Symbol 
 Unit 
 Description 

 Kinetic exponent in the RD model  

 Electronic matrix element in the FranckCondon approximation  

 Prefactor of the permanent component in the NBTI fit formula  

 Prefactor of the recoverable component in the NBTI fit formula  

 Interface area in the yzplane  

 Parameter in the empirical relation of the universal recovery  

 Electron capture coefficient  

 Hole capture coefficient  

 Hole capture coefficient in the NMP model  

 Temperature independent prefactor of  

 Areal gate capacitance  

 Diffusion coefficient in the RDD model  

 Density of states of a onedimensional, confined electron gas  

 Density of states of a threedimensional, confined electron gas  

 Interface trap density of states  

 Electron density of states in the conduction band  

 Density of states of a onedimensional electron gas  

 Product of and  

 Density of states of a twodimensional electron gas  

 Oxide trap density of states  

 Hole density of state in the valence band  

 Density of states of a threedimensional, confined hole gas  

 Density of states of a onedimensional hole gas  

 Product of and  

 Density of states of a twodimensional hole gas  

 Diffusion coefficient of the species in the RD model  

 Electron emission coefficient  

 Hole emission coefficient  

 Hole emission coefficient in the NMP model  

 Temperature independent prefactor of  

 Electron energy in the band edge energy diagram  

 Activation energy  

 Electron energy in the conduction/valance band  

 Conduction band edge energy  

 Conduction band edge energy in DFT calculations  

 Conduction band edge energy in the flat band case  

 Demarcation energy  

 Dissociation barrier in the reactionlimited model  

 Mean value of the dissociation barriers in the reactionlimited model  

 Fermi energy  

 Energy of the electron system in the state  

 Energy of a channel electron in the quasibound state  

 Energy of a channel hole in the quasibound state  

 Switching trap level for a transition from charge state to  

 Trap level  

 Trap level in the flat band case  

 Trap level of the oxygen vacancy in the TSM  

 Trap level of the center in the TSM  

 Trap level in the NMP model  

 Energy of the combined system of electrons and nuclei in the state  

 Valence band edge energy  

 Valence band edge energy in DFT calculations  

 Valence band edge energy in the flat band case  

 component of electron energy  

 Exchangecorrelation energy  

 Lineshape function  

 FranckCondon factor  

 Equilibrium occupancy for the trap  

 Occupancy of a trap in state  

 Occupancy for the trap in state  

 Interface trap occupancy  

 Electron occupancy  

 Oxide trap occupancy  

 Hole occupancy  

 Trap occupancy  

 Equilibrium trap occupancy  

 Electron occupancy of the center in the TSM  

 FermiDirac distribution  

 Oxide field  

 Reference field for the MPFAT mechanism  

 Oxide field during relaxation  

 Oxide field during stress  

 Trap occupancy for a set of states  

 Force on atom  

 Hydrogen trap density of states in the RDD model  

 Degeneracy of the valley  

 Hydrogen concentration in the RDD model  

 Magnetic field strength  

 General hamilton operator in the derivation of Fermi’s golden rule  

 Free hydrogen concentration in the RDD model  

 Hamilton operator of the channel in the derivation of Fermi’s golden rule  

 Hamilton operator of an atomic system  

 Drain current  

 Initial drain current  

 Electron wavevector  

 Coupling constant between and in Yang’s model  

 Forward rate of a reaction/transition  

 Attempt frequency in the reactionlimited model  

 Reverse rate of a reaction/transition  

 component of the electron wavevector  

 Length of the substrate in the direction  

 Effective mass of the electrons  

 Effective mass of the electrons for the valley index  

 Effective mass of the holes  

 Effective mass of the holes for the valley index  

 Tunneling mass of the charge carriers  

 Oscillator mass in the harmonic approximation  

 Matrix element for a vibronic transition from state to state  

 Matrix element for a transition from state to state  

 Electron density  

 Power law exponent of permanent component in the NBTI fit formula  

 Power law exponent of recoverable component in the NBTI fit formula  

 Power law exponent in the RD model  

 Acceptor concentration  

 Effective conduction band weight  

 Effective density of conduction states in the RDD model  

 Donor concentration  

 Concentration of interface states per area  

 Initial concentration of interface states per area  

 Number of oxide charges per area  

 Trap density  

 Effective valence band weight  

 Number of states for a free electrons/holes gas in the direction  

 Number of states for a free electrons/holes gas in the plane  

 Number of states for a free electrons/holes gas in the volume  

 Hole density  

 Transition probability from state to state  

 Configuration coordinate  

 Configuration coordinate at the energy minimum  

 Areal interface charges  

 Areal oxide charges  

 Vibronic transition rate from state to state  

 Electron capture rate  

 Hole capture rate  

 Electron tunneling rate  

 Transition rate of a trap during equilibrium conditions  

 Electron tunneling rate from the charge state to in the LSM  

 Electron emission rate  

 Hole emission rate  

 Rate for the transition  

 Hole tunneling rate  

 Hole tunneling rate from the charge state to in the LSM  

 Ratio of the vibration frequencies in an NMP transition  

 Spatial coordinates of electron  

 Transition rate matrix  

 Spatial coordinates of atom  

 Scaling factor for stress/relaxation curves  

 Scaling factor during relaxation  

 Scaling factor during stress  

 Prefactor of the scaling factor  

 Action in the WKB method  

 HuangRhys factor for an NMP transition  

 Time  

 Thickness of the insulator  

 Relaxation time  

 Stress time  

 First measurement point during stress  

 Temperature  

 Transmission coefficient for tunneling through the conduction band  

 Transmission coefficient for tunneling through the valence band  

 Temperature during equilibrium conditions  

 Transition from state to state  

 Transitions between the states to state  

 Chain of the transitions and  

 Temperature during relaxation  

 Temperature during stress  

 Electron kinetic energy operator  

 Nucleus kinetic energy operator  

 Adiabatic potential of an atomic system  

 for charge state  

 in the minimum configuration of state  

 Effective electron potential  

 Thermal velocity of the electrons  

 Thermal velocity of the holes  

 Velocity of atom  

 Defect potential  

 Channel potential in the derivation of Fermi’s golden rule  

 Gate bias during equilibrium conditions  

 Interatomic empirical potential  

 Gate bias  

 Energy of the system in state in the TWM and the CDW  

 Initial energy of the system in state in the TWM  

 Gate bias during relaxation  

 Gate bias during stress  

 Threshold voltage  

 Initial threshold voltage  

 Threshold voltage extracted from OTF measurements  

 Initial threshold voltage extracted from OTF measurements  

 Trap potential in the derivation of Fermi’s golden rule  

 Operator for the electronnucleus Coulomb interactions  

 Operator for the electronelectron Coulomb interactions  

 Operator for the nucleusnucleus Coulomb interactions  

 WKB factor for tunneling through the conduction band  

 WKB factor for tunneling through the valence band  

 Direction perpendicular to the substrateinsulator interface  

 Position of the substrateinsulator interface  

 Characteristic tunneling length for electrons  

 Characteristic tunneling length for holes  

 Position of the trap  

 Position of the tunneling hole front  

 Density of the diffusing species in the RD model  

 Direction parallel to the substrateinsulator interface  

 Direction parallel to the substrateinsulator interface  

 Charge state of the diffusing species in the RD model  

 Charge state of the diffusing species in the RDD model  

 Characteristic exponent in the reactionlimited model  

 Parameter in the empirical relation of the universal recovery  

 Field dependence factor of the thermal barrier in the TSM  

 Stress parameter in the TWM  

 Stress parameter in the CDW model  

 Time step in molecular dynamics  

 Change in the interface trap density of states  

 Change in the trap occupancy in state  

 Change in the oxide trap occupancy  

 Change in the trap occupancy  

 Energy barrier for charge trapping in the model of Kirton and Uren  

 Energy barrier for hole capture of the oxygen vacancy in the TSM  

 Energy barrier for hole capture of the center in the TSM  

 Relaxation barrier to the oxygen vacancy in the TSM  

 Thermal barrier for the hydrogen transition in the TSM  

 referenced to the substrate valence bandedge  

 referenced to the substrate valence bandedge  

 Change in the number of interface charges per area  

 Change in the number of oxide charges per area  

 Change in the areal interface charges  

 Change in the areal oxide charges  

 Change in the threshold voltage  

 Change in the threshold voltage during relax  

 Change in the threshold voltage during stress  

 Change in threshold voltage extracted from OTF measurements  

 NMP barrier for the transition  

 Electric permittivity  

 Energy level of the bound state  

 KohnSham eigenvalue  

 Energy barrier for the transition in the NMP model  

 Thermodynamic trap level for a transition from charge state to  

 Energy difference between the state and in the NMP model  

 Square root of the WKB factor  

 Mean value of the distribution of in Yang’s model  

 Mobility in the RD model  

 Mobility of the diffusing species in the RDD model  

 Valley index  

 Attempt frequency  

 Normalized relaxation time  

 Occupation probability for being in state  

 Occupation probability for set of states  

 Equilibrium occupation probability for set of states  

 Charge density  

 Density of traps  

 Trapped hydrogen density in the RDD model  

 Ground state charge density  

 Spread of the distribution of in Yang’s model  

 Spread of dissociation barrier in the reactionlimited model  

 Cross section for an electon transition in the TSM model  

 Cross section for an electron tunneling in the ETM  

 Temperatureindependent prefactor of  

 Cross section for a hole transition in the SRH model  

 Cross section for a hole transition in the eNMP model  

 Cross section for a hole transition in the TSM model  

 Cross section for hole tunneling in the ETM  

 Temperatureindependent prefactor of  

 Temperatureindependent prefactor of  

 Temperatureindependent prefactor of  

 Transition time constant in the reactionlimited and the Yang model  

 Hole capture time constant over the state in the eNMP model  

 Hole capture time constant over the state in the eNMP model  

 Capture time constant  

 Electron capture time constant  

 Hole capture time constant  

 Minimal in the eNMP model  

 Minimal in the eNMP model  

 Emission time constant  

 Hole emission time constant over the state in the eNMP model  

 Hole emission time constant over the state in the eNMP model  

 Electron emission time constant  

 Hole emission time constant  

 Minimal in the eNMP model  

 Minimal in the eNMP model  

 Electron capture time constant as defined in the TSM model  

 Hole capture time constant as defined in the ETM  

 Hole capture time constant as defined in the eNMP model  

 Hole capture time constant as defined in the SRH model  

 Hole capture time constant as defined in the TSM model  

 Reduced electron capture time in the ETM  

 Reduced hole capture time in the ETM  

 Wavefunction of the combined system of electrons and nuclei  

 Electric potential  

 Surface potential  

 Potential energy of electrons/holes  

 Left/Right border of the tunnel barrier  

 Wavefunction of an nuclei system in state  

 Singleelectron wavefunction in state  

 KohnSham orbitals  

 Electron channel wavefunction of the quasibound state  

 Hole channel wavefunction of the quasibound state  

 Wavefunction of an electron system in state  

 Wavefunction of an electron system in the ground state  

 Oscillator frequency in the harmonic approximation  