Introduction

The semiconductor properties of bulk silicon have catapulted the world into the digital age. This very important material forms the basis of transistor technology, microprocessors, and light-emitting diodes. An in-depth study of the different forms of silicon can generate a deeper understanding of this technologically useful material. This research monograph project focuses on three major topics of this ever-expanding, exciting field.

The first section is a discussion of the surface structure of crystalline silicon as well as the most commonly used methods of analysis. Low index surfaces , Si(100) and Si(111), will be highlighted in an extensive look on how thes structures bond with group III elements. The surface structure of Si is important due to the common thin film preparation of silicon.

The second section deals with developing a thorough understanding of the structure of amorphous hydrogenated silicon as well as it's consequent electrical and optical properties. These properties are useful in determining potential applications of this material. Since this substance is produced as a thin film, familiarity with the surface structure is important in generating useful properties, as well as it's bulk structural properties.

The third section of this monograph presents an introduction to quantum dot structures, followed by a glance into the future of quantum dot applications. Aside from the utility of quantum dots, the scientific model provided by the exploration of quantum dots can be studied from many different fields of science.

Besides being fascinating topics of study from a purely intellectual perspective, these ideas focus upon an area of hot current research that has broad applications for the technology industry. The development of a deeper understanding of the above mentioned topics may prove fruitful in generating interest into the exciting world of technology.

Section 1

Aspects of The Surface Chemistry of Crystalline Silicon

By Hayden McGuiness

Crystals of silicon are most commonly cleaved in three ways, two of which are of importance to the semiconductor industry. This paper is designed to discuss the theoretical model used to describe crystalline solids, explore the real models accepted to explain the three surface structures of silicon and to give examples of how Si(100) and Si(111) surfaces are manipulated for industrial use. The real model discussion will be limited to these cleavages, excluding the other common cleavage, Si(110). Included is a brief discussion of two of the most widely used experimental tools in surface research.

LEED

LEED , or Low-Energy Electron Diffraction, pioneered in 1957 to gather information about the surface structure of solids. LEED studies provide information on both the symmetry of the surface structure and the distance between atoms relative to one another. Earlier, researchers used either x-rays or high energy electron diffraction to study a given solid. This allowed them to determined properties of the bulk crystal; for example, x-rays of energies around 30 KeV were used which penetrated the crystal lattice on the order of 105 nm, approximately 105 layers. In contrast, Electrons used in LEED are on the order of 100 eV which penetrate about 1 nm, one layer, into the solid before scattering.1 This is why it is such an effective tool for studying surfaces - nearly all of the electron/lattice collisions and subsequent diffractions take place within the first couple layers of the solid.

In a LEED experiment, electrons are excited from a heated filament, accelerated and hit the surface of a sample at a 90° angle, normal, to the crystal surface. These electrons may either scatter elastically or inelastically; only the elastically scattered electrons are used to gather information (see Figure1.1). The first screen, the one closest to the crystal, is at the electrical potential of the crystal, the second is a repelling grid set at the same potential as that of the electrons when they are ejected from the heated filament. The electrons that inelastically collide with the first few crystal atoms are stopped since they are of lower energy than the elastically scattered electrons. The final grid accelerates the chosen electrons onto the fluorescent screen, which allows the diffraction pattern to be photographed.2

The nomenclature used to describe LEED patterns is derived from how the structure absorbs atoms. It follows the pattern (U x V)RØ where RØ means the structure is rotated Ø°. If a and b are lattice parameters (2-D) for the substrate, the spacing of the adsorbate atoms (the atoms that are being absorbed) are Uoa and Vob (multiplied). For example, when the spacing of the adsorbate follows that of the substrate, but the atoms are double the spacing of the host lattice apart, the structure is called a p(2x2) overlayer and is described as a superlattice. The letter p stands for "primitive," meaning the until cell of the adsorbed atoms follows the unit cell of the substrate, although it can be expanded like in p(2x2). The letter "p" is usually left out. The letter c in c(2x2) refers to the case where the absorbed atoms follow the substrate atoms, with double the spacing, but the unit cell of the adsorbate also has atoms in the center of the 2x2 group (see Figure 2). (2x1) means rows of adsorbate atoms are between substrate atoms, where the distance between the rows is twice the distance between the substrate atoms. ( sqr.3 x sqr.3)R30° means the surface atoms are sqr.3 times as far apart as the substrate atoms and the entire network is rotated by 30°.

STM

Advances in the understanding of surface point defects and other structural surface properties have allowed imaging to be done at the atomic level. By predicting structure, phenomenon such as electron tunneling that would otherwise be unpredictable can be utilized as a measuring technique. In the STM, or Scanning Tunneling Microscopy, technique a fine metal tip, several hundred Å from the beginning of curvature to the other side (see figure 1.2) , is positioned within 10-20 Å of the surface. Due to electron tunneling there is a small current running between the tip and the surface of the crystal.3 Since the radius of curvature of the tip (see figure 1.2) is much larger than the distance between the tip and surface it is commonly thought that only one atom, cluster or molecule on the tip is within tunneling distance. Naturally, the current is very sensitive to the distance between the tip and the surface, which allows for very accurate measurement of the distance between the tip and surface. The tip is then moved over areas of the surface. Variations in the current allow a topographical map to be made of the surface; single atoms can be easily made out upon analysis as the metal tip scans over the surface. One of celebrated accomplishments of this technique was the characterization of the Si(111) surface.

The Theoretical Approach to Surfaces

Ideal surface structure of a crystal is one in which the surface is the perfect termination of the bulk crystal; the atoms on the surface have the same position relative to other atoms in the bulk lattice (see Figure 3-A). This ideal surface is said to be formed without allowing any relaxation (explained below) to take place. Terrace-Ledge-Kink, or TLK model, is commonly used to describe ideal surfaces, splitting surfaces up into three categories: rough, vicinal and singular. Terraces are flat, one atom thick planes of atoms (see Figure 3-B), ledges are the edges of these terraces and kinks are defects in the plane-like structure of the terraces, usually denoting a missing or displaced extra atom, or line of atoms, along the ledge (See Figure 3-C). For a surface to be rough it would have to show a high degree of disorder at low temperatures on the surface.4 A rough surface is rarely thought to exist at equilibrium. The vicinal surface is made up of flat terraces of constant width separated by a height of a single atom (see Figure 3-B). Silicon for industrial purposes is usually made to exhibit a singular surface, the ideal surface shown in Figure 2-A, in which the surface orientations lie along a low index plane of the bulk crystal lattice. In the case of silicon, the Miller planes of the crystals would be 100, 111 or 110 (See figure 4).

Unfortunately for researchers and theorists, real surfaces do not behave like ideal TLK surfaces. There are generally two types of deviations from ideal structure: large scale relaxations and surface point defects.

The easiest type of relaxation to consider is the movement of the first few layers of atoms of the surface relative to the bulk of the material, that is, in the direction of the normal. The second and more complicated relaxation involves atom movement relative to the other atoms of the first several surface layers. The movement can be in the plane of the surface or perpendicular to it and can involve individual atoms or the surface plane of atoms moving laterally relative to the bulk of the crystal. Relaxations of these types are called reconstructions. Reconstructions are usually analyzed experimentally by LEED. Interestingly, most clean metal surfaces do not exhibit a large degree of reconstruction. Semiconductor surfaces, on the other hand, show many examples of reconstruction due to the nature of covalent bonding, leading to the formation of complicated surface structures with large unit cells. 5

Single surface TLK crystals are said to exhibit kinetically stable surface point defects. Kinetically stable defects are dislocations, line defects arising from mismatches in the bulk lattice of the surface atoms which interrupt the structure of the atoms. These line defects must form closed loops or networks that terminate themselves at the surface. They come in two types: edge dislocations and screw dislocations (see Figures 3-D,E). An edge dislocation is when an extra string of atoms forms in the surface layer. These atoms bond differently with regularly structured surface atoms, making reactions or adsorptions at the surface behave differently than expected. Screw dislocation is when one half of the crystal lattice is sheared with respect to the other, creating a "step" on the surface of the crystal beginning at some point on the surface. The other type of surface defect is the thermodynamically stable defect, called kinks, which has been described above.

Various Si Surface Structures

The actual structure of the surface layer of diamond structured silicon is far from the ideal terminating unit as theorized in the TLK model. Extensive reconstruction and transformation from one ordered structure to another can take place as the temperature is increased.6 This is theorized to occur due to the localized covalent character of the Si-Si bonds (The atoms of the silicon diamond structure are sp3 hybridized) and the material's low coordination number of 4 (tetrahedral). Metals, which do not usually exhibit this behavior are generally pictured as having delocalized bond characteristics and have higher coordination numbers.7 When the crystal is cut or cleaved, bonds are broken, forming "dangling bonds," which are unshared electron(s). (See Figures 4, 5) Data obtained from LEED analysis has determined the structure of Si(100)p(2x1) which shows surface atoms (each with dangling bonds) bond together by pairing up dangling bonds. This behavior affects the other atoms several layers down.8

The Si(100) planes have a square unit cell with each silicon atom below the surface bonded to two atoms in the plane below and to two in the plane above, creating two dangling bonds for the surface atoms. The accepted model for singular surface, or nominally flat, Si(100) is the dimer model.9 In this model dangling bonds are decreased by 50% through the creation of dimers, where each surface silicon atom bonds to a neighboring atom along the 110 direction using one of its dangling bonds. The theory has changed to allow the dimer to be asymmetric (buckled), allowing different configurations such as (2x1), (2x2) and (4x2) (See Figure 6.1). The additional lattice strain created by the buckling of the dimers causes adjacent dimers to buckle in opposite directs, creating two possible orderings of these buckled rows. If a neighboring dimer buckles in the same direction, a local (2x2) structure is created while if buckled in the opposite direction, a local (4x2) is created. These buckling structures have been observed by LEED and STM to be stable and calculations have shown that buckling lowers the overall surface tension and energy.10

Si(111) has a double layered structure, with each atom having three bonds to atoms in the other layer of the double layer and one bond to an atom in a different double layer (See Figure 4). depending on which layer becomes the surface layer, each atom at the surface can have either one or three dangling bond(s). Because of this, two very different types of reconstructions have been found.

One of them is the annealed surface-(7x7) LEED pattern. The model currently accepted to explain this complex structure is called the Dimer-Adatom-Stacking fault (DAS) model (See Figures 7.1,7.2). In the top layer, the "adatom" layer, each atom has four bonds; the next layer, the layer that terminates the bulk, called the "restatom" layer, has one dangling bond as can be seen in Figure 7.1. The layer after that, the layer consisting of dimers (See Figure 6) is largely uninhibited except for the creation of strings of dimers, connecting the missing atoms, along the edge of the (7x7) unit cell(See figure 7.2) and between the two triangular halves of the unit cell (See 7.2-C. The single bonds are connecting the two triangular halves of the unit cell). The surface that results from this has 21 dangling bonds almost normal to the surface. It is not possible to bond all of these dangling bonds with normal Si atoms. The best solution to this problem is to have six adatoms in each triangular subunit occupying sites of a local (2x2) structure. The dangling bonds of the remaining three rest layer atoms, or restatoms, are untouched. The structure resulting from this complicated pattern reduces the number of dangling bonds in the (7x7) unit cell from 49 to 19, reducing surface tension, energy and making the structure stable.10

Group III Absorption

Group III elements are important to the silicon semiconductor industry for two applications: they are used as dopants (acceptors) in bulk silicon crystals and for the fabrication of III-V semiconductor films on silicon surfaces.10

Group III metals (Al, Ga and In) are usually deposited on Si surfaces when in the gas phase, due to their suitable vapor pressures. When deposited on Si(100), these adsorbates form different structures depending on the level of metal coverage and temperature. The (2x2) structure, a common structure for all absorbents is the most well understood and was proposed based on evidence from LEED, STM and experimental analyses. Adsorbate strings were observed to form in directions perpendicular to the Si dimer rows. These were seen by theorists as adsorbate dimers forming in between the Si dimers, bonding with the dangling bonds of the Si dimers. In this model the adsorbate dimers were perpendicular to the Si dimers. Later it was found that the adsorbate dimers were parallel to the Si dimers (See Figure 8).

Ga and In have been reported to have bonded better to the doubled-stepped Si(100) (a structure not discussed in this paper due to its complexity) than to the singular surface (nominally flat) Si(100) crystal, although at room temperature Ga reacts similarly to both structures.

As for Si(100), Si(111) exhibits several different reconstructions for the deposit of Al, In and also B. The most accepted structure is the (sqr3 x sqr3)R30° structure. This structure is obtained when several monolayers of the adsorbate are deposited on the Si(111)-(7x7) structure surface. From several studies it has been concluded that Al, Ga and In atoms occupy adatom sites(See figure 7.1) while B atoms occupy subsurface (S5) sites (See Figures 9.1, 9.2). This has been explained by the observation that B has the smallest covalent radius, smaller than Si, while Al and In have larger covalent radii. The absorbates in the adatom sites bond with all the dangling bonds of the Si surface atoms. Since they have three valence electrons, no new dangling bonds are introduced.10

Conclusion

Although the silicon surface deviates from idealized TLK theory and is therefore hard to predict and understand, its deviation is what gives it its unique and useful properties, such as how it accepts and structures adsorbates on its surface. These properties make it useful as a doped semiconductor, which has many important applications such as the important p-n junction, a material combination in which thin layers of materials exhibit useful electrical properties. Understanding the structure and nature of the surface of silicon is necessary to understanding the many important electronic devises used in the everyday and not so everyday world.

References

1. J.B. Hudson, Surface Science , Butterworth-Heinemann, New York, 1992 pg. 6

2. A.W. Adamson, A.P. Gast , Physical Chemistry of Surfaces Wiley-Interscience, New york, 1997 pg. 302

3. S.R. Morrison, The Chemical Physics of Surfaces , Plenum Press, New York & London, 1990 pg. 96

4. J.B. Hudson, Surface Science , Butterworth-Heinemann, New York, 1992 pg. 4

5. J.B. Hudson, Surface Science , Butterworth-Heinemann, New York, 1992 pg. 20

6. G.A. Somorjai, Chemistry in Two Dimensions , Cornell University Press, Ithica & London, 1981 pg. 148

7. Edited by H. C. Gatos, The Surface Chemistry of Metal and Semiconductors , John Wiley & Sons, New York & London, 1960 pg. 382

8. G.A. Somorjai, Chemistry in Two Dimensions , Cornell University Press, Ithica & London, 1981 pg. 149

9. Edited by H. C. Gatos, The Surface Chemistry of Metal and Semiconductors , John Wiley & Sons, New York & London, 1960 pg. 383

10. H.N. Waltenburg, J.T. Yates, Jr , Chem. Rev. , 1995, 1589-1673

Section 2

Gina Hennen

Return of the Blob:

The Effects on Optical and Electrical Properties as a Result of Structure in the Amorphous Phase of Hydrogenated Silicon

Chemists have a preference for studying easily described materials that contain high levels of internal symmetry. Perhaps this is why virtually all inorganic textbooks focus primarily on crystalline solids, which are materials having a repetitive unit cell that is translatable in all directions. Solids without this feature are dubbed "glasses" or amorphous compounds; these terms apply to all substances that are non-crystalline. As the properties of a solid are, to a high degree, related to their structure, it seems probable that a compound without a regularly repeating structural unit might have unusual and potentially useful electrical and optical properties. One of the most widely studied non-crystalline compounds of the past thirty years is the semiconductor material amorphous hydrogenated silicon (a-Si:H). This substance is the photovoltaic material most commonly found in solar cells, large-area flat-panel displays, thin-film transistors, optical scanners, and in LCD's. It is also used as a substrate material for microcrystallites, which are of obvious use to the electronics industry as the drive for smaller and faster microprocessors becomes more intensive. Many of the reasons for its common use in these, among other, applications are due to the properties generated by its amorphous "structure".

Amorphous does not mean a total lack of order, though it is the disorder of the atomic structure that distinguishes amorphous compounds from crystalline ones. The long range order of crystalline solids--i.e. the long range periodicity of the lattice, the ability for point groups to be assigned, and the predictability of structure in a perfect crystal in all directions--is completely absent for amorphous compounds. However, short range order is present which places emphasis on localized bonding and the coordination environment of the atoms. In a crystalline material, the extensive overlap of the orbitals generates a non-localized model, which relies on bands instead of individual, isolated atomic orbitals to describe the bonding and structure. For an amorphous semiconductor, the solutions to Schrödinger's wave equation for a crystalline solid, known as the Bloch solutions, do not apply because the potential energy term V(r) in the equation is not periodic. In terms of the physical structure of an amorphous material, this aperiodic potential energy is related to the lack of a periodic, crystalline structure. The disorder of an amorphous material is such that it causes frequent scattering of electrons due to lattice vibrations, thereby creating an inconstant potential; for the wavefunction this means that it loses phase coherence over a distance of one or two atomic spacings. Thus, new theoretical approaches are required to describe amorphous materials, most of which focus on the localized, short range chemical bonding interactions of the atoms. However, it is interesting to note that one model, developed by Thorpe and Weaire in 1971[1], which describes bonding using a wavefunction involving overlap of only the nearest neighbors--and so contains no information about the long range structure--can therefore be used in the description of both crystalline and amorphous solids. But the most commonly used model to describe amorphous materials was introduced by Zachariasen in 1932[2] and is known as the continuous random network. In it, the idea of a periodic crystalline structure is replaced by that of a random network in which each atom has a specific number of bonds to its nearest neighbors, known as its coordination environment (Fig.1). In the continuous random network, each atom is able to take on its preferred coordination environment so as to create the most bonding orbital interactions possible; for example, in Fig. 1 the network might be composed of silicon (four-fold coordinated), gallium (three-fold), and hydrogen (one-fold). Zachariasen's proposed theory of glasses was the first-ever to describe the structure of non-crystalline materials. He defined three features that are common to both amorphous and crystalline materials: each atom has the same coordination number, the nearest neighbor distances are nearly constant, and there are no dangling bonds. He also indicated the two fundamental ways in which the two structures differ: amorphous materials have a spread of possible values for the bond angle--which is not possible in a perfect crystal--and there is no long range order for a non-crystalline material.

Experimental determination of the actual structure (as opposed to the theoretical structure outlined by Zachariasen) of amorphous solids is difficult, at best. The usual techniques for determining the structures of crystalline materials, for example X-ray crystallography, simply do not work for amorphous materials as there are no Miller planes that would produce constructive interference. One technique that has generated considerable attention in the characterization of amorphous structures is that of Small Angle Scattering, a conventional diffraction method using electron[3], X-ray[4], or neutron scattering[5]. This diffraction technique uses one of these three incident sources directed at a small angle to the surface of the amorphous substance, resulting in information about the average atomic density at a certain distance r from any particular reference atom. NMR[6] and Extended X-ray Absorption Fine Structure (EXAFS)[7,8] have been used intensively to improve knowledge of local order in amorphous compounds. These methods allow for investigation of the specific geometric environment of a particular type of atom; for example, these methods could determine the bonding environment of a dopant atom in the a-Si network.

Bonding in amorphous materials is theoretically, as well as experimentally, described by a radial distribution function (RDF). This function determines the probability of finding an atom at a distance r from another atom; put another way, it is the average atomic density at a distance r from any atom in the random network. A schematic diagram of this function for a crystalline solid, an amorphous solid, and a gas displays this quite well (Fig. 2). Over short distances the relative positions of the atoms are completely random for a dilute gas, whereas for a perfect crystal they are extremely ordered, even at large distances between the atom pairs. For the amorphous material, there is some degree of order over relatively short distances, but for large pair distances there is no observable ordering. The RDF can generally be resolved out to the twelfth neighbor from a reference atom for a crystalline material, compared to only the fourth neighbor for an amorphous compound[9]. Thus, some of the properties found in crystalline materials are akin to those found in amorphous ones, due to the shared local order. More specifically, the covalent bonds in crystalline and amorphous silicon share similar qualities in terms of coordination environments (typically, CN=4 in a roughly tetrahedral geometry), bond angles (on average, 109û but it generally varies between +/- 4.5 for the amorphous phase)[9], and average bond lengths (2.35 Å), leading to a similar overall electronic band structure; for example, silicon dioxide is an insulator in both its crystalline and amorphous phases, and both crystalline silicon and a-Si are semiconductors. Most of the information about the local order of silicon atoms in the amorphous phase comes from the RDF obtained experimentally from X-ray or neutron scattering. Thus, while it is accepted that short range order exists, the total lack of any long range ordering for amorphous silicon results in many new optical and electrical properties that are not found in its crystalline counterpart, mostly due to the defect states that lie in the electronic band gap.

One of the fundamental properties of an insulator or a semiconductor is the presence of a forbidden energy band gap between the unoccupied conduction band and the filled valence band. According to the free electron theory, the band gap is due to the periodicity of the crystalline lattice. The experimental observation of a band gap in an amorphous material created heated controversy in the 70's, when the theory of amorphous materials was first being hashed out. There was considerable debate as to why an amorphous material such as a-Si:H could have a band gap at all (experimentally determined at 1.5-1.6 eV)[10], much less one that is comparable in magnitude to its crystalline counterpart (1.1 eV). Subsequent work yielded conclusive theoretical "evidence" for the explanation that the band gap can be equivalently described by the splitting of the bonding and the anti-bonding states of the covalent bond--a localized model. That is, it was proven using complicated mathematics that the band gap can be interpreted as either the result of the structurally repetitive nature of the lattice or as the result of the energy difference due to linear combinations of orbitals of both bonding and anti-bonding nature. With this in mind, the energy bands are thus most strongly influenced by the short range order, which is effectively the same for both crystalline and amorphous silicon.

Deviations from the ideal band gap are due primarily to the presence of defects in the structure of the material. In a crystalline material, any atom that is out of place from its position predicted by the periodicity of the lattice is considered a defect; two common defects are vacancies in lattice positions and interstitials. An example of an interstitial is an atom in a position between the expected lattice positions. With the random network of amorphous substances, the only specific structural feature is the coordination of an atom to its neighbor; thus, the only type of structure that could be considered a defect is that of the coordination defect. A coordination defect occurs when an atom has too many or too few bonds. In a-Si:H, this would mean CN=3 or 5 for the Si atoms. The intrinsic disorder of an amorphous solid is difficult to characterize in terms of defects, as there are many possible configurations for the atoms to obtain, all equally probable and of equivalent energy. That is, if the coordination environment is the same for the silicon atoms, then all structures are equivalent and represent various permutations--they display natural variability. Since there are no "correct" structures as there are in a crystalline solid, then it is difficult to define a specific structure as a defect. For example, if the coordination number for a-Si is four for every atom in the network then the structure is essentially defect-free. There are, however, deviations of both bond length and angle that are not considered defects if the coordination number is the expected one, arising as they do from the long range structural disorder and consequent natural deviations. These deviations, along with the coordination defect, result in alterations to the band structure relative to the crystalline one.

Deviations of bond length and angle due to the long range structural disorder cause a collection of "tail" states occurring at the edges of the delocalized conduction and valence bands (Fig. 3, Label a). The abrupt band edges of a crystal broaden and trail off into these tail states in amorphous compounds, which extend into the band gap region. These band tails are important, as some electronic transport, and hence conduction, occurs at the band edges. Additionally, the defect states located deep in the band gap are due to the coordination defects (Fig. 3, Label b). Examples of this are broken Si-Si bonds, which have corresponding energy states in the middle of the band gap, or dangling bonds found on the surface of the a-Si:H film, the existence of which has been conclusively shown through electron spin resonance measurements[11]. These defects have a great effect upon the electronic transport properties, as they control the trapping, recombination, and hole hopping of charge carriers. When an electron is excited, if there are energy states lying in the interim region above the valence band in energy and below the edge of the conduction band, it can be "trapped" in these localized states, and is subsequently rendered immobile--it has little to no drift velocity or mobility. Through predominately non-radiative, thermal processes, the electron will eventually return to the ground state, and recombine with a hole without ever obtaining the status of charge carrier and aiding in the conduction. The phenomenon of hole hopping occurs when an electron is energetic enough to reach one of the localized states in the tail of the valence band, resulting in a hole of positive charge left in the delocalized valence band. This hole can also be considered an effective charge carrier as electrons from a nearby atom will fill in the hole, creating another hole, which will begin the cycle again. This process generates a flow of current once a potential is applied. A final type of charge transport occurs when an electron is promoted to the extended conduction state, where it acquires a large drift velocity and has high mobility, thereby aiding in conduction with relatively low resistance. This type of charge carrier transport occurs in both amorphous and crystalline semiconductor compounds.

Defects in the amorphous structure also affect the photosensitivity of the material. A sample with high defect density will have a large number of localized electronic states between the conduction and valence bands (Fig. 3, Regions a and b), which consequently hampers conduction as charge carriers are trapped in these localized states and return to ground state without radiating photons. It has been clearly established by experiment[12] that the addition of hydrogen into the amorphous structure of silicon reduces the defect density greatly. The high defect density of pure a-Si prevents both doping and photoconductivity, which are desirable aspects of semiconductor materials. Atomic hydrogen is small enough so that it can move in and out of the surface of a-Si during the film growth stage. This diffusion allows H to react with weak Si-Si bonds; excess H is evolved from the film. Hydrogen chemically bonds with the Si dangling bonds to create 4-fold coordination and thus reduces the coordination defects. Atomic H can also react with very strained, and consequently weak, Si-Si bonds in order to create a more stable bond.

The role of local chemistry in both crystalline and amorphous networks in the bonding of a dopant atom exemplifies one of the major structural differences between the two types of materials. Since each atomic site in a crystal is defined by the lattice, the dopant is restricted to the specifications of that site in terms of its geometry, bond angles, and bond lengths. Even the size of the dopant is limited by the size of the host atom creating the lattice. If this template is not followed by the dopant atom, it must form a defect (e.g. an interstitial). As amorphous silicon has no rigidly defined lattice sites, the dopant can adapt to the local environment such that it optimizes its own bonding configuration by "adjusting" the bond lengths and angles, without creating a defect. In crystal semiconductors, dopants have definite determined energies for the localized states in the band gap, which is an important design parameter. By contrast in a-Si:H, from all possible defect configurations, those are created which yield a lower total energy. That is, the dopant atom can actually change its coordination so as to lower the free energy of the material; it can exist in three-fold or four-fold states. The same holds for silicon atoms in amorphous structures. Thus, even though the number of dopant atoms is fixed once the sample is prepared, the number of donors or acceptors (4-fold coordination of n- or p-type dopant atoms respectively) or defects (3-fold coordinated silicon atoms) can change with temperature and also with light- and field-induced carrier density. Additionally, it is unclear whether the ability of a dopant atom to change its coordination is specifically a consequence of the presence of hydrogen in the random network, or whether it is a more general property of amorphous compounds.

Now that an introductory knowledge of the structure of amorphous materials has been attained, the process of creating amorphous hydrogenated silicon--as well as the characterization of a particular sample's properties--can be better understood. The first synthesis of a-Si:H, performed by Chittick, Alexander, and Sterling[13] occurred in 1969. The technique they used was radio-frequency glow discharge (see Fig.4 for a schematic diagram), which involves vapor depositions of silane gas (SiH4) onto a glass (SiO2) substrate material, creating films of amorphous hydrogenated silicon. As an interesting aside, it should be noted that adding H2 in large amounts in order to dilute the reactant gases in the plasma is known to produce micro-crystalline Si embedded in the thin film at temperatures of 150û to 350ûC [10]. Deposition of a-Si:H occurs on the walls of the reaction tube and coats the substrate at a rate of a few microns per hour; thus only thin films are available for experimentation, and so surface states will affect the measured properties. In the Chittick et al. experiment, an apparatus was included allowing for the substrate to be heated during deposition from 25û-650ûC. With this set-up structural changes as a result of temperature--associated with the ordering of the network, the onset of crystallization, and the subsequent electrical effects--could be studied. They determined that resistivity decreased with increasing deposition temperature, with this effect being most marked between 250û and 500ûC (Fig 5, Curve a). At temperatures above 500ûC, the resistivity stabilized, due perhaps to a metastable structure. It has been determined in numerous experiments[10, 14, 15] since the Chittick et al. experiment that the conditions under which deposition occurs definitely affects the properties of the material.

The first experiment that effectively doped a sample of amorphous silicon was performed by Spear and LeComber in 1975[16]. Prior to this experiment, it was generally agreed that the doping of an amorphous compound was virtually impossible, as the random network could change its structure to accommodate an impurity atom having a different preferred coordination relative to silicon. It was believed that even if it were possible to incorporate a relatively large amount of shallow donor or acceptor impurity atoms into the random network, the excess charge carriers would condense into defect states located in the band gap region without changing the probability of transition into a conducting state. A more technical way of stating this is that the Fermi level wouldn't change by more than a few kT with the addition of large amounts of dopant atoms. However, Spear and LeComber showed that if a sample has both a very low overall density of defect states, and a narrow range of band tail states, then it is indeed dopable. Through experiments on electrical and optical properties, and on determinations of the distribution of localized states, it was concluded that specimens deposited at a high temperature (227û-327ûC) through the gas phase decomposition of silane (SiH4) in a radio-frequency glow discharge fit this criterion. They showed that electrical conductivity could be controlled over four orders of magnitude by doping with either pentavalent or trivalent impurities. The conductivity increased with the addition of either phosphorus (n-type doping) or boron (p-type doping), which is analogous to the doping of crystalline compounds.

There are not many solid materials known that have a wide range of tunable properties dependent upon both the method of preparation and the conditions under which preparation occurs. This is one of the many reasons why the compound amorphous hydrogenated silicon is so fascinating. Current research is focusing on fine-tuning the defect states lying within the band gap so as to control the wavelength of emitted light. Research is also underway that is focused on increasing the absorption efficiency of radiation in the hopes of creating better solar panels. The unique structure of amorphous-phase compounds, and the ability for this structure to change as a function of environment, makes these substances interesting in the abstract as well as useful for technological applications

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A large demand for the production of smaller and smaller electronic devices has spurn the progress of fabrication of low dimensional semiconductor structures. Although technological applications are a major motivating force for the study of semiconductors, there are many phenomena pertaining to semiconductors that are interesting from a purely scientific perspective. This paper endeavors to reveal the interesting aspects of the study of quantum dots.

Although an answer to the question&endash;What is a quantum dot?&endash;shall be an underlying theme of the entire paper, it will be helpful to present a definition a priori. A quantum dot is an electron-hole pair confined to zero dimensions[1]. That is, it is confined by some sort of electrostatic potential in all three dimensions. These electrostatic potentials usually come from interactions with the structure of the material combined with an applied potential. A pair that is confined in one dimension is termed a quantum well and a pair that is free to move in one dimension while being confined in two dimensions is known as a quantum wire[2]. It is useful to note that the dimension of freedom plus the dimension of confinement always equals the dimension of the space, in our world that would be three. These areas of three-dimensional confinement of electron-hole pairs can actually be seen if viewed with the right prescription, in this case an atomic force microscope. As Fig. 1 shows, for microcrystallites the electron-hole pair is typically confined by a sphere.

FIG.1 Atomic force microscope image of the surface of quantum dots showing a typical dot density of ~1011 dots/cm2. From Philips, Kamath, and Bhattacharya, J.Appl.Phys.,Vol 85 Num 5, 2997.

The first quantum dots were made by imbedding crystallites into an amorphous glass material. This was probably done hundreds of years ago by people who made colored glass by melting a certain amount of semiconductor material, like ZnS or ZnSe, into the usual glass material[2]. Loosely speaking, the difference between a glass doped with microcrystallites and a polycrystalline material depends on the amount of amorphous material present and the size of the crystals imbedded in it. If the material is composed of relatively large crystals with amorphous material merely filling in the spaces, the material is considered polycrystalline. A material with a large amount of amorphous material and a distribution of relatively small crystals is considered microcrystalline. This difference is highlighted in Fig. 1.

FIG.1 The picture on the left shows small crystals embedded in a largely amorphous material, typical of a microcrystalline material. The picture on the right shows some remnants of amorphous material filling the space between large crystals, typical of a polycrystalline material. Adapted from Holden and Singer,Crystals and Crystal Growing,(1960).

The preparation of quantum dots by embedding microcrystallites in optical glasses or preparing the microcrystallites in colloidal form are two techniques that are widely in use today. Quantum dots can also be fabricated by the lateral confinement of preexisting quantum wells by implantation-enhanced interdiffusion or by electron-beam lithography.[1] This way, as in Fig. 2, potential barriers are placed to confine motion along the X axis and along the y axis, and motion along the Z-axis is already confined by the original well. The latter type of quantum dots are usually called quantum boxes. The microcrystallites are usually spherical in shape and the motion inside the structure is usually three dimensional. Quantum boxes are thin disks with the two dimensions defined by lateral confinement much larger than the width of the quantum well that defines the third dimension. For more information on the preparation of quantum dots see chapter two of U. Woggon.

FIG. 2 The Dimensions of a quantum box. Adapted from G.W. Bryant (1998).

Qualitatively the effects of confinement on excitons (electron-hole pairs) is the same for excitons in microcrystallites and the so&endash;called quantum boxes (QB)[1]. An exciton in a large QB behaves as a free quasi-two dimensional exciton. Similarly, an exciton in a large microcrystallite behaves as a free three dimensional exciton. As the size L of the quantum box or microcrystallite decreases, confinement effects become important. For a very small L the exciton acts zero-dimensional, or, is quasi-zero-dimensional with all motion frozen out. Quantitatively, the confinement effects in microcrystallites and QB's differ because one degree of motion is frozen out in QB's for every size L. Fortunately, this paper is concerned mostly with qualitative effects of confinement so a rigorous discourse on the preceding quantitative difference won't be necessary. We will treat microcrystallites and quantum boxes under the general category of quantum dots. Quantum dots are either microcrystallites or QB's as the size L shrinks sufficiently to provide a quasi-zero dimensional exciton.

Now some reconciliation is in order. Earlier, for the sake of brevity, I used electron-hole pair and exciton synonymously without even a bit of commentary linking the two. Well as it turns out the sin was not so grave; after all an exciton is an electron hole pair. Exciton is the name given to an electron and the corresponding hole that the electron left when the two entities are bound together through a coulombic force[4]. They make a hydrogen-like particle, one particle being big and positively charged(hole) and the other being small and negatively charged(electron). This electric interaction that the electron and the hole share is relatively weak, and so each entity (the electron or hole) is independently mobile. It is also sufficiently weak to allow the electon and hole to remain separate, without recombination. When referring to quantum dots, electron-hole pairs mentioned are usually excitons, but they are also bound to each other due to the structure of the QB or microcrystallite. Whether it is the quantum confinement pair or the coulombic attraction of the exciton that keeps the pair bound to each other depends on the degree of confinement. The radius of a quantum dot and the radius of the exciton are large compared to the lattice constant of the material, for Si the lattice constant is about two and a half angstroms. .

Confining an electron and a hole to a QB or a microcrystallite does, in fact, increase their direct coulomb interaction because the two particles are constrained to occupy the same space despite any cost of increased kinetic energy[1]. The importance of coulomb effects is determined by the extent to which the electron and hole can correlate in forming an exciton. Since single particle energy levels scale as 1/L2 and coulomb energies scale as 1/L, confinement effects should become dominant as a box shrinks, and the electron-hole pairs become uncorrelated despite the enhancement of the direct coulomb interaction as the box shrinks.

Now that we have a semi-lucent idea of what a quantum dot is, we are going to cheat a little and jump straight to the punch line: This is what a quantum dot does. This discussion of the applications of glasses doped with quantum dots will consist of two parts. First we will probe the possibilities of applications due to the fast optical switching capabilities of quantum dot materials. Lasers always seem appropriate to discuss within the context of semiconductor materials, so for fear of setting precedence, that too will be included in our discussion of quantum dots.

With a somewhat resolute outlook on the future of computing, that is the limits of our ability to make smaller microchips, people are beginning to conceive of computers that are based on completely different forms of information processing. One type of computer that has been proposed relies on chaos to process and retain information. Computer scientists have even come up with a model using dripping water faucets to illustrate the ability to make logic gates using a chaotic system (See Fig. 3). A much more timely way of performing these operations would be to use nonlinear optics in place of faucets and light instead of water, and that is where quantum dot materials would come in. In this spirit, an optical material will either transmit or not transmit based on what light is incident on it. The first two optical devices can be aimed at another; it's fate dependent on the fate of the first two and so on.

FIG.3 Chaotically driven logic gate. Adapted from Sci. Amer. V279 6, p 47.

With quantum dot materials nonlinear absorption and refraction can be controlled by change of a relatively few parameters of the material. Thresholds of values like incident light intensity or wavelength can be tuned to provide an adequate switching mechanism, where a transmission of light by a particular device would be considered either off or on depending on what side of the threshold the values lie on. Whereas in bulk semiconductors the physical origin of these nonlinear properties is associated with the optically created high-density many particle system causing screening , band-gap renormalization and band filling, the mechanism of the nonlinearity of quantum dots is different.[5] With decreasing size, the nonlinear absorption and refraction is strongly influenced by quantum confinement[5]. In the case where the quantum dot sizes are similar in size to the exciton, the nonlinear optical response is dominated by the saturation of discrete levels of the one-electron-hole pair states and induced absorption of the two-pair states. What this means is that instead of the typical continuous bands in bulk materials these quantum dots can be considered as experimental realization of discrete-level systems in semiconductors[5]. Due to the different physical origin of the nonlinearity it is difficult to compare the switching efficiency of the quantum dot and the bulk material. Because of the current lack of sufficient understanding of the quantum size effect on many bulk properties, the tweaking of quantum size is usually reserved for the tuning of wavelength to which is best suited for a particular switching operation. As we can see, even with the paucity of knowledge that is available now, it is possible to use quantum dot materials as a main component in optical computers.

There are a number of reasons that there are investigations into the applications of quantum dot materials as lasers and LED's. First of all, there is a broad tuning range provided by quantum dots which makes them very attractive for light emitting devices [5]. It has been found that silicon-based structures that contain quantum dots emit in the visible region with a high quantum efficiency when compared to bulk Si. Optical gain has been detected in CdSe quantum dots[6]. Optical gain is the gain in intensity of light that occur when light incident on a material causes additional photons to be emitted. These photons are emitted with the same energy and phase as the incident photon causing the familiar cascade of coherent light that is the fundamental mechanism of solid state lasers.

The demand for better electro-optic devices has caused an impetus of research in the field of low dimensional physics. This new field has been and will continue to be truly interdisciplinary, combining ideas from optics, electronics, solid state physics, quantum and wave mechanics, statistical thermodynamics, inorganic and physical chemistry, etc. The beautiful aspect of dealing with quantum dots is the tunability and compatibility of the material. As we have seen, even with the limited knowledge of their properties, quantum dot materials can be exploited to perform a wealth of tasks, often in the same environment as their primordial ancestor, bulk Si. This versatility and compatibility makes the study of quantum dots a valuable investment.

BIBLIOGRAPHY

[1] G.W. Bryant, Phys.Rev. B37, 8763 (1988).

[2] L.Banyai, S.W Koch, in Semiconductor Quantum Dots, (World Scientific, River Edge,New Jersey, 1993).

[3] G.W. Bryant, Phys. Rev. B40, 1620 (1989).

[4] R.Lerner,G.Trigg Ed., in Encyclopedia of Physics, 2nd Ed,(VCH Publishing, Inc, New York, 1990).

[5] U. Woggon, in Optical Properties of Semiconductor Quantum Dot, (Springer, Berlin, Germany, 1997)

[6] V.S. Dneprovskii, V.I.Klimov,D.K. Okoronov, Y.V.Vandyshev, Sol. State Commun. 81, 227 (1992)