Near-Field Thermal Transistor

Using a block of three separated solid elements, a thermal source and drain together with a gate made of an insulator-metal transition material exchanging near-field thermal radiation, we introduce a nanoscale analog of a field-effect transistor that is able to control the flow of heat exchanged by evanescent thermal photons between two bodies. By changing the gate temperature around its critical value, the heat flux exchanged between the hot body (source) and the cold body (drain) can be reversibly switched, amplified, and modulated by a tiny action on the gate. Such a device could find important applications in the domain of nanoscale thermal management and it opens up new perspectives concerning the development of contactless thermal circuits intended for information processing using the photon current rather than the electric current.

Figure 1

Electric and radiative thermal transistor. Classical field-effect transistor (a). A three-terminal device known as source, gate, and drain, which corresponds to the emitter, base, and collector of electrons. The gate is used to actively control, by applying a potential on it, the apparent conductivity of the channel between the source and the drain. Radiative thermal transistor (b). A layer of IMT material (the gate) is placed at subwavelength distances from two thermal reservoirs (the source and the drain). The temperatures $T_S$ and $T_D$ are fixed so that $T_S>T_D$. The temperature $T_G$ of the gate can be modulated from the external environment around its steady-state temperature $T_G^{\mathrm{eq}}$ (which corresponds to the situation where the net flux ${\mathrm{\Phi }}_G$ received by the gate vanishes) so that the flux ${\mathrm{\Phi }}_D$ received by the drain and lost by the source ${\mathrm{\Phi }}_S$ can be tuned. When $T_G^{\mathrm{eq}}$ is a little bit smaller than the critical temperature $T_c$ of IMT material, a small amount of heat applied on the gate induces a strong switching of heat fluxes ${\mathrm{\Phi }}_D$ and ${\mathrm{\Phi }}_S$ owing to its metal-insulator phase transition.

Figure 2

Transmission probabilities of energy carried by the modes. Efficiency of coupling of modes ($\omega$, $\mathit{\kappa }$) in a ${\mathrm{SiO}}_2\text{−}{\mathrm{VO}}_2\text{−}{\mathrm{SiO}}_2$ system ($\delta =50\mathrm{nm}$ and $d=100\mathrm{nm}$). (a) ${\mathcal{T}}_p^{S/G}$ and (b) ${\mathcal{T}}_p^{G/D}$ with ${\mathrm{VO}}_2$ in its crystalline state. (c) ${\mathcal{T}}_p^{S/G}$ and (d) ${\mathcal{T}}_p^{G/D}$ with ${\mathrm{VO}}_2$ in its amorphous state. Wien’s frequency (where the transfer is maximum) at $T=340\mathrm{K}$ is ${\omega }_{\mathrm{Wien}}\sim 1.3\times {10}^{14}\mathrm{rad}/\mathrm{s}$. The dielectric permittivity of ${\mathrm{SiO}}_2$ is taken from the database [19].

Figure 3

Operating regimes of near-field thermal transistor. When $T_G^{\text{eq}}$ is a little bit smaller than the critical temperature $T_c$ of the IMT material, a small amount of heat applied on the gate induces a strong switching of heat fluxes ${\mathrm{\Phi }}_D$ and ${\mathrm{\Phi }}_S$ owing to its phase transition. By changing the flux ${\mathrm{\Phi }}_G$ supplied to the gate, different functions (thermal switching, thermal modulation, and thermal amplification) can be performed. The fluxes plotted here correspond to a gate of ${\mathrm{VO}}_2$ [8] with thickness $\delta =50\mathrm{nm}$ located at a distance $d=100\mathrm{nm}$ from two massive silica samples [19] maintained at $T_S=360\mathrm{K}$ and $T_D=300\mathrm{K}$.

Figure 4

Amplification factor $\alpha$ of the NFTT. When $T_G\ll T_c$ or $T_G\gg T_c$ the slopes of ${\mathrm{\Phi }}_S$ and ${\mathrm{\Phi }}_D$ are almost identical (modulo the sign) so that $\alpha \approx 1/2$. On the contrary, in the close neighborhood of $T_c$, we have $\alpha >1$, owing to the negative differential thermal resistance in the transition region. Here, the parameters of the NFTT are the same as in Fig. 3. (EMT, effective medium theory; BM, Bruggeman mixing rule.).