Physics of WF Modulation

Field-effect transistors (Appendix C) are miniature cousins of the Kelvin probe. The most common is the insulated gate field-effect transistor. The heart of the insulated gate field-effect transistor is the Metal-Insulator-Semiconductor (MIS) capacitor. Let us form this capacitor from palladium (to be modulated by hydrogen), silicon dioxide (insulator), and p-type silicon (semiconductor), and examine the energy levels in this structure (Fig. 6.32). 

In a Thought Experiment, the junction is disassembled (Fig. 6.32) by division through the insulator and the two halves are first treated as electrically isolated objects. In the ensuing equations, we use the common symbol / for the work function of a material. There are three electron work functions to be considered that of palladium 0pd, that of an arbitrary metal which does not interact with hydrogen 0m, and that of silicon 0su The insulator is considered to be ideal which means that it does not contain mobile charges. Therefore, it does not have a defined Fermi level. Because the two halves are not connected, their energy levels are in an arbitrary undefined position with respect to each other. On the other hand, metal M and palladium (as well as the M and silicon) form ohmic junctions, meaning that the 

Fermi levels in those materials must be equal and the contact potentials appear at their interfaces. 

Now we see that the vacuum levels above the same metal M are not equal. The resulting difference is the flatband voltage Vfb which must be externally applied in order to maintain the flatband condition. Thus, the flatband voltage (multiplied by the test charge) equals the difference in the electron work function of Pd and Si. In the nonideal junctions there are other charges and dipoles in this structure that must be added to the overall Vfb. 

Let us pause and take an inventory of the situation up to this point. (1) We have a plausible mechanism of modulation of both components of WF of a selective layer (palladium) and (2) we have at least two methods of measurement of this effect, the macroscopic Kelvin probe and a field-effect transistor. However, the placement of the selective layer within the structure used for either measurement determines whether the effect is observable. In order to explain this caveat, we add another layer of the same metal M between Pd and the insulator in the structure shown in Fig. 6.33. This would correspond to the real life situation when we would try to connect a selective layer by a wire to the IGFET or a Kelvin Probe. It is not necessary to perform the same cycle as we did in Fig. 6.33. Instead, we add the individual energy contributions in the cycle, which begins and ends at the silicon Fermi level (moving again anticlockwise)  

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