Carrier confinement and bond softening in photoexcited bismuth films

Abstract

Femtosecond pump-probe spectroscopy of bismuth thin films has revealed strong dependencies of reflectivity and phonon frequency on film thickness in the range of 25−40 nm. The reflectivity variations are ascribed to distinct electronic structures originating from strongly varying electronic temperatures and proximity of the film thickness to the optical penetration depth of visible light. The phonon frequency is redshifted by an amount that increases with decreasing film thickness under the same excitation fluence, indicating carrier density-dependent bond softening that increases due to suppressed diffusion of carriers away from the photoexcited region in thin films. The results have significant implications for nonthermal melting of bismuth as well as lattice heating due to inelastic electron-phonon scattering. [4,5]. A prototype sample has been crystalline bismuth [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], which shows strong oscillations in time-resolved reflectivity due to coherent oscillations of the A 1g optical phonon mode that are initiated upon excitation with a femtosecond laser pulse [9]. Measurements in bismuth motivated the development of the displacive excitation of coherent phonons (DECP) model of the lattice response to ultrafast optical absorption, in which sudden excitation of electrons from the valence to the conduction band leads to a nearly instantaneous alteration of the lattice potential energy surface. Hase et al. discovered that the frequency of the A 1g mode in bismuth is redshifted with increasing excitation fluence and is chirped, gradually increasing in frequency with time following excitation [12]. Murray and coworkers showed that the phonon frequency reduction is due to carrier density-dependent softening of the lattice potential, and that photocarrier relaxation dynamics are responsible for the vibrational frequency chirp [13]. More recently, Fritz et al. conducted density functional theory (DFT) calculations of the lattice potential, and results were consistent with bond softening as a function of carrier density [16]. The calculations further showed that increasing carrier density reduces the Peierls distortion continuously and removes the distortion completely at about 2.7% excitation of the valence electrons, indicating that bismuth may undergo a photoinduced structural phase transition to a higher symmetry phase. The experimental and theoretical results reveal that the lattice structure and interatomic forces are influenced heavily by the carrier density, which varies in space and time due to the short (15 nm) optical penetration depth into the sample and the dynamics of carrier diffusion and recombination. In this paper, we investigate the effect of carrier diffusion and spatial distribution on ultrafast bond softening in highly photoexcited bismuth. To this end, we performed transient reflectivity experiments on bulk and thin-film bismuth samples. The results show distinct changes in both the transient reflectivity sign and magnitude and in the coheren...

Real-Time Observation of a Coherent Lattice Transformation into a High-Symmetry Phase

“…4. The parameters used for the extended two-temperature model agree well with previous results at moderate excitation density 10,23,24,28 . We found that the maximum lattice temperature T max is reached 15 ps after excitation, and 90% of the lattice temperature jump is complete within 5 ps.…”

“…The parameters used in our model are summarized below. They agree roughly with the results of 28,31,32 15 W m -3 K -(1 27,28) Thermal Interface Conductivity C TI 1,950 W/cm 2 /K (23) Carrier Diffusion Constant D e 1,300 nm 2 /ps (31) Numerical solutions for the 20 nm and 275 nm films as a function of fluence for short and long timescales are shown below. Starting at 80 K, it takes 20 mJ/cm 2 for the 275 nm film to reach the melting point under this model, and over 50 mJ/cm 2 to reach the melting point plus the heat of fusion.…”

“…2c, open circles). As has been discussed earlier 23 , confinement of excited carriers in the thin film preserves a higher carrier density than in the thicker sample, in which fast carrier diffusion quickly reduces the photoexcited electron density. This accounts for more pronounced thin film responses at lower pump fluences, as has been noted in several studies 10,24 .…”

“…This accounts for more pronounced thin film responses at lower pump fluences, as has been noted in several studies 10,24 . Quantum confinement and backreflections from the substrate in the 20-nm thin film reverse the sign of the reflectivity change and reduce the amplitudes of the reflectivity oscillations compared to the bulk sample 23 , but do not affect the excitation density-dependence of the lattice potential. The fluence-dependent trend in bond softening does not change significantly with sample temperature between 300 K and 80 K ( Fig.…”

Ultrafast transport mediated homogenization of photoexcited electrons governs the softening of the $A_\mathrm{1g}$ phonon in bismuth

“…Bismuth as a Peierls-Jones distorted semimetal [1] with its low equilibrium carrier density and its low effective masses is prone to carrier induced structural instabilities. One of them is the distinct displacive excitation of coherent A 1g optical phonons which has turned bismuth into one of the most studied materials by ultrafast timeresolved pump-probe techniques [2][3][4][5][6][7][8][9][10][11][12][13][14]. Upon photoexcitation the charge carrier density can be transiently increased by orders of magnitude thus drastically changing the potential energy surface of the atoms [9,10,15].…”