Crystal defects in silicon

Defects in the Si lattice can either be structural imperfections of the lattice itself or foreign atoms which are introduced into the crystal e.g. during crystallisation or other high temperature steps. Regardless of their size and shape, all defects influence the mechanical, electrical and chemical properties of the Si crystal as the valence electrons near the defective region are forced to reconfigure in bonds of “unusual” length and orientation. The resulting change of the mechanical properties usually generates stress in the crystal and is e.g. detectable by Raman spectroscopy [43]. The stress can even lead to the generation of micro-cracks in the crystal. Mechanical stress generally destabilizes the crystal and renders it more fragile. The electrical influence of defects is due to band bending or introduction of defect levels in the band gap. This alters e.g. the recombination behaviour (see chapter 1.1.2) and due to increased scattering at (charged) defect sites also the mobility and thus the diffusion constant D of the charge carries. The diffusion properties of foreign atoms may also be affected. With the change of bond-length and orientation of course also the chemical properties of the Si crystal around a defect are altered. This can even prove useful e.g. for the determination of the surface dislocation density of a Si wafer via Sirtl, Secco or Dash etch [44] or to introduce an optically rough surface to increase the EQE via better light coupling [45].

2.1.1 0D defects (vacancies and impurities)

Zero-dimensional defects are point defects. They can consist of foreign atoms which are either situated on a lattice point, replacing a Si atom (substitutional), or interstitially as so-called interstitials. Si atoms themselves also can “leave” the crystal lattice, forming self-interstitials. Missing Si atoms in the lattice also form point defects, which are called vacancies. Especially the numbers of the last two defect types are temperature driven, as they increase the entropy as well as the internal energy of the crystal. Thus, even the most perfect Si single crystal exhibits a certain number of point defects at temperatures above 0 K [46].

2.1.2 1D defects (dislocations)

Dislocations are typical one-dimensional defects. They are characterized by a crystallographic plane that is “ending” in the middle of a crystal. This can occur when crystal planes are slipped against each other to release stress that is built up e.g. during inhomogeneous crystallisation, around included point defects or by a mechanical load.

When talking about dislocations, a distinction is drawn between screw and edge dislocations. At elevated temperatures dislocations are mobile, and move mainly along the <111> planes (slipping planes) in the crystal. Mirror-inverse dislocations can thereby be annihilated when they coincide, leaving an undisturbed crystal. Dislocations also disappear when they are moved to a free surface of the Si crystal [47]. The recombination

Crystalline silicon and wafer materials behaviour of dislocations is mainly determined by their decoration with impurities (see chapter 2.1.4). Undecorated dislocations themselves usually do not introduce defect levels deep in the Si band gap [48].

2.1.3 2D defects (grain boundaries and stacking faults)

When two areas of different crystal orientations adjoin, the lattice configuration between these two areas is disturbed. Some valence electrons of the border atoms have to reconfigure, forming bonds of “unusual” length and orientation compared to bonds in the undisturbed lattice. This leads to a plane in the crystal where the electrical, chemical and mechanical properties of the crystal are different. They are called grain boundaries and are mainly observed (as the name already implies) in multicrystalline (mc) Si materials.

One important parameter for the characterization of grain boundaries is the so-called  value. It describes how many atoms are shared with undisturbed bonds between two adjoining grains [49]. A very common configuration value is 3, meaning that every third atom of one grain is shared with the neighbouring grain without disturbance. Higher  values indicate less common atoms and thus a more disturbed grain boundary region.

Stacking faults, which are another type of two-dimensional defect, occur, when an additional crystal half-plane is generated.

The largest 2D defect, however, is the free surface of the Si crystal, where a quasi continuum of defect states is present, demanding a separate treatment in the SRH recombination theory (see equation (1.11)). Similar to the dislocations described before, also the recombination behaviour of grain boundaries and stacking faults is determined to a large extent by their decoration with impurities (see next chapter).

2.1.4 3D defects (voids and precipitates)

The aforementioned defect types are often nucleation points for the development of three-dimensional defects. They consist of voids (agglomeration of vacancies), foreign atoms or silicides, which preferably agglomerate at disturbed areas of the crystal where the nucleation barrier is reduced [50]. The number and size of these defects strongly depends on type and concentration of the contaminants in the crystal as well as on the crystals thermal history. Si crystals are mainly formed by solidifying liquid Si. The three-dimensional defects hereby are formed by precipitation, as the solubility of most impurities in crystalline Si decreases with decreasing temperature. If, during the cooling process of the crystallisation, the solubility limit of a certain impurity falls below the impurity concentration, the crystal becomes supersaturated. At a certain degree of supersaturation, the impurity starts to form precipitates in the crystal. While a rather slow cooling process provides enough time for impurities to diffuse long distances through the crystal and form a small number of large precipitates, which is energetically favourable, a very fast cooling of the crystal (quenching) leads to the formation of many small, finely dispersed precipitates throughout the whole crystal [51]. The above described mechanism is especially important concerning the defect engineering during high temperature processing steps in the solar cell process. For Si ribbon materials it also defines the defect distribution in the wafer material during wafer growth (chapter 2.6.2).

Another aspect for the formation of precipitates is the presence of other impurities.

called co-precipitation at the same site can be energetically favourable. One example is the co-precipitation of oxygen (O) together with carbon (C) in ribbon silicon [52].

The number and distribution of impurities in a Si wafer also strongly depends on the purity of the feedstock, more specifically on the composition, diffusivity and solubility limits of the included impurities. All defects and impurities that induce energy levels in the Si band gap can serve as SRH recombination centres which reduce the minority charge carrier lifetime. The most common and most detrimental impurities in Si are transition metals like iron (Fe) and copper (Cu). Fe can induce highly recombination active defect levels near the centre of the Si band gap [53] (see Figure 1-4), which severely affect the bulk lifetime even at relatively low concentrations [54]. The detrimental effect of Cu is mainly due to its very high diffusivity and solubility in Si, even at very low temperatures [55]. A good overview concerning transition metals in Si is given by Weber in [55].

The differing solubility of a specific impurity in molten Si Sil and solid Si Sis can be of use when large amounts of molten Si are solidified very slowly, e.g. during a block casting process (chapter 2.6.1). The so-called segregation coefficient k0 is defined as:

l s

Si

k₀ Si (2.1)

With this coefficient the distribution of the impurity concentration C over a slowly solidified Si crystal can be described according to an equation first proposed by Scheil [56]:

) 1 (

0 (1 )

)

(f_s k_sC   f_s ^ks

C (2.2)

where fs represents the fraction of the crystal that is already solidified and C0 the initial impurity concentration (evenly distributed) in the melt. ks represents the effective segregation coefficient, which is almost equal to the equilibrium segregation coefficient k0 if a temperature distribution close to the thermal equilibrium is maintained at every stage of the solidification i.e. for very low crystallisation velocities. The segregation coefficient in Si is < 1 for most impurities (e.g. B, P and especially transition metals) resulting in a higher concentration of these impurities in the melt and thus in the part of the crystal that is solidified last (Figure 2-1). There are few exceptions, however. For oxygen (O) some authors report a segregation coefficient k0 > 1 [57].

After the solidification of the Si most impurities are still mobile and can diffuse depending on temperature and crystal structure more or less quickly through the crystal.

Compared to the common doping elements like boron and phosphorous, especially transition metals like Cu and Fe are very mobile, resulting in significant impurity redistribution after the solidification during the cooling of the ingot (Figure 2-3).

Crystalline silicon and wafer materials

impurity concentration C [% of C0]

0 20 40 60 80 100

impurity concentration C [% of C0]

Figure 2-1: Impurity distribution after very slow directional solidification (ks ≈ k0) for impurities with different segregation coefficients k0 according to Scheil’s equation. Dopants B and P as well as oxygen (O) with k0 close to one (left) and transition metals Fe and Cu with very small k0 (right; log scale). Segregation coefficients are obtained from [42].