INTERBAND SINGLE-PHOTON ABSORPTION OF POLARIZED LIGHT IN CRYSTALS WITH ALLOWANCE FOR THE EFFECT OF COHERENT SATURATION. 1-PART Текст научной статьи по специальности «Физика»

https://doi.org/10.29013/ESR-21-7.8-37-40

Rasulov Voxob Rustamovich, associate professor of Fergana State University.

Rasulov Rustam Yavkachovich, professor of Fergana State University Mamatova Makhliyo Adkhamovna, doctoral student of Fergana State University Isomaddinova Umida Mamirjonovna, teacher of the Kokand State Pedagogical Institute.

Kodirov Nurillo Ubaydullo ogli, doctoral student of Fergana State University

INTERBAND SINGLE-PHOTON ABSORPTION OF POLARIZED LIGHT IN CRYSTALS WITH ALLOWANCE FOR THE EFFECT OF COHERENT SATURATION. 1-PART

Abstract. The spectral-temperature dependence of the coefficient of single-photon absorption of light in crystals of tetrahedral symmetry, due to optical transitions occurring from the subbands of light and heavy holes to the conduction band, is calculated. In this case, the contribution of the coherent saturation effect to the single-photon light absorption coefficient is taken into account.

Keywords: polarized light, spectral and temperature dependence of the single-photon light absorption coefficient, crystal of tetrahedral symmetry, coherent saturation effect.

not calculated. This work is devoted to the solution of this issue. For this, we consider various variants of single-photon interband absorption of polarized light, which differ from each other by intermediate states. In particular, in the case of single-photon interband absorption of light, these intermediate states can be located both in the subbands of the valence band, and in the conduction band, or in the spinorbital splitting band. And also, depending on the

energy of photons, optical transitions can occur,

which differ from each other by initial states. In particular, in the frequency range Eg < ha < Eg + ASO, optical transitions are allowed between subbands of

light or heavy holes, but in the frequency range

ha > Eg + ASO , optical transitions from the spinorbit splitting zone to the conduction band are allowed. Therefore, we will consider them separately,

As indicated in the first part of this work, the nonlinear absorption of light in a semiconductor with a degenerate valence band, which is due to direct optical transitions between the subbands of heavy and light holes and depends on the state of radiation polarization, was studied in [1-8]. In these papers, it is assumed that the nonlinearity in the intensity dependence of the single-photon absorption coefficient arises due to resonant absorption saturation. This saturation is due to the photoinduced change in the distribution functions oflight and heavy holes in the region of m omentum space near the surface corresponding Ehh (k) - Ehj (k) - hrn = 0 to the resonance condition. Here, Ehh(k)(em(k) j isthe energy spectrum ofheavy (light) holes, and œ is the frequency of light.

In [1-10], the spectral-temperature dependence of the single-photon light absorption coefficient was

where ha is the photon energy, Eg is the band gap, [5-10], in further calculations ofthe spectral and tem-

ÀSO is the spin-orbit splitting energy. perature dependence of the single-photon light absorp-

Let us first consider the one-photon absorption of tion coefficient, we neglect the light wave vector, i.e. we

light between the subbands ofthe valence band and the assume that the wave vector of current carriers in the

conduction band (at E < ha < E + ASO ). Following final (initial and intermediate) state). Then

K(1)

C,±l/2;V,±3/2

2n l = — hœ-p(hœ)F (fi,1,rn) x h I

M (1) (k) C,±1/2;V,±3/2 V / 2

w 1 + 4 ^ h a> m (1) (k ) C,±1/2;V,±3/2 ^ ' 2

M(1)

C,±1/2;V,+3/2

T3/2(k)

1 + 4-

a

hV

M

(i)

C ,M 1/2;V, T 3/2

T 3/2(k )

(1)

where I, (a) is the intensity (frequency) of light, p(hœ) is the density of states of current carriers involved in optical transitions, where the law of conservation of energy is taken into account, F (j3,l, o) is the distribution function of current carriers in the initial state, kB is the Boltzmann constant, T is the sample temperature, F (fi,1,m) = [l - exp (l fihm))

transitions) where ^ (I) - *

j=

naœ2 4

2nc

is the light

exp El __hh (kCU ))

(hœ- Eg p(hm)

m_

EL=hh (kC, L=hh )

^ is the square of the absolute value ofthe matrix element Mr averaged over the

n k ,nk

/ „ A \2

a„

4-2 2

h a>

ch

2

m + m

(k2 h2)

hh

H is the

reduced effective mass of current carriers, the form of which depends on the type of optical transitions. Now we need to calculate

solid angles of the vector k, Za= 4

the wave vector kw is determined from the energy conservation law. In particular, for the optical transition

considered above kœ = kc, L =.

h2 k2

2m

( c, L)

M

(1)

C,±1/2;V,±3/2

(k )

A

(c, L ) _ mcmL

, E (k ) =

J h2

Eg, El () = ■

(hœ-EJ ,

h2k2

1 + 4 a \M (!) (tf

^KZC,±1/2;V,±3/2^)|

(2)

_f A ch

2

p2 [( I ) + K2(I )],

(it is these integrals that determine the averaged values of the matrix elements of the considered optical

mc + mL v ' 2mc v ' 2mL

mc (mL ) are the effective masses in the conduction band and in the valence band, L = Ih ( hh) are for the subband oflight (heavy) holes.

Calculation of single-photon absorption of polarized light due to optical transitions from the subband of light and heavy holes to the conduction band is performed by the formula

K (1)=-

4ne

or

K

(i) _

cam0 nH nn k 4ne2

I ePnn (k)f (fnk - fnk)5(En k-En(k)-H

(3)

c, SO

chn„

illiPV |e± |2 (( - fci )(( (it ) - Ehh (k) - ho)

+UJJ[f P

cV |

2

+1 Plv\e'±\ 6

+

(( - fci )(( (it)- Elh (it)- hffl)'

(4)

x

2

e

2

2

2

e

h2k2

where Eck =

Eg is the energy spectrum of

2/ 2

t2k

electrons in the conduction band, EL - = —— is the

Then, from the energy conservation law, we have expressions for the wave vectors of photoexcited current carriers involved in interband optical transitions as

2mr

energy spectrum of holes in the subband of light

h2 k2

(L = lh) and heavy (L = hh) holes, ESok =

=

c ,lh

2m

(c,lh)

2m„

- + A

SO

, h1 where ^Jh]

(Es), kCi

hh

2m

(c,hh)

mm

lh

M

(c ,hh)

h mm

{ha-Eg),

hh

is

the

E = ^

SOk 2m.

+ ASO is the energy spectrum ofholes in

the spin-orbital splitting zone.

mc + mih mc + mhh

reduced effective mass of electrons and holes.

The spectral-temperature dependence of the coefficient of interband single-photon absorption oflight, taking into account the latter relations, has the form

„2 „2

K(1) - 1 p2 ^IcL. {( f

J^-v — PcV U J hh,

ch n„

kc hh

- f ^ )hh)k(% + f ^ ) - fc ^ ) }

or

K (i) = 1

c,v 6 ch3n

2 2

cv

f h(Xm)u(c>hh) + f .,( c, lh)k(1s) Jhh, k? $Kc, hhH-+ Jih, kl S c, lh

1-exp

kT

( x -1)

(5)

(6)

hrn

where x =-, the distribution functions of photoexcited light and heavy holes are defined as

Eg

1 ^ Eg)

1" E 1

exp _ kBT _ ■ exp

kBT mih

fh

hh, ea

= exp

hBT

exp

hh

(kC,hh )

hBT

= exp

hBT

■ exp

i l,(c,hh)

(ha-Eg )

kBT mhhK g

(7)

(8)

and the Fermi energy is determined by the relation

1

ekT =- p 2

kBT 2 nh2

-3/2

(ml'C + m

13/2 ■ lhh

32 )-1

lh

(9)

Calculations show that the spectral and temperature dependences of the coefficient of single-photon absorption of polarized light in GaAs, due to optical transitions between the subbands of light (k^I j and heavy holes (d^ and the conduction band, as well as the resulting single-photon absorption of light, first increases with increasing temperature and photon energy and reaches a maximum, then falls. This behavior K<y(]h and K(1hh is due to the peculiarity of the temperature Fermi energy, as well as the temperature and spectral dependences of the distribution function of current carriers in the initial state.

Above, the temperature dependence of the band gap is not taken into account, the inclusion ofwhich will lead to a noticeable change in the spectral and temperature dependence of the single-photon absorption coefficient of polarized light.

Thus, we have received:

1. Spectral-temperature dependence of the coefficient of single-photon absorption of polarized light in GaAs, due to optical transitions between the subbands of light holes and the conduction band, where the contribution of the coherent saturation effect to the coefficient of single-photon light absorption is not taken into account.

2. Results are obtained both with and without allowance for the temperature dependence of the band gap.

References:

1. Ivchenko E. L. Two-photon absorption and optical orientation of free carriers in cubic crystals // Semiconductors.- Vol. 14.- Issue 12. 1972.- P. 3489-3485. (in Russian).

2. Rasulov R. Ya. Polarization optical and photovoltaic effects in semiconductors with linear and nonlinear absorption of light. Dissertation for thesis. of doctor's degree phys.-math. sciences. - St. Petersburg. 1993.- 206 p. (in Russian).

3. Ganichev S. D., Ivchenko E. L., Rasulov R. Ya., Yaroshetskii I. D. and Averbukh B. Ya. Linear and circular dichroism of drag current due to nonlinear inter subband absorption oflight in p-type Ge // Phys. Solidi State.- V. 35.- No. 1. 1983.- P. 104-108.

4. Parshin D. A., Shabaev A. R. Theory of nonlinear absorption of infrared radiation in semiconductors with degenerate bands. // ZhETF.- Moscow, 1987.- T.92.- Issue 4.- P. 1471-1484. (in Russian).

5. Rasulov V. R. Rasulov R. Ya., Eshboltaev I. Linearly and circular dichroism in a semiconductor with a complex valence band with allowance for four-photon absorption of light // Physics of the Solid State.-Springer,- Vol. 59.- No. 3. 2017.- P. 463-468.

6. Rasulov R. Ya., Khoshimov G. Kh., Kholitdinov Kh. / Linear-circular dichroism of the nonlinear absorption of light in n-GaP / / Semiconductors.- T. 30.- No. 30.- No. 2. 1996.- P. 274-277. (in Russian).

7. Rasulov R. Ya., Drag effect at three-photon absorption of light in semiconductors of the Ge type // Semiconductors.- T. 22.- No. 11. 1988.- P. 2077-2080. (in Russian).

8. Rasulov R. Ya. Linear circular dichroism in multiphoton interband absorption in semiconductors // Semiconductors.- T. 35.- No. 6. 1993.- P. 1674-1678. (in Russian).

9. Rasulov R. Ya., Rasulov V. R., Eshboltaev I. The theory of the four photon of polarized radiation in a semiconductor with complex band structure // American Scientific journal.- New York,- No. 2. 2016.-P. 93-96.

10. Rasulov V. R., Rasulov R. Ya., Eshboltaev I. Linear-Circular Dichroism of Four-Photon Absorption of Light in Semiconductors with a Complex Valence Band // Russian Physics Journal.- Springer,-Vol. 58.- No. 12. 2015.- P. 1681-1686.