<div> Challenges in the semiconductor industry have resulted in the discovery of a plethora of promising materials and devices such as the III-Vs (InGaAs, GaSb, GaN/InGaN) and 2D materials (Transition-metal dichalcogenides [TMDs]) with wide-ranging applications from logic devices, optoelectronics to biomedical devices. Performance of these devices suffer significantly from scattering processes such as polar-optical phonons (POP), charged impurities and remote phonon scattering. These scattering mechanisms are long-ranged, and a quantitative description of such devices require non-local scattering calculations that are computationally expensive. Though there have been extensive studies on coherent transport in these materials, simulations are scarce with scattering and virtually non-existent with non-local scattering. </div><div> </div><div>In this work, these scattering mechanisms with full non-locality are treated rigorously within the Non-Equilibrium Green's function (NEGF) formalism. Impact of non-locality on charge transport is assessed for GaSb/InAs nanowire TFETs highlighting the underestimation of scattering with local approximations. Phonon, impurity scattering, and structural disorders lead to exponentially decaying density of states known as Urbach tails/band tails. Impact of such scattering mechanisms on the band tail is studied in detail for several bulk and confined III-V devices (GaAs, InAs, GaSb and GaN) showing good agreement with existing experimental data. A systematic study of the dependence of Urbach tails with dielectric environment (oxides, charged impurities) is performed for single and multilayered 2D TMDs (MoS2, WS2 and WSe2) providing guideline values for researchers. </div><div><br></div><div>Often, empirical local approximations (ELA) are used in the literature to capture these non-local scattering processes. A comparison against ELA highlight the need for non-local scattering. A physics-based local approximation model is developed that captures the essential physics and is computationally feasible.</div>