Signatures of dynamic screening in interfacial thermal transport of graphene

The interaction between graphene and various substrates plays an important and limiting role on the behavior of graphene films and devices. Here we uncover that dynamic screening of so-called remote substrate phonons (RPs) has a significant effect on the thermal coupling at the graphene-substrate interface. We calculate the thermal conductance $h_{\text{RP}}$ between graphene electrons and substrate, and its dependence on carrier density and temperature for SiO${}_2$, HfO${}_2$, h-BN, and Al${}_2$O${}_3$ substrates. The dynamic screening of RPs leads to one order of magnitude or more decrease in $h_{\text{RP}}$ and a change in its dependence on carrier density. Dynamic screening predicts a decrease of $\sim$1 MW K${}^{-1}$ m${}^{-2}$ while static screening predicts a rise of $\sim$10 MW K${}^{-1}$ m${}^{-2}$ when the carrier density in Al${}_2$O${}_3$-supported graphene is increased from 10${}^{12}$ to 10${}^{13}$ cm${}^{-2}$.

Figure 1

(a) Dispersion of the graphene electron (dotted line), plasmon (dashed lines), IPP (solid lines), and SPP branches (dashed lines) in the graphene-SiO${}_2$ system at $n={10}^{12}$ cm${}^{-2}$. The vertical dashed line represents the Landau damping cutoff $q_c$. (b) Corresponding plot of $M_{\mathbf{q}}^{\gamma }{(\Omega /A)}^{1/2}$ vs $q$ for interfacial plasmon-phonons (IPP${}_1$, IPP${}_2$, and IPP${}_3$), unscreened surface polar phonons (u-SPP${}_1$ and u-SPP${}_2$) and surface polar phonons with static screening (s-SPP${}_1$ and s-SPP${}_2$).

Figure 2

Calculated thermal conductance ($h_{\text{u-SPP}}$) between electrons in SLG and unscreened SPPs of various substrates: (a) SiO${}_2$, (b) HfO${}_2$, (c) h-BN, and (d) Al${}_2$O${}_3$ over the range $n={10}^{12}$ to ${10}^{13}$ cm${}^{-2}$ from 50 to 400 K.

Figure 3

Calculated thermal conductance ($h_{\text{s-SPP}}$) between electrons in SLG and substrate SPPs with static screening. (a) SiO${}_2$, (b) HfO${}_2$, (c) h-BN, and (d) Al${}_2$O${}_3$ over the range $n={10}^{12}$ to ${10}^{13}$ cm${}^{-2}$ from 50 to 400 K. Note approximately an order of magnitude lower thermal coupling compared to the unscreened results from Fig. 2.

Figure 4

Calculated thermal conductance ($h_{\mathrm{IPP}}$) between electrons in SLG and interfacial plasmon phonons (IPPs, i.e., dynamically screened SPPs) with various substrates: (a) SiO${}_2$, (b) HfO${}_2$, (c) h-BN, and (d) Al${}_2$O${}_3$ over the range $n={10}^{12}$ to ${10}^{13}$ cm${}^{-2}$ from 50 to 400 K. Note the opposite dependence on carrier density from that of Fig. 2 (unscreened SPPs) and Fig. 3 (statically screened SPPs)

Figure 5

Comparison of the three different models of thermal coupling (hRP) between graphene electrons and remote substrate phonons considered in this paper, over the range $n={10}^{12}$ to ${10}^{13}$ cm${}^{-2}$ at 300 K. (a) $h_{\text{IPP}}$ for interfacial plasmon phonons, (b) $h_{\text{s-SPP}}$ for statically screened SPPs, and (c) $h_{\text{u-SPP}}$ for unscreened SPPs. The four plotted sets correspond to SiO${}_2$, HfO${}_2$, h-BN, and Al${}_2$O${}_3$ substrates. Note the different $y$-axis scales.