PART I: The thermal, electronic and electromagnetic properties of nanostructures vary significantly due to quantum confinement which results in breaking of symmetry and loss in periodicity. Collective atomic vibrations or phonons play a significant role in controlling all the above-mentioned properties in semiconductor and biological nanostructure. The goal of the present study is focused towards understanding the underlying nanoscale mechanisms and its implementations in specific systems. It has been observed that semiconductor devices tend to overheat (formation of hotspot) in high power and high frequency applications thus reducing the device performance efficiency. The generation of hotspot can be attributed to difference in decay rate of electron relaxation via optical phonon emission and decay rate of acoustic phonon generation from optical phonons, hence evaluation of the phonon dynamics can provide an useful insight towards heat generation and dissipation processes. For the first part of the research, phonon dynamics in cubic (GaAs) and wurtzite (GaN) crystal structure has been explored. According to Fuchs-Kliwer (FK) slab model, phonon modes in a layered structure can be represented as confined (CF) and interface (IF) modes. The CF phonon modes lie in the bulk, whereas IF phonon modes are limited within the surface of the layers and plays more important role in determining the properties of the nanostructure because of its comparatively higher surface-to-volume ratio. The effect of quantum confinement on the anharmonic decay rate of confined longitudinal optical phonon has been evaluated for free-standing quantum well (FSQW) and double-interface heterostructure quantum well (DHSQW) - two most widely used constructs for nanoscale optoelectronic and electronic devices. The potential role of interface phonon modes in the dissipation of heat in these structures has been discussed along with the preliminary demonstration of temperature measurement using Raman spectroscopy in semiconductor superlattices. Phonons play a significant role in functioning of phononic and phoxonic waveguides, acoustic metamaterials, which are profoundly used in nanostructures designed for precise and coherent controls of phonons. In this section of the study, the role of phonons has been explored in performance evaluation of an acoustic waveguide fixed on a perfectly elastic substrate. The continuum acoustic fields are represented as acoustic phonons using quantum mechanical second quantization. The quality factor of the waveguides in terms of phonon-phonon interaction is also analyzed. Electromagnetic signatures of biosystems and biological subunits (proteins, bio-macromolecules) can be ascribed to collective vibration of atoms. Viruses have shown to possess different structural vibrations depending on their morphological features, and shows activity towards electromagnetic excitation in terahertz frequency range. This research hypothesizes that the origin of terahertz vibrational signature of Bacillus endospores arises from acoustic vibrations of the nanocylinders present on its external surface. Parts 2: Nanosensors based on Aptamers Exploiting thermal, vibrational and electrical properties of nanoscale, highly selective biological, chemical and optical sensors with ultra-low detection capability. An electrochemical and an optical hybrid sensor with primary transducer and secondary transducer as DNA aptamer and nanomaterial are used. The electrochemical sensor consisted of graphene based ion-sensitive FET device functionalized with DNA aptamer and exhibited detection limit of 87 pM, whereas the optical sensing scheme consist of an analyte sensitive FRET probe. Semiconductor CdSe/ ZnS core shell quantum dot, DNA aptamer and gold nanoparticle are the integral part of the FRET probe and have shown detection limit of 2 pM.