The Schottky barrier height

Assuming that the band-bending and the interfadal charge transfer are negligible, Schottky (1939) wrote Ob as the difference between the metal 

Subsequently, a number of experiments have proved that Ob is not given by Schottky s equation, and that it does not depend upon the metal properties. Such a result may be found if the Fermi level is pinned by a surface state band (Bardeen, 1947), in which case Ob is equal to the energy difference between the bottom of the conduction band and the surface state. The same is true in the presence of defect states or of high MIGS densities, such as those seen at the interfaces between metals and covalent semi-conductors (Rhoderick, 1978 Schluter, 1982 Brillson, 1982 Flores and Tejedor, 1987). 

The analytical approach developed above yields an expression of Ob as a function of the MIGS density, which is valid whatever the ionicity of the insulator  

In this limit, Ob depends only upon the insulator characteristics, because the Fermi level is pinned at the zero-charge point Ezcf- This is similar to Bardeen s result, although the nature of the states which pin the Fermi 

The most general expression of valid in the whole ionicity range, is obtained by combining (5.5.6) for the interfacial potential with the definition (5.5.8) of 4 b  

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The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

Fig. 4.1. Example energy band diagrams for a semiconductor/metal contact and and a semiconductor p/n-heterocontact. The Schottky barrier height for electrons B,n is given by the energy difference of the conduction band minimum Ecb and the Fermi energy Ey. The valence and conduction band offsets A/ An and AEcb are given by the discontinuities in the valence band maximum Eyb and the conduction band minimum, respectively...

Very little work has been performed on Schottky barrier contacts to the other III-N semiconductors, although a strong dependence of the Schottky barrier height of metal contacts to AIN on the electronegativity of the metal was reported in 1969 [35],... 

Fig. 9.6. Measurements of the Schottky barrier height versus metal work function for various metal contacts to a-Si H and crystalline silicon. The dashed line shows the relation for an ideal Schottky contact (Wronski and Carlson 1977).

It is well known that the existence of an insulating layer may have a strong Influence on the diode characteristics and on the determination of the Schottky barrier height, and may give rise to an interface state charge with bias owing to an additional field in the oxide layer. 

As a consequence of Fermi level pinning, the Schottky barrier height < ) =... 

In eq. (3), for simplicity, we shall assume that the pair potential, zl, equals to the energy gap of the superconductor, F is the Schottky barrier height, is the semiconductor doping density, s is the permittivity of the semiconductor. Now, by substituting eq.(3) into eq.(2) and integrating we get... 

The Schottky barrier height can be calculated if the thermionic emission model is regarded as valid ... 

The initial increase in the sensitivity is due to the reduction in the Schottky barrier height. 

In N-polar GaN Schottky diodes, because of the higher surface reactivity with hydrogen inducing higher polarity, the Schottky barrier heights are reduced much more than those of Ga-polar Schottky diodes. Therefore, the N-polar GaN Schottky diodes have much higher sensitivity than Ga-polar GaN. 

Nowadays, a consensus has been reached in the sense that both virtual gap states and defects are needed to explain the complete set of experimental data on real interfaces. Only when the experimental conditions can be controlled to reduce the defect density to below lO cm , the Schottky barrier height is determined by the virtual gap states. In highly defective interfaces, defect states play a role in the control of the barrier height [87M6n, 90M6n]. 

Similarly, the Schottky barrier height for holes is the difference between the valence band maximum of the semiconductor and the metal Fermi level, measured with respect to... 

In this section, three major theories explaining how the electronic bands of semiconductors and metals align after contact will be outlined. These are the Schottky, Bardeen, and Tersoff theories. These models are employed to predict the Schottky barrier height at the metal/semiconductor junction. Comprehensive reviews on the general issue of heterojunctions, which also include other lineup theories, can be found in [47-50,52,53],... 

One of the earliest models for the metal/semiconductor contact is due to Schottky. Here the reference level, is the vacuum level vac at the solid s surface. This is a valid approximation if one neglects dipole layers and charged interface states. In this case, the Schottky barrier height for electrons is given by (Figure 19.2a) ... 

Similarly, in a metal/semiconductor junction, in which the metal work function lies between the valence band maximum and the conduction band minimum, the tails of the metallic wave function decrease exponentially in the adjacent semiconductor gap states, inducing transfer of charge, which in turn creates the dipole. The mismatch between the metal Fermi level and E is reduced by this dipole (by a factor inversely proportional to the semiconductor s optical dielectric constant, s o, in first approximation [51]). Only in the case of semiconductors with a large optical dielectric constant or high density of interface states is the Fermi level almost completely pinned at E- In this case, since E is an intrinsic property of the semiconductor, the Schottky barrier height of a particular semiconductor is independent of the metal (and its work function) utilized as contact. In order to define the CNL, one... 

Heteroepitaxial growth leads to buried interfaces with very important structural properties that determine, e.g., the Schottky barrier heights in the case of metal-semiconductor junctions. With the improved depth resolutions of the detection systems, structural studies by ion scattering of such interfaces are becoming increasingly feasible. 

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