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. 2020 Jun 11;10:9470. doi: 10.1038/s41598-020-65971-5

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Forward biased CMOS modulator for cryogenic optical readout. (a) Optical readout system. The superconducting device (an SNSPD here) directly drives an optical modulator, which encodes the data into an optical carrier. Right: Micrograph (top) and layout (bottom) of the T-shaped silicon ring modulator. (b) Modulator’s p-n junction conduction band and free electron distribution $n (E)$ for voltages V and V + ΔV. Due to $n (E)$ being tightly distributed at low temperatures, the same ΔV results in a stronger current injection. (c) Modulator’s transmission spectra at different bias voltages. (d) Modulator’s I-V curve. Low temperature operation increases the turn-on voltage (due to increased built-in potential) and the I-V slope (because of tighter $n (E)$ distribution). (e) Modulator’s differential resistance ( $r_{d} = d V / d I = k_{B} T / q I + R_{s}$ ). At 3.6 K and currents >5 μA, ionization decreases the series resistance. (f) Modulation efficiency versus voltage. An exponential increase is measured in forward bias. (g) Modulation efficiency versus DC electrical power. Higher efficiency is obtained for the same power at 3.6 K. (h) Transmission change versus detuning between laser wavelength λ and resonance wavelength λ₀ for a 1.3 μW DC power consumption and 2 mV AC signal. Increased modulation efficiency makes ΔT much stronger at low temperatures.