Physical properties of defect parameters

A defect center can be mono- or multivalent. The former characterizes a defect center which can appear in exactly two different states leading to one energy level within the band gap, while for the latter multiple states are possible leading to several distinct energy levels within the band gap. A common example for a monovalent defect center is interstitial iron, whose charge states are neutral and positively charged, leading to one single donor level within the band gap. If this interstitial iron is paired with substitutional boron, a completely new defect configuration occurs. This paired defect configuration is multivalent, having a neutral, positively charged and negatively charged appearance, leading to a donor level and an acceptor level within the band gap.

Tab. 11.4: Overview of the different defect states common for metallic impurities in silicon.

Defect level

State 1 (captures electrons)

State 2 (captures

holes)

Impact on capture cross

sections

Double acceptor aa − − −

Acceptor a 0 − σn < σp

Donor d + 0

Double donor dd + + + σn > σp

In general, donor levels alternate between a positively charged and a neutral state, while double donor levels alternate between a two-times positively charged and a positively charged. The same holds for acceptor and double acceptor levels, alternating between a neutral and a negatively charged or a negatively charged and a two-times

negatively charged, respectively. Looking at a donor level, the positively charged state is more attractive to electrons than the neutral state is for holes, resulting in a larger capture cross section for electrons than for holes (σ^{n >} σ^p , k > 1). The opposite trend holds for acceptor defect levels. These implications are summarized in Tab. 11.4.

Lemke [131] observed that the behavior of the different transitional metals depends mainly on the number of outer electrons N, given by the sum of the s and d electrons of the free atom. Transition metals with 9 ≤ N ≤12 are likely to be substitutional, while on the other hand transition metals with 3 ≤ N ≤8 are likely to be interstitial. Due to the partly filled sp-shells of interstitial metals, a donor-like behavior is likely, while for substitutional metals an acceptor-like behavior is likely because of their nearly filled outer shells.

It can thus be summarized that transitional metals with 3 ≤ N ≤8 tend to be located on interstitial sites within the silicon lattice, act donor-like and hence have a symmetry factor k > 1. On the other hand, transitional metals with 9 ≤ N ≤12 tend to be located on substitutional sites within the silicon lattice, act acceptor-like and hence have a symmetry factor k < 1. There are of course exceptions for this general rule, however, the known acceptor states of interstitially located transitions metals are mostly quite shallow [107] and are hence unlikely to dominate the recombination activity under most circumstances. These trends were compared with experimental data from literature for various transition metals by Macdonald [150], which generally agree with these general rules.

Furthermore, for every defect level within the band gap, there exist excited states in addition to the ground state (see Fig. 11.7). From a hydrogen atom it is known that an ionization energy of E_I = 13.6 eV is necessary in order to remove the electron from the isolated atom. Besides that there exist numerous excited states, for example the eight 2s and 2p states, the eighteen 3s, 3p and 3d states and so on. It is not that this analogy between an isolated hydrogen atom and a defect center within the silicon lattice should be overstretched, but Shifrin [31] was able to show that defect centers exhibit excited states within the silicon band gap.

Fig. 11.7 shows the ground state and the excited states of a donor-like defect center.

For an acceptor-like defect center the excited states would be located between ground state and valence band. The excited states of a defect center are difficult to determine experimentally, due to the fact that most characterization methods measure the transition from state 1 and state 2. However, the electronic configuration stays the same if a valence electron from the ground state transits into an excited state.

11.2 Lifetime spectroscopy vs. deep-level transient spectroscopy 149

Fig. 11.7: Ground state and excited states of a donor-like defect center.

One possibility to access the energy levels of the excited states would be to use a modified DLTS technique. After filling the ground state of the defect center with electrons using a fill pulse, transitions between the ground state and one distinct level of the excited state could be induced using a coupled laser with the appropriate frequency. Afterwards the electrons are emitted from the exited state into the conduction band. By using this technique, the defect parameters of the excited state would be accessible. More information about excited states of defect centers can also be found in [31].

The energy depth, which is the distance of the defect level to the conduction band or valence band, (of the ground state) of the defect center is being determined by the ionization energy of the defect atom. If the defect atom was not located within the silicon lattice but in free space, the bond energy of the outer electron would be needed in order to ionize the atom. Iron, for example, has a first ionizing energy of 7.903 eV.

If this same atom is located within the silicon lattice, this bond energy is strongly reduced. For iron it is reduced to 0.38 eV [120]. Two reasons may be given for that.

Firstly, the electrostatic potential that an electron experiences has to be reduced by the permittivity ε of the semiconductor. For silicon this is ε = 11.9. Please note that the use of macroscopic electrostatics is justified since the wave function of the electron is expanded for several hundreds Angstrom.

Secondly, the bond energy is reduced due to the fact that the electron within the silicon lattice can be described by the energy momentum relationship of free space, if the electron rest mass m₀ is substituted by the effective mass m_e*. In silicon this effective electron mass can be calculated using the transversal effective mass m_t* and the longitudinal effective mass m_l* according to

( ) [

( )

]

*

l t

e T m T m

m = ^(11.1)

At room temperature the effective electron mass is m_e*(300 K) = 0.33 m₀. For these calculations the transversal and longitudinal effective masses from eq. (2.8) and (2.9) were used. Please note that generally the effective electron mass (eq. (11.1)), the density-of-states effective mass of electrons in the conduction band (eq. (2.7)) and the thermal effective electron mass (eq. (2.12)) have to be distinguished from another.

11.2.2 Theoretical comparison of lifetime spectroscopy and deep-level transient