Electron random semiconductors

Light is generated in semiconductors in the process of radiative recombination. In a direct semiconductor, minority carrier population created by injection in a forward biased p-n junction can recombine radiatively, generating photons with energy about equal to E. The recombination process is spontaneous, individual electron-hole recombination events are random and not related to each other. This process is the basis of LEDs [36]. 

Semiconductor devices ate affected by three kinds of noise. Thermal or Johnson noise is a consequence of the equihbtium between a resistance and its surrounding radiation field. It results in a mean-square noise voltage which is proportional to resistance and temperature. Shot noise, which is the principal noise component in most semiconductor devices, is caused by the random passage of individual electrons through a semiconductor junction. Thermal and shot noise ate both called white noise since their noise power is frequency-independent at low and intermediate frequencies. This is unlike flicker or ///noise which is most troublesome at lower frequencies because its noise power is approximately proportional to /// In MOSFETs there is a strong correlation between ///noise and the charging and discharging of surface states or traps. Nevertheless, the universal nature of ///noise in various materials and at phase transitions is not well understood. 

Charge carriers in a semiconductor are always in random thermal motion with an average thermal speed, given by the equipartion relation of classical thermodynamics as m v /2 = 3KT/2. As a result of this random thermal motion, carriers diffuse from regions of higher concentration. Applying an electric field superposes a drift of carriers on this random thermal motion. Carriers are accelerated by the electric field but lose momentum to collisions with impurities or phonons, ie, quantized lattice vibrations. This results in a drift speed, which is proportional to the electric field = p E where E is the electric field in volts per cm and is the electron s mobility in units of cm /Vs. 

As is to be expected, inherent disorder has an effect on electronic and optical properties of amorphous semiconductors providing for distinct differences between them and the crystalline semiconductors. The inherent disorder provides for localized as well as nonlocalized states within the same band such that a critical energy, can be defined by distinguishing the two types of states (4). At E = E, the mean free path of the electron is on the order of the interatomic distance and the wave function fluctuates randomly such that the quantum number, k, is no longer vaHd. For E < E the wave functions are localized and for E > E they are nonlocalized. For E > E the motion of the electron is diffusive and the extended state mobiHty is approximately 10 cm /sV. For U <, conduction takes place by hopping from one localized site to the next. Hence, at U =, )J. goes through a... 

In summary, NMR techniques based upon chemical shifts and dipolar or scalar couplings of spin-1/2 nuclei can provide structural information about bonding environments in semiconductor alloys, and more specifically the extent to which substitutions are completely random, partially or fully-ordered, or even bimodal. Semiconductor alloys containing magnetic ions, typically transition metal ions, have also been studied by spin-1/2 NMR here the often-large frequency shifts are due to the electron hyperfine interaction, and so examples of such studies will be discussed in Sect. 3.5. For alloys containing only quadrupolar nuclei as NMR probes, such as many of the III-V compounds, the nuclear quadrupole interaction will play an important and often dominant role, and can be used to investigate alloy disorder (Sect. 3.8). 

Metal to insulator Semiconductor to insulator, or Insulator to insulator Light contact (touching) Ion migration (due to inherent or unavoidable ion contamination electron traps (a) by random adhesion of ions for contact of dissimilar materials (b) by diffusion due to differences in ion concentration or mobilities (c) by image attraction Anomalous (due to avoidable surface contamination)... 

We turn now to an evaluation of nc, the concentration of centres at which the transition occurs. We remark first of all that an experimental value is difficult to obtain. We do not know of a crystalline system, with one electron per centre in an s-state, that shows a Mott transition. Figure 5.3 in the next chapter shows the well-known plot given by Edwards and Sienko (1978) for nc versus the hydrogen radius aH for a large number of doped semiconductors, giving ncaH=0.26. In all of these the positions of the donors are random, and it is now believed that for many, if not all, the transition is of Anderson type. In fluid caesium and metal-ammonia solutions the two-phase region is expected, but this is complicated by the tendency of one-electron centres to form diamagnetic pairs (as they do in V02). In the Mott transition in transitional-metal oxides the electrons are in d-states. 

As we shall see below, for dilute solutions the electron is not attached to the alkali ion but is trapped in a cavity, around which the ammonia is polarized. The problem of the metal-insulator transition, then, is one of a random array of one-electron centres, as in a doped single-valley semiconductor. On the other hand, the disorder is less because the strong overlap between the wave functions of some pairs of centres characteristic of doped semiconductors is absent. In doped semiconductors there is no discontinuity in s2 at the transition. As explained in Chapter 5, this may be because of the very strong disorder or, in many-valley systems, because of self-compensation. In metal-ammonia solutions, as in the fluid alkali metals discussed in Section 4, both are absent. 

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