Lesson plan
Quantum capacitance
Quantum capacitance, also known as chemical capacitance is defined as the variation of electrical charge q with respect to the variation of internal chemical potential \mu , i.e., C_{q} = \frac{dq}{d\mu} . It was first introduced theoretically by Serge Luryi (1988). In the simplest example, if a parallel-plate capacitor is made so that one or both of the plates has a low density of states, then the capacitance is not given by the normal formula for parallel-plate capacitors, C_e . Instead, the capacitance is lower, as if there was another capacitor in series, C_q . This second capacitance, related to the density of states of the plates, is the quantum capacitance and is represented by C_q . The combination of regular geometric capacitance with chemical/quantum capacitance is called electrochemical capacitance \frac{1}{C_{\bar{\mu}}} = \frac{1}{C_e} + \frac{1}{C_q} . Quantum capacitance is especially important for low-density-of-states systems, such as a 2-dimensional electronic system in a semiconductor surface or interface or graphene, and can be used to construct an experimental energy functional of electron density.
Article summary
Quantum capacitance, also known as chemical capacitance is defined as the variation of electrical charge q with respect to the variation of internal chemical potential \mu , i.e., C_{q} = \frac{dq}{d\mu} . It was first introduced theoretically by Serge Luryi (1988). In the simplest example, if a parallel-plate capacitor is made so that one or both of the plates has a low density of states, then the capacitance is not given by the normal formula for parallel-plate capacitors, C_e . Instead, the capacitance is lower, as if there was another capacitor in series, C_q . This second capacitance, related to the density of states of the plates, is the quantum capacitance and is represented by C_q . The combination of regular geometric capacitance with chemical/quantum capacitance is called electrochemical capacitance \frac{1}{C_{\bar{\mu}}} = \frac{1}{C_e} + \frac{1}{C_q} . Quantum capacitance is especially important for low-density-of-states systems, such as a 2-dimensional electronic system in a semiconductor surface or interface or graphene, and can be used to construct an experimental energy functional of electron density.
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Discussion questions
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