Institute for Microelectronics, Vienna University of Technology, Gußhausstraße 27–29/E360, 1040 Wien, AustriaDepartment of Physics and Astronomy and London Centre for Nanotechnology, University College London, Gower Street, London WC1E 6BT, UK
Two typical ΔVth recovery traces of a small-area pMOSFET from a TDDS experiment. The measured data are given by the noisy black lines (a). The thick blue and red lines together with the symbols mark the emission times and step heights, unambiguous fingerprints of each defect which constitute the spectral map (b).
Two TDDS spectral maps at two stress times, (a) ts=100 μs and (b) ts=10 ms. With increasing stress time, the number of defects in the map increases. The width of each cluster is given by the exponential distribution of τe (considered on a log scale) and the extracted defects/clusters are marked by ‘plus’ symbols.
Two charge states of the hydroxyl-E′ centre calculated using DFT, (a) neutral and (c) positive. H atoms are shown as silver, Si atoms as yellow and O atoms as red. The localized highest occupied orbital is shown as the turquoise bubble for the neutral charge state, whereas it represents the lowest unoccupied orbital for the positive charge state. Note that all atomic positions around the defect change when the charge state is changed. In panel (b), the diabatic potentials of the two states are shown qualitatively as a function of the reaction coordinate. In the classical limit of the NMP transition, charge capture takes place at the intersection of the two parabolas. The intersection point determines the barrier that has to be overcome for this reaction.
Four-state defect model used to analyse the results of TDDS measurements show a schematic presentation of a cross section of the potential energy surface along a configuration coordinate (CC). The schematic illustrates the energy parameters needed for calculating the rates of vibronic transitions described using NMP theory ( as ) and thermally activated transitions described using transition-state theory ( and ).
Diagram illustrates the distribution of the potential energy surface parameters shown in figure 4 arising in TDDS experiments. It shows an average CC diagram extracted experimentally for 35 defects using TDDS. Additionally, the envelope curves of the potential energy surfaces for calculated standard deviations of the characteristic parameters are schematically shown up to a deviation of 1.5σ.
Atomic configurations corresponding to states 1, 1′, 2′ and 2 for the oxygen vacancy (OV, top row panels) hydrogen bridge (HB, middle row panels) and the hydroxyl-E′ centre (H-E′, bottom). H atoms are shown as silver, Si atoms, yellow and O atoms, red. The turquoise bubble represent the localized highest occupied orbitals for the neutral charge states and the lowest unoccupied orbital for the positive charge states. Upon hole capture, the defect can go into state 2′ and the Si atoms move closer together in all the defects. Depending on the gate bias, the defect either goes back to state 1 or, eventually into the positive state 2 or the neutral state 1′, where the right Si has moved through the plane of its three O neighbours, forming a puckered configuration by bonding to a neighbouring O in the right.
Distribution of the thermodynamic charge-trapping levels, ET, a fundamental parameter that decides on which trap can be charged for a combination of certain stress- and recovery voltages. The top of the Si valence band is set to zero. Note that all defects close to the valence band of Si, EV(Si), will contribute to RTN in a pMOS. Clearly, the OV/E′ centre is too low in energy, whereas both the hydrogen bridge and the hydroxyl-E′ centre are in good agreement with the data inside the experimental window. Recall the uncertainty in DFT energy-levels and the −0.4 eV energy shift used.
The experimental and calculated barriers for the various transitions in the four-state model. The parameters are shown on the diabatic potential energy diagram in figure 4. While overall good agreement is obtained, the theoretical barrier ε22′ is too small in general. Note that the defects with negative εT2′ are two-state defects at the border of our experimental window.
TDDS measurements for three selected defects which were monitored over three months. The plots show when the defect is electrically active or inactive (volatile). Occasionally, the experimental conditions did not allow for an observation (‘blind’ phases), for instance during a long high-temperature bake around the beginning of the third month.
Barriers EB from NEB-calculations for the transition (in the case of the HB also ) into the electrically inactive state 0+. For the HB (a) even the lowest values found are much too high to be able to explain the observed volatility. Even though the mean value for the barrier height (black arrow) for the hydroxyl-E′ (b) is very high too, one can also find very low barriers that could easily be overcome during experimental conditions, giving a possible explanation for defects becoming volatile.
Top: schematic shows the relocation of the proton for the case of the hydroxyl-E′ centre. The proton moves from the defect site in state 2′ (left) onto a neighbouring bridging oxygen atom (right). Owing to the amorphous nature of the structure, in general, the new location does not favour the creation of a new defect. We name this new positively charged state 0+. Bottom: when the state 0+ is charged neutrally, three different possible states 0n have been found: the H atom becomes interstitial (left), the H atom causes one of the oxygen-silicon bonds to break (middle), forming a new hydroxyl-E′ centre or the H-atom remains attached (right). The latter is only possible when the hydrogen can transfer its electron to an electron-accepting site nearby.
Example of a potential energy surface of a hydroxyl-E′ centre defect along the reaction coordinates between different states. Possible transitions can occur by charge capture or emission (green arrows) or barrier hopping (purple arrows). The defect is electrically active when on the left side of the plot (orange). When it overcomes the barrier it is electrically inactive (grey) and therefore, in general, not visible in the measurements (given certain conditions for the barrier between the states 0+ and 0n as described in the text). Depending on the applied gate bias, the parabolas of the neutral states (blue) will be shifted up or down along the energy axis, thereby changing the barriers and time constants for charge-trapping and emission. Note that in this extended model there are now three possibilities to leave state 2′ (to 1, 2 or 0+).
Correlations of the barrier heights EBr and Er with respect to Ef (figure 12) for the hydroxyl-E′ centre. We distinguish between the three possible states 0n (figure 11 bottom): the hydrogen atom can either stay attached (stick), break one of the bonds at the bridging oxygen (break) or become interstitial (inter). For about two-thirds of the defects EBr is higher than Ef (a). Even though this means that defects should be electrically active, this does not mean that they would be visible in RTN measurements. This is due to the height of Ef and, even more importantly, owing to the large difference between Ef and Er (b), which moves them far outside of the RTN detection window. However, as discussed in the text, those defects should be visible in TDDS, but the signal would most probably not be identified as being related to the initial defect.