Abstract

Random numbers are fundamental elements in different fields of science and technology such as computer simulation like Monte Carlo-method simulation, statistical sampling, cryptography, games and gambling, and other areas where unpredictable results are necessary. Random number generators (RNG) are generally classified as “pseudo”-random number generators (PRNG) and "truly" random number generators (TRNG). Pseudo random numbers are generated by computer algorithms with a (random) seed and a specific formula. The random numbers produced in this way (with a small degree of unpredictability) are good enough for some applications such as computer simulation. However, for some other applications like cryptography they are not completely reliable. When the seed is revealed, the entire sequence of numbers can be produced. The periodicity is also an undesirable property of PRNGs that can be disregarded for most practical purposes if the sequence recurs after a very long period. However, the predictability still remains a tremendous disadvantage of this type of generators. Truly random numbers, on the other hand, can be generated through physical sources of randomness like flipping a coin. However, the approaches exploiting classical motion and classical physics to generate random numbers possess a deterministic nature that is transferred to the generated random numbers. The best solution is to benefit from the assets of indeterminacy and randomness in quantum physics. Based on the quantum theory, the properties of a particle cannot be determined with arbitrary precision until a measurement is carried out. The result of a measurement, therefore, remains unpredictable and random. Optical phenomena including photons as the quanta of light have various random, non-deterministic properties. These properties include the polarization of the photons, the exact number of photons impinging a detector and the photon arrival times. Such intrinsically random properties can be exploited to generate truly random numbers. Silicon (Si) is considered as an interesting material in integrated optics. Microelectronic chips made from Si are cheap and easy to mass-fabricate, and can be densely integrated. Si integrated optical chips, that can generate, modulate, process and detect light signals, exploit the benefits of Si while also being fully compatible with electronic. Since many electronic components can be integrated into a single chip, Si is an ideal candidate for the production of small, powerful devices. By complementary metal-oxide-semiconductor (CMOS) technology, the fabrication of compact and mass manufacturable devices with integrated components on the Si platform is achievable. In this thesis we aim to model, study and fabricate a compact photonic quantum random number generator (QRNG) on the Si platform that is able to generate high quality, "truly" random numbers. The proposed QRNG is based on a Si light source (LED) coupled with a Si single photon avalanche diode (SPAD) or an array of SPADs which is called Si photomultiplier (SiPM). Various implementations of QRNG have been developed reaching an ultimate geometry where both the source and the SPAD are integrated on the same chip and fabricated by the same process. This activity was performed within the project SiQuro—on Si chip quantum optics for quantum computing and secure communications—which aims to bring the quantum world into integrated photonics. By using the same successful paradigm of microelectronics—the study and design of very small electronic devices typically made from semiconductor materials—, the vision is to have low cost and mass manufacturable integrated quantum photonic circuits for a variety of different applications in quantum computing, measure, sensing, secure communications and services. The Si platform permits, in a natural way, the integration of quantum photonics with electronics. Two methodologies are presented to generate random numbers: one is based on photon counting measurements and another one is based on photon arrival time measurements. The latter is robust, masks all the drawbacks of afterpulsing, dead time and jitter of the Si SPAD and is effectively insensitive to ageing of the LED and to its emission drifts related to temperature variations. The raw data pass all the statistical tests in national institute of standards and technology (NIST) tests suite and TestU01 Alphabit battery without a post processing algorithm. The maximum demonstrated bit rate is 1.68 Mbps with the efficiency of 4-bits per detected photon. In order to realize a small, portable QRNG, we have produced a compact configuration consisting of a Si nanocrystals (Si-NCs) LED and a SiPM. All the statistical test in the NIST tests suite pass for the raw data with the maximum bit rate of 0.5 Mbps. We also prepared and studied a compact chip consisting of a Si-NCs LED and an array of detectors. An integrated chip, composed of Si p+/n junction working in avalanche region and a Si SPAD, was produced as well. High quality random numbers are produced through our robust methodology at the highest speed of 100 kcps. Integration of the source of entropy and the detector on a single chip is an efficient way to produce a compact RNG. A small RNG is an essential element to guarantee the security of our everyday life. It can be readily implemented into electronic devices for data encryption. The idea of "utmost security" would no longer be limited to particular organs owning sensitive information. It would be accessible to every one in everyday life.