lithium niobateLiNbO3
PPLN Λ = 6.82 µm · 1064 → 532 nm · 2 px/µm
lithium niobate / 01 Crystal / 1.9

1.9 Poling and periodic poling

L1 Writing domains

2Ps per area; PPLN; Volk & Wöhlecke 2008

To pole is to set the polarization with a field. A uniform field across a whole wafer makes one domain; a field applied through a comb of electrodes flips only the stripes under the teeth. The result, periodically poled lithium niobate (PPLN), alternates the sign of the crystal’s nonlinear and electro-optic coefficients every few micrometres. That alternation lets light waves of different colours stay in step over centimetres of crystal (quasi-phase-matching, Chapter 02).

Every flipped domain moves a fixed charge: twice the spontaneous polarization times its area. Flipping one square centimetre takes 142 microcoulombs with Ps = 0.71 C/m2 (160 with 0.80 C/m2 conflict) derived, so the current trace of a poling pulse is a direct record of how much crystal has switched.

Poling bench: z-cut patch 20.8 × 16.0 µm, top view of the +z face, comb on +ztemplate template
Statedone
Time, voltaget  70.00 ms V  0.00 kVtemplate
I = 2Ps dA/dt + C dV/dt   0.0 nAderived
Q = ∫(I − C dV/dt) dt197.0 pCderived
2PsA of the map197.0 pCderived
Reversed area A138.7 µm²template
Q / A 142.0 µC/cm²derived
Switched fraction X0.417derived
Domain duty / comb w/Λ0.42 / 0.41derived
Backswitched0.00template
KAI fitn 2.06template
t₀  6.81 ms r² 0.88
22.0 kV/mm = 11.00 kV
ms, window  70 ms
After pulse
Comb Λ, w/Λ
Ps, C/m2
conflict
Time axis
Run
Measured P–E, along the applied fieldderived template
* live, P = −Ps + 2PsX  o reference  : Ec 21 kV/mm P-comp, Ec − 2Eint, Eint 2.5 kV/mm P(abs) misprint
# reversed, −z up+ one of two rows reversed. original, +z up= comb fingero KAI fit- - comb w/ΛPs P-comp, Ec P-comp, Eint P(abs), facets P-comp, rates template, map template
22.0 kV/mm = 11.00 kV
10 ms
After the pulse
Comb period, finger fraction template
Ps for current and charge conflict
Image template
 7
013V, kV−20080I, nA0472Q, pC01X0.1110t, ms
Measured P–E loop, along the applied fieldderived template
−0.7100.71−26−1602126P, C/m²E along the applied field, kV/mm
live, −Ps + 2PsXreference branchEc 21 kV/mm P-comp and Ec − 2Eint▲ centre Eint 2.5 kV/mm P(abs) misprint
Time axis
State
done
Time, voltage
t  70.00 ms V  0.00 kV
Current I derived
   0.0 nA
Charge Q derived
197.0 pC
2PsA of the map
197.0 pC
Q / A
 142.0 µC/cm²
Switched fraction X derived
0.417
Comb w/Λ
0.41
Backswitched template
0.00
KAI fit template
n 2.06
t₀  6.81 ms r² 0.88
Ps out of the page, originalPs into the page, reversedcomb finger on +z trace2PsA from the mapKAI fitcomb w/Λplanned V Ps P-comp Ec P-comp Eint P(abs) facets P-comp rates template

Press Pulse: domains nucleate on the +z face, mostly at the finger edges, grow as hexagons, touch and merge into stripes while the current trace draws itself; the integrated charge Q equals 2Ps times the reversed area at every step. Set the field to 0 after the pulse and press again: the fresh domains shrink back (backswitching, a negative current) template; hold Ec/2 and they stay. A longer pulse spreads domains past the fingers (domain merging) and lifts the duty cycle above w/Λ. The P–E panel plots P = −Ps + Q/A against the applied field as the pulse plays: a unipolar pulse drives only the forward branch, so the return branch, at −(Ec − 2Eint) = −16 kV/mm, is never reached and is not drawn. Any parameter change loads a fresh single-domain patch; the same seed replays the same run. Rates are template values; Ps, Ec, Eint, the hexagon facets and nucleation at +z are sourced.

L2 Charge, history, practice

2Ps; 1962–1995; Volk & Wöhlecke 2008 pp. 177–180
QA=2Ps=142µC/cm2derived
QuantityValueStatus
Switched charge per area, Q/A = 2Ps1.42 C/m2 = 142 µC/cm2 (Ps = 0.71 C/m2); 160 µC/cm2 (Ps = 0.80 C/m2) conflictderived
Charge to invert a whole 76.2 mm (3 inch) wafer6.5 mC (Ps = 0.71 C/m2); 7.3 mC (0.80 C/m2); area π (38.1 mm)2derived
Optimum duty cycle for first-order QPM0.5P-comp

Milestones of domain engineering, dates as published (Chapter 07 holds the full chronology):

YearStepSource
1962Periodic reversal of the nonlinear coefficient proposed for phase matchingP
1965Domains revealed by etchingP
1966Preparation of single-domain crystalsP
1979Ti in-diffusion inverts a surface layer on the +c faceP(abs)
1980Periodic laminar domains grown in by Czochralski growth striations; SHG enhanced by QPM on d33; Y-doped, period 7 µmP(abs) P-comp
1993First-order QPM waveguide poled by an external field at room temperature; 20.7 mW blue, 600 %/(W cm2); pulse 24 kV/mm, 100 µs, period 2.8 µmP(abs) P-comp
1994–1995Liquid-electrode poling, period from 9 µm to 4.5 µm; deff from 2 to 19 pm/V against a 22 pm/V limitP-comp
1995Bulk PPLN optical parametric oscillators; backswitching found and controlledP P-comp

Poling practice reported for bulk congruent crystal P-comp:

  • Backswitching. If the pulse is too short the new domains flip back; at 25 kV/mm the critical time was at least 50 ms. Remedies: hold at about Ec/2 after the pulse, or use ramped fields.
  • Domain merging. Domains spread beyond the electrode, so the electrode duty cycle is set below the target.
  • Electrodes. Al stripes on +z under photoresist (or resist openings under a conductor), contacted through LiCl electrolyte; electrolyte on −z.
  • Stability. PPLN survived heating to 800 °C.

L3 Kinetics and current

nucleation and growth; KAI; switching current; thin films

Kinetics. Switching proceeds by nucleation (at the +z surface in undoped crystal), forward growth along c, and sideways wall motion; wall motion itself proceeds by nucleation of steps on the existing wall, which accounts for the activation-type field dependence P-comp P. In congruent crystal the walls run parallel to the yz glide planes P-comp; DFT finds Y-walls lower in energy than X-walls, so domains are hexagons bounded by Y-walls, and antisite–wall interactions in congruent LiNbO3 are too weak to change that P(abs). A Kolmogorov–Avrami–Ishibashi switched fraction is the fit form used below:

X(t)=1−exp[−(t/t0)n]

In the bench above all rates are template values; only Ps, the Ec anchor, Eint and the domain shape are sourced. Fitted to the default pulse, the automaton gives n = 2.06, t0 = 6.81 ms (r2 = 0.88) template: a property of the template, not of LiNbO3.

What the switching current measures. The current through the electrodes is the switching term plus the charging of the electrode capacitance:

I(t)=2PsdAdt+CdVdtderived
∫(I−CdVdt)dt=2PsAderived

Integrated current minus the capacitive part equals 2PsA of the switched area. In the bench, Q = 196.992 pC against 2PsA = 196.992 pC for the default pulse derived; the displacement term uses C = 0.067 fF derived. The Ps disagreement (0.71 vs 0.80 C/m2 conflict) is therefore an 11% uncertainty in any area inferred from charge derived.

Thin films. Poling of x-cut and z-cut thin-film LN (TFLN; coplanar electrodes, sub-micrometre periods, incomplete depth) is treated with process detail in Chapter 05.

How the bench is computed. Stochastic cellular automaton on a triangular lattice in the z-cut top view, seeded generator, synchronous update. Nearest neighbours lie at 30° + k · 60° from x, so facets run along y and ±60° from y, the traces of the three mirror planes. Untouched sites under a finger nucleate (edge sites 50 times more often than interior ones); sites next to reversed ones switch at step rates (1 or 2 reversed neighbours) or kink rates (3 or more), each with the activation form of Volk & Wöhlecke 2008 Eq. (7.32) referenced to Ec − Eint. Domains younger than the stabilization age revert from their boundary while E < Ec/2. The map has no depth: domains are assumed through the thickness.

ParameterValueStatus
Spontaneous polarization Ps0.71 C/m2 (0.80 offered)P-comp conflict
Coercive field Ec, congruent21 kV/mmP-comp
Internal field Eint, congruent2.5 kV/mmP(abs)
Hold level that suppresses backswitching0.5 Ecreported
Stabilization age50 mstemplate
Nucleation rate at Ec, finger-edge site; interior factor; α200 s−1; 0.02; 10template
Step rates, 1 / 2 reversed neighbours20 / 100 s−1template
Kink rate, 3 or more reversed neighbours; wall α2 × 104 s−1; 6template
Backswitching rate at domain boundaries200 s−1template
Field between fingers / applied0.7template
Lattice spacing; patch; time step0.25 µm; 20.8 × 16.0 µm; 0.05 mstemplate
Electrode capacitance (displacement term)0.067 fFderived

Sources

13 cited in 1.9
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  2. Hsu et al. 1997R. Hsu, E. N. Maslen, D. du Boulay, N. Ishizawa, "Synchrotron X-ray studies of LiNbO3 and LiTaO3", Acta Cryst. B 53, 420-428 (1997). doi:10.1107/S010876819600777X
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  4. Kitamura et al. 1998K. Kitamura, Y. Furukawa, K. Niwa, V. Gopalan, T. E. Mitchell, "Crystal growth and low coercive field 180 ° domain switching characteristics of stoichiometric LiTaO3", Appl. Phys. Lett. 73, 3073-3075 (1998). doi:10.1063/1.122676
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  6. Nassau et al. 1965K. Nassau, H. J. Levinstein, G. M. Loiacono, "The domain structure and etching of ferroelectric lithium niobate", Appl. Phys. Lett. 6, 228-229 (1965). doi:10.1063/1.1754147
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  13. Lee et al. 2011D. Lee, H. Xu, V. Dierolf, V. Gopalan, S. R. Phillpot, "Shape of ferroelectric domains in LiNbO3 and LiTaO3 from defect/domain-wall interactions", Appl. Phys. Lett. 98, 092903 (2011). doi:10.1063/1.3560343