Investigation and modeling of impact ionization spatial-transient effects in silicon devices
Impact ionization (II) has played an important role in semiconductor devices; yet the understanding of II has not been mature. Abnormal behaviors related to II in deep sub-micrometer devices were observed and have not been fully explained. Existing models are not rigorously applicable to predicting II in different device structures and different operational regimes. Monte Carlo (MC) programs simulating transport of both electrons and holes are developed to investigate II in homogeneous electric field and in scaled devices. The programs' accuracy is verified by accurately producing many different transport parameters obtained from both experiments and previous MC simulations' results.
Impact ionization, for the first time, is modeled as a positive feedback loop in which electrons create holes, and the secondary holes feed back secondary electrons. This model is analytically proven to be valid for short devices due to the existence of the II dead-space. This model is also numerically proven to be accurate by producing a good fit to the experimental data. It is easy to conclude from the positive feedback model that the breakdown voltage is the same for both the electron-initiating and hole-initiating II processes in a high field region. In addition, the positive feedback model also shows that the current gain from the electron-initiating II process is always higher than the current gain from the hole-initiating II process within the same high field region. More importantly, the positive feedback loop enables successful simulations of the II process in which both electrons and holes participate simultaneously. This is particularly important at high current gain. An efficient algorithm is also developed to speed up spatial transient simulations by implementing temporal meshes rather than the traditional spatial meshes.
The II current gain in short p-i-n diodes is studied. The calculated results fit well to the experimental data of diodes with different lengths. Various physical insights are learned from the simulations. The minimum breakdown voltage for highly doped junctions is extrapolated to be at least 4.41V. Franz-Keldysh effect plays a significant role at low bias, especially for short devices. For the first time, Franz-Keldysh effect is invoked to explain the experimental current gain. II threshold energy is not constant with respect to the electric field, which partly explains various values of the reported threshold energy. II threshold energy is higher for holes than for electrons. Both electron and hole II coefficients come to equilibrium with the electric field after a dead-space distance. This spatial transient effect is a major cause for the disagreements among the experimentally-extracted values of the II coefficients. The values extracted from the double drift p-n junction experiments are more reliable in terms of accounting for the II spatial-transient effect. The II spatial-transient effect is identified to be the main cause for the failures of different well-known II models for semiconductor devices. A pseudo-local electric field model and the positive feedback model are proposed and proven to be sufficient in predicting the II current gain in short devices.
MC simulations are conducted to study mixed tunneling and II process in short p-n diodes, which are potential terahertz source devices. Tunneling current is treated as generation current, which is also subject to the tunneling dead-space distance. Another gain stage is added on top of the positive feedback model to account for the tunneling dead-space. II is less important for more heavily doped p-n junctions. The contribution of the diffusion current and its II is negligible compared to the tunneling counterparts.
Abnormal behaviors of II in deep sub-micrometer MOSFETs are investigated and explained. Channel carrier distribution functions are generated by MC simulations employing the rare-state algorithm. The thermal tail of the distribution function is Maxwellian with the lattice temperature as the effective temperature. By formulating the thermal tails as functions of position and bias voltage, an analytical formula of the substrate current is successfully derived for the first time. The formula is then used to explain experimental results of the substrate current in a sub-micrometer pMOSFET. The newly-developed formula is able to explain different abnormal behaviors of the substrate current that cannot be explained by the conventional formulas.