4.7 DC bias drift in modulators

L1 Phenomenon

bias point walks under constant voltage

A lithium niobate modulator is set to its operating point with a DC voltage. Over seconds to hours that voltage stops doing its job: mobile charge inside and around the crystal rearranges and cancels part of the applied field, so the operating point walks away (DC bias drift). Bulk telecom modulators have been engineered against it since at least 1981 (Yamada & Minakata 1981reported; Gee et al. 1985reported). Thin-film modulators show the same effect on much shorter time scales, and the 2024-2026 literature traces it to interfaces, cladding and contacts.

The footer bias meter uses a single RC with a 40 s display time constant.

Drift mitigations, 1981-2026: metric as reported, no common scale17 rows; filters dim the others

Year	Platform	Class	Mitigation or finding	Metric	Source
1981	bulk	diagnosis	Ti:LN directional coupler	two components: seconds (buffer leakage), hours (photorefraction)	Yamada & Minakata 1981reported
1985	bulk	buffer/cladding	ITO buffer instead of SiO2	< 0.3% drift in 8 h	Gee et al. 1985reported
1986	bulk	cut choice	x-cut instead of z-cut interferometers	x-cut thermally stable; z-cut unstable	Bulmer et al. 1986reported
1996	bulk	material processing	OH reduction	improved long-term drift (title)	Nagata et al. 1996reported (title)
2004	bulk	diagnosis	DC-induced thermal shift	title-level	Nagata et al. 2004reported (title)
2011	bulk	control	analysis and control of drift	title-level	Salvestrini et al. 2011reported (title)
2021	TFLN	temperature	LNOI MZI at cryogenic temperature	bias-drift-free 12 h	Lomonte et al. 2021reported
2022	TFLN	interface and anneal	LN/metal interface preparation, forming-gas anneal	anomalous sub-MHz response improved	Puma et al. 2022reported
2024	TFLN	interface and anneal	LN-metal interface control and annealing	relaxation slowed > 10⁴-fold	Holzgrafe et al. 2024reported
2024	TFLN	heterogeneous	wafer-scale Si/TFLN	weak bias drift	Li et al. 2024reported
2024	TFLT	material swap	thin-film LiTaO3	< 1 dB vs 5 dB (TFLN) output fluctuation over 46 h	Powell et al. 2024reported
2025	TFLN	surface treatment	Ar+ milling pre-treatment	no drift under DC within 1 h	Shi et al. 2025reported
2025	TFLN	temperature	liquid-nitrogen temperature	stable DC operation	Warner et al. 2025reported
2026	TFLN	buffer/cladding	cladding on vs off	RC 11.9 ms (clad, positive) vs 88.6 µs (unclad, negative)	Li et al. 2026reported
2026	TFLN	reset protocol	zero or reverse bias reset	hysteresis reversible; active reset	Yeh et al. 2026reported
2026	TFLT	material swap	thin-film LiTaO3, hot	DC-bias stable at 120 °C (preprint)	Al Sayem et al. 2026reported (preprint)
2026	TFLN	thermal bias	thermo-optic bias, visible and NIR	title-level	Liu et al. 2026reported (title)

Platform

Class

DC drift mitigations, 1981-2026

one marker per reported result, rows by class of fix; metric as reported, no common scale

Hover a markeryear, platform, mitigation, metric as reported

Platform

circle: bulk Ti:LN
diamond: TFLN
hatched square: thin-film LiTaO₃

Click a row name to filter by class.

The same two levers recur 40 years apart: a conductive buffer in 1985, cladding and interface control in 2024-2026. Metrics are not comparable across rows and are printed as reported.

preprints marked in the hover card

L2 Layered relaxation

Maxwell-Wagner, two and three layers

Two-layer model: layer 1 = LN, layer 2 = buffer or cladding, each a parallel capacitance C_i and conductance G_i, in series under a voltage step V:

V_{1} (t) = V [\frac{G_{2}}{G_{1} + G_{2}} + (\frac{C_{2}}{C_{1} + C_{2}} - \frac{G_{2}}{G_{1} + G_{2}}) e^{- t / τ}], τ = \frac{C_{1} + C_{2}}{G_{1} + G_{2}}

(1)

The LN voltage moves from capacitive division (t = 0+) to resistive division (t → ∞). If the LN share grows with time the drift is called positive here; if it shrinks, negative. Sign conventions differ between papers; each reported drift below keeps the paper's own term.

Drift simulator: series RC layers, voltage share on the LN film1D series stack, unit area

τ: 1.19e−02 s
V_LN(0+)/V: 0.077 V/V
V_LN(∞)/V: 1.000 V/V
drift: LN share grows (positive)
t cursor: 1.00e−02 s
bias phase, unwrapped: 702.2 deg

layer	t	ε_r	σ(T), S/m
LN	600 nm	28.0	1.0e−15
SiO2 cladding	1000 nm	3.9	3.8e−08
interface off

Preset

σ LN film 1.00e−15 S/m

σ cladding 3.76e−08 S/m

ε_r partner 3.9

σ interface 1.00e−12 S/m

Temperature 295 K

Bias dot time 1.00e−02 s

Square period 3.16e−02 s

Interface

Waveform

The footer bias meter on every page now runs this stack with your settings.

presets tuned to the RC fits 11.9 ms (clad) and 88.6 µs (air-clad) reported 1-20 kHz band reported bulk σ_d range P-comp thicknesses, oxide ε and σ, interface layer, E_a 0.5 eV, V/V_π 0.5: model parameters, no data template Li⁺ migration: not a mechanism here U

Bias walk after a DC step

series RC layers, unit area; voltage share on the LN film

Stack

Cladding conductivity3.8e−08 S/m

LN film conductivity1.0e−15 S/m

Time after the bias step 10.0 ms

Temperature (Arrhenius, 0.5 eV)295 K

Interface layer, 10 nm

Relaxation time: 11.9 ms
LN share, start to end: 0.08 → 1.00
Drift: positive
Transmission now: 0.976
Bias phase, unwrapped: 702°
LN: 600 nm, ε 28.0, σ 1.0e−15 S/m
SiO2 cladding: 1000 nm, ε 3.9, σ 3.8e−08 S/m
interface layer: off
E_a, V/V_π at 0+: 0.5 eV, 0.5

The footer bias meter on every page now runs this stack with your settings.

preset time constants 11.9 ms (clad) and 88.6 µs (air-clad) reported1-20 kHz band reportedbulk σ_d range P-complayer values: model parameters, no data templateLi⁺ migration not modelled U

Result	Value	Device	Source
Two drift components	short: several seconds (buffer-layer leakage); long: several hours (photorefraction from guided light)	Ti:LN directional coupler, bulk	Yamada & Minakata 1981reported
Conductive buffer	ITO buffer (about 20 Ω/sq) instead of SiO₂: long-term drift < 0.3% in 8 h; equivalent-circuit model	Ti:LN modulator, bulk	Gee et al. 1985reported
Pyroelectric drift	z-cut interferometers unstable with temperature; x-cut stable	Ti:LN	Bulmer et al. 1986reported
OH reduction	improved long-term drift (title)	bulk LN intensity modulators	Nagata et al. 1996reported (title)
DC-induced thermal shift	DC voltage causes a thermal shift of the bias point (title)	bulk LN	Nagata et al. 2004reported (title)
Analysis and control	title-level	bulk LN MZM	Salvestrini et al. 2011reported (title)
EO response 1 mHz to 1 MHz	relaxation enhances EO modulation at 1-20 kHz, confounding V_π measurements; relaxation slowed > 10⁴-fold by LN-metal interface control and annealing	TFLN	Holzgrafe et al. 2024reported
Anomalous sub-MHz response	improved by LN/metal interface preparation and high-temperature anneal in forming gas	x-cut TFLN phase modulators	Puma et al. 2022reported
RC fit	11.9 ms with SiO₂ cladding (positive drift); 88.6 µs without cladding (negative drift); relaxation more than 100× shorter than bulk; optical intensity changes the low-frequency response via photoconductivity	TFLN MZM	Li et al. 2026reported
Hysteresis	reversible under zero or reverse bias; short-time drift attributed to charge trapping near the contact junction; active reset protocol	TFLN	Yeh et al. 2026reported
Ar⁺ milling pre-treatment	no drift under DC within 1 h; modulator > 40 GHz, stable 30 min at 4.5 V	TFLN	Shi et al. 2025reported
Thin-film LiTaO₃	< 1 dB output fluctuation vs 5 dB for TFLN, quadrature bias, 46 h, 12.1 dBm input	TFLT vs TFLN	Powell et al. 2024reported
Thin-film LiTaO₃, hot	DC-bias stable at 120 °C	TFLT	Al Sayem et al. 2026reported (preprint)
Cryogenic	bias-drift-free 12 h	LNOI MZI with superconducting nanowire single-photon detectors	Lomonte et al. 2021reported
Liquid-nitrogen temperature	stable DC operation	TFLN	Warner et al. 2025reported
Heterogeneous Si/TFLN	weak bias drift; V_πL about 2.9 V cm; 176 Gb/s PAM4 (four-level pulse amplitude modulation)	wafer-scale SOI/TFLN	Li et al. 2024reported
Thermal biasing	heaters bias TFLN modulators stably but cost power, cross-talk and bandwidth; thermo-optic bias in visible and near-infrared TFLN modulators (title)	TFLN	Holzgrafe et al. 2024reported Liu et al. 2026reported (title)

Derived numbers derived

Quantity	Value	Formula and inputs
Relaxation time from bulk dark conductivity	6.9 h to 29 d	ε₃₃ε₀/σ_d; ε₃₃ = 28; σ_d = 10⁻¹⁴ to 10⁻¹⁶ S/m (Volk & Wöhlecke p. 60)
Effective conductivity implied by the TFLN RC fits	2.1×10⁻⁸ S/m; 2.8×10⁻⁶ S/m	ε₃₃ε₀/τ with τ = 11.9 ms; 88.6 µs
Ratio to bulk dark conductivity	2×10⁶ to 3×10¹⁰	above / (10⁻¹⁴ to 10⁻¹⁶ S/m)

Bulk LN dark conduction cannot produce millisecond relaxation. Some other path, 6 to 10 orders of magnitude more conductive, carries the screening charge; the papers above point to the LN-metal interface, the cladding, and traps near contacts.

L3 Mechanisms and measurement

candidates by evidence

Candidate	Status
Conduction through buffer or cladding layers	reported for bulk (Yamada & Minakata 1981reported, Gee et al. 1985reported) and TFLN (Li et al. 2026reported)
LN-metal interface and contact traps	reported (Holzgrafe et al. 2024reported, Puma et al. 2022reported, Yeh et al. 2026reported)
Photoconductivity from guided light	reported (Yamada 1981 bulk; Li 2026 TFLN)
Pyroelectric charge from temperature changes	reported (Bulmer et al. 1986reported; 4.6)
Protons (H⁺) in bulk LN	dominant dark carrier in bulk LN (Volk & Wöhlecke 2009, pp. 59-60P-comp); OH reduction helps bulk drift (Nagata 1996, title)
Li⁺ ion migration	not established for TFLN by any primary source found U; not used in the model

The two-layer formula has one time constant. Real devices show several (Yamada 1981) and stretched behavior; the simulator adds a thin interface layer (three layers, three-pole network solved exactly) and an Arrhenius factor σ_i(T) = σ_i(T₀) exp[−(E_a/k_B)(1/T − 1/T₀)] with E_a a template.
Frequency response: H(f) = V₁(f)/V(f) for the same network; the relaxation step appears between the RC corners. Holzgrafe et al. measured the enhancement band at 1-20 kHz in their devices; the figure shades it as a reported band, not a model output.
Measurement: slow square wave or step bias while monitoring optical output at quadrature; low-frequency EO response by lock-in from mHz up; long-term bias-voltage logs under a control loop.
Error sources: optical power during the test (photoconductivity), temperature (pyroelectric and Arrhenius), humidity and surface state for unclad devices (assumption, no source found), and bias history (hysteresis, Yeh et al. 2026).

Sources

Yamada & Minakata 1981S. Yamada, M. Minakata, DC Drift Phenomena in LiNbO3 Optical Waveguide Devices. Japanese Journal of Applied Physics 20 733 (1981), doi:10.1143/JJAP.20.733.Read: abstract
Gee et al. 1985C. M. Gee, G. D. Thurmond, H. Blauvelt, H. W. Yen, Minimizing dc drift in LiNbO3 waveguide devices. Applied Physics Letters 47 211-213 (1985), doi:10.1063/1.96220.Read: abstract
Bulmer et al. 1986C. H. Bulmer, W. K. Burns, S. C. Hiser, Pyroelectric effects in LiNbO3 channel-waveguide devices. Applied Physics Letters 48 1036-1038 (1986), doi:10.1063/1.96640.Read: abstract
Nagata et al. 1996Hirotoshi Nagata, Junichiro Ichikawa, Naoki Mitsugi et al., Improved Long-Term DC Drift in OH-Reduced Lithium Niobate Optical Intensity Modulators. Applied Optics 35 6828 (1996), doi:10.1364/AO.35.006828.Read: title
Nagata et al. 2004H. Nagata, N. F. O'Brien, W. R. Bosenberg, G. L. Reiff, K. R. Voisine, DC-Voltage-Induced Thermal Shift of Bias Point in LiNbO3 Optical Modulators. IEEE Photonics Technology Letters 16 2460-2462 (2004), doi:10.1109/LPT.2004.834928.Read: title
Salvestrini et al. 2011J. P. Salvestrini, L. Guilbert, M. Fontana, M. Abarkan, S. Gille, Analysis and Control of the DC Drift in LiNbO3-Based Mach-Zehnder Modulators. Journal of Lightwave Technology 29 1522-1534 (2011), doi:10.1109/JLT.2011.2136322.Read: title
Puma et al. 2022E. Puma, R. Cheng, J. Holzgrafe, A. Shams-Ansari, R. Shankar, M. Lončar, Mitigating Anomalous Sub-Megahertz Frequency Response of Electro-Optic Phase Modulators in X-Cut Lithium Niobate on Insulator. Conference on Lasers and Electro-Optics (CLEO) 2022, SF2O.1 (2022), doi:10.1364/CLEO_SI.2022.SF2O.1.Read: abstract
Holzgrafe et al. 2024Jeffrey Holzgrafe, Eric Puma, Rebecca Cheng et al., Relaxation of the electro-optic response in thin-film lithium niobate modulators. Optics Express 32 3619 (2024), doi:10.1364/OE.507536.Read: abstract
Li et al. 2024Zhuoyun Li, Yang Chen, Shuxiao Wang, Mingbin Yu, Xin Ou, Yan Cai, A Weak DC-Drift Silicon/Lithium Niobate Heterogeneous Integrated Electro-Optical Modulator. CLEO 2024, AM4J.2 (2024), doi:10.1364/CLEO_AT.2024.AM4J.2.Read: abstract
Powell et al. 2024K. Powell, X. Li, D. Assumpcao, L. Magalhães, N. Sinclair, M. Lončar, DC-stable electro-optic modulators using thin-film lithium tantalate. Optics Express 32 44115 (2024), doi:10.1364/OE.538870.Read: abstract
Shi et al. 2025Jiakang Shi, Zhilin Ye, Zhen Liu et al., Alleviation of DC drift in a thin-film lithium niobate modulator utilizing Ar+ ion milling. Optics Letters 50 1703 (2025), doi:10.1364/OL.549975.Read: abstract
Warner et al. 2025H. K. Warner, Y. Zhao, Y. Zhang, M. Zhang, M. Lončar, DC-stable thin-film lithium niobate modulator at liquid nitrogen temperatures. Optics Letters 50 5398 (2025), doi:10.1364/OL.571632.Read: abstract
Lomonte et al. 2021E. Lomonte, M. A. Wolff, F. Beutel et al., Single-photon detection and cryogenic reconfigurability in lithium niobate nanophotonic circuits. Nature Communications 12 6847 (2021), doi:10.1038/s41467-021-27205-8.Read: abstract
Li et al. 2026Run Li, Jinye Li, Zongyu Lu et al., Low-Frequency Time-Domain Response of Thin-Film Lithium Niobate Electro-Optic Modulator. Photonics 13 339 (2026), doi:10.3390/photonics13040339.Read: abstract
Yeh et al. 2026Matthew Yeh, C. J. Xin, Donald Witt, David R. Barton, Evelyn L. Hu, Marko Lončar, Hysteresis and Trap Emission in dc-Biased Integrated Lithium Niobate Electro-optic Modulators. Nano Letters 26 13450-13456 (2026), doi:10.1021/acs.nanolett.6c03406.Read: abstract
Al Sayem et al. 2026Ayed Al Sayem, Shiekh Zia Uddin, Ting-Chen Hu et al., Stable thin-film lithium tantalate modulators operating at high temperature for uncooled operation. arXiv (2026), arXiv:2604.27285.Read: arXiv abstract
Liu et al. 2026Tianyi Liu, Engjell Bebeti, John N. Straguzzi, Joyce K. S. Poon, Wesley D. Sacher, Visible and Near-Infrared Thin-Film Lithium Niobate Modulators with Thermo-Optic Bias. ACS Photonics 13 3951-3962 (2026), doi:10.1021/acsphotonics.6c00668.Read: title
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)