Geometry of the problem. N-layer graphene with thickness h on a ferroelectric substrate of thickness L clamped to a gate wafer (thermostat).
Pyroelectric mechanism of the carrier density high-frequency modulation in graphene. Free charges , located at graphene-ferroelectric interface, follow the high-frequency temperature variation due to the pyroelectric effect in the single-domain ferroelectric at the given moment of time (a) and (b). Spontaneous polarization is . Electrostatic charges are sluggish and cannot screen the high-frequency pyroelectric field. (c) Domain structure appearance in a ferroelectric substrate leads to the in-plane carrier density modulation.
Finite-size effect of carrier density modulation in multi-layer graphene. Dependence of the concentration variation absolute value ((a) and (c)) and phase ((b) and (d)) on graphene thickness calculated for dimensionless frequency ωτ from 0.1 to 10 (as listed near the curves), interfacial resistance 10−8 K m2/W ((a) and (b)) and 0 ((c) and (d)), Curves are calculated for parameters = 0.1, 0.1, 3 nm, 150 nm, W/(m·K), pyroelectric constant 306 μC/m2 K and electric field amplitude 5 × 104 V/m. Other parameters are listed in the Table S1. 41
Frequency spectrum of carrier density variation in multi-layer graphene. Dependence of the concentration variation absolute value ((a) and (c)) and phase ((b) and (d)) on dimensionless frequency ωτ calculated for graphene thickness from 5 to 50 (as listed near the curves), interfacial resistance 10−8 K m2/W ((a) and (b)) and 0 ((c) and (d)). Other parameters are the same as in Figure 3 .
Contour map of the concentration variation absolute value in coordinates graphene thickness -frequency ωτ. Interfacial resistance 10−8 K m2/W; other parameters are the same as in Figure 3 . Color bar indicate concentration variation in 1010cm(−2).
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