1.8 Domains, internal field, coercive field

L1 Domains and the field to flip them

Volk & Wöhlecke 2008 Table 7.1; Gopalan et al. 1998; Chen et al. 2003

A region of crystal with one polarization direction is a domain. In LiNbO₃ the polarization can point only up or down c, so neighbouring domains always differ by 180° and are separated by thin walls P(abs). Wafers are sold single-domain.

Flipping a domain takes a field of about 21 kV per millimetre in congruent crystal (10.5 kV across a standard 0.5 mm wafer), but only 6.0–6.5 kV/mm (or 2.1–2.5 kV/mm on another page of the same compilation) in near-stoichiometric crystal conflict and under 2 kV/mm in near-stoichiometric crystal with a little MgO P-comp P(abs). Congruent crystal also remembers which way it grew: it flips more easily back to its original direction than away from it, as if a built-in bias field of about 2.5 kV/mm pointed along the original polarization P(abs). That bias is attributed to the same antisite defects as optical damage and vanishes in stoichiometric crystal (L3) P-comp.

Seen from above, domains in LiNbO₃ grow as hexagons whose walls are parallel to the crystal's mirror planes, an image of the threefold symmetry P-comp P(abs).

Hysteresis comparator: P–E loops on sourced anchors, room temperature, virgin P_s along +zP-comp derived template

Emphasize

     |                                        :                                       
+0.8_|                                        :                                       
     |        ########################################################################
     |        ###                  +++  xx@@  : @@*   +++o            #######         
     |       ##                    +++  xx@@  : @@*   ++oo           ######           
     |       #                     ++   xx@@  : @@*   ++o            ######           
     |       #                     ++   xx@@  : @@*   ++o            #####            
     |      ##                     ++   xx@@  : @@*   ++o            #####            
     |      #                      ++   xx@@  : @@*   ++o           ######            
   0_|______#______________________++___x*@@__:_@@*__+++o___________#####_____________
     |      #                      ++   x*@@  : @@   +++o           #####             
     |     ##                     +++   x*@@  : @@   +++o           #####             
     |     #                      +++   x*@@  : @@   +++o          ######             
     |     #                      +++   x*@@  : @@   +++o          #####              
     |    ##                      +++   x*@@  : @@   ++oo          #####              
     |    ##                      +++   x*@@  : @@   ++oo         ######              
     |  ###                      +++   xx*@@  :x@@  +++o        #######               
−0.8_|#################################################################               
     |                                        :                                       
     |                                        :                                       
     +--------+---------------+---------------+---------------+---------------+-------
             −20             −10              0              10              20  kV/mm
                                        <==---| Eint 2.2–3.4 kV/mm

#CLNonear-SLN+CLN:5%MgOxCLN:8%ZnO*nSLN:1%MgO@nSLN:2%MgO!near-SLN E_c 2.1–2.5, p. 118 conflict<==|E_int, E = 0 to loop centrerow 0.1 C/m², column 0.625 kV/mm; _ P = 0, : E = 0

Ec 21 kV/mm Eint 2.2–3.4 kV/mmV 10.5 kV @ 0.50 mm

Crystal	Congruent
P_s	0.71–0.80 C/m²	conflict
E_c, forward	21 kV/mm	P-compP-compconflictP-compP-compP-compP(abs)
E_int	2.2–3.4 kV/mm	misprint P(abs)P-compP-compP-compP-compP(abs)
E_int as drawn
Forward switching, −E_c, kV/mm	−21.0	derived
Reverse switching, E_c − 2E_int, kV/mm	14.2–16.6	derived
Loop centre, −E_int, kV/mm	−3.4 to −2.2	derived
Loop width, kV/mm	35.2–37.6	derived
V = E_c t, kV	10.5	derived
V, near-SLN E_c of p. 118, kV		conflict

Crystal	E_c fwd, kV/mm	E_int, kV/mm	V at t, kV	Source
Congruent	21	2.2–3.4	10.5	P-compmisprint
Near-stoichiometric	6.0–6.5 / 2.1–2.5	→ 0	3.00–3.25	P-compconflict
CLN + 5% MgO	6.0–6.8	0.5	3.00–3.40	P-comp
CLN + 8% ZnO	2.5–3.5	0.5	1.25–1.75	P-comp
Near-SLN + 1% MgO	2.5	→ 0	1.25	P-comp
Near-SLN + 2.0 mol% MgO (VTE)	1.8 ± 0.2	not reported	0.90 ± 0.10	P(abs)

Wafer thickness t0.50 mm

switching fields derivedtanh shape, w = 0.05 E_c templateP_s band 0.71–0.80 C/m² conflictV = E_c t derived

Crystal

Other crystals

CongruentP-compmisprint P(abs)P-compconflictP-compP-compP-compP(abs)

selected: band over P_s 0.71–0.80 C/m² conflict and the E_c, E_int ranges other crystals near-SLN E_c 2.1–2.5 kV/mm, p. 118 conflict E_int: E = 0 to loop centre derived congruent E_int about 2.5 kV/mm P(abs) tanh shape template

Voltage across the wafer derived10.5 kV

Wafer thickness0.50 mm

E_c, forward: 21 kV/mm
E_int: 2.2–3.4 kV/mm
Forward switching: −21.0 kV/mm
Reverse switching: 14.2–16.6 kV/mm
Loop centre: −3.4 to −2.2 kV/mm
Loop width: 35.2–37.6 kV/mm

Select congruent, then near-stoichiometric: the forward switching field drops from 21 to 6.0–6.5 kV/mm, the loop narrows from 35.2–37.6 to 12.0–13.0 kV/mm, and its centre slides from −3.4 to −2.2 kV/mm back to zero as E_int vanishes derived. Drag the thickness: at 0.50 mm the voltage is 10.5 kV for congruent and 0.90 ± 0.10 kV for near-SLN + 2% MgO derived. Ranges are drawn as bands; the loop shape is a template template.

L2 Field anchors and switching

E_c, E_int; V = E_c t; switching time; domain shapes; etching

Coercive and internal fields at room temperature (literature averages compiled by Volk & Wöhlecke 2008, plus individual reports):

Crystal	E_c (forward, from virgin state)	E_int	Source
Congruent	21 kV/mm (210–220 kV/cm)	2.2–3.4 kV/mm (22.2 kV/cm refined; 33.5 kV/cm first report) misprint	P-comp
Congruent		about 2.5 kV/mm	P(abs)
Near-stoichiometric	6.0–6.5 kV/mm (Table 7.1) \| 2.1–2.5 kV/mm (p. 118) conflict	tends to 0	P-comp
Ratio congruent / near-stoichiometric (C = 0.484 vs 0.498)	4–5		P(abs)
Ratio, another near-stoichiometric crystal	about 3		P-comp
Congruent + 5% MgO	6.0–6.8 kV/mm (table average); switching at 4.45 kV/mm (0.5 mm wafer); poling with 2.5 kV/mm pulses (4.8% MgO, 0.3 mm)	0.5 kV/mm	P-comp
Congruent + 8% ZnO	2.5–3.5 kV/mm	0.5 kV/mm	P-comp
Near-stoichiometric + 1% MgO	2.5 kV/mm	tends to 0	P-comp
Near-stoichiometric + 2.0 mol% MgO (VTE)	1.8 ± 0.2 kV/mm	not reported	P(abs)

Wafer voltage

Voltage that puts the forward coercive field across a wafer of thickness t, V = E_c t derived:

Crystal	t = 0.5 mm	t = 1 mm	Status
Congruent, 21 kV/mm	10.5 kV	21.0 kV	derived
Near-stoichiometric, 6.0–6.5 kV/mm (Table 7.1)conflict	3.0–3.3 kV	6.0–6.5 kV	derived
Near-stoichiometric, 2.1–2.5 kV/mm (p. 118)conflict	1.1–1.3 kV	2.1–2.5 kV	derived
Near-stoichiometric + 2% MgO, 1.8 kV/mm	0.9 kV	1.8 kV	derived

Switching time

Empirical activation law with internal field P-comp:

t_{s} \sim \exp (\frac{δ}{E \pm E_{int}})

P-comp

+ for reverse switching, − for forward switching: the internal field aids the return to the original direction and opposes the first reversal.

Domain shapes

Domain-shape observation	Source
Congruent LiNbO₃: almost equilateral hexagons, walls parallel to the yz (glide) planes	P-comp
Congruent LiNbO₃: nucleate and grow as six-sided polygons; spike-like wall velocity, pinning-depinning	P(abs)
Stoichiometric LiNbO₃ and LiTaO₃: Y-walls, parallel to (112̅0), lower in energy than X-walls, parallel to (101̅0), so domains are hexagons bounded by Y-walls (DFT)	P(abs)
Congruent LiNbO₃: antisite–wall interactions too weak to reverse that order, domains remain hexagonal; congruent LiTaO₃: triangles bounded by one type of X-wall	P(abs)
Antiparallel domains nucleate near the +z surface (without illumination)	P-comp

Etching reveals domains: the −c end of a domain etches much faster than the +c end P-comp, first used on LN by Nassau, Levinstein and Loiacono P.

L3 Unipolarity, conflicts, temperature

Volk & Wöhlecke 2008 pp. 176-199; Gopalan & Gupta 1996; Gopalan et al. 1998

Unipolarity and its origin. The asymmetric P–E loop (forward field larger than reverse) was measured with liquid electrodes on z-cut plates; E_int did not depend on thickness (0.5 and 0.25 mm), so it is a bulk property P-comp. Hydrogen content has no effect on switching or internal field P(abs). After reversal, E_int keeps its original direction at room temperature and realigns with the new P_s after heating above a threshold of about 100 °C in LN (150 °C in LiTaO₃) P-comp. The proposed mechanism is a frozen defect dipole, an Nb_Li antisite with its four Li vacancies, that cannot reorient with P_s at room temperature; Volk & Wöhlecke 2008 notes that no spectroscopic proof of dipole realignment exists and that the model does not explain the very low E_c of highly doped crystals, which contain other defects P-comp. In LiTaO₃ the internal field correlates with changes in the OH⁻ band after reversal P(abs).

Conflicts in the numbers. (1) Near-stoichiometric E_c: Volk & Wöhlecke 2008 Table 7.1 gives 60–65 kV/cm, while its p. 118 gives 21–25 kV/cm citing Gopalan et al. 1998, whose abstract gives only a ratio P-comp conflict. A factor of 10 between two pages of one book suggests a unit slip (speculation); the figure draws the table value and marks the other. (2) The congruent E_int is printed “2–33 kV/cm” in Table 7.1; the text on p. 181 gives 33.5 and later 22.2 kV/cm, so the table entry is read as 22–33 kV/cm misprint. (3) E_c depends on how it is defined (threshold of first domains, half-switched charge, loop midpoint), ramp rate, temperature and Li content within “near-stoichiometric” P-comp.

Temperature. E_c falls with temperature; in laser-heated crystal at 800–900 °C antiparallel domains appeared at 200 V/cm P-comp. Ultraviolet light lowers the coercive field of Mg-doped crystal near threshold by more than 30% at 305 nm and 10–12 mW/cm² P-comp.

How the figure is computed. Each loop is built from the forward coercive field and the internal field only: E_down = −E_c, E_up = E_c − 2E_int, centre −E_int derived. The branches are tanh curves of template steepness template; the drawn band is the pointwise minimum to maximum over the bounds of E_c, E_int and P_s (0.71 and 0.80 C/m² conflict), so a range never collapses to one invented value.

E_{down} = - E_{c}, E_{up} = E_{c} - 2 E_{int}, P = P_{s} \tanh \frac{E - E_{sw}}{w}

derived template

Sources

11 cited in 1.8

Gopalan et al. 2007V. Gopalan, V. Dierolf, D. A. Scrymgeour, "Defect-domain wall interactions in trigonal ferroelectrics", Annu. Rev. Mater. Res. 37, 449-489 (2007). doi:10.1146/annurev.matsci.37.052506.084247
Volk & Wöhlecke 2008T. Volk, M. Woehlecke, Lithium Niobate: Defects, Photorefraction and Ferroelectric Switching, Springer Series in Materials Science 115 (Springer, Berlin Heidelberg, 2008). doi:10.1007/978-3-540-70766-0
Gopalan et al. 1998V. Gopalan, T. E. Mitchell, Y. Furukawa, K. Kitamura, "The role of nonstoichiometry in 180 ° domain switching of LiNbO₃ crystals", Appl. Phys. Lett. 72, 1981-1983 (1998). doi:10.1063/1.121491
Chen et al. 2001Y.-L. Chen, J.-J. Xu, X.-J. Chen, Y.-F. Kong, G.-Y. Zhang, "Domain reversion process in near-stoichiometric LiNbO₃ crystals", Opt. Commun. 188, 359-364 (2001). doi:10.1016/S0030-4018(00)01137-8
Chen et al. 2003Y. Chen, C. Lou, J. Xu, S. Chen, Y. Kong, G. Zhang, J. Wen, "Domain switching characteristics of the near stoichiometric LiNbO₃ doped with MgO", J. Appl. Phys. 94, 3350-3352 (2003). doi:10.1063/1.1597960
Gopalan et al. 1999V. Gopalan, Q. X. Jia, T. E. Mitchell, "In situ video observation of 180 ° domain kinetics in congruent LiNbO₃ crystals", Appl. Phys. Lett. 75, 2482-2484 (1999). doi:10.1063/1.125055
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
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
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
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
Gopalan & Gupta 1996V. Gopalan, M. C. Gupta, "Origin of internal field and visualization of 180 ° domains in congruent LiTaO₃ crystals", J. Appl. Phys. 80, 6099-6106 (1996). doi:10.1063/1.363684