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Picosecond electron and phonon phenomena in amorphous Ge and As2Te3
Journal of Non-CrystallineSolids77 & 78 (1985) 1113-1116 North-Holland,Amsterdam
1113
['ICOSt,](I()NI) ELECTRON AND PHONON PHENOMENA IN AM()RI'11OUS Ge AND As2T %
C. TIIOMSEN, tt. T. GRAIIN, It. J. MARLS, and J. TAUC
I)epar(ment of Physics and Division of Engineering, Brown University, Providence, Rhode Island 02912, USA
Picosecond optical nleasurements of photoindueed absorption are used to determine hot carrier thermalization rates in a-Ge and a-Si. In a-As2Te a phonon generation and propagation has been observed and applied to determine the temperature dependence of velocity and attenuation of 30 GHz phonons in this material.
1.
INTRODUCTION
In this paper we present results of picosecond measurements performed on thin films of amorphous Ge and As2T % with the pump and probe technique using a photon energy of 2 eV. These materials exhibit different responses although their gaps Eg arc approximately equal. We find that in a-Ge the response is dominated by electronic processes (similarly as in our previous work 1 on amorphous Si and a As2S3 xSex) while in a-As2Te a photogenerated acoustic waves make an observable contribution. This is due to different material parameters of a-Ge and a As2Te a. We compare the results obtained on a-Ge with those on a-Si and discuss the origin of the differences. Then we show how the oscillatory responses observed in a As2T % can be used for studying acoustic phonon velocity and attenuation.
2.
EXq'ER IMENT
All measurements are done with a passively mode-locked CPM ring dye laser 2 with pulses 0.2 ps long and an energy of 0.2 nJ per pulse. The photon energy is 2 eV, roughly twice the bandgap of both, a-Ge (Eg = 1 eV) and a-AseT % [ E g = 0.8 eV). The absorption depth f for light of this energy is quite small in the studied materials (~.30 nm), so that fihns not thicker than 200 nm were used for transmission measurements. Fihns used in reflection measurements were up to 500 nm thick. The density of excited carriers in both materials are estimated to be 2X1019 em 3. The films were sputlered on quartz or sapphire substrates.
3.
PttOTOINDUCED ELECTRONIC PROCESSES IN a-Ge
In our previous work I on a-Si we measured the induced change in transmission A T to obtain the change in the absorption coefficient Aa. But in general the determination 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
1 1 14
C. Thomsen et al. / Picosecond electron andphonon phenomena
of A a requires also information on the change in reflection AR, since for small changes a Aa/a:=
AT/T
AR/(1-R).
(1)
Since A R / ( 1 - R ) is much smaller than A T / T in a-Si at 2 eV, A a is practically determined by AT. This is not the case in a-Ge, where A T / T and A R / ( 1 - R ) are of the same order, so t h a t both quantities have to he measured in order to obtain Aa. In Fig. l a A a is shown for a-Ge and a-Si as a function of time delay between the pump and the probe pulse. In a-Ge Ac~ is negative (photoinduced bleaching) in the first 4 ps, then it becomes positive (photoinduced absorption) and saturates after 20 ps. At longer times (up to 2 ns) this positive signal does not decrease significantly. We propose that the peak at zero time delay is associated with free carriers produced by the pump. The bleaching is due to a decrease in the number of initial states in the valence band and of final states in the conduction band. After thermalizing to the band edge the carriers become trapped in the band tail, which gives a positive Aa. Then most carriers sit in traps near the band edge and subsequent processes occur on a much longer time scale, so that no significant decay is seen in 2 ns. In a-Si a similar behavior is observed, except that A a has a positive peak at zero time delay. Here free carrier absorption previals over bleaching in the first 4 ps. The peak decays in about 15 ps to a positive finite signal, which again can he ascribed to trapped carriers. The change in the index of refraction An, which is proportional to AR in these materials, is shown in Fig. lb for a-Ge. It also exhibits a strong peak at zero time delay, which decays approximately with the same time constant as At~. The change is negative as expected for free carriers. But in As2Te a An is positive in the first picoseconds; we may speculate that in this material photoinduced effects have a different origin, for example a shift in the absorption edge produced by the pump. From the decay of Ac~ in the first 4 ps the excess energy dissipation rate Rex has been calculated from the equation Rex (tiw - Eg)/2r where 1 ~ - - 2 eV is the photon energy of the pump, Eg the energy gap of the material and r the thermalization time. It is assumed that the excess energy llw - Eg is equally divided between the electron and the hole. The data were fitted to a single exponential between 0.5 ps and 4 ps resulting in a value for r of 1.3 4- 0.1 ps in a-Ge and 1.2 4- 0.1 ps in a-Si. Taking the energy gap
g
::
°
t.d
I
40
O
I
I
20 TIME DELAY (psec) io
I
50
FIGURE l a Time dependence of the change in the absorption coefficient A a in a-Si and a-Ge at 295 K.
-IO
0
I
I
I0 20 TIME DELAY (psec)
"30
HGURE lb Time dependence of the change in the index of refraction An in a-Ge at 295 K.
C Thomsen et al. / Picosecond electron and phonon phenomena
11 15
of a-(;e to Ire 1.0 eV and of a-St 1.4 eV leads to an excess energy dissipation rate of 0.39 + 0.03 eV/ps in a-Ge and 0.25 :i: 0.02 eV/ps in a-St. Kuhl 4 et al. obtained a similar value for r in a-St.
-1.
A('OU.~'I'IC t']H"I",CTS IN a As2Te 3
In thin films of As2Te a we have observed picosecond time responses that are clearly due to acoustic phenomena. We have extensively studied these responses in amorphous As2Te 3, but rot)re recently they were also seen in polycrystalline samples. Photoinduced refieclivity ()f a sample of a As2Te 3 (thickness d ~ 240 nm) is shown in Fig. 2. Superimposed on an initial increase anti a following decrease of refiectivity are three equally spaced sharp oscillations which stand in remarkable contrast to the expec(~,d behavior of electrorlic and thermal relaxations in glasses. The velocity derived from the sample thickness and the time interval between these features shows that they are associated with ultrasound prot)agation in the samlrle. The different glitches are subsequent echoes of the sound pulse generated at time t 0 ps by the pump at the free surface and reflected :it the interface with the substrate. We have ascribed s the generation process It) thernnd exl):lnsion of the region near the surface where incident light is absorbed. Strain originaling from this process propagates in the sample and modifies the optical 1)r~)])erties as measured by changes in transmission AT and reflectivity AR. The dependence of A T on strain ~(z,t) has been shown to be 5 /',T(t} c~ f ( ( z , t ) d z ,
(2)
i.e. AT is prt)l)ortional to the spatial average of the strain through the sample and thus nol sensiliw, to the details of the acoustic pulse shape. The change in reflectivity, however, is related to strain in the sample through a "sensitivity function" f(z) At{{t) 0< ff(z) E(z,t) dz
(3)
where f(z) measures the contribution of strain ((z,t) in the sample at depth z to Ate(t). For salnples with au absorption depth S'<,~:d f(~'~)is nonzero only in a small region near the surface, lhus yielding a mr)re accurate picture of the propagating strain t(z,t). We have calcul'lted the integral of strain ¢{z,t) with an estimate of f(z] and compare it to the experimentai echo shape in the inset of Fig. 2. The agreement is reasonable. The a~erage magnitude of ( ( z , t 0) can be approximated by the product of the average temperature increase ~.~A0 ..... Q/(C ~'A) and the expansion coefficient /~ of the mat(,rial with Q being tire absorbed energy', C the heat capacity, and A the illuminated area of the sample. If Gr(ineisen's law h()lds, we can write •<¢(z,t
0)>
: "/Q/(BcA)
(4)
where -/is (;riineisen's constant. The difference in bulk moduli B of a As2Te a and a-Ce thus produces a smaller strain in a-Ge and makes soft materials more suitable for the observation of acoustic phenomena. The shift of the echo position in time with temperature can be used to determine the temperature dependence of the longitudinal phonon velocity in a sample. The data in Fig. 3 shc)w an approximately linear increase in velocity V when the sample is cooled. We have neglected the thickness change due to thermal expansion. The decrease in amplitude of the echoes is mainly due to the reflection loss at the sample substrate interface (in Fig. 2 the acoustic reflection coefficient Ra¢ == 54%), however, a contribution to attenuation is measurable. The frequency spectrum of the echo
C Thomsen et aL / Picosecond electron and phonon phenomena
1 116
~-
;
oo
o.o4
~- .=
~
003
tt ttt
;
T
s g
t
6
oo.o tt!
z °
I
-200
0
]
I
I
200 400 600 TIME DELAY (psec)
O.O0
800
z~I
0
°
_ _
~00 200 TEMPERATURE (K)
t
0
500
FIGURE 2 FIGURE 3 Photoinduced reflectivity AR in a-As2Te s Temperature dependence of velocity V and at 295 K. The inset is an expanded view of attenuation of 30 Gllz phonons ill the first echo showing a data set ( - - ) and a As2Te 3 between 30 and 300 K. a fit according to the theory ( ..... ).
ill the inset of Fig. 2 peaks at 25 GHz and thus allows us to measure acoustic attenuation in this frequency range. The attenuation per unit distance may be defined as
a(0~) = log{R,¢ I Al(w)I/I A:(~ I }/2d
(5)
where Al(W) and A2(:o) are the Fourier spectra of two pulses separated by one roundtrip. The attenuation at 30 GHz in a-As2Te a is plotted as a function of temperature in Fig. 3. Note the extremely high attenuation typical of glasses ~ which could not have been measured with a conventional transducer.
ACKNOWLEDGEMENT The authors would like to thank T. R. Kiist for technical assistance. One of us (II.T.G.) had an IBM Predoctoral Fellowship. The work was supported in part by the National Science Foundation grant DMR 82-09148 and the NSF Materials Research Laboratory Program at Brown University.
REFERENCES 1) J. Tauc, Physica l17B & 188B, 889 (1983). 2) R. L. Fork, B. I. Greene, and C. V. Shank, Appl. Phys. Lett. 36, 671 (1981). 3) J. Strait, Ph.D. Thesis (Brown University, 1985). 4) J. Kuhl, E. O. GSbel, Th. Pfeiffer, and A. Jonietz, Appl. Phys. A34, 105 (1984). 5) C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, and J. J. Hauser, Phys. I~ev. Lett. 53, 989 (1984). 6) S. Hunklinger and W. Arnold, Ultrasonic Properties of Glasses at Low Temperatures, in: Physical Acoustics, Vol. XII, ed. W. P. Mason (Academic, New York, 1976), p. 115.
1113
['ICOSt,](I()NI) ELECTRON AND PHONON PHENOMENA IN AM()RI'11OUS Ge AND As2T %
C. TIIOMSEN, tt. T. GRAIIN, It. J. MARLS, and J. TAUC
I)epar(ment of Physics and Division of Engineering, Brown University, Providence, Rhode Island 02912, USA
Picosecond optical nleasurements of photoindueed absorption are used to determine hot carrier thermalization rates in a-Ge and a-Si. In a-As2Te a phonon generation and propagation has been observed and applied to determine the temperature dependence of velocity and attenuation of 30 GHz phonons in this material.
1.
INTRODUCTION
In this paper we present results of picosecond measurements performed on thin films of amorphous Ge and As2T % with the pump and probe technique using a photon energy of 2 eV. These materials exhibit different responses although their gaps Eg arc approximately equal. We find that in a-Ge the response is dominated by electronic processes (similarly as in our previous work 1 on amorphous Si and a As2S3 xSex) while in a-As2Te a photogenerated acoustic waves make an observable contribution. This is due to different material parameters of a-Ge and a As2Te a. We compare the results obtained on a-Ge with those on a-Si and discuss the origin of the differences. Then we show how the oscillatory responses observed in a As2T % can be used for studying acoustic phonon velocity and attenuation.
2.
EXq'ER IMENT
All measurements are done with a passively mode-locked CPM ring dye laser 2 with pulses 0.2 ps long and an energy of 0.2 nJ per pulse. The photon energy is 2 eV, roughly twice the bandgap of both, a-Ge (Eg = 1 eV) and a-AseT % [ E g = 0.8 eV). The absorption depth f for light of this energy is quite small in the studied materials (~.30 nm), so that fihns not thicker than 200 nm were used for transmission measurements. Fihns used in reflection measurements were up to 500 nm thick. The density of excited carriers in both materials are estimated to be 2X1019 em 3. The films were sputlered on quartz or sapphire substrates.
3.
PttOTOINDUCED ELECTRONIC PROCESSES IN a-Ge
In our previous work I on a-Si we measured the induced change in transmission A T to obtain the change in the absorption coefficient Aa. But in general the determination 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
1 1 14
C. Thomsen et al. / Picosecond electron andphonon phenomena
of A a requires also information on the change in reflection AR, since for small changes a Aa/a:=
AT/T
AR/(1-R).
(1)
Since A R / ( 1 - R ) is much smaller than A T / T in a-Si at 2 eV, A a is practically determined by AT. This is not the case in a-Ge, where A T / T and A R / ( 1 - R ) are of the same order, so t h a t both quantities have to he measured in order to obtain Aa. In Fig. l a A a is shown for a-Ge and a-Si as a function of time delay between the pump and the probe pulse. In a-Ge Ac~ is negative (photoinduced bleaching) in the first 4 ps, then it becomes positive (photoinduced absorption) and saturates after 20 ps. At longer times (up to 2 ns) this positive signal does not decrease significantly. We propose that the peak at zero time delay is associated with free carriers produced by the pump. The bleaching is due to a decrease in the number of initial states in the valence band and of final states in the conduction band. After thermalizing to the band edge the carriers become trapped in the band tail, which gives a positive Aa. Then most carriers sit in traps near the band edge and subsequent processes occur on a much longer time scale, so that no significant decay is seen in 2 ns. In a-Si a similar behavior is observed, except that A a has a positive peak at zero time delay. Here free carrier absorption previals over bleaching in the first 4 ps. The peak decays in about 15 ps to a positive finite signal, which again can he ascribed to trapped carriers. The change in the index of refraction An, which is proportional to AR in these materials, is shown in Fig. lb for a-Ge. It also exhibits a strong peak at zero time delay, which decays approximately with the same time constant as At~. The change is negative as expected for free carriers. But in As2Te a An is positive in the first picoseconds; we may speculate that in this material photoinduced effects have a different origin, for example a shift in the absorption edge produced by the pump. From the decay of Ac~ in the first 4 ps the excess energy dissipation rate Rex has been calculated from the equation Rex (tiw - Eg)/2r where 1 ~ - - 2 eV is the photon energy of the pump, Eg the energy gap of the material and r the thermalization time. It is assumed that the excess energy llw - Eg is equally divided between the electron and the hole. The data were fitted to a single exponential between 0.5 ps and 4 ps resulting in a value for r of 1.3 4- 0.1 ps in a-Ge and 1.2 4- 0.1 ps in a-Si. Taking the energy gap
g
::
°
t.d
I
40
O
I
I
20 TIME DELAY (psec) io
I
50
FIGURE l a Time dependence of the change in the absorption coefficient A a in a-Si and a-Ge at 295 K.
-IO
0
I
I
I0 20 TIME DELAY (psec)
"30
HGURE lb Time dependence of the change in the index of refraction An in a-Ge at 295 K.
C Thomsen et al. / Picosecond electron and phonon phenomena
11 15
of a-(;e to Ire 1.0 eV and of a-St 1.4 eV leads to an excess energy dissipation rate of 0.39 + 0.03 eV/ps in a-Ge and 0.25 :i: 0.02 eV/ps in a-St. Kuhl 4 et al. obtained a similar value for r in a-St.
-1.
A('OU.~'I'IC t']H"I",CTS IN a As2Te 3
In thin films of As2Te a we have observed picosecond time responses that are clearly due to acoustic phenomena. We have extensively studied these responses in amorphous As2Te 3, but rot)re recently they were also seen in polycrystalline samples. Photoinduced refieclivity ()f a sample of a As2Te 3 (thickness d ~ 240 nm) is shown in Fig. 2. Superimposed on an initial increase anti a following decrease of refiectivity are three equally spaced sharp oscillations which stand in remarkable contrast to the expec(~,d behavior of electrorlic and thermal relaxations in glasses. The velocity derived from the sample thickness and the time interval between these features shows that they are associated with ultrasound prot)agation in the samlrle. The different glitches are subsequent echoes of the sound pulse generated at time t 0 ps by the pump at the free surface and reflected :it the interface with the substrate. We have ascribed s the generation process It) thernnd exl):lnsion of the region near the surface where incident light is absorbed. Strain originaling from this process propagates in the sample and modifies the optical 1)r~)])erties as measured by changes in transmission AT and reflectivity AR. The dependence of A T on strain ~(z,t) has been shown to be 5 /',T(t} c~ f ( ( z , t ) d z ,
(2)
i.e. AT is prt)l)ortional to the spatial average of the strain through the sample and thus nol sensiliw, to the details of the acoustic pulse shape. The change in reflectivity, however, is related to strain in the sample through a "sensitivity function" f(z) At{{t) 0< ff(z) E(z,t) dz
(3)
where f(z) measures the contribution of strain ((z,t) in the sample at depth z to Ate(t). For salnples with au absorption depth S'<,~:d f(~'~)is nonzero only in a small region near the surface, lhus yielding a mr)re accurate picture of the propagating strain t(z,t). We have calcul'lted the integral of strain ¢{z,t) with an estimate of f(z] and compare it to the experimentai echo shape in the inset of Fig. 2. The agreement is reasonable. The a~erage magnitude of ( ( z , t 0) can be approximated by the product of the average temperature increase ~.~A0 ..... Q/(C ~'A) and the expansion coefficient /~ of the mat(,rial with Q being tire absorbed energy', C the heat capacity, and A the illuminated area of the sample. If Gr(ineisen's law h()lds, we can write •<¢(z,t
0)>
: "/Q/(BcA)
(4)
where -/is (;riineisen's constant. The difference in bulk moduli B of a As2Te a and a-Ce thus produces a smaller strain in a-Ge and makes soft materials more suitable for the observation of acoustic phenomena. The shift of the echo position in time with temperature can be used to determine the temperature dependence of the longitudinal phonon velocity in a sample. The data in Fig. 3 shc)w an approximately linear increase in velocity V when the sample is cooled. We have neglected the thickness change due to thermal expansion. The decrease in amplitude of the echoes is mainly due to the reflection loss at the sample substrate interface (in Fig. 2 the acoustic reflection coefficient Ra¢ == 54%), however, a contribution to attenuation is measurable. The frequency spectrum of the echo
C Thomsen et aL / Picosecond electron and phonon phenomena
1 116
~-
;
oo
o.o4
~- .=
~
003
tt ttt
;
T
s g
t
6
oo.o tt!
z °
I
-200
0
]
I
I
200 400 600 TIME DELAY (psec)
O.O0
800
z~I
0
°
_ _
~00 200 TEMPERATURE (K)
t
0
500
FIGURE 2 FIGURE 3 Photoinduced reflectivity AR in a-As2Te s Temperature dependence of velocity V and at 295 K. The inset is an expanded view of attenuation of 30 Gllz phonons ill the first echo showing a data set ( - - ) and a As2Te 3 between 30 and 300 K. a fit according to the theory ( ..... ).
ill the inset of Fig. 2 peaks at 25 GHz and thus allows us to measure acoustic attenuation in this frequency range. The attenuation per unit distance may be defined as
a(0~) = log{R,¢ I Al(w)I/I A:(~ I }/2d
(5)
where Al(W) and A2(:o) are the Fourier spectra of two pulses separated by one roundtrip. The attenuation at 30 GHz in a-As2Te a is plotted as a function of temperature in Fig. 3. Note the extremely high attenuation typical of glasses ~ which could not have been measured with a conventional transducer.
ACKNOWLEDGEMENT The authors would like to thank T. R. Kiist for technical assistance. One of us (II.T.G.) had an IBM Predoctoral Fellowship. The work was supported in part by the National Science Foundation grant DMR 82-09148 and the NSF Materials Research Laboratory Program at Brown University.
REFERENCES 1) J. Tauc, Physica l17B & 188B, 889 (1983). 2) R. L. Fork, B. I. Greene, and C. V. Shank, Appl. Phys. Lett. 36, 671 (1981). 3) J. Strait, Ph.D. Thesis (Brown University, 1985). 4) J. Kuhl, E. O. GSbel, Th. Pfeiffer, and A. Jonietz, Appl. Phys. A34, 105 (1984). 5) C. Thomsen, J. Strait, Z. Vardeny, H. J. Maris, J. Tauc, and J. J. Hauser, Phys. I~ev. Lett. 53, 989 (1984). 6) S. Hunklinger and W. Arnold, Ultrasonic Properties of Glasses at Low Temperatures, in: Physical Acoustics, Vol. XII, ed. W. P. Mason (Academic, New York, 1976), p. 115.