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Edited by: Derek Abbott, University of Adelaide, Australia

Reviewed by: Junichi Fujikata, Photonics Electronics Technology Research Association, Japan; Bernard Gelloz, Nagoya University, Japan

*Correspondence: Zahra Bisadi

This article was submitted to Optics and Photonics, a section of the journal Frontiers in Physics

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

A small-sized photonic quantum random number generator, easy to be implemented in small electronic devices for secure data encryption and other applications, is highly demanding nowadays. Here, we propose a compact configuration with Silicon nanocrystals large area light emitting device (LED) coupled to a Silicon photomultiplier to generate random numbers. The random number generation methodology is based on the photon arrival time and is robust against the non-idealities of the detector and the source of quantum entropy. The raw data show high quality of randomness and pass all the statistical tests in national institute of standards and technology tests (NIST) suite without a post-processing algorithm. The highest bit rate is 0.5 Mbps with the efficiency of 4 bits per detected photon.

Thanks to the quantum properties of light, “truly” random numbers can be produced by photonic quantum random number generators (PQRNG). Cryptographic tasks of encryption and decryption of private data can be executed using secret keys based on high quality random numbers. Even though mathematical algorithms are extensively used to generate random numbers, they suffer from high guessability provided the seed of the algorithm is known. If they have a short periodicity, their repeatability would be a serious flaw, as well.

PQRNGs benefit from the intrinsically random and unpredictable properties of physical processes involving photons as the quanta of light. The randomness in path taken by photons arriving on a beam splitter^{1} [^{1}

However, in all the above-mentioned approaches a bulky setup is used to generate random numbers. A small-sized and compact PQRNG, easy to be implemented in small electronic devices such as mobile phones and cameras for secure data encryption and decryption as well as other applications, is highly essential for facile accessibility to everyone. Here, we present a first step toward this goal: a PQRNG with a novel, compact configuration comprising a silicon nanocrystals large area LED (Si-NCs LLED) coupled with a silicon photomultiplier (SiPM) in free space. Based on some statistical analyses described in section 5, it is proved that the generated hexadecimal random symbols have a very high quality and the corresponding random bits pass all the statistical tests in NIST tests suite with no post-processing operations. The highest bit rate of 0.5 Mbps is achieved with the efficiency of 4-bits per detected photon.

In a previous work [

This work is organized as follows. In section 2, the Si-NCs LLEDs and their electrical and optical characteristics are described. In section 3, the SiPM is introduced and explained. Section 4 describes the experimental procedure and random numbers extraction. Randomness analyses are discussed in section 5 and at the end the conclusions are presented.

Si-NCs are silicon quantum dots which emit light at room temperature in the visible range due to quantum confinement. The emitted photons are emitted independently by a quantum process named spontaneous emission and their statistics obey Poisson statistics (see more in section 4).

Si-NCs LEDs are fabricated by complementary metal-oxide-semiconductor (CMOS) processing, they can be easily incorporated in integrated configurations, they emit photons with wavelengths in the spectral range detectable by silicon detectors allowing the fabrication of an all-silicon-based device and since the spontaneous emission of photons in a Si-NCs LED is a non-deterministic, quantum mechanical and random process, they can be used as a quantum source of randomness to generate random numbers. The Si-NCs LEDs were fabricated with a large emitting surface in order to illuminate large area detectors like the SiPM we use here. The matching of the emitter and detector surfaces allows their direct coupling, i.e., without any coupling optics. The Si-NCs LLED (large area LED) has the active layer structure formed by a multilayer structure with 5 periods of silicon rich oxide (SRO)/SiO_{2} layers of 3.5–4 nm and 2 nm thicknesses, respectively (Figure

_{2}.

The Si-NCs LLEDs have been prepared in three different sizes: big (b), medium (m) and small (s) with emitting surface area of 1.3 mm × 0.99 mm, 0.99 mm × 0.82 mm and 1.02 mm × 0.11 mm, respectively (see Figure

The electroluminescence (EL) spectra of the Si-NCs LLEDs can be seen in Figure ^{2} for the (b), (m) and (s) LLEDs, respectively. It should be noted that the applied currents to the (b), (m) and (s) LLEDs are 30, 3 and 3 μA, respectively.

The efficiency (EL over injected power) of (b), (m), and (s)LLED.

^{2}) |
^{2}) |
||||
---|---|---|---|---|---|

b | 1.29 | 2.52 | 2.33 | ~533 | 70 |

m | 0.81 | 2.34 | 0.37 | ~363 | 517 |

s | 0.11 | 3 | 2.67 | ~364 | 413 |

At currents lower than 30μA to the (b) LLED, no appreciable EL is observed. Therefore, by applying the previously-mentioned currents to the LLEDs, we tried to keep the voltages and hence the electric field through the active area of the LLEDs (with actual thickness of ~22.5 nm) more or less the same. The low current density and high EL intensity of the (m)LLED yield the higher efficiency of this LLED compared with the (b) and (s) LLEDs. In addition to the efficiency, the active area of (m)LLED allows a suitable coupling with the large area SiPM since the SiPM dimensions are of 1 mm × 1 mm. It should be noted that all three LLEDs result in the generation of high quality random numbers since they are fabricated in a very similar way and the detected photons from all of them follow a Poisson distribution.

The current-voltage (I/V) characteristics of Si-NCs LLED are presented in Figure ^{2}

These LLEDs can emit light over long hours of operation. Figure

EL of the (m) LLED vs. time at the applied current density of 0.62 mA/cm^{2} (corresponding to an applied voltage of 2.61 V). The right hand side of the figure (blue axis) shows the EL variation percentage.

The analog SiPM is an array of many (hundreds) of single photon avalanche diodes (SPADs). They are all connected in parallel to a common anode and cathode, each one with its own quenching resistor. Each cell (i.e., SPAD+resistor) is sensitive to a single photon and provides a current pulse at the output. Therefore, the counts at the SiPM output are proportional to the number of triggered cells, thus to the number of detected photons. Different technologies for SiPM have been developed in FBK during last few years, with peak sensitivity in the green part (RGB-SiPM) or in the blue part (NUV-SiPM) of the visible spectrum, and with different cell sizes. The NUV technology, in particular, benefits from an upgraded silicon material [

In this work we employ a 1 mm × 1 mm NUV SiPM (inset in Figure _{bd})), as shown in Figure ^{2} at 5 V of excess bias (see Figure

We designed a custom front-end board to amplify and digitalize the analog output signal from the detector (see Figure

The experimental setup is schematically shown in Figure

In order to verify that the Si-NCs emit independent photons, cross correlation measurements can be performed. The measurement is based on the random transmission of the emitted photons from the source (i.e., a Si-NCs LLED) into two arms of a fiber beam splitter (see Figure ^{2}(τ), is computed. A peak in the cross-correlogram indicates photon bunching while a dip shows anti-bunching. Photon bunching occurs in the case of chaotic or thermal light which has a super-Poissonian distribution with the mean greater than the variance and photon number fluctuations larger than in a coherent light beam. Photon antibunching refers to a sub-Poissonian distribution with the mean lower than the variance and photon number fluctuations smaller than in a coherent light beam [^{2} statistic [

In order to characterize afterpulsing and crosstalk in the SiPM, autocorrelation, g^{2}(τ), measurements of its signal were performed via a multitau digital correlator with 4 ns resolution [^{2}(τ) exhibits a main peak within ~140 ns from the main autocorrelation peak at τ = 0 (Figure ^{2}(τ) approaches the normalization value of 1 at about 950 ns.

Autocorrelation function (g^{2}(τ)) of the SiPM signal (peak at zero is out of scale). Dead time and afterpulsing distribution of the SiPM can be seen here. The dead time of ~110 ns is not due to limitation of the SiPM, but it is set by the monostable in the electronics (front-end shown in Figure

The measurements for random number generation were performed on the (m)LLED with an active area of ~ 0.99 mm × 0.82 mm (see Figure _{bias} to SiPM was 32 V corresponding to an excess bias of ~6 V (V_{bd} = 26^{2}.

The methodology to generate random numbers is similar to our recent work [

The duration of the “double length” interval is determined by the afterpulsing and crosstalk distribution of the SiPM (Figure ^{−4}, 1.05 × 10^{−4} and 1.45 × 10^{−5} corresponding to the “double length” interval of 640, 1280, and 1920 ns, respectively. Therefore, we fixed the “double length” interval to 1920 ns and acquired sequences of random symbols.

A very straightforward way to detect an observable pattern among the random symbols or codes is to create a 2-dimensional map of them. A 512 × 512 map of the 16 hexadecimal symbols generated by our methodology from a recording of our system is presented in Figure

A 512 × 512 map of the hexadecimal symbols. No particular, periodic pattern is observable among the symbols.

Figure

Probability distribution of 16 hexadecimal symbols in a sequence of 1 G symbols raw data. The solid red line shows the theoretical value of 1/16.

The high quality of random symbols is proved through the evaluation of the joint probability mass function (JPMF) [^{−6} from the expected theoretical value of (1/16) × (1/16) = 0.00390625 (Figure ^{−7} bits considering 1 G random symbols.

Joint probability mass function for 1 G symbols showing the probability of having each symbol after the other one.

To further analyze the quality of generated random numbers, each symbol is replaced with its corresponding 4-bit binary values. In this way, we obtain a binary sequence of random bits. We then apply the 15 statistical tests in the NIST tests suite to the generated raw data. Various datasets with 1 and 2 Gbits length at different applied currents to the (m)LLED were obtained. They all passed the NIST tests without the application of a post-processing algorithm irrespective of the EL variations of the (m)LLED during data acquisition. The results for a dataset of 2 Gbits are tabulated in Table

NIST tests results for 2 G random bits (2 × 10^{9} bits). The significance level is α = 0.01. In order to pass, the p-value should be larger than 0.01 and the proportion should be more than 0.983.

Frequency | 0.2861 | 0.9930 | Passed |

Block frequency | 0.2868 | 0.9935 | Passed |

Cumulative sum | 0.1657 | 0.9920 | Passed |

Runs | 0.3298 | 0.9935 | Passed |

Longest run | 0.4817 | 0.9910 | Passed |

Rank | 0.3611 | 0.9860 | Passed |

FFT | 0.0401 | 0.9910 | Passed |

Non-overlapping template | 0.5666 | 0.9905 | Passed |

Overlapping template | 0.4064 | 0.9900 | Passed |

Universal | 0.1404 | 0.9850 | Passed |

Approximate entropy | 0.2854 | 0.9930 | Passed |

Random excursions | 0.5310 | 0.9938 | Passed |

Random excursions variant | 0.3127 | 0.9883 | Passed |

Serial | 0.3376 | 0.9870 | Passed |

Linear complexity | 0.2550 | 0.9905 | Passed |

We realized a compact quantum random number generator with a novel configuration comprising a Si-NCs LLED directly interfaced with a SiPM without any coupling optics. This paves the way to the further integration of the photon source and the single photon detectors in a single integrated circuits. Indeed, both the devices were fabricated by using the FBK technology. Our research is currently focusing to define a single fabrication process allowing the fabrication of both devices in a single silicon chip.

Remarkably the Si-NCs LLED have similar emission properties and statistics as the standard small Si-NCs which we have previously developed for PQRNG application [

This compact QRNG, with the capability of producing high quality random numbers, can be implemented in small electronic devices providing utmost security accessible to everyone. The proposed device configuration has several advantage with respect to what we already reported in Bisadi et al. [

ZB prepared the setup, conducted the experiments and analyzed the acquired data. She also made some suggestions to adapt the robust methodology to generate high quality random numbers with the structure. FA partially designed the silicon photomultiplier (SiPM) and characterized it. GF created the robust methodology to generate high quality random numbers and implemented the target function on the FPGA. NZ designed most part of the SiPM. CP supervised the development of the technology used in the SiPM. GP designed and fabricated the large area silicon nanocrystals LED (Si-NCs LLED). LP supervised the whole research work.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

This work has been supported by the Provincia Autonoma di Trento via the project “SiQuro.”

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