Despite being well documented, nonlinearity—its theory and applications—is often viewed as a novelty or strange anomaly. Here, we’ll argue the opposite point of view. Nonlinear and negative resistances may simply be misunderstood, and the standardization of terms and performance claims would further advance their common understanding (see Beyond Ohm’s Law).
This article particularly emphasizes the materials used to fabricate working nonlinear components. The list of materials that may result in non-ohmic behavior is lengthy:
• Simple compounds
• Multi-material composites
• Multilayer structures and junctions
• Germanium (Ge), silicon (Si), and group III-V semiconductors
• Group VI elements (chalcogenides)
• Transition metals
• Organics (carbon-based)
• Organo-metallics
Now, as advances in materials research open the door to new device fabrication techniques, customized performance for the desired application is possible. If silicon does reach its ultimate size limitations at the end of the Moore’s Law curve, nonlinear materials may offer another path to the next generation of electronic devices. In fact, there has been increased observation of nonlinear behavior in the shrinking world of nano-structures and molecular electronics.
COMING TO NONLINEAR TERMS
Negative but linear: The current-voltage (I-V) response of a linear theoretical resistance element may have either positive or negative slope. Furthermore, resistance can be time-invariant or time-variant. For this article, time invariance is assumed.
Linear resistance may have either an ohmic positive I-V slope or a negative slope. A typical, lossy resistor is by definition the ratio of voltage over current (R = E/I, according to Ohm’s Law). Conversely, an op-amp circuit can synthesize a negative resistance through positive feedback. The representation for negative resistance is simply –R. In this case, a linear but negative or decreasing slope appears in the I-V curve, rather than the positive or increasing slope of a lossy resistor.
Interestingly, The Illustrated Dictionary Of Electronics, 7th Edition (McGraw-Hill, 1997) defines “ohmic contact” as one that exhibits none of the properties of a rectifying junction or nonlinear resistance. In other words, ohmic can be defined as the absence of nonlinearity.
“Ohmic region” is defined as the portion of the response curve of a negative-resistance device that exhibits positive (ohmic) resistance. One type of nonlinear current-voltage curve is commonly called a voltage-controlled “N” shaped curve (Fig. 1a). A complementary type of relationship is the current-controlled “S” curve (Fig. 1b). Yet another variation of the S-shape is its mirror image or “Z” curve (Fig. 1c). Subsequent sections of this article will refer to these basic qualitative curves.
The curve in Figure 1a is typical for tunnel diodes. Other familiar forms of negative-resistance devices include the backward diode, Gunn diode, IMPATT diode, and neon lamp. We will not discuss temperature-dependent resistors, or thermistors, which generally remain ohmic at a given temperature.
The schematic symbol for a linear resistor (Fig. 2a) is universally known. Found less often is the symbol for a nonlinear resistor (Fig. 2b), likely because no device manufacturer makes anything called a nonlinear resistor. Figure 2c shows the symbol for tunnel diodes; more about them shortly.
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