Nanoscale Heat Transport through Epitaxial Ultrathin Hetero Films: Bi(111)/Si(001) and Bi(111)/Si(111)
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Nanoscale Heat Transport through Epitaxial Ultrathin Hetero Films: Bi(111)/Si(001) and Bi(111)/Si(111) Anja Hanisch-Blicharski, Simone Wall, Annika Kalus, Tim Frigge and Michael Horn- von Hoegen Faculty of Physics and Center for Nanointegration Duisburg-Essen (CeNIDE), University of Duisburg-Essen, 47057 Duisburg, Germany ABSTRACT The cooling process of ultrathin hetero films upon excitation with short laser pulses was studied for epitaxial Bi(111) films on Si(001) and Si(111) substrates by means of the DebyeWaller effect with ultrafast electron diffraction. From the exponential decay of the temperature, a cooling time constant was determined as a function of thickness for both substrates. For Bi/Si(111), a linear dependence between the decay constant and thickness was observed, even for 2.8 nm thin films , as predicted from the diffuse mismatch model (DMM) and the acoustic mismatch model (AMM). However, with Bi/Si(001), a significant deviation from this linear dependence was observed for film thicknesses below 5 nm. INTRODUCTION The interface between two materials can be understood as a barrier for thermal heat transport. This interface between a film and an underlying substrate is characterized by a thermal boundary conductance σK, which was first described by Kapitza [1-3]. Experimentally, σK is determined from the cooling behavior of such a thin heterofilm upon excitation by ultrashort laser pulses [1-3]. With the equation: ∂T f (t ) (1) c⋅d = −σ K (T f (t ) − Ts (t )) , ∂t the temporal cooling of the film with the temperature Tf on a substrate with the temperature Ts is given by specific heat c and the thickness d of the film, the thermal boundary conductance σK and the temperature discontinuity at the interface [3]. In our experiments, the film was excited with fs-laser pulses, that led to a heating of the film. Assuming a constant substrate temperature, Eq. 1 can be solved with an exponential function with the decay constant [3, 4]: τ = c ⋅ d /σ K . (2) The assumption of a constant substrate temperature is justified for our model system of Bi on Si, because of a large absorption length of 13 µm for 1.55 eV photons and the high thermal conductivity of the silicon substrate in comparison to the Bi film [4]. This results in a linear dependence between the decay constant and the film thickness. Within the two well-accepted models for the calculation of the heat transport across a hetero interface – the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM) – the energy is carried by phonons [2,3]. The thermal boundary conductance σK calculated with the AMM is between 1,350 (W/cm2K) for 80 K and 1,450 (W/cm2K) for 300 K [5]. For the DMM we get values between 1,440 (W/cm2K) for 80 K and 1,560 (W/cm2K) for 300 K [5].
EXPERIMENT The preparation of the hetero films was performed under ultrahigh vacuum conditions of pbase < 3x10-10 mbar. The Bi films were prepared in-situ through Bi-deposition (99.9999%) from a Knudsen cell [6] onto Si(001) and Si(111) substrates using recipes described in Refs. 7-11. The
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