Mobility in semiconductors

A. Miller, Transient Grating Studies of Carrier Diffusion and Mobility in Semiconductors... 

Evaluation of Charge Transport and Ion Mobility in Semiconductors, Organic Crystais, Poiymer Composites and Polymer Electrolytes (Nad et al. 2000 Karlinsey et al. 2004 Baskaran et al. 2004)... 

The great interest at present being shown in MBE can be ascribed to the control of composition and crystalline perfection which it permits, together with the excellent carrier mobilities in semiconductors amenable to the technique. The LB technique, too, can be used to fabricate semiconductors Lieser, Tieke, Wegner,... 

The electrons have low mobility in semiconductors. Consequently, there is no transfer of electrons and the link between the molecule and surface on a semiconductor is local. Moreover, the electronic structure of a semiconductor is unlike and so more complicated to explain the adsorption phenomena [1]. 

The vacancy is very mobile in many semiconductors. In Si, its activation energy for diffusion ranges from 0.18 to 0.45 eV depending on its charge state, that is, on the position of the Fenni level. Wlrile the equilibrium concentration of vacancies is rather low, many processing steps inject vacancies into the bulk ion implantation, electron irradiation, etching, the deposition of some thin films on the surface, such as Al contacts or nitride layers etc. Such non-equilibrium situations can greatly affect the mobility of impurities as vacancies flood the sample and trap interstitials. 

In perfect semiconductors, there are no mobile charges at low temperatures. Temperatures or photon energies high enough to excite electrons across the band gap, leaving mobile holes in the Fermi distribution, produce plasmas in semiconductors. Thermal or photoexcitation produces equal... 

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. 

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. 

The data indicate that elastic shock-compression resistance measurements can provide data on the effects of strain on energy gaps and deformation potentials in semiconductors. Drift mobility measurements on holes in germanium and resistivity measurements on samples with different dopings would appear to be of considerable interest. 

Microwave Hall experiments have been performed in our laboratory.16 They have shown that the mobility of charge carriers in semiconductors can be measured quite reliably even if the semiconductors are only available in the form of a powder. The measurement technique itself is relatively complicated and involves, for example, rectangular waveguides, which can be rotated against each other on opposite sides of the sample to monitor the phase rotation. In the two-mode resonator, two modes of... 

Zinc oxide is a thoroughly studied typical semiconductor of n-type with the width of forbidden band of 3.2 eV, dielectric constant being 10. Centers responsible for the dope electric conductivity in ZnO are provided by interstitial Zn atoms as well as by oxygen vacancies whose total concentration vary within limits 10 - 10 cm. Electron mobility in monocrystals of ZnO at ambient temperature amounts to 200 cm -s". The depth of donor levels corresponding to interstitial Zn and oxygen vacancies under the bottom of conductivity band is several hundredth of electron volt [18]. 

Note that the above model is for a simple system in which there is only one defect and one type of mobile charge carrier. In semiconductors both holes and electrons contribute to the conductivity. In materials where this analysis applies, both holes and electrons contribute to the value of the Seebeck coefficient. If there are equal numbers of mobile electrons and holes, the value of the Seebeck coefficient will be zero (or close to it). Derivation of formulas for the Seebeck coefficient for band theory semiconductors such as Si and Ge, or metals, takes us beyond the scope of this book. 

Electron mobility, in direct gap semiconductors, 22 143-144 Electron paramagnetic resonance (epr), 17 418... 

The existence of two types of mobile charge carriers in semiconductors enables us to distinguish between a majority charge carrier transferred from the electrode into the electrolyte and a minority charge carrier injected from the electrolyte into the electrode. Minority carrier injection causes significant reverse currents, but may also contribute to the total current under forward conditions. 

It should also be briefly recalled that semiconductors can be added to nanocarbons in different ways, such as using sol-gel, hydrothermal, solvothermal and other methods (see Chapter 5). These procedures lead to different sizes and shapes in semiconductor particles resulting in different types of nanocarbon-semiconductor interactions which may significantly influence the electron-transfer charge carrier mobility, and interface states. The latter play a relevant role in introducing radiative paths (carrier-trapped-centers and electron-hole recombination centers), but also in strain-induced band gap modification [72]. These are aspects scarcely studied, particularly in relation to nanocarbon-semiconductor (Ti02) hybrids, but which are a critical element for their rational design. 

Both electrons and holes are mobile charge carriers in semiconductors. The mobile charge carrier whose concentration is much greater than the other is called the majority carrier, and the minority carrier is in much smaller concentrations. In n-type semiconductors, the mcgority carriers are electrons in the conduction band and the minority carriers are holes in the valence band. The product of the concentrations of majority and minority carriers (electrons and holes) in a semiconductor of extrinsic type (containing impurities) equals the square of the concentration of electron-hole pairs, ni, in the same semiconductor of intrinsic type (containing no impurities) ... 

In the case of aqueous solutions containing dissolved particles (solutes), a number of localized electron levels associated with solute particles Eirise in the mobility gap of aqueous solutions as shown in Fig. 2-34. These localized electron levels of solutes may be compared with the localized impiuity levels in semiconductors. In electrochemistry, the electron levels of the solutes of general interest are those located within the energy range from - 4 eV to - 6 eV (around the electron levels of the hydrogen and oxygen electrode reactions) in the mobility gap. 

Superlattices result from the periodic infinite repetition of heterostructures. MBE-grown superlattices of III-V semiconductors exhibit sharp interfaces and high carrier mobilities of the resulting 2D carrier gas at low temperature (Ando et al, 1982). To date no superconductivity has been found for such engineered solids, although some expectations were raised in 2000 after some reports on the obten-tion of superconductivity in semiconductor/insulator interfaces by field-induced... 

Klenkler RA, Xu G, Aziz H, Popovic ZD (2006) Charge-carrier mobility in an organic semiconductor thin film measured by photoinduced electroluminescence. Appl Phys Lett 88 242101... 

Arkhipov VI, Emelianova EV, Heremans P, Bassler H (2005) Analytic model of carrier mobility in doped disordered organic semiconductors. Phys Rev B 72 235202... 

Sakanoue T, Sirringhaus H (2010) Band-like temperature dependence of mobility in a solution-processed organic semiconductor. Nat Mater 9 736... 

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