Schottky effect

Other types oflow-lying energy levels can also lead to Schottky effects. For example, rotational energy levels can give rise to a Schottky effect. We will limit our discussion here to electronic levels. 

Schottky effect in solids 580-5 Second law of thermodynamics 56-90 absolute temperature, identification of as integrating factor 71-8 Caratheodory principles differentials 63-7 and inaccessible states 68-71... 

Einstein heat capacity equation 569-72 Schottky effect 580—5 solid + solid phase transitions 399-404 first-order 402-4 solutes 6... 

Debye heat capacity equation 572-80 Einstein heat capacity equation 569-72 heat capacity from low-lying electronic levels 580-5 Schottky effect 580-5 statistical weight factors in energy levels of ideal gas molecule 513 Stirling s approximation 514, 615-16 Streett, W. B. 412... 

As we can see from Fig. 3.9, the magnitude of the Schottky effect may be several orders greater than that due to lattice and electronic contributions even at liquid helium temperatures. 

Schottky diodes Schottky contact Schottky effect Schottky barrier Schwabe, Kurt... 

Schottky anomaly is determined from the difference between an RY compound and LaX or LuX compound. Then the crystal field parameters are deduced from the Schottky anomaly data. The accuracy of the method is limited by spin-phonon interactions and exchange effects in rare earth ions which affect the Schottky effect, ft is used to find crystal field parameters, W, x which fit the specific heat data as shown in Fig. 8.4. The figure refers to a plot of C/Rq vs. T for TmAF [19]. 

Thermionic Emission Sommerfeid Formula and Schottky Effect... 

The thermionic current grows with electric field until the negative space charge near the cathode is eliminated and saturation is achieved. This saturation, however, is rather relative. A further increase of electric field leads gradually to an increase of the saturation current level, which is related to a reduction of work function due to an electric field known as the Schottky effect ... 

This decrease of work function W is relatively small at reasonable values of electric field E. The Schottky effect can result, however, in essential change of the thermionic current because of its strong exponential dependence on the work function in accordance with the Sommerfeld formula (2-100). Dependence of the Schottky W decrease and thermionic emission current density on electric field are illustrated in Table 2-12 together with corresponding data on field and thermionic field emission (Raizer, 1997). The 4x change of electric field results in 800 x increase of the thermionic current density. 

Figure 2-15. Schottky effect in thermionic and field emission.

Because thermionic emission is based on the synergistic effect of temperature and electric field, these two key parameters of electron emission can be just reasonably high enough to provide a significant emission current. Results of calculations of the thermionic field emission are also presented in Table 2-12. The thermionic field emission dominates over other mechanisms at T = 3000 K and > 8 10 V/cm. We should note that at high temperatures but lower electric fields < 5- 10 V/cm, electrons of the third group usually dominate the emission. The Sommerfeld relation in this case includes the work function diminished by the Schottky effect. 

To determine the height of the barrier in an applied electric field F 0, we must take into account the so-called Schottky effect (Fig. 8.23) an injected electron at a distance x from the metal surface produces a positive image charge in the metal through influence, whose field gives rise to what is termed the image force and... 

A thermaUy-emitted electron must reach at least this distance in order that it is not able to recombine. At a typical applied-field strength of F = 1 MV/cm and e = 4, we have A<1> = 0.19 eV and = 9.5 A. The Schottky effect thus makes a non-neghgible... 

The current density jj s for this process, which at high temperatures is also called glow emission, was originally calculated by Richardson for glow cathodes in vacuum valves and, taking the Schottky effect into account, is given by ... 

Schottky effect A reduction in the work function of a substance when an external accelerating electric field is applied to its surface in a vacuum. The field reduces the potential energy of electrons outside the substance, distorting the potential barrier at the surface and causing field emisslorL A similar effect occurs when a metal surface is in contact with a semiconductor rather than a vacuum, when It Is known as a Schottky barrier. The effect was discovered by the German physicist Walter Schottky (1886-1976). 

Simmons, J.G. 1967. Pool-Frenkel effect and Schottky effect in metal-insulator-metal systems. Phys Rev Lett 155 657. 

Rikken, G.L.J.A., D. Braun, E.G.J. Staring, and R. Demandt. 1994. Schottky effect at a metal-polymer interface. Appl Phys Lett 65 219-221. 

Is the observed effect of decreasing analogous to a Schottky effect in the heat capacity ... 

Is the effect of resonant phonon scattering by paramagnetic impurities on an analogue of the Schottky effect in the heat capacity Let us compare the temperature dependences of Csch md — AK e, in crystals (PrS) and glasses (Pr2S3(Ga203)2). 

The effect of — Ak s and the Schottky-effect differ in sign Kl decreases, whereas C increases (fig. 88). 

Up to now we have discussed the influence of the crystal field eflect on (due to phonon resonance scattering by the rare earth ions) and the heat capacity (Schottky effect). It is known that the crystal field can significantly influence the behaviour of the elastic constants (Luthi et al. 1973), the thermal expansion coefficient (Ott and Liithi 1976), the magnetostriction and thermoemf (Sierro et al. 1975), the electrical conductivity (Liithi et al. 1973, Friederich and Fert 1974, Andersen et al. 1974) and the electron part of the thermal conductivity (Smirnov and Tamarchenko 1977, Wong 1978, Matz et al. 1982, Muller et al. 1982). 

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