This section will discuss the electronic structure of amorphous silicon and carbon found in the above simulations. There have been many calculations on the electronic density of states of amorphous group IV materials in recent years, each result varying from the others depending on the model used to obtain the atomic coordinates[115, 116]. Amorphous carbon is atypical of the group IV semiconductors because of the large number of different bonding types that it can form. The electronic structure is governed by the relative importance of three and four fold sites. A purely four fold coordinated model of amorphous carbon predicts only bonding to occur which gives a large gap in the electronic density of states. The electronic structure predicted by this model is similar to a broadened diamond-carbon density of states. It is now clear that this is not the correct model for diamond-like amorphous carbon and later tight-binding calculations[122, 125, 137] have found states which close the gap and have been associated to 3-fold coordinated atoms exhibiting bonding. The total number of states in the ` gap' increase when orbitals are introduced into the simulation. However, some models produced from the Tersoff potential have a significant density of states near the Fermi level. This is in contradiction to experimental and other ab initio calculations[117, 125] which show only a small density of states at the Fermi level.
The electronic structure of the amorphous carbon simulation performed here is shown in Figure 8.13.
Figure 8.13: Electronic density of states for diamond-like amorphous carbon. Each of the different bonding regions are labelled.
The method detailed in Chapter 3 for calculating band structures is used here, where diagonalisation of the Hamiltonian matrix consisting of 128 occupied bands and a further 64 unoccupied bands is performed. The part of the density of states corresponding to bonding is very similar to a broadened diamond-like electronic structure. Most of the states around the Fermi level are found to be -like in nature leaving no band gap. Therefore the optical properties of amorphous carbon will be dominated by the bonded sites. There are however, relatively few of these (less than 10% of the atoms in the sample are 3-fold coordinated). They are not found to be clustered together as some earlier models of amorphous carbon predicted. Instead they are found either bonded to three 4-fold coordinated atoms leaving a single electron in a localised p-like orbital, or rather often to two 4-fold atoms and another 3-fold site. This structure is similar to a recent ab initio calculation on diamond-like amorphous carbon where 3-fold sites are found to group in pairs. Due to the lack of clustering of sites, it follows that it is the intermediate range correlations of the sites which will have profound effects on the optical spectrum.
It is also rather interesting to note that the density of states of diamond-like amorphous carbon calculated here is remarkably similar to ab initio calculations on the less dense graphitic form of amorphous carbon[117, 121, 122].
Contrary to that of carbon, the electronic structure of amorphous silicon is found to be predominantly composed of -bonding orbitals. It is now well established that the effects of structural disorder on -bonded tetrahedral systems are governed almost entirely by short ranged correlations. It is this fact that makes the `complex crystal model' of amorphous silicon a good approximation, but fails to do so in carbon where the medium range correlations play an important role.
The electronic density of states for systems-I and II of amorphous silicon are given in Figures 8.14 and 8.15 respectively.
Figure 8.14: Electronic density of states for system-I of amorphous silicon.
Figure 8.15: Electronic density of states for system-I of amorphous silicon.
On comparison of the two density of states diagrams, they are found to be very similar. Thus, a relatively large change in density and structure does little to change the electronic nature of the samples. Both exhibit a zero density at the Fermi level which agrees well with models based on random tetrahedral networks, although they are not in agreement with other ab initio calculations of amorphous silicon which show a non-zero density at the Fermi level. This indicates that there are probably a large number of structural defects in their sample. However, experiment shows a gap does exist in the density of states, in agreement with our calculations. On reconstruction of the charge density from the occupied bands around the Fermi level, these states are found to be localised mainly on the 3-fold coordinated atoms and can be classified as dangling bonds. Other localised states are found at atoms which are five-coordinated. These eigenstates are distributed throughout the five highly strained bonds at each 5-fold site. All of these localised states are found between the Fermi level and the large peak in the density of states at -2.5eV.