Amorphous materials are of interest because of their complexity and unique structural and electronic properties. While crystalline and amorphous silicon are widely used in the manufacture of semiconductor devices, the carbon analogues at first seem of limited value in that context. This is due to the lack of electronic levels in the band gap of diamond on the introduction of n or p doping. However this is not true of the dense form of diamond-like amorphous carbon as opposed to the lower density graphitic form of amorphous carbon. To investigate the properties of such structures a model is first required of pure amorphous carbon. It is this problem which will be discussed in this chapter.
Of fundamental interest is the microscopic origins of such properties ranging from mechanical and elastic characteristics to the electronic and optical properties. As seen in Chapter 3, and in many recent publications (for example [115, 116, 117, 118]), carbon can display many different bonding configurations with varying coordination number due to the ability to form both bonding such as in graphitic structures and bonding as in diamond, although it seems energetically unfavourable to distort the bonding angles. Silicon also forms an amorphous phase which has generally been modelled using 4-fold coordinated continuous random networks of bonded atoms[115, 119]. These have used empirical and tight-binding force models which agree well with experiment. It is possible that this type of model may not be complete in view of the unusual interstitial configuration found in the previous chapter which was associated with a low defect formation energy. This implies that such a bonding topology could easily be formed in amorphous silicon.
In chapters 3 and 4, calculations were performed on complex forms of silicon and carbon which are characterised by short range order but still retain long range crystalline order. In view of the difficulties associated with performing full theoretical calculations on amorphous structures they proved to be a useful insight into the physics of short range disorder. It therefore seems a natural conclusion to attempt a molecular dynamics calculation on the amorphous structures of silicon and carbon and examine their differences.
Previous experimental and theoretical studies of the microscopic structure of amorphous carbon[121, 122, 123, 124] show that it is dependent on the macroscopic density which in turn depends on the method in which the sample was made. The trend in structures is from graphitic-like structures embedded in a matrix of both two-fold and four-fold coordinated atoms at a low density of 2.20 to 2.69 g/cm (found from tight binding molecular dynamics), to diamond-like amorphous carbon containing `defected' three fold sites at a high density of 3.35 g/cm [121, 125]. This change in density also changes the bonding properties considerably, where the ratio of is found be inversely proportional to the density of the amorphous carbon.
Studies of amorphous silicon seem to show a somewhat simpler behaviour[116, 119] where the microscopic structure consists of distorted tetrahedral units. Numerous hand built and computer models have been constructed[127, 128, 129]. In the relaxed continuous random network models various potentials and bond charge models have been used (for example, the Keating and Stillinger-Weber potentials) in order to minimise total energies. Other models have included `defect' atoms that are three fold coordinated which have been obtained from various molecular dynamics techniques by cooling from the melt.
One of the main methods used recently for obtaining better models of both amorphous carbon and silicon is that of reverse Monte Carlo simulations. This method involves fitting the structure factors for trial atomic configurations to experimental results (measured, for example, by neutron diffraction) by moving the atoms at random and accepting the move by a probability given by the difference in the new structure factor and the experimental measurements. Configurations are accepted under certain constraints, such as bond length, coordination number, etc. Some configurations are not accepted such as those containing three membered rings. This may be incorrect given the results presented in Chapter 6 and the results for carbon given below. Also calculations on very small cells of silicon atoms arranged randomly have been found to contain 3-fold rings which was found to be relatively stable under small atomic displacements.