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Rasulov Voxob Rustamovich, Researcher of Fergana State University E-mail: r_rasulov51@mail.ru Rasulov Rustam Yavkachovich, Professor of Fergana State University Karimov Ibrohim Nabiyevich, Professor of Andijan State University Abduxoliqov Akmaljon, undergraduate of Fergana State University Sultanov Ravshan Rustamovich, undergraduate of Fergana State University
TWO QUANTUM ABSORPTION OF POLARIZED RADIATION IN n-GaP
Abstract: The two quantum absorption of polarized radiation in a semiconductor with a camel's back band structure is theoretically researched.
An expression is for the spectral and temperature dependence of the absorption coefficient ofpolarized radiation due to optical transitions between the subbands of the conduction band obtained. In this case, the camel's backness of the lower subband of the semiconductor conduction band is taken into account.
Keywords: matrix element, photon, polarized radiation, optical transition, electrons, conduction band, semiconductor, light absorption coefficient.
Nonlinear absorption of light in a semiconductor with a degenerate valence band, due to direct optical transitions between subbands of heavy and light holes and depending on the state of polarization of the radiation, was studied in [1-8]. In these researches, it is taken to account that nonlinearity in the dependence of the single-photon absorption coefficient on intensity occurs due to resonance absorption saturation. This saturation is due to the photoinduced change in the distribution functions of current carriers in the region of the momentum space near the surface Exc (k ) - Exc (k) - ha = 0 corresponding to the resonance condition. Here Exc (k ) [exc (k ) J is the energy spectrum of electrons in the upper (lower) X3 (Xf) subzone of the semiconductor conduction band, m is the frequency of light.
However, the issue of absorption of polarized radiation in a semiconductor with a complex zone consisting of two subbands (branches) [9], between which there is an energy gap, remains open. The solution of this issue is devoted this work.
Next, we consider two quantum absorption of polarized radiation in n-GaP type semi-conductors, due to direct optical transitions between the subbands of the conduction band without taking into account the effect of coherent absorption saturation [10], i.e. consider the absorption of polarized radiation, where it is assumed that the photon energy hm satisfies the inequalities, where Eg is the band gap, Aso is the spinorbit splitting of the valence band.
Due to the smallness of the wave vector of the photon
compared to the wave vector of the electron (hole) formed as a result of absorption, when calculating the N-photon absorption coefficient of light (K(Na,T), we can assume q << k and assume q = 0. Then, according to [2; 3], the absorption coefficient can be written as
K (Nv,T ) = N 2n— x
H 1 (1) x X (( -fXN,l)KW(k)|2-Exfk -Nno) '
k ,m=±l/2;m'=±3/2
where Mxc,xc (k) is the matrix element of the optical transition from the state |xf to |x3,k^, k is the wave vector of elec-
n û)2 A2
trons, I = —~ is the light intensity, Ek is the energy spectrum of electrons in the subzone l ( l = Xf, Xf ), fkN' is their nonequilibrium distribution function for N-photon absorption of light, nm - is light refraction index at frequency m . Other quantities are well known.
It is clear from the last relation that to determine the spectral or temperature dependence of the optical parameters of a semiconductor, for example K (Nm,T ), it is necessary to calculate the composite matrix elements of the considered optical transitions and we will analyze them below for specific cases.
In the future, to calculate K(2®,T) in the case of absorption of linearly polarized light, we choose the following geometry of the experiment e = (0,0,ez) ,i.e. light propagates across to the main axis of symmetry of n-GaP. Then
Section 14. Physics
* (4 ) = ^f A | X faj f (Ek )s( - Ek - 2ha),
fia-A((a))'
*(2®T) = ^{A) X\r?Jf (EkHEk - Ek - 2M>(*6)
where the intersubband matrix element of the momentum operator for the vertical optical transition will be as
P, = %H (k)Xf ) = m [Perf* + no^D (( + exky )]
kp3i.= mH X 3C )| V î H (k)Xf) = ^ [Pe^+n^D ( + exkr )],
h
where n '
A2
A2 + 4P 2k
,(31) -.
2Pk
(31) _ .
^A2 + 4P 2k: A '
2 ; °y h
■\Ja2 + 4Pk2 '
f (ex(C) (k)j isdistribution function of electrons with
en-
ergy EXC) (k) = E.
1. Spherical zone. Energy spectrum
A
Ex,,x, (k) = A3,ik2 + B,,ki ±-, Next, we consider the following geometry of the experiment: ez = 0, ex # 0, ey # 0, where
lepJ2 = m2n'D2 (ek + ek )2 2 A 2 2 I n2 i y x y! A2 + 4P k
z
Then the light absorption coefficient in the spherical approximation in the energy spectrum will be as
* (2»;T>=cnMU)k■f (0,
Ef - Ak--
F 1 " 2
kBT
. From the law of conserva-2fia- A
where f ( ) = exp
tion of energy s (( - E^ - 2ft®) we have k2m = 2nC°—A.
(A3 - A3 )
Next, choose the following geometry of light absorption:
2
ez ± 0, ex = 0, ey = 0, then it is easy to get that |ep3112 = ^ P2e2z. Then the light absorption coefficient is determinedly the formula
* (2a, T)
e2 kBT l
fiffl-Ak; ef _ kBT JB
cnmh B k?
Now choose the following light absorption geometry that satisfies the conditions ez = 0, ex # 0, ey # 0. Then the intersub-band absorption coefficient of polarized radiation is determined by the ratio
l
c^ (2n) A2
( - Ek -
K ±(a,T) =
xfdkkdkmD2(ek + ek ) 2 2 2 J x y z n2 \ x y x y) A2 + 4P k2 From the law of energy conservation, the wave vector of electrons participating in intersubband optical transitions depends on the frequency of the light and on the band parameters: k(a = —^4h2a2 - A2. Then for the spectral and temperature dependence we have
K ±(2a,T ) = -
D2
kBT
_A_ fia
l
32cnah P2 y B J y ha J k(a)
a v XV y Z
where nm is the refractive index of light for n-GaP at the frequency m . This shows that the spectral dependence of
K±(<o,T) is inversely proportional to kz0, and therefore when
2 —1-1/2
ha^A it has a root feature of the type ^" 1 , which
arises due to the presence of a "camel's back" in the lower subband X . If the light propagates along the main axis of symmetry of n-GaP, then
K±(a,T ) =
l e_ J_ 8 cfi n„
kBT
D2 A
exp
V kBT
exp
ha- 2Ak(f kBT
B ) P2 ha
and the above root feature is not. This is due to the absence of a "camel's back" in the Xx and X3 subzones in the direction perpendicular to the main axis of symmetry in n-GaP (It does not take into account the anisotropy in the refractive index of light). Further, the intersubband light absorption coefficient is
investigated in the approximation A+=-(A + A1), 12
B+ — — (B3 + Bj ,when the electron energy spectrum has the form
Ex,,xi = AA2 + B+ki ±|T-
p 2k 2
In this case, the intersubband matrix element of the pulse operator takes the form
|ep3if = D (ek + ek )2 A2
h2 A2 + 4P2kz2
From the law of conservation of energy we get
k«=A
z 2P
ha A
-1
Then K±(2a,T) in this case it is defined as in case 2.1, where in the results it is necessary to make the following replacement A+ A, B+ ^ B, i.e.
K ±(2a,T ) =
22 D21 kT ^ A l
32cn fi P2
ha! k
lr(a
fia-A+(k(a) )
. kBT ! kT
x ev B ! ek"' So for various geometry of the experiment, the relations
for the spectral and temperature dependences of the absorption coefficient of polarized radiation in a semiconductor camel's back band structure were derived and limited only to qualitative analysis due to the absence of experimental results.
In conclusion, we note that a similar problem can be solved for hole conduction tellurium, since one subband of the valence band in which has a camel's back structure. This case requires separate consideration.
The work was partially funded by a grant 0T-02-66.
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