Super-diffusion of excited carriers in semiconductors

Abstract

The ultrafast spatial and temporal dynamics of excited carriers are important to understanding the response of materials to laser pulses. Here we use scanning ultrafast electron microscopy to image the dynamics of electrons and holes in silicon after excitation with a short laser pulse. We find that the carriers exhibit a diffusive dynamics at times shorter than 200 ps, with a transient diffusivity up to 1,000 times higher than the room temperature value, D0≈30 cm2s−1. The diffusivity then decreases rapidly, reaching a value of D0 roughly 500 ps after the excitation pulse. We attribute the transient super-diffusive behaviour to the rapid expansion of the excited carrier gas, which equilibrates with the environment in 100−150 ps. Numerical solution of the diffusion equation, as well as ab initio calculations, support our interpretation. Our findings provide new insight into the ultrafast spatial dynamics of excited carriers in materials.

Scanning ultrafast electron microscopy: A novel technique to probe photocarrier dynamics with high spatial and temporal resolutions

“…While the temperature of the gas is set by the photon energy, the pressure is determined by the number density of photocarriers that depends on the pump laser fluence. The initial fast expansion of the hot carrier gas can be modeled as a result of its initial high temperature and pressure [30], which decrease rapidly with the expansion. These observations illustrate the drastic difference between the hot photocarrier dynamics and the charge transport near equilibrium.…”

“…Like the built-in potential at a p-n junction, this surface potential separates electrons and holes, driving one group to the surface and the other to the bulk. This vertical transport process determines whether electrons or holes are observed in SUEM, since the secondary-electron-detection mode is only sensitive to the top few nanometers of the sample, and explains why a bright (dark) contrast is observed in heavily doped p-type (ntype) silicon [30], as shown in Fig. 4 (c).…”

“…In practice, the rising time of the SUEM signal from a standard sample, such as intrinsic silicon [27] or cadmium selenide [26], is used to estimate the temporal resolution of this instrument -typically a few picoseconds. It should be noted that the experimental rising time only sets an upper limit for the temporal resolution, since the rising time can also be affected by the vertical transport of photocarriers caused by surface potentials [30]. It is observed that the rising time is affected by the number of electrons per pulse as well [26], which indicates the contribution from the electron pulse width.…”

“…SUEM experiences the same charging issue as the normal SEM, so in principle is not suitable to study electrically insulating materials, although the environmentalmode SUEM [29] can be a potential solution. SUEM has been utilized to image ultrafast photocarrier dynamics on the surface of a wide range of materials, including crystalline semiconductors [28,30], semiconducting nanowires [31] and nanocrystals [32], amorphous semiconductors [33], semiconductor p-n junctions [34] and two-dimensional materials [35], and these applications have resulted in intriguing observations such as ballistic transport of photocarriers across a p-n junction [34], superdiffusion of photocarriers in heavily-doped semiconductors [30] and spontaneous spatial separation of electrons and holes in amorphous semiconductors [33]. Whereas there has been an abundance of recent reviews of ultrafast electron microscopy [8,9,[36][37][38], we dedicate this article specifically to SUEM, with an emphasis on the current understanding of various physical processes that contribute to the contrast images observed in SUEM from a users' perspective.…”

60 dB high-extinction auto-configured Mach–Zehnder interferometer

“…This is owing to the photon's properties of long coherence time and ease of manipulation [13][14][15][16][17][18][19][20][21][22]. A vast array of key components in integrated quantum photonics (IQP) have been reported in recent years including integrated photon sources [16][17][18], linear optical circuits [14,15], and waveguide photon detectors [19,20]. Many such uses of photonic technology, including sensing, mode conversion, IQP, and linear optical circuits generally, require quite precise interference of beams, for example in Mach-Zehnder interferometers (MZIs).…”