Electronic Structure of Dislocations

Dislocations existing in solar-grade multicrystalline silicon can be of different types depending on their origin. A significant part of dislocations are produced by plastic deformation at T > 600°C caused by mechanical stresses of different nature. These dis­locations are usually 60° or screw dislocations of the glide set in {111} glide planes and their Burgers vectors are of type a /2(110). It is energetically favorable for such dislo­cations to be dissociated into two parallel Shockley partial dislocations with a stacking fault ribbon in between. A screw dislocation is dissociated into two 30° partials while 60° dislocations are dissociated into 90° and 30° partials. The geometry of the dangling bonds in their cores is such that the energy gain due to forming new covalent bonds between the dangling bonds (bond reconstruction) is larger than the associated increase of elastic energy (see [149] for a more detailed discussion).

As an example, Figures 4.10(a) and (b) illustrate how the core of the 30° and 90° partials can be reconstructed. In addition, unsaturated bonds at RD are shown that are reconstruction defects associated with a deep donor and an acceptor level in the band gap. At elevated temperatures, reconstruction defects can move along the dislocation and that leads to pairwise annihilation. It is evident that the concentration of dangling bonds related to reconstruction defects depends on the thermal history of the silicon material and it should be possible to reduce their concentration by suitable thermal annealing. All available experimental data support the theoretical predictions that recon­struction of partial dislocations in silicon is energetically favorable. EPR measurements show that the concentration of paramagnetic dangling bonds can be sometimes quite

Подпись: (c)
Подпись: (a)
Подпись: RD

image159Figure 4.10 Fundamental properties of straight dislocations in silicon. Core views on the (111) glide plane of a the reconstructed 30° Shockley partial dislocation (a) and 90° Shockley partial dislocations (b). RD denotes a reconstruction defect which is mobile at high temperature and gives rise to deep states at dislocations, (c) Schematic density-of-states for a dislocation: one-dimensional bands split from the valence (1D hole band) and conduction (1D electron band) resulting from the dislocation stress field via the deformaton potential; core defects and impurities give rise to deep localized states as indicated.

significant for dislocations introduced at T < 700°C. Their density is strongly reduced after annealing at T > 800°C with an almost complete removal using suitable thermal treatments [150-152].

Theoretical and experimental investigations consistently show that straight and clean segments of such dislocations have electronic spectra of semiconductor type, i. e., con­sisting of an empty one-dimensional energy band (lD-bands) split from the conduction band of bulk silicon and a filled quasi-lD band split up from the valence band (see Figure 4.10(c)). The energy positions of the bottom EDe of the empty band and of the top EDh of the occupied 1D band have been found as (EC-EDe) ~ (EDh-EV) ~ 75-85 meV from electron dipole spin resonance (EDSR) and conductivity measurements [153-155], where EC and EV denote the bottom of the conduction band and the top of the valence, respectively.

In addition to those dissociated dislocations, some other types of dislocations may exist in solar-grade multicrystalline Si: for example, nondissociated Lomer dislocations, appearing as a reaction of two 60° dislocations moving in two different {111} planes, Frank partial dislocations bounding stacking faults can appear due to condensation of silicon self-interstitials and nondissociated edge dislocations that can be found at grain boundaries. Not all types of dislocations are well investigated. However, in all cases when dislocation energy spectra were investigated they were found to be of 1D-semiconductor type. For example, for Lomer dislocations it was found that the core is most likely reconstructed [156] and the 1D electronic energy band observed by EDSR is empty in a neutral state [157-159] so that there is an energy gap between empty and filled energy bands.

Nondissociated edge a/2(110) dislocations in silicon that can often be found in some grain boundaries and hetero-interfaces (for example, in Si/Ge interfaces) also do not contain dangling bonds in their cores and are associated with a filled 1D band split up
by about 0.2 eV from the valence band of bulk silicon and an empty 1D band split down by about 0.07-0.1 eV from the conduction band (see [160]).

For dislocations with a semiconductor-type energy spectrum consisting of such rather shallow empty and filled 1D bands it can be expected that excess carrier recombination rates should not be high for two fundamental reasons. On the one hand, the bands are not sufficiently deep to break the momentum conservation in the directions perpendic­ular to the dislocation, thus allowing fast radiative transitions between 1D bands. On the other hand, nonradiative recombination caused by multiphonon transitions is also suppressed compared to the case of deep localized states at defects since electrons and holes are delocalized along dislocations [161]. This expectation agrees well with many experimental measurements of carrier recombination rates at dislocations. It was shown by using electron-beam-induced current (EBIC) that in cases where dislocations seem to be sufficiently ‘clean’ from deep-level defects, their recombination activity is small and nearly not observable at room temperature (see, e. g., [61, 162]).

Further insight has been gained from experiments showing that the recombination activity of dislocations is strongly influenced by processing conditions and impurity contamination with in some cases very high rates of carrier recombination at dislocations [162-168]. In order to explain existing experimental data it was supposed that in addition to the 1D bands real dislocations could also have localized deep electronic states that may originate from intrinsic core defects like reconstruction defects and core defects caused by vacancies and self-interstitials incorporated into the dislocation core, or from impurity atoms in the dislocation core, in the strain field of dislocations or small impurity precipitates at dislocations.

It should be noted that the electronic energy levels of impurities incorporated into the dislocation core in general should differ significantly from the energy levels of the same impurities incorporated as individual atoms within the bulk. Recent calculations for substitutional copper in the dislocations core confirm this basic argument [169]. In contrast to the number of states of one-dimensional bands, concentrations of deep electronic states related to core defects and impurities strongly depend on the sample history and can vary in a very wide range.

This statement is strongly supported by numerous experimental data obtained by deep level transient spectroscopy (DLTS), which permits measurement of the concentrations of electrons and holes captured by dislocation-related deep states and to get some param­eters of these deep electronic states, like the energy and capture cross section. Deep dislocation-related energy levels have been intensively investigated by DLTS (see, e. g., [170-177]). However, the exact origin of the defects responsible for even well known dislocation-related energy states detected by DLTS is not yet completely clear. A typical DLTS spectrum of deep dislocation-related defect states in the upper half of the band gap after deformation below 750-800°C usually consists of several overlapping non­uniformly broadened lines which – adopting Omling’s notation [176]-are: ‘A’ at about EC — 0.19 eV, ‘B’ at about EC — 0.3 eV, ‘C’ at about EC — (0.37-0.43) eV, and ‘D’ at about EC — 0.54 eV. These defect lines are well known in the literature [148]. Line broadening is typical for dislocation-related deep defects and is usually in the order of 10-50 meV. They show all characteristic features of deep localized states at extended defects, like the logarithmic dependence of the signal amplitude on refilling time duration tp, which is due to the Coulomb potential вФ of a charged dislocation line caused by electrons captured by deep states at dislocations. This potential is repulsive for electrons thus slowing down further electron capture. The defects A, B and D are known to be thermally unstable and their concentration can be strongly reduced by annealing at tem­peratures above 800°C. Hence, they may correspond to some metastable intrinsic core defects. In particular, the D-line might be related to dangling-bond defects at disloca­tions observed in such samples by the EPR technique. It is generally observed that the C-line remains nearly unaffected by usual thermal annealing or even increases in some cases. At the same time, the concentration of defects associated with the C-line can be drastically reduced by aluminium gettering [178]. Therefore, one can suppose that they are related to some impurities at dislocations, which can be reduced in concentrations by external gettering processes. This may be taken as a strong hint that transition metal impurities play an important role for the C-line.

Additional evidence supporting the idea that C-defects correspond to some impurity atoms at dislocations were demonstrated [174] by the observed dependence of DLTS spectra on the velocity of dislocations. A few thousand dislocation loops were generated in n-type silicon at 600°C from indentation pits. The DLTS signal from the same dis­locations in the same sample was measured after sequential deformation steps at 600°C at different loads forcing dislocations to move at different velocity. It turned out that the DLTS C – and C1-lines appear with large amplitude when the dislocation speed is small (vdis 2 pm/min) or zero, whereas the concentration of the related defects strongly decreases for larger vdis. Typical results are summarized in Figure 4.11 where DLTS spec­tra sequentially measured on the same 60° and screw dislocations in the same sample after their motion at 600°C with different velocity vdis.


150 200 250 300

T [K]

Figure 4.11 DLTS spectra of the C-line sequentially measured on the same 60° and screw dislocations in the same sample after their motion at 600°C with different velocity vdis during

time tann: (1) – vdis = 2Pm/min durng tann = 360 min (2) vdis = 0 during tann = 180 min

(3) vdis = 5-6pm/min during tann = 5 min. (DLTS spectra measured with frequency f = 6.7 Hz and pulse length of 100 ps). The highest signal is measured without dislocation motion, whereas a high dislocation velocity reduced the signal. A possible interpretation includes defect accumulation at stationary and slow-moving dislocations, whereas dislocations detach from defects for a high velocity.

Directly following dislocation-loop generation, dislocations were moved with a veloc­ity of about 5-10 pm/min up to a loop diameter of about 150 pm no DLTS signal was observed in this sample. Spectrum (1) was measured after the dislocation was moving for 6 h with a velocity vdis = 2 pm/min under a stress of 30 MPa. One can see that a DLTS signal appeared consisting of broadened and overlapping lines B, C, C1 and D. After the measurement of this spectrum the sample was annealed at 600°C for 3 h with­out applying stress (vdis = 0). As a result, the C line increased strongly (see spectrum (2)). Subsequently, a stress of 50 MPa was applied and dislocations were moving with vdis = 5 pm/min for 5 min. As a result, the amplitude of the C-line decreased significantly (see spectrum 3). The most probable explanation of this experiment is the following: When the dislocation velocity is smaller than some critical value, they collect impurities resulting in an increase of the DLTS C – and C1-lines. However, if dislocations are forced to move with a high velocity, impurity atoms will not be able to follow the dislocations. The latter will then lose nearly all impurity atoms accumulated before, as has been shown by calculations [179].