Summary
The electrical impedance of a semiconductor supporting two waves contains an entire transcendental function of the form f(z)=exp(−z)−1−cz, wherec is a complex parameter. This function has an infinity of zeros in the left half z-plane when c is finite (0<¦c¦<+∞). Several approximate expressions for the location of zeros as function of c are obtained. For certain values of c (cf. Fig. 3) one or several zeros are located in the right half z-plane. The real part of some of those exceeds an arbitrarily large positive number, provided c is properly chosen. This corresponds to resonances which represent growing oscillations.
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References
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Falnes, J. Complex zeros of a transcendental impedance function. J Eng Math 2, 389–401 (1968). https://doi.org/10.1007/BF01579580
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DOI: https://doi.org/10.1007/BF01579580