amorphous semiconducter and thin film preparation

A Progress Report
on
AMORPHOUS SEMICONDUCTOR
AND
THIN FILM PREPARATION
Submitted to: DR. KAILASH SIR
DEPTT. OF PHYSICS

Lovely Professional University, Jalandhar

“Bachelor of Technology”
(2008-09)
Submitted By

Rahul Mahajan & Ashwani Soni

Btech(CSE) Ist Sem


Uni Roll No.R237A27


Acknowledgement

Gratitude cannot be seen or expressed. It can only be felt in heart and is beyond description. Often words are inadequate to serve as a model of expression of one’s feeling, specially the sense of indebtedness and gratitude to all those who help us in our duty.

It is of immense pleasure and profound privilege to express my gratitude and indebtedness along with sincere thanks to DR. KAILASH SIR, Faculty of Lovely University for providing me the opportunity to work for a project on “AMORPHOUS SEMICONDUCTOR AND THIN FILM PREPARATION “

In particular I would like to mention the efforts of DR.KAILASH SIR, Lecturer of LPU Jalandhar, without whose encouragement the project could not have been started . He helped me on the project as an advisor and offered his help when needed in every aspect of project.

I am beholden to my family and friends for their blessings and encouragement.

Always Obediently
Rahul Mahajan



Introduction
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[120].
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[124]), 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[126], 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[130].
One of the main methods used recently for obtaining better models of both amorphous carbon and silicon[131] is that of reverse Monte Carlo simulations[132]. 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[133].

























Structural Details


Silicon
Two samples of amorphous silicon have been generated at slightly different densities using the same initial random configuration. The higher density sample will be referred to as system-I, the other being system-II. After relaxation, the final configurations are found to be rather different. Given in Figures 8.1 and 8.2 are the radial distribution functions, g(r), of each sample.

Figure 8.1: Radial distribution function of amorphous silicon calculated at a density of 2.6g/cm .

Figure 8.2: Radial distribution function of amorphous silicon calculated at a density of 2.3g/cm .
The radial distribution function of system-I is in excellent agreement to that of experiment[131, 135]. For comparison, an experimental radial distribution function for an amorphous silicon sample which has a density of 2.45g/cm is given in Figure 8.3.


Figure 8.3: Experimental radial distribution function of amorphous silicon as found from neutron diffraction measurements.
System-II differs slightly in that the second neighbour peak at 3.5-4Å is too low and slightly wider than experiment. Integration under this part of the curve (taken from 2.9Å to 4.3Å) however indicates that the average number of nearest neighbours per atom is similar in each case. The lower density of system-II allows for a wider spread in second neighbour distances than system-I.
In both cases the height and width of the first peak of the radial distribution functions are in agreement with experiment. This implies that the average coordination number is correct in both cases. To find the coordination number, the maximum length of a silicon bond must be known. Unfortunately, the first minimum in the radial distribution function does not go to zero showing that there is a continuous range of neighbour distances. For this reason a maximum bond length is chosen arbitrarily to be 2.55Å. This then defines all the bonds within the structure. Some structural details of systems I and II are summarised in Table .
The coordination number of each atom can now be calculated. It is found that most atoms are four-fold coordinated (70.3% for system-I and 81.3% for system-II) while only a few atoms are either 3 or 5 fold coordinated. In system-I a single two-fold coordinated site is found. Such a feature has not been included in reverse Monte Carlo studies of amorphous silicon. In figure 8.4 is a schematic diagram of some 2, 3, and 4 fold coordinated atoms found in system-I. The 4-fold coordinated site is typical of the atomic structure of most of the atoms in the sample. It consists of a distorted tetrahedral bonding arrangement with a more distant, but unbonded, 5 neighbour, somewhat similar to that found in the BC8 structure. In the case shown in Figure 8.4, the bond angles for each site are given in Table .

Figure 8.4: Schematic diagram showing a group of atoms in the amorphous silicon structure of various coordination numbers. The full lines show covalent bonds while the dashed lines indicate unbonded close neighbouring atoms. The bonded/unbonded nature of neighbouring atoms is determined by examining 3d charge density plots. The distances are shown in Å.
The average bond angle for each coordination number is also shown in Table . As expected, the mean angle for the 4-fold coordinated sites are approximately that of the perfect tetrahedral angle. It may have been expected that the mean bond angle at a 3-fold site to be similar to that of an graphitic-like region, but instead it is found that it is less than . This leads to the implication that 3-fold sites are tending to have p-like character (at an angle of ). The bonding topology of the 3-fold site resembles a triangular pyramid with a well defined bond to the three neighbours of a central atom. A non-bonding orbital is formed at the top of the pyramid indicating that the `defect' site still retains bonding characteristics.
A typical five fold site is shown in Figure 8.5.

Figure 8.5: A five-fold coordinated silicon atom. The solid lines show the five covalent bonds from the central atom. The bond lengths are given in Å.
On examination of the valence electron charge density it is found that there are no bonds formed between atoms more that 2.6Å distant (hence the choice of when calculating the coordination number). There exist several sites with 5 atoms much closer than this (there are no 6-fold sites found) and hence covalent bonding is expected to occur. On examination of the valence electron charge density around these sited, we find that the sites tend to be fully 3 or 4 fold coordinated where the remaining atoms are relatively close and form slightly weaker bonds. When a fifth atom is found in an otherwise tetrahedral configuration it tends to weaken the longer bonds further. Such a configuration is shown in Figure 8.5 where the two more distant atoms form much weaker bonds that the three closer ones. Also, it is found that usually one of the neighbours of a five-fold coordinated atom has only three neighbours. This suggests that the electrons for the fifth bond is `donated' from the undercoordinated atom. Note that this is similar to the five-fold configuration found in the Si-BC8 surface in Chapter 5.
The average coordination number for system-I is 4.03 while the slightly lower density structure of system-II is found to have a coordination number of 3.97. Most models of amorphous silicon, such as random networks, assume from experimental measurements that the structure is fully four-fold coordinated. The fact that both simulations have found a structure which is very close to those found in other calculations from an initial random packing indicates that a full annealing treatment may not be necessary. There have been previous ab initio calculations on amorphous silicon and germanium (for example, see [135, 130]) which have rapidly cooled the melt in order to form models of their amorphous structure which reduces the percentage of `wrongly' coordinated sites, but giving an average coordination number similar to that found here. This suggests that cooling from the melt followed by annealing may not be the most efficient method of obtaining a reasonable model of amorphous silicon since there results do not differ significantly from those given here.
The ring statistics are also given in Table for both systems. This can be compared to the BC8 and ST12 structures which contain a range of small ring sizes from 5 to 7 fold rings. There are no three fold rings (and therefore no three-centre bonding orbitals) found in either sample which is somewhat unexpected considering the low formation energy of the interstitial configuration found in Chapter 6.
Since the bond lengths found in amorphous silicon (and also in the BC8 and ST12 structures) are similar to that found in the diamond structure it is generally assumed that the energy associated with straining the bond angle away from the perfect tetrahedral value gives the main proportion of excess energy of the amorphous structure relative to that of diamond Si[130]. This distortion of angles away from is illustrated in Figures 8.6 and 8.7 which show the bond angle distribution functions for systems I and II respectively.

Figure 8.6: Bond angle distribution function of amorphous silicon system-I.

Figure 8.7: Bond angle distribution function of amorphous silicon system-II.
As can be seen, a relatively small change in the size of the unit cell of the 64 atom simulation (a change of 3.5%) makes a rather large change to both the radial and bond angle distribution functions despite the same random starting configurations. The main features however seem to remain similar in both cases. There is a very large spread in bond angles centred about the maximum of .



Figure 8.8: A comparison between the first five neighbour distances in BC8, ST12 and amorphous silicon. The points on the BC8 and ST12 graphs show the neighbour distances at several different compressions.
The average first five neighbour distances for the two amorphous silicon simulations are shown along side a similar plot silicon in the BC8 and ST12 structures. Also shown is a plot of these distances for a third simulation of amorphous silicon as a much reduced volume to emphasize this trend. The neighbour distances for BC8 and ST12 are shown over a wide range of pressures. Firstly, it should be noticed that the distance to the first four bonded neighbours remains relatively unchanged with respect to the (generally unbonded) fifth neighbour distance. It can be seen that this is increasingly true in the trend of BC8 ST12 amorphous as the structure becomes more disordered. In the similar plot for a highly compressed amorphous silicon simulation the trend in neighbour distances becomes linear. It should be noted, however, that this third simulation is done only to show this reduction in the trend of reducing the distance in the extreme case where experimental verification of this linear trend in neighbour distances may be infeasible.
Carbon
The amorphous carbon structure is generated by the same method used above for silicon where the same initial random configuration is used. This allows a direct comparison between the amorphous silicon and carbon structures. Figures 8.9 and 8.10 show the radial and angle distribution functions of the final atomic configuration of the sample.

Figure 8.9: Radial distribution function of amorphous carbon calculated at a density of 3.4g/cm .

Figure 8.10: Bond angle distribution function of amorphous carbon.
It should be noticed that, unlike both silicon simulations, the radial distribution function drops to zero after the first neighbour peak. This leads to an unambiguous method of locating bonded pairs of atoms: 1.85Å. Examination of the electronic charge density indicates that this definition of a bond is correct. Using this the coordination numbers and ring statistics can be found. These are summarised in Table 8.1.

Table 8.1: Structural data for the amorphous carbon simulation.
As can be seen from the coordination numbers there exists no atom to which a fifth nearest neighbour is bonded. On consideration of the case of BC8 carbon this is expected. It was found that carbon is unable to form highly distorted tetrahedral bonding, favouring instead multiple bonding to a single atom. In order for silicon to form a 5-fold coordinated atom it is necessary to form a wide range of bond angles (from about to was found in the two silicon samples for ). Although the chemistry of carbon allows it to form many bonding configurations, this one is unstable with respect to multiply covalent bonds.
Although the radial distribution function is a very useful quantity in determining averages for shells of neighbouring atoms it is not unambiguously related to the spatial distribution of the carbon atoms. The bond angle distribution function is also necessary to determine the types of bonding. The bond angle distribution function contains several interesting features. Other experimental and theoretical results indicate that amorphous carbon contains mainly four-fold coordinated bonded atoms. This is also evident here in the large peak at about . Averaging the bond angles subtended by all four-fold coordinated atoms gives an angle of . Also of note is the shoulder at indicating planar graphitic-like bonding is also present, although in a smaller amount. Averaging the bond angles of three-fold coordinated atoms gives which is slightly less than the expected for perfect -like bonding although the statistics are rather limited since only six sites are found. There is also an indication that the amorphous carbon may be forming some p-like bonding due to the peak in the distribution function at . A small peak also appears at . Such a small bond angle indicates the possibility of 3-fold rings exist in the sample. A ring counting calculation in fact confirms that there are two such 3-fold rings (Table 8.1).
There have been several studies on the structure of amorphous silicon and carbon using the method of reverse Monte Carlo simulations which fits trial atomic configurations to the experimental radial distribution function. This may not fully describe all the atomic bonding environments in view of the large number of possible bonding topologies evident in the bond angle distribution function. Unfortunately obtaining this three-body function experimentally proves to be extremely difficult.
The amorphous structure is found to contain only three and four-fold coordinated atoms. Example of their bonding topologies are illustrated in Figure 8.11.

Figure 8.11: Schematic diagram illustrating a typical bonding topology of a 3-fold and 4-fold coordinated carbon atom. The dashed lines indicate close, but unbonded neighbours. The 4-fold coordinated atom forms a slightly distorted tetrahedral structure. It is this type of structure which dominates the amorphous carbons structure at this density.
There is a large number of 4-fold coordinated sites (90.6%) formed from slightly distorted bonding. All of the remaining sites are found to be 3-fold coordinated, but are not all necessary bonded. Of particular interest is the 3-fold rings that are found in the structure (see Figure 8.12).

Figure 8.12: A 3-fold ring of carbon atoms found in the amorphous structure. On examination of the charge density it was found that the electronic structure within the ring is best described as a 3-centre orbital, rather than three simple covalent bonds. Also shown is a four fold ring of carbon atoms is formed from a ring of covalent bonds unlike the 3-fold ring.
Like the silicon interstitial configuration found in Chapter 6 which formed a three fold ring, the charge density for this configuration in amorphous carbon formed a three-centre bonding orbital. Such a feature will not be found on examination of a radial distribution function alone since the inter-atomic distances are close to the C-C bond length. To find the electronic band(s) which are associated with the three-centre orbital, the electronic charge density was constructed from each individual band. This unusual feature is found to be very stable with its eigenvalue lying 24eV below the highest occupied band. However, another localised bonding orbital was found be be associated with it whose eigenvalue showed that it occupied the most energetic band.


















Electronic properties
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[136] 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[137] 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[116]. 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[138]. 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[130] 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[139] 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.






THIN FILM PREPARATION
The preparation of thin films of high quality is prerequisite for the realization of modern devices and sensors. Thus, the investigation and control of the growth process of new materials as thin films suitable for sensors is of great interest. We are working on superconducting, semiconducting, metallic, magnetic and ferroelectric materials for fundamental properties and applications in devices.
To deposit thin films we employ three different methods: Sputtering, thermal evaporation and pulsed laserdeposition (>>PLD) with in-situ Reflection High Energy Electron Diffraction (>>RHEED). The advantage of sputtering is its scalability to large areas. Thermal evaporation provides a simple means to prepare metallic contacts to devices. With PLD it is possible to prepare thin films from new oxide materials with interesting electronic properties in high quality within short time. The in-situ RHEED-analysis allows to control the thin film growth with monolayer precision up to a total film thickness of 1 um. Further analysis is done by x-ray diffraction (XRD) and scanning atomic force microscopy (>>AFM).
All optimization experiments are planned and evaluated with support of statistical methods for the design of experiments (DOE). To machieve highly reproducible thin films of high quality we develop further automatization in our processes. Also, we attach our thin film deposition equipment to the cleanroom area of class 100 by vacuum locks.