Carrier 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]. 

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. 

All the preceding mechanisms of the carrier packet spread and transit time dispersion imply that charge transport is controlled by traps randomly distributed in both energy and space. This traditional approach completely disregards the occurrence of long-range potential fluctuations. The concept of random potential landscape was used by Tauc [15] and Fritzsche [16] in their models of optical absorption in amorphous semiconductors. The suppressed rate of bimolecular recombination, which is typical for many amorphous materials, can also be explained by a fluctuating potential landscape. 

With the experimental results in mind we retium to the analysis of the trap-limited transport. The time-dependent decrease in the apparent mobility is obviously consistent with our earlier argument that the average trapping time will increase with the number of trapping events for an exponential band tail. Scher and Montroll (1975) were the first to point out this property of a very broad distribution of release times and to associate the effect with transport in disordered semiconductors. They analyzed the random walk of carriers with such a distribution and... 

As described above, the electrons in a semiconductor can be described classically with an effective mass, which is usually less than the free electron mass. When no gradients in temperature, potential, concentration, and so on are present, the conduction electrons will move in random directions in the crystal. The average time that an electron travels between scattering events is the mean free time, Tm. Carrier scattering can arise from the collisions with the crystal lattice, impurities, or other electrons. However, during this random walk, the thermal motion is completely random, and these scattering processes will therefore produce no net motion of charge carriers on a macroscopic scale. 

This always holds when the semiconductor is clean, without any added impurities. Such semiconductors are called intrinsic. The balance (4.126) can be changed by adding impurities that can selectively ionize to release electrons into the conduction band or holes into the valence band. Consider, for example, an arsenic impurity (with five valence electrons) in gennanium (four valence electrons). The arsenic impurity acts as an electron donor and tends to release an electron into the system conduction band. Similarly, a gallium impurity (three valence electrons) acts as an acceptor, and tends to take an electron out of the valence band. The overall system remains neutral, however now n p and the difference is balanced by the immobile ionized impurity centers that are randomly distributed in the system. We refer to the resulting systems as doped or extrinsic semiconductors and to the added impurities as dopants. Extrinsic semiconductors with excess electrons are called n-type. In these systems the negatively charged electrons constitute the majority carrier. Semiconductors in which holes are the majority carriers are calledp-type. 

However, in most experimental systems, the manifestations of the polaronic character of the charge carriers are masked by the effects of disorder. In any solution-deposited thin him, disorder is present and causes the energy of a polaronic charge carrier on a particular site to vary across the polymer network. Variations of the local conformation of the polymer backbone, presence of chemical impurities or structural defects of the polymer backbone, or dipolar disorder due to random orientation of polar groups of the polymer semiconductor or the gate dielectric result in a signihcant broadening of the electronic density of states. 

Figure 8 A schematic representation of the motion of charge carriers in a semiconductor iattice. (a) A charge carrier in the absence of any externai fieid. The thermai motion is random, and will not iead to any motion of the charge carrier on a macroscopic level, (b) A charge carrier in the presence of an electric field. The charge carrier motion due to the electric field is imposed upon its thermal motion, (c) The carrier drift shown at the macroscopic level. The random thermal motion of the charge carrier again leads to no motion on the macroscopic level. The charge carriers are propelled by the electric field at a constant velocity, Vd, either parallel or antiparallel to the applied field...

When electrons move toward the interface, lattice sites from where electrons are originated become positively charged (Fig. 4b). Creation of positively charged carriers occurs randomly in the semiconductor (shown by a curved vertical line in Fig. 4b), but are situated not very far from the interface. Any mathematical treatment for such random distribution or even approximated exponential distribution of charged ions becomes a complicated system to deal with. 

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