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3.1 Silicon Dangling Bonds

Figure 3.1: (a) At the silicon surface silicon atoms are missing and unpaired valence electrons exist forming electrically active interface traps. (b) After oxidation most interface states are saturated with oxygen bonds. (c) After annealing the surface with a hydrogen related species the amount of interface defects is further decreased.
Silicon surface

Unpassivated \ensuremath {\textrm {Si/SiO$_2$}} interface

After hydrogen passivation

The silicon atom possesses four valence electrons and therefore requires four bonds to fully saturate the valence shell. In the crystalline structure each silicon atom establishes bonds to its four neighboring atoms, leaving no unsaturated bond behind. At the surface of the silicon crystal atoms are missing and traps are formed as shown in Figure 3.1(a). The density of these interface states, \ensuremath {D_\textrm {it}}, in this regime is approximately $\ensuremath{D_\textrm{it}}\approx
10^{14}$cm$^{-2}$eV$^{-1}$. After oxidation most interface states are saturated with oxygen atoms (Figure 3.1(b)). The density is then approximately $\ensuremath{D_\textrm{it}}\approx 10^{12}$cm$^{-2}$eV$^{-1}$ [16].

This number is already a major improvement of the interface quality. But in an MOS transistor with a gate length of 100nm and a gate width of 1$\mu $m this density still translates to 1000 dangling bonds. With such a high number of interface defects a transistor would still not operate properly. Therefore, it is mandatory to increase the quality of the \ensuremath {\textrm {Si/SiO$_2$}} interface in MOS device technology as much as possible. Each electrically active interface state leads to degradation of important transistor parameters such as the threshold voltage, the on-current, or the surface carrier mobility. To further improve the interface, the number of dangling valence bonds is further reduced by annealing the interface in forming gas with hydrogen atoms, as shown in Figure 3.1(c). The dangling silicon bonds are passivated by forming Si-H bonds. With this treatment the amount of electrically active interface states can be reduced to around $\ensuremath{D_\textrm{it}}\approx

This is an acceptable number and a first-class \ensuremath {\textrm {Si/SiO$_2$}} interface can be formed. Ironically, exactly these Si-H bonds are the cause for NBTI, as extensively described in Chapter 6. The bonds can break at elevated temperatures and high electric fields due to their lower binding energy and re-activate the interface states.

The exact properties of the interface defects, which are trivalent silicon atoms with one unpaired valence electron

\ensuremath{\textrm{Si}}_3 \ensuremath{\!\!\equiv\!\!}\ensuremath{\textrm{Si}}^\bullet   ,
\end{displaymath} (3.1)

\ensuremath{\textrm{Si}}_2\mathrm{O} \ensuremath{\!\!\equiv\!\!}\ensuremath{\textrm{Si}}^\bullet   ,
\end{displaymath} (3.2)

depends on the exact atomic configuration and on the orientation of the substrate. While \ensuremath {P_\textrm {b}} centers (3.1) are formed on (111) oriented substrates, \ensuremath {P_\textrm {b0}} (3.1) and \ensuremath {P_\textrm {b1}} (3.2) centers can only exist on (100) orientations. Figures 3.2 and 3.3 depict the atomic configurations of all three trap types.

Figure 3.2: \ensuremath {P_\textrm {b}} defect located at a \ensuremath {\textrm {Si/SiO$_2$}} interface with (111) orientation. The defect is formed by an unpaired valence electron of a silicon atom back-bonded to three other silicon atoms. The defect's trap energy lies in the silicon band-gap. Thus, the charge state of the trap depends on the Fermi-level and it is electrically active [17].

Figure 3.3: \ensuremath {P_\textrm {b0}} and \ensuremath {P_\textrm {b1}} defects located at a \ensuremath {\textrm {Si/SiO$_2$}} interface with (100) orientation. The \ensuremath {P_\textrm {b0}} center is back-bonded to three silicon atoms and electrically very similar to the \ensuremath {P_\textrm {b}} center. The silicon atom of the \ensuremath {P_\textrm {b1}} center is back-bonded to two other silicon atoms and an oxygen atom. Both traps are electrically active as their energy lies in the silicon band-gap making their charge state Fermi-level dependent [17].

Recent works show [18,19,20] that all three types of \ensuremath {P_\textrm {b}} centers give rise to trap levels in the silicon band-gap. The charge state of the traps therefore depends on the Fermi-level.

3.1.1 Amphoteric Nature of Dangling Bonds

All three types of silicon dangling bonds investigated up to now ( \ensuremath {P_\textrm {b}}, \ensuremath {P_\textrm {b0}}, and \ensuremath {P_\textrm {b1}}) are reported to be of amphoteric nature. Their energy distribution comprises of two distinct peaks in the silicon band-gap, as seen in Figure 3.6.

The two peaks have different properties regarding their possible charge states and their energetic positions depend on the type of the trap center. For \ensuremath {P_\textrm {b}} and \ensuremath {P_\textrm {b0}} these are:

  1. Donor-like energy levels: They are located in the lower half of the band-gap around 0.25eV [21] above the valence band edge. The trap levels are positively charged when empty and electrically neutral when occupied by an electron. In the empty state they are diamagnetic, a very weak form of magnetism triggered by an external magnetic field changing the orbital motion of the atoms core electrons. With one unpaired electron the trap levels are paramagnetic, a stronger form of magnetism initiated by the presence of a magnetic field and unpaired electrons. The possible charge states of the \ensuremath {P_\textrm {b}} centers can be written as $\ensuremath{P_\textrm{b}}+ h^+ = \ensuremath{P_\textrm{b}}^+$ and $\ensuremath{P_\textrm{b}}^+
+ e^- = \ensuremath{P_\textrm{b}}$.
  2. Acceptor-like energy levels: They are located in the upper half of the band-gap, around 0.85eV [21] above the valence band. The trap levels are electrically neutral when empty and negatively charged when occupied by an electron. They are therefore paramagnetic when empty (the same state as the filled donor like level, with one electron in the \ensuremath {P_\textrm {b}} center), and diamagnetic when occupied, as the total amount of electrons in the \ensuremath {P_\textrm {b}} center is then two. The charge states are $\ensuremath{P_\textrm{b}}^- + h^+ = \ensuremath{P_\textrm{b}}$ and $\ensuremath{P_\textrm{b}}+ e^- = \ensuremath{P_\textrm{b}}^-$.

\ensuremath {P_\textrm {b1}} centers have the same, amphoteric nature but the energy levels of the peaks are different, as shown in Figure 3.6(b).

Figure 3.4: Energy diagram of a \ensuremath {P_\textrm {b}} center at the \ensuremath {\textrm {Si/SiO$_2$}} interface in weak inversion. The trap consists of donor like states in the lower and acceptor like states in the upper half of the band-gap due to its amphoteric nature. The Fermi-level determines the filling and therefore the charge state. In this configuration the trap is slightly positively charged.
Figure 3.4 illustrates the determination of the charge state of an amphoteric interface trap in weak inversion. At these conditions the upper peak is totally empty and therefore electrically neutral. The lower peak is filled to approximately two thirds and positively charged.

3.1.2 Characterization of Trap Centers

A tool with the analytical power and sensitivity to identify the atomic-scale structure of the different traps is the electron spin resonance (ESR) measurement [22,23]. The ESR measurement is suited to investigate the NBTI induced interface state generation [24,25,23]. The draw-back is that after stressing the device at the poly-gate with high voltages, the gate has to be etched off before ESR measurements can be performed. For the investigation of fully processed devices the spin-dependent recombination (SDR) technique can be used [26,27].

The SDR technique can be explained by using the Shockley-Read-Hall (SRH) model (Section 2.3.2) for recombination and the Pauli exclusion principle as follows [28]. The device under test (DUT) is operated as a gate controlled diode with the source/drain to substrate slightly forward biased. With this forward bias the current is dominated by recombination at the trap centers of the \ensuremath {\textrm {Si/SiO$_2$}} interface. At a certain gate voltage the recombination current has its maximum, as determined by the DCIV method described in Section 4.2. The DUT is exposed to a large DC magnetic field which is slowly varied to partially align the spins of the paramagnetic charge carriers and the paramagnetic trapping centers. Because of the Pauli exclusion principle it is not possible that a carrier is trapped by a trap having the same spin orientation. When the ESR condition is satisfied, the electron spins are flipped. This increases the probability of different spin orientations for carriers and traps and therefore increases the measured recombination current. This spin dependent increase in recombination current is evaluated in SDR.

Figure 3.5: Energy distribution, \ensuremath {D_\textrm {it}}, of traps at the (111) \ensuremath {\textrm {Si/SiO$_2$}} interface after Ragnarsson et al. [21]. The two peaks of Gauss'ian form are observed in the upper and lower half of the band-gap. After annealing at zero and -0.8 V bias the trap density is reduced.
Early works [29,16,30] concentrated on the investigation of (111) oriented substrates, mainly due to the higher defect density compared to other wafer orientations and therefore easier experimental evaluation. Figure 3.5 gives the energy distribution of the interface trap density \ensuremath {D_\textrm {it}} for \ensuremath {P_\textrm {b}} centers at (111) oriented interfaces after Ragnarsson [21]. It can be seen that the interface trap energies are spread according to a Gauss'ian peak in the upper and another peak in the lower half of the band-gap. During passivation with hydrogen at elevated temperatures of 170 ^C the electrically active dangling bonds are saturated with hydrogen atoms. The peaks of the maximum trap concentration stay approximately at the same energy levels whereas the concentration decreases continuously.

Figure 3.6: Estimated density-of-states (DOS) distributions of (a) \ensuremath {P_\textrm {b0}} and (b) \ensuremath {P_\textrm {b1}} centers at the (100) \ensuremath {\textrm {Si/SiO$_2$}} interface. The data are from Lenahan et al. [20] and give only a ``crude, semi-quantitative estimation'' as precise measurements are not yet available. Important details are the broader distribution of the \ensuremath {P_\textrm {b0}} centers and the distribution of most \ensuremath {P_\textrm {b1}} levels within the \ensuremath {P_\textrm {b0}} levels.
\ensuremath {P_\textrm {b0}} defect

\ensuremath {P_\textrm {b1}} defect

Recent works [19,21,20,18,31] concentrate on the technologically much more important (100) substrate orientation. The standard silicon CMOS processes of most applications use this crystal orientation. The \ensuremath {P_\textrm {b0}} defects found at interfaces of this wafer orientation are very similar to the \ensuremath {P_\textrm {b}} centers found at (111) interfaces. The \ensuremath {P_\textrm {b1}} centers, in contrast, are found to comprise of completely different levels in energy. Lenahan et al. [20] gives an estimation of the energy distribution of \ensuremath {P_\textrm {b0}} and \ensuremath {P_\textrm {b1}} centers, as seen in Figure 3.6.

The number of \ensuremath {P_\textrm {b1}} centers is assumed to be lower than that of \ensuremath {P_\textrm {b0}} centers. Still, around the peak levels of the \ensuremath {P_\textrm {b1}} centers a small change in the Fermi-level can have a significant impact on the charge state because of these \ensuremath {P_\textrm {b1}} centers and their narrow distribution.

3.1.3 Effects of Trap Centers

Although the density of silicon dangling bonds is rather small, they still lead to worse device characteristics. Therefore, it is of major interest to reduce the amount of electrically active interface traps as much as possible.

It has been shown that by subjecting the MOS device to a post metallization anneal or to a forming gas anneal, the density of electrically active traps can be reduced dramatically. As a model for the passivation process the reactions

\ensuremath{P_\textrm{b}}+ \ensuremath{\textrm{H$_2$}} \ri...
...textrm{b}}\ensuremath{\textrm{H}}+ \ensuremath{\textrm{H}}  , \end{displaymath} (3.3)

\ensuremath{P_\textrm{b}}+ \ensuremath{\textrm{H}} \rightarrow  \ensuremath{P_\textrm{b}}\ensuremath{\textrm{H}}  ,
\end{displaymath} (3.4)

have been suggested in the literature [32,33,34,35].

The electrical activity of the \ensuremath {P_\textrm {b}} center is eliminated by a hydrogen atom as it shifts the energy levels of the trap out of the silicon band-gap [16], and thus passivates the defect.

During the negative bias temperature (NBT) stress exactly these hydrogen passivated silicon bonds can be broken. Broken bonds have, again, electrically active states in the band-gap which lead to additional charge on the interface and thus to degradation of important transistor parameters, as described in detail in Chapter 6.

next up previous contents
Next: 3.2 Centers Up: 3. The Silicon/Silicon-Dioxide Interface Previous: 3. The Silicon/Silicon-Dioxide Interface

R. Entner: Modeling and Simulation of Negative Bias Temperature Instability