Schottky model

Table 11-2 shows the built-in potential in metal/MEH-PPV/metal structures measured by either electroabsorption [15] or photocurrenl techniques [37] for a variety of contact metals. The uncertainty in both the work function differences and the built-in potential measurements is about 0.1 eV. For all of the structures except the Pt-Ca and Al-Sm devices there is good agreement between the metal work function difference, AW, and the built-in potential, Vhi. This indicates that for a wide range of metal contacts the Schottky energy barrier between the metal and MEH-PPV is well approximated by the ideal Schottky model and that state chaiging, which pins the Schottky energy barrier, is not significant. A built-in potential smaller than the difference between the contact work functions implies that... 

Surface states, then, are states in or near the surface of semiconductors that can be occupied by electrons or holes. They are always discussed as existing energetically in the energy gap they are most noticeable here because in the first approximation of the Schottky model, there should be no states for electrons at all in this energy region. 

Field emission is characterized by its temperature independence. Here meff is the effective mass of the carrier in the dielectric. The essential assumption of the Schottky model is that a carrier can gain sufficient thermal energy to cross the barrier that results from superposition of the external field and image charge potential. Neither tunnelling nor inelastic carrier scattering is taken into account. The following current characteristic is predicted for the Schottky junction ... 

The clearest test of the Schottky model is the comparison of the barrier heights for metals of diflerent work function. Fig. 9.6 shows this dependence for a variety of metals (Wronski and Carlson 1977). The values are such that most metals form a barrier for electrons to undoped a-Si H. There are a few metals with low work functions such as samarium and ytterbium, which are blocking for holes and should give an ohmic contact for electrons (Greeb, Fuhs, Mell and Welsch... 

In the prior studies, contact resistance was estimated by measurements of two-probe OFETs and fitting the data with the Schottky model at different T and... 

Fig. 13. ER spectra generated theoretically for the Ex and E1 + A, transitions of p-GaP (Nk = 1018 cm 3) assuming (a) that the depletion layer can be modelled as a single slab of thickness IF in which the electric field is fixed at a constant value corresponding to half that calculated at the surface using the classical Schottky model and (b) that the depletion layer can be modelled by dividing the depletion layer into twelve slabs within each of which the electric field is fixed at the value obtained from the Schottky model for the mid-point of the slab.

However, experimental ]V curves often deviate from the ideal /scl- In these cases, the measured current /inj is injection limited caused by a nonohmic contact or poor surface morphology. When the MO interface is nonohmic, carrier injection can be described by the Richardson-Schottky model of thermionic emission the carriers are injected into organic solid only when they acquire sufficient thermal energy to overcome the Schottky barrier ((()), which is related to the organic ionization potential (/p), the electron affinity (AJ, the metal work function (O, ), and the vacuum level shift (A) [34,35]. Thus, the carrier injection efficiency (rj) can be calculated by the following equation ... 

The shortcoming of the Schottky model in many real heterojunctions between metals and semiconductors lies in the fact that it ignores the role of dipoles and of interface states at these junctions. The latter are, instead, central to the Bardeen model. 

Metal/polymer interfaces which do follow the Schottky model theory, and PLEDs, for which Equation 19.12a is valid, have been often observed in experiments where deposition and test conditions were carefully controlled [4,6,8,73,74,77,78]. 

The measured values of Vbi were compared against those calculated from the difference between the work functions to which Vbi would be equal to in the Schottky model according to the following equation ... 

Impedance spectroscopic investigations on PPV-based LEDs are reported in the literature by several groups with different results and interpretations. Impedance spectra on ITO/PPV/Al devices were described by two semicircles within a Schottky model representing bulk and junction region [122] or by the presence of an interfacial oxide layer at the PPV/Al contact [123]. Equivalent circuits using three RC elements suggested a spatial variation of the conductivity in the PPV film [124]. A more complex equivalent circuit was proposed by analyzing the Poisson s and the hole and electron continuity equations [125]. 

Mott-Schottky model, with a modification to include an impurity gradient near the layer interface. 

---