This thesis offers modeling of a newly discovered gain mechanism for various photodetection applications. Conventional avalanche photodetectors have been in use for the past four decades with impact ionization being the underlying carrier multiplication mechanism.However, tradeoff between sensitivity, dynamic range and bandwidth are some of the drawbacks of the present day photodetection technology. The newly discovered cycling excitation process (CEP) can be a potential candidate to address these issues with linear photo response, single photon sensitivity and high gain bandwidth product. The key feature of CEP is introduction of counter dopants in p-n junction silicon diode, with which the efficiency of auger excitation can be enhanced to great extent by facilitating relaxation of k selection rule. Higher uncertainty in k spaces dictates localization of carriers in real space. Hence, an initial hot carrier can excite electron-hole pair between localized states (e.g. from states closer to valence band to states closer to conduction band) at much lower bias. Another essential component of CEP is phonon/field assisted tunneling from localized states to mobile bands. Contrary to other photodetectors, phonons, actually, play a positive role in achieving gain. Experimentally gain of ~4000 at only 4V have been achieved in the CEP test structure along with photo response dependence on input light power, which is helpful for photon number resolving. Temperature dependent measurement also shows the positive role of phonons. Density functional theory calculation shows the change in band structure with doping bulk crystalline silicon with boron (B) and phosphorous (P) simultaneously. Comparison of density of states exhibits existence of states inside band gap. Furthermore, charge density plot clearly demonstrates electron and hole localization centered around P and B atoms respectively. Hence, highly counter doping with BP atoms turns the crystalline silicon into a quasi-disordered material. Since, highly counter doping introduces disorder in silicon, with this notion naturally disordered materials are explored as possible CEP gain media. Amorphous materials have low mobility due to their nature of disorder. Surprisingly, amorphous silicon (a-Si) photodiodes with thin a-Si layer (~40nm) have shown a gain-bandwidth product of over 2 THz with very low excess noise. To unveil the true gain mechanism, the thesis further delves into theoretical modeling and numerical analysis along with experimental data at different frequencies. Evidence of highly effective carrier multiplication process within a-Si as the primary gain mechanism, especially at high frequency is shown. There is also trap-induced junction modulation at much lower frequency. The analysis further suggests that the carrier multiplication process in thin a-Si can be much more efficient than in thick a-Si, even stronger than single crystalline Si in some cases. Although seemingly counter intuitive, this is consistent with the proposed cycling excitation process (CEP) where the localized states in the bandtails of disordered materials such as a-Si relax the k-selection rule and increase the rate of carrier multiplication. A more rigorous quantum mechanical scattering rate calculation also demonstrates the increase of strength of carrier multiplication with the presence of localized states and the increase of ionization coefficient with decreasing thickness of gain medium. A theoretical framework is offered to calculate the carrier multiplication process in a-Si or other disordered materials involving donor acceptor pairs (DAPs) and to answer several key and seemingly counter intuitive questions such as why amorphous silicon can be more efficient carrier multiplication material than single crystal silicon, why low carrier mobility of amorphous material helps rather than hurt carrier multiplication process, and why thin a-Si is more efficient than thick a-Si in carrier multiplication
