Porous silicon exhibits unique electronic and optical properties that are strongly influenced by its nanostructured morphology. Unlike quantum dots, which exhibit discrete energy levels due to three-dimensional quantum confinement, or two-dimensional materials where charge carriers are confined in one dimension, porous silicon presents a complex network of interconnected nanocrystals and pores. The size-dependent behavior arises from the quantum confinement effects within the silicon nanocrystals that form the porous matrix, while the luminescence properties are further modulated by surface states and the surrounding dielectric environment.

The electronic properties of porous silicon are primarily governed by the size distribution of silicon nanocrystals embedded within the porous framework. When the dimensions of these nanocrystals approach the excitonic Bohr radius of bulk silicon (approximately 5 nm), quantum confinement effects become significant. This leads to a widening of the bandgap as the nanocrystal size decreases, following a power-law relationship. Experimental studies have shown that the bandgap can be tuned from the near-infrared (1.1 eV for bulk silicon) to the visible range (up to 2.5 eV) by controlling the nanocrystal size between 5 nm and 2 nm. Unlike quantum dots, where the energy levels are sharply defined, porous silicon exhibits a broader distribution of states due to the inhomogeneous size distribution of nanocrystals and the presence of surface-related defects.

Luminescence in porous silicon is a result of both quantum confinement and surface-related effects. The visible photoluminescence, first observed in the early 1990s, was initially attributed solely to quantum confinement. However, further research revealed that surface passivation plays an equally critical role. Hydride-terminated surfaces exhibit different emission characteristics compared to oxide-passivated surfaces, with the latter showing improved stability and a redshift in the emission spectrum. The luminescence efficiency is strongly dependent on the nanocrystal size, with smaller nanocrystals exhibiting higher quantum yields due to enhanced radiative recombination rates. The emission wavelength can be tuned across the visible spectrum by adjusting the porosity and etching conditions during fabrication, which in turn controls the average nanocrystal size.

The charge transport properties in porous silicon differ markedly from those in bulk silicon or quantum dot arrays. The interconnected network of nanocrystals creates a percolation path for carriers, but the presence of surface states and the inherent disorder lead to hopping conduction mechanisms at room temperature. The electrical conductivity decreases exponentially with increasing porosity due to the reduction in available conduction pathways. Unlike two-dimensional materials where carrier mobility is primarily limited by surface scattering, transport in porous silicon is dominated by tunneling between nanocrystals and trapping at interface states.

Optical absorption in porous silicon shows a blueshift relative to bulk silicon, consistent with the quantum confinement effect. However, the absorption spectrum lacks the sharp features observed in quantum dots due to the size distribution of nanocrystals. The absorption coefficient remains high in the visible range, making porous silicon suitable for photovoltaic applications despite its indirect bandgap nature. The effective refractive index can be tuned by varying the porosity, enabling the design of optical waveguides and filters integrated with silicon technology.

Surface chemistry plays a pivotal role in determining the electronic and optical properties of porous silicon. Freshly etched porous silicon with hydrogen-terminated surfaces exhibits different electronic behavior compared to oxidized or chemically modified surfaces. Oxidation leads to the formation of silicon oxide layers around the nanocrystals, which introduces additional interface states that can trap charge carriers or act as recombination centers. Chemical functionalization with organic molecules can further modify the electronic properties by introducing dipole layers or creating new electronic states within the bandgap.

The thermal properties of porous silicon are also size-dependent, with reduced thermal conductivity compared to bulk silicon due to phonon scattering at the nanocrystal boundaries and pores. This property has been exploited in thermoelectric applications where a low thermal conductivity is desirable. The mechanical properties show a similar dependence on porosity, with Young's modulus decreasing as the porosity increases, following a power-law relationship.

In optoelectronic applications, the tunability of both electronic and optical properties makes porous silicon attractive for light-emitting devices, photodetectors, and sensors. The large surface area enhances sensitivity to environmental changes, while the adjustable bandgap allows optimization for specific wavelength ranges. Unlike quantum dots that require precise size control during synthesis, porous silicon offers a more cost-effective route to achieving size-dependent properties through electrochemical or chemical etching processes.

The stability of porous silicon devices remains a challenge due to surface oxidation and degradation under ambient conditions. Various passivation techniques have been developed to address this issue, including thermal oxidation, chemical functionalization, and encapsulation in polymer matrices. These treatments not only improve stability but can also modify the electronic properties through surface dipole effects or strain induction in the nanocrystals.

Recent advances in fabrication techniques have enabled better control over pore morphology and nanocrystal size distribution, leading to improved reproducibility of electronic and optical properties. The development of multilayer structures with varying porosity has opened new possibilities for bandgap engineering and photonic applications. Compared to quantum dots or two-dimensional materials, porous silicon offers unique advantages in terms of compatibility with existing silicon technology and the ability to create three-dimensional nanostructured devices.

The size-dependent properties of porous silicon continue to be an active area of research, with ongoing investigations into surface modification techniques, hybrid structures combining porous silicon with other materials, and novel device architectures. The understanding of charge transport mechanisms and recombination pathways has improved significantly, enabling more sophisticated device designs that take advantage of the unique properties of this material system. While challenges remain in terms of stability and reproducibility, the ability to tune electronic and optical properties through simple processing steps makes porous silicon a versatile platform for various applications in electronics and photonics.