lithium niobateLiNbO3
PPLN Λ = 6.82 µm · 1064 → 532 nm · 2 px/µm
lithium niobate / 04 Quirks / 4.9

4.9 Lithium out-diffusion

L1 Phenomenon

Li2O leaves the hot surface

At the temperatures used for diffusion and annealing, lithium oxide leaves the surface (Li out-diffusion; Carruthers et al. 1974reported (title); Ranganath & Wang 1977reported). The lithium-poor skin has a higher extraordinary index than the crystal below, so it guides light: the 1973 "thin-film LiNbO3" modulator was such a skin, not a film (Kaminow et al. 1973reported). The same loss became a problem when titanium was diffused in to make waveguides; Ti indiffusion can also flip the ferroelectric domain at the +c surface (Miyazawa 1979reported); and lithium loss remains a question for every high-temperature anneal of thin films.

Li2O out-diffusion: deficit, index change, Curie temperature vs depthbulk 48.38 mol% Li2O, 24.5 °C
012345600.511.5051015108011101140Li2O deficit (mol%)Δn ×10³: e solid, o dashedCurie temperature (°C): Bordui solid, Iyi dotteddepth z / √(Dt) (1 unit =  1.00 µm, template)
Δcs, surface deficit
 0.50 mol%
Δne(0)
 4.85e−03
Δno(0)
−3.00e−04
Tc(0), Bordui fit
 1124 °C
Tc(0), Iyi fit
 1119 °C
surface index raised
e: yes o: no
dne/dc, 632.8 nm
−9.70e−03 /mol%
dno/dc, 632.8 nm
 6.00e−04 /mol%

Guided means the surface index is raised (Δn(0) > 0); whether a mode exists also depends on depth and wavelength. Losing Li2O raises ne and lowers no slightly.

 0.50 mol%
  1.00 µm
Wavelength
n(c, λ): generalized Sellmeier, 400-1200 nm, about 2×10−3 accuracy S Tc slope 39.06-39.26 °C per mol% P-comp D, dcs: model parameters, no data template

A skin that guides one polarization

bulk 48.38 mol% Li₂O, 24.5 °C; ne rises, no falls
surface (Li-poor)e: index raised in the skino: leaks into the substrateLi-site thinning exaggerated: 90% of dots removed at a 1.5 mol% deficit
0.50 mol%
 1.00 µm
Light
Surface Δne
  +4.85×10⁻³
Surface Δno
  −0.30×10⁻³
Surface Tc, Bordui / Iyi
 1124 /  1119 °C

A raised surface index (Δn(0) > 0) is necessary for guiding; whether a mode exists also depends on depth and wavelength.

Raise the deficit and the extraordinary ray locks into the skin while the ordinary ray spills out: the physics of the 1973 out-diffused "thin-film" modulator.

index model SCurie fits P-compdeficit and diffusion length: model parameters, no data template632.8 nm in computed spectral color; 1064 nm in false color, dashed

L2 Events and index model

generalized Sellmeier
Event or quantityValueSource
Out-diffused planar guide modulatorbroadband EO phase modulator; modulation index per volt 0.13 V−1; base bandwidth 3.2 GHz (50 Ω); 0.2 mW/MHz for 1 radKaminow et al. 1973reported
Diffusion kinetics and waveguiding of out-diffused layerstitle-levelCarruthers et al. 1974reported (title)
Ti-indiffused waveguidesTi, V, Ni diffused into LN; single-mode guides within about 1 µm of the surfaceSchmidt & Kaminow 1974reported
Side effect of Ti indiffusionaccompanying Li2O out-diffusion gives unwanted guided modes in y-cut; suppressed with Li2ORanganath & Wang 1977reported
Suppression by pre-annealy-cut substrate annealed in Li2CO3 powder, 600 °C, 72 h, before Ti diffusion: single TE and TM modes, no out-diffusion modes at 632.8 nmMiyazawa et al. 1977reported
Li2O compensation in planar and channel guidestitle-levelBurns et al. 1978reported (title)
Domain inversionTi diffusion on the +c face forms a surface layer with reversed polarization; none on the −c faceMiyazawa 1979reported
Reversal undone by Li-rich vaporerasure of domain inversion in Ti:LN by Li-rich vapor transport (title)Hua et al. 2015reported (title)
Annealed TFLN material Qabout 1.6×108 (0.2 dB/m) after a post-fabrication annealShams-Ansari et al. 2022reported
HypothesisLi out-diffusion during anneals as one cause of higher coercive fields in thin filmsZhu et al. 2021S (hypothesis)

Derived numbers derived

QuantityValueStatus
dne/d(mol% Li2O), 632.8 nm−9.7×10−3 per mol%derived
dno/d(mol% Li2O), 632.8 nm+6.0×10−4 per mol%derived
dne/d(mol% Li2O), 1064 nm−9.1×10−3 per mol%derived
Curie temperature slope39.06-39.26 °C per mol% Li2OVolk & Wöhlecke 2009, Eqs. 6.2-6.3 (Iyi 1992, Bordui 1992)P-comp

Loss of Li2O raises ne (about +10−2 per mol% lost) and slightly lowers no, so a Li-depleted surface layer guides extraordinary light and not ordinary light, and has a locally lower Curie temperature. These are predictions of the generalized Sellmeier, valid 400-1200 nm with about 2×10−3 accuracy.

L3 Gaps and history

  • Diffusion coefficient for Li2O out-diffusion under LNOI anneal conditions: none found. The figure's D is a template; the depth axis is in units of √(Dt).
  • Why the domain inverts on +c during Ti indiffusion: the common attribution to Li2O out-diffusion is unverified U.
  • Bulk dark conduction is protonic, not Li+ (Volk & Wöhlecke pp. 59-60; 4.1 L3). Out-diffusion is a high-temperature surface process, separate from room-temperature charge transport; no cited source links it to DC drift (4.7 L3).
  • Out-diffused guides (1973-1974) preceded Ti indiffusion (1974) and proton exchange (1982); the Li2O compensation work of 1977-1978 is the earliest Li2O-compensation work found for LN integrated optics. The near-stoichiometric route (Li-rich vapor transport equilibration) runs the same chemistry in reverse.

Sources

  1. Kaminow et al. 1973I. P. Kaminow, J. R. Carruthers, E. H. Turner, L. W. Stulz, Thin-film LiNbO3 electro-optic light modulator. Applied Physics Letters 22 540-542 (1973), doi:10.1063/1.1654500.Read: abstract
  2. Carruthers et al. 1974J. R. Carruthers, I. P. Kaminow, L. W. Stulz, Diffusion Kinetics and Optical Waveguiding Properties of Outdiffused Layers in Lithium Niobate and Lithium Tantalate. Applied Optics 13 2333 (1974), doi:10.1364/AO.13.002333.Read: title
  3. Schmidt & Kaminow 1974R. V. Schmidt, I. P. Kaminow, Metal-diffused optical waveguides in LiNbO3. Applied Physics Letters 25 458-460 (1974), doi:10.1063/1.1655547.Read: abstract
  4. Ranganath & Wang 1977T. R. Ranganath, S. Wang, Suppression of Li2O out-diffusion from Ti-diffused LiNbO3 optical waveguides. Applied Physics Letters 30 376-379 (1977), doi:10.1063/1.89438.Read: abstract
  5. Miyazawa et al. 1977S. Miyazawa, R. Guglielmi, A. Carenco, A simple technique for suppressing Li2O out-diffusion in Ti:LiNbO3 optical waveguide. Applied Physics Letters 31 742-744 (1977), doi:10.1063/1.89523.Read: abstract
  6. Burns et al. 1978W. K. Burns, C. H. Bulmer, E. J. West, Application of Li2O compensation techniques to Ti-diffused LiNbO3 planar and channel waveguides. Applied Physics Letters 33 70-72 (1978), doi:10.1063/1.90149.Read: title
  7. Miyazawa 1979S. Miyazawa, Ferroelectric domain inversion in Ti-diffused LiNbO3 optical waveguide. Journal of Applied Physics 50 4599-4603 (1979), doi:10.1063/1.326568.Read: abstract
  8. Hua et al. 2015Ping-Rang Hua, Jia-Ji Dong, Kun Ren, Zhao-Xi Chen, Erasure of ferroelectric domain inversion in Ti-diffused LiNbO3 optical waveguide by Li-rich vapor-transport equilibration. Journal of Alloys and Compounds 626 203-207 (2015), doi:10.1016/j.jallcom.2014.12.001.Read: title
  9. Shams-Ansari et al. 2022Amirhassan Shams-Ansari, Guanhao Huang, Lingyan He et al., Reduced material loss in thin-film lithium niobate waveguides. APL Photonics 7 081301 (2022), doi:10.1063/5.0095146.Read: abstract
  10. Zhu et al. 2021Di Zhu, Linbo Shao, Mengjie Yu et al., Integrated photonics on thin-film lithium niobate. Advances in Optics and Photonics 13 242 (2021), doi:10.1364/AOP.411024.Read: secondary use only
  11. Volk & Wöhlecke 2009Tatyana Volk, Manfred Wöhlecke, Lithium Niobate: Defects, Photorefraction and Ferroelectric Switching. Springer Series in Materials Science 115 (2009), doi:10.1007/978-3-540-70766-0.Read: selected chapters: Ch. 2.2 (pp. 14-19), Ch. 3 (pp. 51-61), Ch. 4 (pp. 75-77, 82-85, 94-97), Sec. 7.1.3 (p. 168)