveloftheelectrode\end{array}$ $\begin{array}{r}(thestepiszeroforidenticalelectrodes\\ andmustbeobtainedwithtwodifferent\\ electrodesordifferentinterfaces;each\\ stateshiftstheaveragebarrierby\\ \mp \Delta U/2,sothestatesdifferby\Delta U)\end{array}$
TER from the average barrier height	$TER\approx \exp \left[\frac{2t\sqrt{2m^{\ast }}}{\hslash }\left(\sqrt{{\phi }_{OFF}}-\sqrt{{\phi }_{ON}}\right)\right]$	$TER\approx \exp \left[\frac{t}{\hslash }\sqrt{\frac{2m^{\ast }}{{\phi }_0}}\Delta U\right]\left(\Delta U\ll {\phi }_0\right)$	$\begin{array}{r}TER:ratioofthecurrentdensitiesofthe\\ twostatesfromtheexponentialfactorof\\ therectangular-barriermodel(prefactors\\ aretakenasequal;changesofbarrier\\ shapeandthicknessareneglected;\\ measuredTERrangesfromabout10to\\ above10^4)\end{array}$ $t:ferroelectricbarrierthickness$ $m^{\ast }:effectivetunnellingmass$ $\begin{array}{r}{\phi }_{ON},{\phi }_{OFF}:averagebarrierheightsofthe\\ twostates\end{array}$ ${\phi }_0:averagebarrierheightatzeropolarization$ $\begin{array}{r}\Delta U:barrierstepbetweenthestates(see\\ therowabove)\end{array}$
Fowler-Nordheim tunnelling (high bias)	$J_{FN}=\frac{q^3{E}^2}{8\pi h{\phi }_B}\exp \left(-\frac{8\pi \sqrt{2m^{\ast }}{\phi }_B^{3/2}}{3hqE}\right)$	$qV>{\phi }_B$	$J_{FN}:Fowler-Nordheimcurrentdensity$ $E:electricfieldinthebarrier$ $\begin{array}{r}{\phi }_B:barrierheightattheinjecting\\ electrode(inenergyunits)\end{array}$ $m^{\ast }:effectivetunnellingmass$ $\begin{array}{r}qV>{\phi }_B:conditiononthevoltageacross\\ thebarrierforwhichthebarrierbecomes\\ triangularandthedirect-tunnelling\\ expressionnolongerapplies\end{array}$ $\begin{array}{r}(thefieldusedisthefieldinthe\\ barrieratthereadvoltage;fora\\ ferroelectricbarrieritincludesthe\\ fieldfromthepolarization)\end{array}$
Depolarizing field from imperfect screening	$E_{dep}=-\frac{PX}{{\epsilon }_0\left(t_{FE}+{\epsilon }_{b}X\right)}\approx -\frac{PX}{{\epsilon }_0{t}_{FE}}$	$V_{dep}=-E_{dep}{t}_{FE}$ $X=\frac{{\delta }_1}{{\epsilon }_1}+\frac{{\delta }_2}{{\epsilon }_2}$	$\begin{array}{r}{E}_{dep}:depolarizingfieldinthe\\ ferroelectricatzeroappliedvoltage\\ (oppositetothepolarization)\end{array}$ $P:polarization$ $t_{FE}:ferroelectricthickness$ $\begin{array}{r}{\delta }_1,{\delta }_2,{\epsilon }_1,{\epsilon }_2:screeninglengthsand\\ relativepermittivitiesofthetwo\\ electrodes\end{array}$ $\begin{array}{r}{V}_{dep}:voltagedroppedinthescreening\\ regionsoftheelectrodes\end{array}$ $\begin{array}{r}(exactforshortedelectrodeswithlinear\\ screening;theapproximationholdswhen\\ t_{FE}\gg {\epsilon }_{b}X.Itisthesame\\ constructionasthedead-layerrowonthe\\ FeRAMpage;Xisthesumofthetwo\\ effectivescreeningthicknesses)\end{array}$
Write voltage with a dielectric layer (metal-ferroelectric-insulator-metal)	$V_{write}\approx V_c+\frac{\left(P_r+{\epsilon }_0{\epsilon }_b{E}_c\right)t_{DE}}{{\epsilon }_0{\epsilon }_{DE}}$	$V_c=E_c{t}_{FE}$ $D={\epsilon }_0{\epsilon }_b{E}_{FE}+P={\epsilon }_0{\epsilon }_{DE}{E}_{DE}$	$\begin{array}{r}{V}_{write}:voltageneededtocomplete\\ thereversalofthepolarizationina\\ stackofaferroelectricandadielectric\\ layer(P_r+{\epsilon }_0{\epsilon }_b{E}_{c}isthe\\ displacementattheendoftheswitching,\\ asontheFeFETpage)\end{array}$ $\begin{array}{r}{V}_c,E_c:coercivevoltageandcoercive\\ fieldoftheferroelectric\end{array}$ $P_r:remanentpolarization$ $\begin{array}{r}{\epsilon }_b:backgroundrelativepermittivityof\\ theferroelectric\end{array}$ $\begin{array}{r}{t}_{DE},{\epsilon }_{DE}:thicknessandrelative\\ permittivityofthedielectriclayer\end{array}$ $t_{FE}:thicknessoftheferroelectriclayer$ $\begin{array}{r}D:electricdisplacement,continuous\\ throughthestackifthereisnointerface\\ charge\end{array}$
Multi-domain (analog) conductance	$G=x{G}_{ON}+\left(1-x\right)G_{OFF}$	$x=\frac{A_{\uparrow }}{A_{total}}$	$\begin{array}{r}G:conductanceofthejunctionwitha\\ partlyswitchedferroelectric,from\\ domainsactingasparallelconductors\end{array}$ $\begin{array}{r}{G}_{ON},G_{OFF}:conductancesofafullyswitched\\ junctioninthelowandhighresistance\\ state\end{array}$ $\begin{array}{r}x:fractionoftheareaoccupiedby\\ domainswiththepolarizationthatgives\\ thelow-resistancestate\end{array}$ $\begin{array}{r}{A}_{\uparrow },A_{total}:areaofthesedomainsandtotal\\ junctionarea\end{array}$ $\begin{array}{r}(themodelignoreslateralcurrent\\ spreadingandtheeffectofdomainwalls)\end{array}$

Important Questions

Ques: How does the polarization of the barrier change the tunnelling current in a ferroelectric tunnel junction?

The ferroelectric layer is the tunnel barrier, so reversing its polarization changes the barrier seen by the electrons. Three effects are usually named: (i) the screening charge in the two electrodes is different when the electrodes or interfaces differ, which gives a polarization-dependent potential step across the barrier ($\Delta U$ in the screening row); (ii) the piezoelectric strain changes the barrier thickness and the effective mass slightly; and (iii) the bonding at the two interfaces changes, which changes the local barrier height. The first effect is the one with the simplest model and gives a TER that grows exponentially with the barrier thickness. A junction with two identical electrodes and identical interfaces shows no TER at low bias at all, because the two polarization states are then mirror images of each other, whatever the mechanism, which is why the electrodes are made different (for example a metal and a semiconductor, or two metals with different screening lengths). Reference: E.Y. Tsymbal and H. Kohlstedt, “Tunneling across a ferroelectric,” Science 313, 181 (2006); M.Ye. Zhuravlev, R.F. Sabirianov, S.S. Jaswal and E.Y. Tsymbal, “Giant electroresistance in ferroelectric tunnel junctions,” Phys. Rev. Lett. 94, 246802 (2005).

Ques: Why does the current of a ferroelectric tunnel junction depend so strongly on the barrier thickness, and what limits the minimum thickness?

Direct tunnelling gives a current that falls as $\exp (-2\kappa t)$. For a barrier height of 1 eV and the free electron mass, $\kappa =\sqrt{2m\phi }/\hslash \approx 5.1\times 10^9$ m${}^{-1}$, so each 0.1 nm of thickness changes the current by a factor of about 2.8, and a 2 nm barrier has $2\kappa t\approx 20$ (transmission of order $10^{-9}$). The same exponential gives the TER, and the example in the TER row (t = 2 nm, ${\phi }_0$ = 1 eV, $\Delta U$ = 0.2 eV) gives a TER of about 8. A thicker barrier gives a larger TER but a read current that is too low to measure, and a thinner barrier carries more current but may lose ferroelectricity because of the depolarizing field. The experimental junctions are therefore a few nanometres thick, with a lower limit given by the critical thickness for stable polarization. Reference: J. Junquera and P. Ghosez, “Critical thickness for ferroelectricity in perovskite ultrathin films,” Nature 422, 506 (2003); J.G. Simmons, “Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film,” J. Appl. Phys. 34, 1793 (1963).

Ques: How does a ferroelectric tunnel junction differ from FeRAM and from the FeFET?

In FeRAM the polarization is read by switching it and measuring the charge, which destroys the state and needs a write-back. In the FeFET the polarization is read through the threshold voltage of a transistor. In the FTJ the polarization is read as a resistance of a two-terminal junction at a voltage well below the coercive voltage, so the read is non-destructive, and the cell needs no transistor channel. The price is a small read current (set by the exponential in the barrier thickness) and a TER that must be large enough to be separated from the variation between devices. Because the polarization can be set to a fraction of the junction area, the junction also works as an analog memory element (multi-domain row). Reference: A. Chanthbouala et al., “A ferroelectric memristor,” Nat. Mater. 11, 860 (2012); V. Garcia and M. Bibes, “Ferroelectric tunnel junctions for information storage and processing,” Nat. Commun. 5, 4289 (2014).

Ques: Why is a composite barrier of a ferroelectric and a dielectric layer used, and what does the write voltage look like?

A thin dielectric layer in series with the ferroelectric makes the barrier asymmetric and raises the TER, because polarization reversal changes the voltage dropped in the dielectric layer and therefore the shape of the barrier. A second reason is the extra control of the current. It also increases the voltage required to switch: in the write voltage row the dielectric layer adds a term proportional to $t_{DE}/{\epsilon }_{DE}$ to the coercive voltage, which is the same division of the voltage as in the FeFET stack without the semiconductor surface potential. A high-permittivity dielectric or a thinner dielectric reduces this penalty. A related scheme uses a semiconductor electrode, where the polarization opens or closes a depletion layer that acts as an extra barrier. Reference: M.Ye. Zhuravlev, Y. Wang, S. Maekawa and E.Y. Tsymbal, “Tunneling electroresistance in ferroelectric tunnel junctions with a composite barrier,” Appl. Phys. Lett. 95, 052902 (2009) (ferroelectric plus dielectric barrier); Z. Wen, C. Li, D. Wu, A. Li and N. Ming, “Ferroelectric-field-effect-enhanced electroresistance in metal/ferroelectric/semiconductor tunnel junctions,” Nat. Mater. 12, 617 (2013) (semiconductor electrode); see also the Ferroelectric Field Effect Transistor (FeFET) page for the same voltage division.

Ques: Which tunnelling regime is the read operation in, and why does that matter?

The read voltage is kept below the coercive voltage, which is a few tenths of a volt for a barrier of a few nanometres, and it is smaller than the barrier height (about 1 eV or less), so the read is in the direct-tunnelling regime and the low-bias and Simmons expressions apply. At a higher voltage the barrier becomes triangular (the Fowler-Nordheim condition qV > ${\phi }_B$) and the current grows faster with the voltage, which also changes the ratio between the two states. The TER therefore depends on the read voltage and must be quoted at a stated voltage. For a barrier with a polarization-dependent step the transition to the FN regime occurs at different voltages in the two states. Reference: J.G. Simmons, J. Appl. Phys. 34, 1793 (1963); H. Kohlstedt, N.A. Pertsev, J. Rodriguez Contreras and R. Waser, “Theoretical current-voltage characteristics of ferroelectric tunnel junctions,” Phys. Rev. B 72, 125341 (2005).

Ques: What is the difference between the TER of a junction and the memory window of a FeFET, and can the two be compared?

The TER is a ratio of two currents at the same read voltage, so it expresses the separation of the states on a logarithmic scale and depends on the barrier thickness and on the shape of the barrier. The memory window of a FeFET is a voltage difference between two threshold voltages and is limited by the coercive voltage (about $2E_c{t}_{FE}$), while the current ratio of a FeFET depends on the subthreshold slope ($10^{MW/S}$). Both are set by the polarization, but the one is a voltage and the other a ratio, so a direct comparison needs the read conditions of each. For barriers thick enough to stay ferroelectric, the FTJ usually carries a much smaller read current than a FeFET of the same area, because the current has to tunnel through the full thickness; the exact ratio depends strongly on the barrier thickness. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007; V. Garcia and M. Bibes, Nat. Commun. 5, 4289 (2014).

Ques: Which materials are used for ferroelectric tunnel junctions?

Early experimental junctions used perovskite ferroelectrics such as BaTiO${}_3$ and Pb(Zr,Ti)O${}_3$ with oxide electrodes (for example SrRuO${}_3$ or La${}_{0.7}$Sr${}_{0.3}$MnO${}_3$), where the thickness could be a few unit cells. More recent work uses doped HfO${}_2$ (for example Hf${}_{0.5}$Zr${}_{0.5}$O${}_2$) between metal or semiconductor electrodes, because it is compatible with CMOS processing and stays ferroelectric to a few nanometres (down to about 1 nm in some reports), although its tunnelling mass and barrier height are different from those in the perovskites. The choice of electrodes sets the screening lengths ${\delta }_1$ and ${\delta }_2$ and so the barrier step. Reference: A. Gruverman et al., “Tunneling electroresistance effect in ferroelectric tunnel junctions at the nanoscale,” Nano Lett. 9, 3539 (2009); S.S. Cheema et al., “Enhanced ferroelectricity in ultrathin films grown directly on silicon,” Nature 580, 478 (2020); T. Mikolajick et al., “Next generation ferroelectric materials for semiconductor process integration and their applications,” J. Appl. Phys. 129, 100901 (2021).

Related pages in this vault: Ferroelectric Field Effect Transistor (FeFET), Ferroelectric Random Access Memory (FeRAM), Organic Ferroelectric Polymer Memory (PVDF and P(VDF-TrFE)), Ferroelectric NAND and 3D Ferroelectric Memory (Vertical FeFET and Stacked FeRAM), Ferroelectric Random Access Memory (FeRAM, PZT and HfO2), Piezoresponse Force Microscope (PFM), Two-Dimensional Material Memristor (Atomristor and Memtransistor), Resistive Random Access Memory (ReRAM, RRAM), Spin-Transfer Torque Magnetic Random Access Memory (STT-MRAM).