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DOI:10.29013/AJT-23-11.12-39-44
INTERZONE ONE-PHOTON ABSORPTION OF POLARIZED LIGHT WITH ACCOUNT OF THE COHERENT
SATURATION EFFECT IN
A3B5
SEMICONDUCTORS
Rasulov Rustam Yavkachovich 1, Kasimov Forrukh Kasimovich 2, Isomiddinova Umida Mamurjonova 3, Urinova Kamola Komoljonovna 3
1 Department Physics, Fergana State University, Uzbekistan
2 Department Physics, And^n State University, Uzbekistan
2 Department Physics, Kokand State Pedagogical Institute, Uzbekistan
Cite: Rasulov R. Y., Kasimov, F. K., Isomiddinova, U.M., Urinova, R. K. (2023). Interzone One-Photon Absorption of Polarized Light With Account of the Coherent Saturation Effect in A3B5 Semiconductors. Austrian Journal of Technical and Natural Sciences 2023, No 11-12. https://doi.org/10.29013/AJT-23-11.12-39-44
Abstract
The polarization, spectral, and temperature dependences of the one-photon absorption coefficient of polarized radiation are calculated, and its linear-circular dichroism in crystals of tetrahedral symmetry is studied. In this case, the contribution to the coefficients of one-photon absorption of light from the effect of coherent saturation of optical transitions is taken into account.
Keywords: polarization, spectral, and temperature dependences of the one-photon light absorption coefficient, linear-circular dichroism, crystal of tetrahedral symmetry, coherent saturation effect
Intraduction
Nonlinear absorption of light in a semiconductor with a degenerate valence band, which is due to direct optical transitions between heavy and light hole subbands and depends on the state of radiation polarization, was studied in (Ivchenko, 1972; Rasulov, 1993; Ganichev, 1983; Parshin D. A., 1987; Rasulov, 2017; Rasulov, 1996; Rasulov, 1988; Rasulov, 1993). In these papers, it is assumed that the nonlinearity in the intensity dependence of the one-photon absorption coefficient arises due to resonant absorption
saturation. This saturation is due to the pho-toinduced change in the distribution functions of light and heavy holes in the region of momentum space near the surface corresponding Ehh (k) - Eu (k) - 0 to the resonance condition. Here, Ehh(k)^Ehl(k)j is the energy spectrum of heavy (light) holes, and © is the frequency of light.
Due to the smallness of the photon wave vector compared to the wave vector of the electron (hole) formed as a result of absorption, when calculating the light absorption
coefficient, we can assume |q| << k and put \q\ = 0, where q (k ) is the wave vector of the photon (holes).
In case hrn > Eg, Eg + ASO, there are two types of interband optical transitions, the first of which satisfies the condition Eg <hrn (Eg + ASO, and in the second case the condition hrn > Eg + ASO is satisfied. Therefore, in the first case, optical transitions occur between the subbands of light and heavy holes in the valence band and the conduction band, and in the second case, optical transitions occur between the spin-orbit splitting
K(1) - —hw
C,±1/2 ;V,±3/2 . nuJ
n
and conduction bands, which we will analyze separately.
Interband one-photon absorption of polarized light with allowance for the effect of coherent saturation
Next, we investigate various variants of one-photon interband absorption of polarized light, where we take into account the contribution of the coherent saturation effect (Parshin, 1987; Rasulov, 2017; Rasu-lov, 1996) to the light absorption coefficient. Then the spectral - temperature dependence of the coefficient of one-photon absorption of light K1 is determined by the formula (Parshin, 1987; Rasulov, 2017; (Rasulov, 1996)
1 p(hrn)F (fi,1,rn) x
M
(!)
C,±1/2;V,±3/2
(k )
1 + 4
a„
f-2 2 n œ
M
(i)
C,±1/2;V,±3/2
(k )
M
(i)
C,±1/2;V,+3/2
(k )
1 + 4
a„
f-2 2 n œ
m:
(1)
C,M1/2; V,+3/2
(k )
(1)
where I,(o) is the intensity (frequency) of light, p(ha>) is the density of states of current carriers involved in optical transitions, where the energy conservation law is taken into account, F(fi,1,a>) is the distribution function of current carriers in the initial state, P'1 — kBT, kB, - is Boltzmann's constant, T is the sample temperature: F(Mffl) = [1 - exp (Ww)] exp - EL=hh (k(c%h ))],
El .hh (Kth ) = Eg ),
mc + mhhy g/ p(hrn) — /u*ka !(n2h2), [ is the reduced effective mass of current carriers, the form of which depends on the type of optical transitions.
It can be seen from (1) that it is necessary to perform angular averaging of the squares of the composite matrix elements over the solid angles of the wave vector of the current carriers, i.e. we need to perform an integration of the type
M W (k) C,±1/2;V,±3/2 W 2
/+4 «a, m ^ (k ) C,±1/2; V,±3/2 V / 2
hW
(2)
where
e-A-\ pV [(I ) + «2 (I )],
«1(1 ) = <
«2 (I ) = <
1e
1ki
i=
2nc
is the light intensity,
f(N) n 'k ',nk
- is the
square of the absolute value of the matrix element Mr averaged over the solid angles
n ' k ' ,nk
of the vector k , £,= 4
a„
-j-2 2 n CO
eAn
ply, the
v c h j
wave vector k is determined from the energy conservation law. In particular, for the optical transition considered above
ic,L) _
(-Eg ), _
ka - kc ,L -
2 ß
(c ,L)
n2
m + mr
The calculation of one-photon absorption of polarized light due to optical transitions from the subband of light and heavy holes to the conduction band is performed using the formula (Rasulov, 1996; Rasulov, 1988; Rasulov, 1993; Rasulov, 2016; Rasulov, 2015)
2
e
2
2
e
2
2
2
K(1)= ^ (()( _f (()En(()_ha) (3)
c^mona tH W V ' V " W W '
whence, in the Luttinger-Kohn approxi- spectral-temperature dependence of the co-
mation and in the three-band Kane model efficient of interband one-photon absorption
(Ivchenko E. L., 1989; Bir G. L., 1972), the of light takes the form
1
K (1) = 1 p 2 e 2
^c ,V „tcV .3
3 ch n
Iff - f ^/(c,hh (lffl) +( f - f ,lh)k <lffl)
\\Jhh ,k™ fc kc ,hh +[ flh^ > Jc ^ >j kc ,lh
where the distribution functions of photoexcited light and heavy holes are defined as
fh & » - exp
LT
■ exp
1 ß
(c ,lh) +
LT m,.
(hœ- Eg )
fhh w = exp
LT
exp
E (k(lffl)V
hhy c,hh )
LT
= exp
LT
■ exp
1 ^
(c ,hh)
LT m.
hh
{hœ~ Eg )
(4)
(6)
(7)
and the Fermi energy is determined by the relation
1
y
ekET =- p 2
' LT v3/2
ml2 + m3i2
). (8)
V 2nh j
Figure 1 shows the spectral and temperature dependences of the coefficient of one-photon absorption of polarized light in GaAs, due to optical transitions between the
subbands of light ^K^ j and heavy *K^ j holes (fig. 1 a) and the conduction band, as well as the resulting one-photon absorption of light (fig. 116 b), where the contribution of the coherent saturation effect to the one-photon light absorption coefficient is not taken into account. In quantitative calculations, the maximum value of Ksl is chosen as one.
Figure 1. Spectral - temperature dependence of the coefficient of one-photon absorption of polarized light in GaAs, due to optical transitions between the subbands of light j and heavy i K^ j holes (a) and the conduction band and their sum (b)
1 V b)
From fig. 2 a and 2 b, it can be seen that the spectral (temperature) dependence of the one-photon light absorption coefficient in GaAs, due to optical transitions between subbands of the valence band and the conduction band, first increases with increasing frequency (temperature) and, passing through a maximum, decreases. This is explained by the fact that the spectral dependence of the
coefficient of one-photon absorption of light by the product of the density of states, with increasing frequency, which increases as a power function of frequency, and the distribution function of current carriers in the initial state, with increasing frequency, which decreases exponentially. The product of these quantities gives the graph shown in fig. 6. We note that here the temperature dependence
of the band gap is not taken into account, taking into account which will lead to a noticeable change in the spectral and temperature dependence of the one-photon absorption coefficient of polarized light, and it is shown in fig. 2 for GaAs. It can be seen from fig. 2 that, when the temperature dependence of the band gap is taken into account, the amplitude value of K + K oscillates with
c ,lh c ,hh
increasing temperature in the region of low frequencies, while in the region of high frequencies, this value remains almost unchanged. In calculations, the temperature dependence of the band gap was chosen as:
7g =
E (T) = Eg (0) + yT, wtere -0,5405 meVIK for ~ ' 2001).
GaAs (Vurgaftman,
Figure 2. Spectral - temperature dependence of the coefficient of one-photon absorption of polarized light in GaAs, due to optical transitions between the subbands of light holes
and the conduction band j without taking into account (a) and taking into account (b) the temperature dependence of the band gap on temperature
a) b)
One-photon absorption of light be- cient due to optical transitions between the tween the spin-orbit splitting zone and spin-orbital splitting zone and the conduc-the conduction band tion band is defined as
The spectral-temperature dependence of the one-photon light absorption coeffi-
K
c ,SO
(1)
4ne2 1
chn,, 3'
pCv UKCI2 + |e ; I2) (( , - f k )
h2 k2 2m„
or
1 n1 fl2
K(i) _i_e_Vcv_ ..(cs
Kc ,SO - 0 t2 <"+ kc SO J SO
3 chn h
,SO)k(lffl) J
*c SO J St
1- exp
kT
; Eg ;^so -
E
x -1 - Eso
f h2k2 ^
— hm
V 2mSO J J
V
J _ J ,
where ß
(c ,SO)
mmso
m + m
SO
hn'c,SO) - . is the reduced effective mass, k(lffl) = J—^-(hco - E ) isthe
c \ h2 ^ g'
vector of current carriers,
JSO kiSSS = exp
KT
■ exp
1 ^
(c ,SO)
k„T m
-(hœ- Eg - Eso )
SO
(10)
wave
(11)
is the distribution function of current carri- in optical transitions between the spin-orbit ers in the spin-orbit splitting zone involved splitting zone and the conduction band.
Figure 3. Spectral and temperature dependence of the coefficient of one-photon absorption of polarized light due to optical transitions between the spin-orbital splitting subband and the conduction band in InSb without (a) and with (b) the temperature dependence of the band gap and their ratio (c), where not the contribution of the coherent saturation effect to the one-photon light absorption coefficient is taken into account
Figure 3 shows the spectral-temperature dependence of the one-photon absorption coefficient of polarized light, due to optical transitions between the spin-orbital splitting subband and the conduction band in InSb without taking into account (a) and taking into account (b) the temperature dependence of the band gap and their ratio (c), where not the contribution of the coherent saturation effect to the one-photon light absorption coefficient
is taken into account. The red line marks the intersection of the spectral and temperature dependences of the one-photon absorption coefficient of polarized light, shown in figs. 3 a and 3 b. From fig. 3 it is seen that the spectral (temperature) dependence of the coefficient of one-photon interband absorption of light in InSb, both without taking into account and taking into account the temperature dependence of the band gap with increasing
frequency (temperature), first increases and reaches a maximum, and then decreases.
Conclusion
Thus, we have defined the following:
1. Spectral-temperature dependence of the one-photon absorption coefficient of polarized light in GaAs, caused by optical transitions between subbands of light holes and the conduction band, without and taking into account the temperature dependence of the band gap on temperature.
2. Spectral and temperature dependences of the one-photon absorption coefficient of polarized light, caused by optical transitions between the spin-orbital splitting subband and the conduction band in InSb without taking into account and taking into account the temperature dependence of the band gap and their ratio, where the contribution of the coherent saturation effect to the one-photon absorption coefficient is not taken into account.
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submitted 20.12.2023;
accepted for publication 26.12.2023;
published 24.01.2024
© Rasulov R. Y., Kasimov F. K., Isomiddinova U. M., Urinova K. K. Contact: r_rasulov51@mail.ru
