In recent years there has been considerable interest in studying the DENSITY-OF-STATES (DOS) functions and Related Applications in Quantized Structures of different technologically important materials in low dimensional electronics. The concept of DOS function is of fundamental importance for not only the characterization of semiconductor nanostructures but also in the study of the carrier transport in quantum effect devices. The acoustic mobility limited momentum relaxation time is inversely proportional to the respective DOS function of a particular semiconductor and the DOS function, in turn, is connected to the twenty five important transport topics of quantum effect devices namely the Landau Dia and Pauli's Para Magnetic Susceptibilities, the Einstein's Photoemission, the Einstein Relation, the Debye Screening Length, the Generalized Raman gain, the Normalized Hall coefficient, the Fowler-Nordheim Field Emission, the Gate Capacitance, the Thermoelectric Power, the Plasma Frequency, the Magneto-Thermal effect in Quantized Structures, the Activity coefficient, the Reflection coefficient, the Heat Capacity, the Faraday rotation, the Optical Effective Mass, the Carrier contribution to the elastic constants, the Diffusion coefficient of the minority carriers, the Nonlinear optical response, the Third order nonlinear optical susceptibility, the Righi-Leduc coefficient, the Electric Susceptibility, the Electric Susceptibility Mass, the Electron Diffusion Thermo-power and the Hydrostatic Piezo-resistance Coefficient respectively.This first-of-a-kind monograph investigates the DOS function and the aforementioned applications in quantized structures of tetragonal and non-linear optical, III-V, II-VI, Gallium Phosphide, Germanium, Platinum Antimonide, stressed, IV-VI, Lead Germanium Telluride, II-V, Zinc and Cadmium diphosphides and Bismuth Telluride respectively. We have also formulated the same and the allied physical properties of III-V, II-VI, IV-VI and HgTe/CdTe quantum well Heavily Doped (HD) superlattices with graded interfaces under magnetic quantization, III-V, II-VI, IV-VI and HgTe/CdTe HD effective mass superlattices under magnetic quantization, quantum confined effective mass superlattices and superlattices of HD optoelectronic materials with graded interfaces in addition to other quantized structures respectively.This book covers from elementary applications in the first chapter up to rather advanced investigations in the later chapters. We have suggested experimental determinations of the Einstein relation for the Diffusivity-Mobility ratio, the Debye screening length and Elastic Constants in various types of quantized structures under different physical conditions. This book contains 222 current open research problems which form an integral part of the text and are useful for both aspiring students and researchers. It is written for graduate / post graduate students, engineers and professionals in the fields of condensed matter physics, solid state sciences, materials science, nanoscience, nanotechnology and nanostructured materials in general and this book will be invaluable to all those researching in academic and industrial laboratories in the said cases worldwide.