Semiconductor constants 232

Several reports have addressed how interfacial electron transfer rate constants vary with thermodynamic driving force. The driving force is tuned by manipulating the conduction band edge through adsorption of specific cations, utilizing different semiconductors, or by keeping the semiconductor constant with a series of sensitizers with known formal potentials. A difficulty in these studies is that the position... 

Another example of epitaxy is tin growdi on the (100) surfaces of InSb or CdTe a = 6.49 A) [14]. At room temperature, elemental tin is metallic and adopts a bet crystal structure ( white tin ) with a lattice constant of 5.83 A. However, upon deposition on either of the two above-mentioned surfaces, tin is transfonned into the diamond structure ( grey tin ) with a = 6.49 A and essentially no misfit at the interface. Furtliennore, since grey tin is a semiconductor, then a novel heterojunction material can be fabricated. It is evident that epitaxial growth can be exploited to synthesize materials with novel physical and chemical properties. 

Dielectric constants of metals, semiconductors and insulators can be detennined from ellipsometry measurements [38, 39]. Since the dielectric constant can vary depending on the way in which a fihn is grown, the measurement of accurate film thicknesses relies on having accurate values of the dielectric constant. One connnon procedure for detennining dielectric constants is by using a Kramers-Kronig analysis of spectroscopic reflectance data [39]. This method suffers from the series-tennination error as well as the difficulty of making corrections for the presence of overlayer contaminants. The ellipsometry method is for the most part free of both these sources of error and thus yields the most accurate values to date [39]. 

III-V compound semiconductors with precisely controlled compositions and gaps can be prepared from several material systems. Representative III-V compounds are shown in tire gap-lattice constant plots of figure C2.16.3. The points representing binary semiconductors such as GaAs or InP are joined by lines indicating ternary and quaternary alloys. The special nature of tire binary compounds arises from tlieir availability as tire substrate material needed for epitaxial growtli of device stmctures. 

Figure C2.16.3. A plot of tire energy gap and lattice constant for tire most common III-V compound semiconductors. All tire materials shown have cubic (zincblende) stmcture. Elemental semiconductors. Si and Ge, are included for comparison. The lines connecting binary semiconductors indicate possible ternary compounds witli direct gaps. Dashed lines near GaP represent indirect gap regions. The line from InP to a point marked represents tire quaternary compound InGaAsP, lattice matched to InP.

Temary and quaternary semiconductors are theoretically described by the virtual crystal approximation (VGA) [7], Within the VGA, ternary alloys with the composition AB are considered to contain two sublattices. One of them is occupied only by atoms A, the other is occupied by atoms B or G. The second sublattice consists of virtual atoms, represented by a weighted average of atoms B and G. Many physical properties of ternary alloys are then expressed as weighted linear combinations of the corresponding properties of the two binary compounds. For example, the lattice constant d dependence on composition is written as ... 

Here, E and s are the band gap energy and the dielectric constant of the bulk semiconductor, and p is the reduced 0 mass of the exciton system, 1/p = + 1/fffi,. The second tenn, proportional to /R, arises from a simple... 

In the electronics industry. Pis find wide appHcations as a dielectric material for semiconductors due to thermal stabiHty (up to 400°C) and low dielectric constant. Pis are being considered for use in bearings, gears, seals, and prosthetic human joints. The intended part can be machined or molded from the PI, or a film of PI can be appHed to a metallic part. Because of their superior adhesion, dielectric integrity, processing compatibUity, and lack of biological system impact. Pis have been used in many biological appHcations with particular success as body implants. 

Epitaxial crystal growth methods such as molecular beam epitaxy (MBE) and metalorganic chemical vapor deposition (MOCVD) have advanced to the point that active regions of essentially arbitrary thicknesses can be prepared (see Thin films, film deposition techniques). Most semiconductors used for lasers are cubic crystals where the lattice constant, the dimension of the cube, is equal to two atomic plane distances. When the thickness of this layer is reduced to dimensions on the order of 0.01 )J.m, between 20 and 30 atomic plane distances, quantum mechanics is needed for an accurate description of the confined carrier energies (11). Such layers are called quantum wells and the lasers containing such layers in their active regions are known as quantum well lasers (12). 

Fig. 6. Band gap versus lattice constant for Group 13—15 (III—V) semiconductors where (—) denotes direct gap and (-) iadirect. Liaes joining the...

Fig. 8. A plot of band gap versus lattice constant for Groups 2—16 and 12—16 (II—VI) semiconductors used for the preparation of green and blue lasers.

Semiconductors (qv) are materials with resistivities between those of conductors and those of insulators (between 10 and 10 H-cm). The electrical properties of a semiconductor determine the hmctional performance of the device. Important electrical properties of semiconductors are resistivity and dielectric constant. The resistivity of a semiconductor can be varied by introducing small amounts of material impurities or dopants. Through proper material doping, electron movement can be precisely controlled, producing hmctions such as rectification, switching, detection, and modulation. 

Table 1 Hsts the properties of several semiconductors relevant to device design and epitaxy. The properties are appropriate to the 2incblende crystal stmcture in those cases where hexagonal polytypes exist, ie, ZnS and ZnSe. This first group of crystal parameters appHes to the growth of epitaxial heterostmctures the cubic lattice constant, a the elastic constants, congment sublimation temperature, T. Eor growth of defect-free...

Electrical and Electronic. Diamond is an electrical insulator (-- lO H/cm) unless doped with boron when it becomes ap-ty e semiconductor with a resistivity in the range of 10 to 100 Q/cm. n-Ty e doping has often been claimed but is less certainly estabUshed. The dielectric constant of diamond is 5.58. 

Where b is Planck s constant and m and are the effective masses of the electron and hole which may be larger or smaller than the rest mass of the electron. The effective mass reflects the strength of the interaction between the electron or hole and the periodic lattice and potentials within the crystal stmcture. In an ideal covalent semiconductor, electrons in the conduction band and holes in the valence band may be considered as quasi-free particles. The carriers have high drift mobilities in the range of 10 to 10 cm /(V-s) at room temperature. As shown in Table 4, this is the case for both metallic oxides and covalent semiconductors at room temperature. 

Early work in ellipsometry focused on improving the technique, whereas attention now emphasizes applications to materials analysis. New uses continue to be found however, ellipsometry traditionally has been used to determine film thicknesses (in the rang 1-1000 nm), as well as optical constants. " Common systems are oxide and nitride films on silicon v ers, dielectric films deposited on optical sur ces, and multilayer semiconductor strucmres. 

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