Symbol |
| Unit |
| Description |
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| Kinetic exponent in the RD model |
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| Electronic matrix element in the Franck-Condon approximation |
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| Prefactor of the permanent component in the NBTI fit formula |
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| Prefactor of the recoverable component in the NBTI fit formula |
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| Interface area in the yz-plane |
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| Parameter in the empirical relation of the universal recovery |
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| Electron capture coefficient |
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| Hole capture coefficient |
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| Hole capture coefficient in the NMP model |
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| Temperature independent prefactor of ![]() |
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| Areal gate capacitance |
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| Diffusion coefficient in the RDD model |
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| Density of states of a one-dimensional, confined electron gas |
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| Density of states of a three-dimensional, confined electron gas |
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| Interface trap density of states |
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| Electron density of states in the conduction band |
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| Density of states of a one-dimensional electron gas |
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| Product of ![]() ![]() |
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| Density of states of a two-dimensional electron gas |
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| Oxide trap density of states |
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| Hole density of state in the valence band |
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| Density of states of a three-dimensional, confined hole gas |
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| Density of states of a one-dimensional hole gas |
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| Product of ![]() ![]() |
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| Density of states of a two-dimensional hole gas |
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| Diffusion coefficient of the species ![]() |
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| Electron emission coefficient |
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| Hole emission coefficient |
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| Hole emission coefficient in the NMP model |
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| Temperature independent prefactor of ![]() |
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| Electron energy in the band edge energy diagram |
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| Activation energy |
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| Electron energy in the conduction/valance band |
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| Conduction band edge energy |
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| Conduction band edge energy in DFT calculations |
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| Conduction band edge energy in the flat band case |
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| Demarcation energy |
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| Dissociation barrier in the reaction-limited model |
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| Mean value of the dissociation barriers in the reaction-limited model |
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| Fermi energy |
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| Energy of the electron system in the state ![]() |
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| Energy of a channel electron in the quasi-bound state ![]() |
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| Energy of a channel hole in the quasi-bound state ![]() |
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| Switching trap level for a transition from charge state ![]() ![]() |
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| Trap level |
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| Trap level in the flat band case |
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| Trap level of the oxygen vacancy in the TSM |
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| Trap level of the ![]() |
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| Trap level in the NMP model |
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| Energy of the combined system of electrons and nuclei in the state ![]() |
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| Valence band edge energy |
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| Valence band edge energy in DFT calculations |
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| Valence band edge energy in the flat band case |
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| ![]() ![]() |
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| Exchange-correlation energy |
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| Lineshape function |
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| Franck-Condon factor |
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| Equilibrium occupancy for the trap ![]() |
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| Occupancy of a trap in state ![]() |
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| Occupancy for the trap ![]() ![]() |
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| Interface trap occupancy |
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| Electron occupancy |
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| Oxide trap occupancy |
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| Hole occupancy |
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| Trap occupancy |
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| Equilibrium trap occupancy |
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| Electron occupancy of the ![]() |
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| Fermi-Dirac distribution |
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| Oxide field |
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| Reference field for the MPFAT mechanism |
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| Oxide field during relaxation |
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| Oxide field during stress |
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| Trap occupancy for a set of states |
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| Force on atom ![]() |
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| Hydrogen trap density of states in the RDD model |
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| Degeneracy of the valley ![]() |
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| Hydrogen concentration in the RDD model |
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| Magnetic field strength |
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| General hamilton operator in the derivation of Fermi’s golden rule |
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| Free hydrogen concentration in the RDD model |
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| Hamilton operator of the channel in the derivation of Fermi’s golden rule |
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| Hamilton operator of an atomic system |
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| Drain current |
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| Initial drain current |
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| Electron wavevector |
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| Coupling constant between ![]() ![]() |
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| Forward rate of a reaction/transition |
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| Attempt frequency in the reaction-limited model |
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| Reverse rate of a reaction/transition |
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| Length of the substrate in the ![]() |
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| Effective mass of the electrons |
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| Effective mass of the electrons for the valley index ![]() |
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| Effective mass of the holes |
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| Effective mass of the holes for the valley index ![]() |
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| Tunneling mass of the charge carriers |
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| Oscillator mass in the harmonic approximation |
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| Matrix element for a vibronic transition from state ![]() ![]() |
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| Matrix element for a transition from state ![]() ![]() |
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| Electron density |
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| Power law exponent of permanent component in the NBTI fit formula |
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| Power law exponent of recoverable component in the NBTI fit formula |
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| Power law exponent in the RD model |
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| Acceptor concentration |
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| Effective conduction band weight |
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| Effective density of conduction states in the RDD model |
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| Donor concentration |
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| Concentration of interface states per area |
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| Initial concentration of interface states per area |
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| Number of oxide charges per area |
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| Trap density |
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| Effective valence band weight |
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| Number of states for a free electrons/holes gas in the ![]() |
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| Number of states for a free electrons/holes gas in the ![]() |
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| Number of states for a free electrons/holes gas in the ![]() |
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| Hole density |
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| Transition probability from state ![]() ![]() |
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| Configuration coordinate |
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| Configuration coordinate at the energy minimum ![]() |
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| Areal interface charges |
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| Areal oxide charges |
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| Vibronic transition rate from state ![]() ![]() |
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| Electron capture rate |
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| Hole capture rate |
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| Electron tunneling rate |
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| Transition rate ![]() ![]() |
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| Electron tunneling rate from the charge state ![]() ![]() |
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| Electron emission rate |
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| Hole emission rate |
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| Rate for the transition ![]() |
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| Hole tunneling rate |
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| Hole tunneling rate from the charge state ![]() ![]() |
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| Ratio of the vibration frequencies in an NMP transition |
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| Spatial coordinates of electron ![]() |
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| Transition rate matrix |
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| Spatial coordinates of atom ![]() |
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| Scaling factor for stress/relaxation curves |
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| Scaling factor ![]() |
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| Scaling factor ![]() |
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| Prefactor of the scaling factor ![]() |
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| Action in the WKB method |
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| Huang-Rhys factor for an NMP transition ![]() |
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| Time |
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| Thickness of the insulator |
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| Relaxation time |
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| Stress time |
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| First measurement point during stress |
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| Temperature |
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| Transmission coefficient for tunneling through the conduction band |
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| Transmission coefficient for tunneling through the valence band |
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| Temperature during equilibrium conditions |
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| Transition from state ![]() ![]() |
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| Transitions between the states ![]() ![]() |
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| Chain of the transitions ![]() ![]() |
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| Temperature during relaxation |
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| Temperature during stress |
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| Electron kinetic energy operator |
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| Nucleus kinetic energy operator |
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| Adiabatic potential of an atomic system |
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| ![]() ![]() |
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| ![]() ![]() |
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| Effective electron potential |
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| Thermal velocity of the electrons |
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| Thermal velocity of the holes |
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| Velocity of atom ![]() |
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| Defect potential |
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| Channel potential in the derivation of Fermi’s golden rule |
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| Gate bias during equilibrium conditions |
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| Interatomic empirical potential |
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| Gate bias |
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| Energy of the system in state ![]() |
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| Initial energy of the system in state ![]() |
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| Gate bias during relaxation |
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| Gate bias during stress |
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| Threshold voltage |
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| Initial threshold voltage |
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| Threshold voltage extracted from OTF measurements |
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| Initial threshold voltage extracted from OTF measurements |
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| Trap potential in the derivation of Fermi’s golden rule |
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| Operator for the electron-nucleus Coulomb interactions |
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| Operator for the electron-electron Coulomb interactions |
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| Operator for the nucleus-nucleus Coulomb interactions |
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| WKB factor for tunneling through the conduction band |
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| WKB factor for tunneling through the valence band |
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| Direction perpendicular to the substrate-insulator interface |
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| Position of the substrate-insulator interface |
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| Characteristic tunneling length for electrons |
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| Characteristic tunneling length for holes |
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| Position of the trap |
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| Position of the tunneling hole front |
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| Density of the diffusing species ![]() |
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| Direction parallel to the substrate-insulator interface |
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| Direction parallel to the substrate-insulator interface |
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| Charge state of the diffusing species ![]() |
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| Charge state of the diffusing species in the RDD model |
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| Characteristic exponent in the reaction-limited model |
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| Parameter in the empirical relation of the universal recovery |
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| Field dependence factor of the thermal barrier in the TSM |
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| Stress parameter in the TWM |
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| Stress parameter in the CDW model |
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| Time step in molecular dynamics |
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| Change in the interface trap density of states |
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| Change in the trap occupancy in state ![]() |
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| Change in the oxide trap occupancy |
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| Change in the trap occupancy |
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| Energy barrier for charge trapping in the model of Kirton and Uren |
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| Energy barrier for hole capture of the oxygen vacancy in the TSM |
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| Energy barrier for hole capture of the ![]() |
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| Relaxation barrier to the oxygen vacancy in the TSM |
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| Thermal barrier for the hydrogen transition in the TSM |
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| Change in the number of interface charges per area |
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| Change in the number of oxide charges per area |
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| Change in the areal interface charges |
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| Change in the areal oxide charges |
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| Change in the threshold voltage |
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| Change in the threshold voltage during relax |
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| Change in the threshold voltage during stress |
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| Change in threshold voltage extracted from OTF measurements |
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| NMP barrier for the transition ![]() |
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| Electric permittivity |
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| Energy level of the bound state ![]() |
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| Kohn-Sham eigenvalue |
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| Energy barrier for the transition ![]() |
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| Thermodynamic trap level for a transition from charge state ![]() ![]() |
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| ![]() |
| Energy difference between the state ![]() ![]() |
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| Square root of the WKB factor |
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| Mean value of the distribution of ![]() |
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| Mobility in the RD model |
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| Mobility of the diffusing species ![]() |
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| Valley index |
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| Attempt frequency |
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| Normalized relaxation time |
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| Occupation probability for being in state ![]() |
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| Occupation probability for set of states |
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| Equilibrium occupation probability for set of states |
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| Charge density |
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| Density of traps |
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| Trapped hydrogen density in the RDD model |
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| Ground state charge density |
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| Spread of the distribution of ![]() |
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| Spread of dissociation barrier in the reaction-limited model |
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| Cross section for an electon transition in the TSM model |
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| Cross section for an electron tunneling in the ETM |
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| Temperature-independent prefactor of ![]() |
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| Cross section for a hole transition in the SRH model |
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| Cross section for a hole transition in the eNMP model |
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| Cross section for a hole transition in the TSM model |
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| Cross section for hole tunneling in the ETM |
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| Temperature-independent prefactor of ![]() |
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| Temperature-independent prefactor of ![]() |
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| Temperature-independent prefactor of ![]() |
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| ![]() |
| Transition time constant in the reaction-limited and the Yang model |
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| Hole capture time constant over the state ![]() |
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| Hole capture time constant over the state ![]() |
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| Capture time constant |
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| Electron capture time constant |
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| Hole capture time constant |
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| Minimal ![]() |
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| Minimal ![]() |
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| Emission time constant |
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| Hole emission time constant over the state ![]() |
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| Hole emission time constant over the state ![]() |
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| Electron emission time constant |
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| Hole emission time constant |
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| ![]() |
| Minimal ![]() |
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| ![]() |
| Minimal ![]() |
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| Electron capture time constant as defined in the TSM model |
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| Hole capture time constant as defined in the ETM |
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| Hole capture time constant as defined in the eNMP model |
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| Hole capture time constant as defined in the SRH model |
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| Hole capture time constant as defined in the TSM model |
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| Reduced electron capture time in the ETM |
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| Reduced hole capture time in the ETM |
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| Wavefunction of the combined system of ![]() ![]() |
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| Electric potential |
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| Surface potential |
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| Potential energy of electrons/holes |
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| Left/Right border of the tunnel barrier |
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| Wavefunction of an ![]() ![]() |
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| Single-electron wavefunction in state ![]() |
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| Kohn-Sham orbitals |
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| Electron channel wavefunction of the quasi-bound state ![]() |
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| Hole channel wavefunction of the quasi-bound state ![]() |
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| Wavefunction of an ![]() ![]() |
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| Wavefunction of an ![]() |
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| Oscillator frequency in the harmonic approximation |