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Section 14. Physics
Section 14. Physics
Rasulov Voxob Rustamovich, researcher of Fergana State University E-mail: [email protected] Rasulov Rustam Yavkachovich, professor of Fergana State University Eshboltaev I. M., resarcher of Kokand State Pedagogical Institute.
Mamadaliyeva N. Z., Graduate student of Kokand State Pedagogical Institute
A SINGLE-QUANTUM SHIFT PHOTOCURRENT IN PIEZOSEMICONDUCTORS
Adsract: The spectral and temperature dependence of the shift photocurrent in piezosemiconductors is calculated, which is due to the carrier current shift in each act of interaction of electrons with photons.
Keywords: electrons, photons, temperature, shift photocurrent, semiconductors.
At the present time, two mechanisms of the LPhGE have become known: the ballistic mechanism due to the asymmetry of the processes of scattering, photoionization and recombination [1-3] and the shift mechanism associated with the shift of the center of gravity of the wave packets of photoex-cited electrons during quantum transitions [4].
A linear photovoltaic effect (LPhGE) is understood as the photoelectric effect caused by the appearance of a photocurrent in homogeneous piezoelectric crystals under uniform bighting. The polarization dependence of the resulting photocurrent density (j ), proportional to the light intensity (I), is described by the phenomenological relation
ja= IXaPy 1 (e/y + eye'fi) (1)
Here e is the polarization vector of the electromagnetic wave, Xapy the LPhGE tensor.
In this work, we consider the photon mechanism of shift LPhGE in n-type gallium phosphide, caused by carrier displacement during direct optical transitions of electrons between the subbands of the conduction band, taking into account the "hump" of the subband n-GaP multivalley semiconductor, the extremes of the valleys of the conduction band are located at points X of the Brillouin zone [6].
This mechanism was first considered in [5] in the spherical approximation in the energy spectrum. Each valley of the conduction band consists of two subzones XC, XC. The energy spectrum of electrons in these subbands is determined with the Hamiltonian [6; 9; 8]
H (k ) =
A3k2 + B3k2 + À /2
-iPk + Dk±,
iPkz + Dkk Afc + Bk - À /2
(2)
where k± = kx + ky is the two-dimensional electron wave vector, A13, B13, P, D are the band parameters of the semiconductor, A is the energy gap between the subbands and at the point X of the Brillouin zone. According to (2), the energy spectrum of the electrons in the subbands XC and XC is described by:
(k ) = ^ [(a, + A3 ))2 + ( + B3 )k 1 ]±
± 1 [[(A3 - A, )k2 +(3 - B, )-a]2 +| 2 i+4Pk2 + 4D2kk2
(3)
In the two-band spherical approximation [7; 8], i.e. when A - A3 = A, Bj - B3 = B, (3) is transformed to the form
E13 (k) = Ak2 + Bki ± + Pk + D2k2xk
(4)
The wave functions of the electrons near the point X in the basis (2)
=
C,
v C2 j
where C12 ±n ,
1
n = 2
Vxç =
A
r C 2^
v-Ci j
A2
(5)
(6)
— + P 2k2 + D 2k2k2 4 z % y
In the further calculations, we restrict by the contribution to the shift LPhGE current of electrons in which the wave
A SINGLE-QUANTUM SHIFT PHOTOCURRENT IN PIEZOSEMICONDUCTORS
vectors lie in the region
2Dkk
« A, 2Pk . Therefore, the
value Dkxky is taken into account only in the mespodzon matrix element of the momentum operator. Because Dkxky is responsible for the appearance ofboth ballistic [5; 7] and shift LPhGE in n-GaP. According to (2)
dH
ep3i = -
dk
X =
= m[iPez -nD(exky + eykx )].
(7)
We note here that for n-GaP the energy gap between the subbands of the conduction band is greater than the energy of the LO phonon and the average thermal energy of the electrons. Therefore, the nonphoton real transitions of thermal-ized electrons from the subband X^ to X33 (and back transitions) are absent. Therefore, optical transitions involving phonons, shown in (Fig) contribute to the n-GaP ballistic LPhGE, where a solid (thick) line is an electron, a wavy one is a photon, and a dashed line is a phonon.
Figure 1. Optical transitions involving phonons Next, we calculate the shift LPhGE current in n-GaP, which is related to the direct optical transitions between the subbands and without the participation of phonons, where we use the formula [4].
•$om _
J a
ee e
2nm„© hcn.
ZJ dk I
Im
r 31;n
dk
p3f
r31;n
(8)
x<5(E 3 (k )- E1 (k )- ha>)
where n is the number of the valley (The remaining notations correspond to the notation of [4])
The substitution of (7) in (8) and the sum over all valleys gives an expression for the shift LPhGE current
1 (e S + e S V
: \ x ay y ax 1'
:<t°m =_\e\ — KL,e
J a 4- €08 "
ha
(9)
•$om _ oi
J a ~ j0
~kT
ch
A
v kbt j
exp
ho (ho) -a2
(2P )2
kT
e(eS
lhoJ x a
+ e S
y ax
I
DN '
where, j0!om = -8n2 \e\—B1A12--, N' is the concentration
Jo 11A 11 P A
of free electrons, K is the light absorption coefficient for a direct optical transition of electrons between the subbands X% and X 3C. It is seen from (9) that the temperature variation of the shift LPhGE current is completely determined by the temperature dependence of the light absorption coefficient.
Let us compare the current of the ballistic contribution to the LPhGE calculated in [5; 7] in the spherical approximation in the energy spectrum (4) (that is, when A1 = B1, A3 = B3, P = O ), taking anisotropy into account in the matrix element of the optical transition X33 - X33, with a shift photo-current (9). Calculations show that at T = 200 K, the ballistic current of the LPhGE is five times greater than the shift current. In the estimation, we assumed that (the energy of the LO phonon), A = 335 MeV, Pa0 = D, a0 = 5,4-10-8sm (lattice constant).
The work is partially financed by the grant OT-F2-66.
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