Supplementary Figure 1. Scanning ultrafast electron microscopy (SUEM) images of the dynamics of (a) electrons and (b) holes in p-type and n-type silicon, ...
a
b
Supplementary Figure 1. Scanning ultrafast electron microscopy (SUEM) images of the
Figure 1S.
dynamics of (a) electrons and (b) holes in p-type and n-type silicon, respectively. These SUEM images complement those in Fig. 2 of the main text. Here, the dynamics is shown at the same time delays for electrons and holes.
2
2
Model 1 2800
2 Second moment R2 (µmSecond ) moment R2 (µm2 )
2600
R2 (t)
R2 (t)
2400 2200
c(R, t) = t
2000
· D0 c(R, t) +
µkB T (t) c(R, t) e t
1800
T (t) = 400000Ke 77ps + 300K
1600 1400
0
500
1000
1500
2000
2500
3000
3500
2
the dynamics at the same time thedelays dynamics for electrons at the same andtime holes. delays for electrons an
n-type silicon, respectively. These n-typeimages silicon,complement respectively.Fig. These 2 inimages the main complement text by
FigureFigure 1S. S1. SUEM images Figure of the Figure 1S. dynamics S1. SUEM of (a) images electrons of theand dynamics (b) holes of in (a)p-t el
Figure S2: Plot of R2 (µm 2) vs. Time
Model 2 2800 2600 2400 2200 c(R, t) = t
2000
· D0 c(R, t) +
µkB µkB T (R, t) c(R, t) + c(R, t) T (R, t) e e
1800
t
1600 1400
R2
T (R, t) = 811000Ke 77ps e (38.9µm)2 + 300K
0
500
1000
1500
2000
2500
3000
3500
Time (ps)
Supplementary Figure 2. Time evolution of the second moment (see eq. 1 in the main
FIG. 1. Figure S2. Time evolution of the second moment (see eq. 1 in the main text) for a
text) for a uniform temperature distribution (top panel) and a non-uniform temperature
uniform temperature distribution (top panel) and a non-uniform temperature distribution with
distribution with a gaussian spatial profile (bottom panel). Using the same relaxation time
a gaussian spatial profile (bottom panel). Using the same relaxation time of 77 ps and initial
of 77 ps and initial e↵ective temperatures within a factor of 2 of each other, both models give effective temperatures within a factor of 2 of each other, both models give excellent agreement excellent agreement with experiment. Hence the choice of using a constant temperature, as withdone experiment. Hencetext, the choice of using a constant temperature, in the The maindi↵erential text, does in the main does not a↵ect the interpretation of as thedone results. not equations affect the interpretation themodels, results.which The differential solved twotext, models, solved for the of two combine eq.equations 3 and eq. 4 infor thethe main are which combine eq.the 3 and eq. 4 in the main text, are also given in the figure. also given in figure.
3
3
