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Two-photon indirect transition in GaP crystal
Volume
10, number
OPTICS
1
TWO-PHOTON
COMMUNICATIONS
INDIRECT
TRANSITION
January
1974
IN GaP CRYSTAL*
Jick H. YEE and H.H.M. CHAU Lawrence Livermore Laboratory, University of California, Livermore, California 94550, USA
Received
18 October
1973
The two-photon indirect transition in n-type GaP crystals was investigated through transmission measurements at 1.17 eV. The value of the two-photon indirect coefficient was found to be approximately 1.7 X 10e3 cm/MW, which is in close agreement with theoretical calculations.
1. Introduction Nonlinear photon processes in GaP crystal have been studied recently through the investigation of the change of the nonequilibrium concentration of the carriers and through the dependence of luminescent intensity on laser intensity [l-3]. The confirmation that the two-photon indirect transition occurred in these experiments was based on the fact that the change of the nonequilibrium concentration of carriers is proportional to the square of the light intensity. The change of the nonequilibrium carrier concentration and the luminescent intensity of the emitted light are complicated functions of physical parameters such as the lifetime of the carriers, carrier mobility, and the surface condition; it was therefore not possible to determine the two-photon indirect absorption coefficient directly from these experiments [l-3]. Two-photon indirect transitionshave been studied theoretically by several workers [4, 51. The numerical estimate of the two-photon indirect transition coefficient deduced from these theoretical works are all of the same order of magnitude’. The purpose of the present paper is to present the numerical value of the two-photon indirect transition coefficient determined from transmission measurements on an n-type GaP crystal.
2. Theory In the presence of both single-photon
absorption
dI/dx = -al-/3Z2. The solution pf
= IO
and two-photon
absorption,
the change in intensity
i:j: (1)
of this equation
can be shown to be:
(1 - R)2 exp(1 +/3Zo(l -R)
[l-
ai)
exp(-&)]a-’
’
(2)
* Performed under the auspices of the U.S. Atomic Energy Commission. The numerical values of the two-photon-indirect absorption coefficient given on page 648 of ref. [4] was in error. These values should be: 010 z 2 X 104/cm for optical polar phonon interaction, and aa = 2 X 10A3/cm for acoustic phonon interaction.
l
56
Volume
10, number
OPTICS
1
COMMUNICATIONS
January
where IO is the excitation intensity, CYis the single-photon absorption /3 = eta/I.The /3 = CY,/I term can be approximated as follows [4]: 2fiow; /3 = a,/I
=
I2
= “2 (l/fiw)3
(m&)3/2
(l/m)2
coefficient,
(kF)2 ~
(,2/,,1/2)2
1974
1 is the length of the crystal, and
I(c,0I&plv,0)12
Pwa
x {[ Igf 12 (2 m,/@)
IEd”
[ lgi I2 (2WI,/R2)lE~v12
t
+ I&
12 (2m,/iQ)
IE,, 121 n+
+ 125 I2 (2t?Z,/Fi2)lE~c12]
(2?iiw + hw,
-E&3
(TZkF+ 1)(2fiW~fiWa~Eg)3}~
(3)
where the g’s are
where 1 nkF =
exp(fio,/kr)
- 1.
The meanings of the notation
3. Experimental
in eq. (3) are shown in fig. 1 and in ref. [4].
results
In our investigation we used an n-type GaP crystal, with an impurity concentration of about 3 X 1016/cm3 with a length of 1.5 cm to 0.5 cm. The excitation source was a Q-switched neodymium laser (1.17 eV) with a pulse width -50 nsec and maximum energy output of 1 J. All experimental runs were performed at ambient temperature. The measured transmission curve is shown in fig. 2. As can be seen from the data, in the laser intensity range from 0 to 4 MW/cm2, the free carrier absorption was at first dominant in the absorption process. In this range of intensity, the transmission coefficient was very constant and ‘he absorption process was mainly due to the single-
E(k)
EC - EC kF
rko
k
LE; 0
Fig. 1. Simple energy
- E” kF
band structure
of GaP crystal
57
OPTICS COMMUNICATIONS
Volume 10, number 1
January 1974
1
6-i
5_
6 ‘-
4
5
3-
z .C
: t
,x-x/x
-X-x
I 0 In$ut
Input
light
intensity
(IO) - MW/cm2
Fig. 2. The transmission curve of GaP crystal as a function of light intensity
-X’
I 80 light
I
I 160
I
intensity
I 240
!
I 320
I
_ 400
(IO) - MW/cm'
Fig. 3. The inverse of the transmission of the GaP crystal vs. input light intensity. The experimental points are shown as well as the theoretical curve of T-’ for (3= I .7 X 10e3 cm/MW, OL= 0.49/cm and for I= 1.5 cm
photon absorption through the interband (X, to X3) transition with the absorption coefficient approximately equal to 0.54/cm. As the intensity was increased beyond 4 MW/cm 2, the transmission coefficient increased momentarily and then approached a constant value with a new absorption coefficient of about 0.49/cm. This increase in transmission was not expected. It was probably due to the depletion of the carrier into the conduction band X3. As the laser intensity was increased beyond 40 MW/cm2, a drastic decrease in transmission occurred. This part of the transmission was approximately linearly dependent on the intensity. This means that in this range of light intensity, the two-photon indirect transition process could no longer be ignored. The inverse of the transmission curve of fig. 2 (in the intensity range from 40 MW/cm2 to 400 MW/cm2) is plotted in fig. 3. From this curve, we can determine the two-photon indirect transition coefficient by equating the slope of the inverse of eq. (1) equal to the slope of fig. 3 and by using the value CY = 0.49/cm. The result is /3g 1.7 X 10e3 cm/MW. Now we estimate /3 from eq. (3) using the following parameters:
.E’& ~ EiF = 0.5 eV,
p = 4.13 g/cm3,
m, 2 0.34 m,
m, Y 0.74 m,
Edc = 6 ev,
fiiw, = 0.03 eV,
Eg Y 2.9 eV at k= 0,
Edv = ,I2 eV,
EiF ~ El,
I(c,Ola.p m2
= -3 eV,
lv,O)l2
Z 1.3 X 1016 cm/set g.
Substituting the parameters given above into eq. (3), we obtain /3r 0.19 X 10e3, which is in semiquantitative agreement with the values determined from the experiments. It is of interest to note that other workers [5] also have predicted approximately the same numerical value for 8.
[II B.M. Ashkinadze, I.P. Kretsu, S.L. Pyshkin and I.D. Yaroshetskii, Fiz. Tekh. Poluprov. 2 (1968) 1511 (Soviet Phys. Semicond. 2) (1969).
[21 B.M. Ashkinadze, A.I. Bobrysheva, E.V. Vitiu, V.A. Kovarskii, A.V. Lelyakov, S.A. Moskalenko, S.L. Pyshkin and S.I. Radautsan, Proc. Ninth Intern. Conf. on Physics of Semiconductors (in Russian), Moscow (1968). [31 S.L. Pyshkin, N.A. Ferdman, S.I. Radautsan, V.A. Kovarsky, E.V. Vitiu, Opto-Electronics 2 (1970) 245. [41 J.H. Yee, J. Phys. Chem. Solids 33 (1972) 643. I51 F. Bassani and A.R. Hassan, Nuovo Cim. 7B (1972) 313.
58
10, number
OPTICS
1
TWO-PHOTON
COMMUNICATIONS
INDIRECT
TRANSITION
January
1974
IN GaP CRYSTAL*
Jick H. YEE and H.H.M. CHAU Lawrence Livermore Laboratory, University of California, Livermore, California 94550, USA
Received
18 October
1973
The two-photon indirect transition in n-type GaP crystals was investigated through transmission measurements at 1.17 eV. The value of the two-photon indirect coefficient was found to be approximately 1.7 X 10e3 cm/MW, which is in close agreement with theoretical calculations.
1. Introduction Nonlinear photon processes in GaP crystal have been studied recently through the investigation of the change of the nonequilibrium concentration of the carriers and through the dependence of luminescent intensity on laser intensity [l-3]. The confirmation that the two-photon indirect transition occurred in these experiments was based on the fact that the change of the nonequilibrium concentration of carriers is proportional to the square of the light intensity. The change of the nonequilibrium carrier concentration and the luminescent intensity of the emitted light are complicated functions of physical parameters such as the lifetime of the carriers, carrier mobility, and the surface condition; it was therefore not possible to determine the two-photon indirect absorption coefficient directly from these experiments [l-3]. Two-photon indirect transitionshave been studied theoretically by several workers [4, 51. The numerical estimate of the two-photon indirect transition coefficient deduced from these theoretical works are all of the same order of magnitude’. The purpose of the present paper is to present the numerical value of the two-photon indirect transition coefficient determined from transmission measurements on an n-type GaP crystal.
2. Theory In the presence of both single-photon
absorption
dI/dx = -al-/3Z2. The solution pf
= IO
and two-photon
absorption,
the change in intensity
i:j: (1)
of this equation
can be shown to be:
(1 - R)2 exp(1 +/3Zo(l -R)
[l-
ai)
exp(-&)]a-’
’
(2)
* Performed under the auspices of the U.S. Atomic Energy Commission. The numerical values of the two-photon-indirect absorption coefficient given on page 648 of ref. [4] was in error. These values should be: 010 z 2 X 104/cm for optical polar phonon interaction, and aa = 2 X 10A3/cm for acoustic phonon interaction.
l
56
Volume
10, number
OPTICS
1
COMMUNICATIONS
January
where IO is the excitation intensity, CYis the single-photon absorption /3 = eta/I.The /3 = CY,/I term can be approximated as follows [4]: 2fiow; /3 = a,/I
=
I2
= “2 (l/fiw)3
(m&)3/2
(l/m)2
coefficient,
(kF)2 ~
(,2/,,1/2)2
1974
1 is the length of the crystal, and
I(c,0I&plv,0)12
Pwa
x {[ Igf 12 (2 m,/@)
IEd”
[ lgi I2 (2WI,/R2)lE~v12
t
+ I&
12 (2m,/iQ)
IE,, 121 n+
+ 125 I2 (2t?Z,/Fi2)lE~c12]
(2?iiw + hw,
-E&3
(TZkF+ 1)(2fiW~fiWa~Eg)3}~
(3)
where the g’s are
where 1 nkF =
exp(fio,/kr)
- 1.
The meanings of the notation
3. Experimental
in eq. (3) are shown in fig. 1 and in ref. [4].
results
In our investigation we used an n-type GaP crystal, with an impurity concentration of about 3 X 1016/cm3 with a length of 1.5 cm to 0.5 cm. The excitation source was a Q-switched neodymium laser (1.17 eV) with a pulse width -50 nsec and maximum energy output of 1 J. All experimental runs were performed at ambient temperature. The measured transmission curve is shown in fig. 2. As can be seen from the data, in the laser intensity range from 0 to 4 MW/cm2, the free carrier absorption was at first dominant in the absorption process. In this range of intensity, the transmission coefficient was very constant and ‘he absorption process was mainly due to the single-
E(k)
EC - EC kF
rko
k
LE; 0
Fig. 1. Simple energy
- E” kF
band structure
of GaP crystal
57
OPTICS COMMUNICATIONS
Volume 10, number 1
January 1974
1
6-i
5_
6 ‘-
4
5
3-
z .C
: t
,x-x/x
-X-x
I 0 In$ut
Input
light
intensity
(IO) - MW/cm2
Fig. 2. The transmission curve of GaP crystal as a function of light intensity
-X’
I 80 light
I
I 160
I
intensity
I 240
!
I 320
I
_ 400
(IO) - MW/cm'
Fig. 3. The inverse of the transmission of the GaP crystal vs. input light intensity. The experimental points are shown as well as the theoretical curve of T-’ for (3= I .7 X 10e3 cm/MW, OL= 0.49/cm and for I= 1.5 cm
photon absorption through the interband (X, to X3) transition with the absorption coefficient approximately equal to 0.54/cm. As the intensity was increased beyond 4 MW/cm 2, the transmission coefficient increased momentarily and then approached a constant value with a new absorption coefficient of about 0.49/cm. This increase in transmission was not expected. It was probably due to the depletion of the carrier into the conduction band X3. As the laser intensity was increased beyond 40 MW/cm2, a drastic decrease in transmission occurred. This part of the transmission was approximately linearly dependent on the intensity. This means that in this range of light intensity, the two-photon indirect transition process could no longer be ignored. The inverse of the transmission curve of fig. 2 (in the intensity range from 40 MW/cm2 to 400 MW/cm2) is plotted in fig. 3. From this curve, we can determine the two-photon indirect transition coefficient by equating the slope of the inverse of eq. (1) equal to the slope of fig. 3 and by using the value CY = 0.49/cm. The result is /3g 1.7 X 10e3 cm/MW. Now we estimate /3 from eq. (3) using the following parameters:
.E’& ~ EiF = 0.5 eV,
p = 4.13 g/cm3,
m, 2 0.34 m,
m, Y 0.74 m,
Edc = 6 ev,
fiiw, = 0.03 eV,
Eg Y 2.9 eV at k= 0,
Edv = ,I2 eV,
EiF ~ El,
I(c,Ola.p m2
= -3 eV,
lv,O)l2
Z 1.3 X 1016 cm/set g.
Substituting the parameters given above into eq. (3), we obtain /3r 0.19 X 10e3, which is in semiquantitative agreement with the values determined from the experiments. It is of interest to note that other workers [5] also have predicted approximately the same numerical value for 8.
[II B.M. Ashkinadze, I.P. Kretsu, S.L. Pyshkin and I.D. Yaroshetskii, Fiz. Tekh. Poluprov. 2 (1968) 1511 (Soviet Phys. Semicond. 2) (1969).
[21 B.M. Ashkinadze, A.I. Bobrysheva, E.V. Vitiu, V.A. Kovarskii, A.V. Lelyakov, S.A. Moskalenko, S.L. Pyshkin and S.I. Radautsan, Proc. Ninth Intern. Conf. on Physics of Semiconductors (in Russian), Moscow (1968). [31 S.L. Pyshkin, N.A. Ferdman, S.I. Radautsan, V.A. Kovarsky, E.V. Vitiu, Opto-Electronics 2 (1970) 245. [41 J.H. Yee, J. Phys. Chem. Solids 33 (1972) 643. I51 F. Bassani and A.R. Hassan, Nuovo Cim. 7B (1972) 313.
58