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7LINEAR-CIRCULAR DICHROISM OF THE PHOTON DRAG EFFECT IN SEMICONDUCTOR SUPERSTRUCTURES
R.Y. Rasulov, G.A. Karimova,
I. Rahmatov
ABSTRACT
This article analyzes the electric field strength resulting from the transfer of momentum from linearly and circularly polarized photons to current carriers in a semiconductor superlattice. The expressions for the electric field strength of the PhDE (photon drag effect) in the case of linear and circular polarization are obtained, revealing a nonlinear and oscillatory character. The analysis also suggests the presence of linear-circular PhDE dichroism in the energy spectrum of a semiconductor superlattice. Finally, the energy parameter of the superstructure is estimated based on the intensity magnitude.
Keywords: Lorentz, consider, linear-circular, photon
АННОТАЦИЯ
В данной статье анализируется напряженность электрического поля, возникающая в результате передачи импульса от линейно и циркулярно поляризованных фотонов носителям тока в полупроводниковой сверхрешетке. Получены выражения для напряженности электрического поля ФДЭ (эффект фотонного увлечения) в случае линейной и круговой поляризации, обнаруживающие нелинейный и колебательный характер. Анализ также свидетельствует о наличии линейно-кругового дихроизма ФДЭ в энергетическом спектре полупроводниковой сверхрешетки. Наконец, энергетический параметр надстройки оценивается на основе величины интенсивности.
Ключевые слова: Лоренц, считать, линейно-круговой, фотон.
INTRODUCTION
It is known [1,2] that an incident electromagnetic wave transmits an impulse to current carriers, as a result of which they participate in directed motion. Depending on the experimental conditions, this leads to the appearance of a direct current (in a closed sample) or a constant voltage (in an open sample). Below, the strength of a constant electric field is calculated, due to the transfer of a momentum of a linearly -and circularly polarized photon of an electromagnetic wave to current carriers.
It is explained as the result of the action of the Lorentz force arising from the movement of carriers in the electric field of the wave in the presence of the magnetic
field of this wave. Consider a circularly polarized transverse electromagnetic wave with frequency ro propagating in a semiconductor superlattice along the z axis
sx = s0 cos («■1 - q ■ z ), sy = sQ sin (a^1 - q ■ z ), (1)
Hx = H0 cos (a ■ t - q ■ z ), # = - H0 sin (a-1 - q ■ z ), where q is the wave vector of the electromagnetic wave. We assume that the x axis is directed along the superstructure axis, and we choose the energy spectrum E( p ) of electrons in the form
ApI+p2)/ _WnJaPx
E(P)=(px + Py2m.-Wcos^ap/h j (2)
Here m* is the effective mass of electrons, is the energy parameter of the superstructure (superlattice).
We write the equations of motion of current carriers neglecting diffusion and recombination in the form
dV V e 1 dVy Vy e lT/rM
^ + ^= Ar(sx -1 V2Hy), —L + T = -*(Sy + -VzHx), (3) dt t m c dt t m c
dV V e , 1
z
^ = — (Sz +-(VH -VH)
j. * V z Vxv y x^
at t m c where x is the time of impulse relaxation, V = h 1 \7itE(p) is the group velocity of
the current carriers. The electric field strength of the photon drag effect Sz is determined from the condition of the absence of an electron flow along the z axis, i.e. from the condition V = 0.
After simple transformations, it is easy to obtain useful expressions for further calculations
Vx =—. (cos 6 + car sin 6) (4a)
x 1 + co2r2X }, (4a)
Vy = , //g0 2 (-ct cos 6 + sin 6), (4b)
y 1 + cr
where 6 = at - q r . Solving the third equation (3), taking into account (4a, 4b), we have
Vy = A + V0 XX [ Am sin(«m^ + W) + Bm sm^-O - W) +
m=1 n=1
Em CO s(«m^ + W) + Fm CO s(«m-10 - W)] +
+Dmn cos^O + (-1)» + R sin^O + (- 1)v W), (5)
where
A = №z + MH ° ( cos^-^rsin^), VQ = MH ,
C(1 + Û?~T~) 2 cfi
J0( x) J2m- 1 ( X2) Am = i,222 '
1 + a„,® r
F _ x)Vi(xj + (-1)m/0(xj/2m-1(x))
^ m =--r;-^^- ' (6)
1 + a ^ r
5 = A (a ^a , ), ^ = A (a ^ ^ a ),
m m\ m m-1' m m V^~m+1 m/'
D(2) = --
(2) _ ( (-1)m a^niœTjJ2m-1 (X ) + J2n (X) - J2m-1 (X) ^n
1 + ai2jVr2
mn
( 2) 2m-1(x) + J2n (X1) - J 2m-1(X1)J2n (x))
Rmn ,~n2 „ „ ( 1) , :
1 + a(2) ®2r2
mn
D{v) = D(2) (a(2} ), RM = R(2} (a(2) ^a{v)], am = 2• m, a2 = 2• (m + n -1),
mn mn \ mn mn / ' mn mn \ mn mn / 7 m 7 mn v J
a{2 = 2 • (m + n), a^ = 2 • (m - n -1), a% = 2 • (m - n -1),
a(,nn =-2• (m-n) , x = wr x, x = ^£0am" h 1 (1 +a>2T2, Jn(x)- Bessel functions
of the first kind of integer order n. In (1.5.5) underline are those expressions m = 1 that in case m = 1 do not depend on time for and contribute to the stationary component Vz. Separating the stationary component Vz in (1.5.5) and assuming that Vz = 0 we get an expression for the electric field strength when illuminated by light of circular polarization:
i) = - fg"H 2, (cosW — cz sin w) — WaH0 [J0(x)J1 (X)siny + J0(X)J1 (x)cosy]
n{\ + COT) en
(V)
The expression for the electric field strength of the EUV in the case of linear polarization £<(l) can be obtained from (7), neglecting the first term in it, i.e.
sZc)-s{zl) =—M£(>H° (cosy — cz sin y), (8) + c z )
As can be seen from (7) and (8), the dependence of the PhDE (photon drag effect) electric field strength on the intensity of the exciting light (1) is nonlinear and
has an oscillatory character, i.e. s'f'' and £<(l) can take both positive and negative
values. It can be seen from (8) that due to the presence of narrow allowed minibands in the energy spectrum of a semiconductor superlattice, it is possible to detect linear-
circular dichroism of PhDE not only with nonlinear but also with linear absorption of light.
Finally, we note that it is possible to estimate the value of the -energy parameter of the superstructure (superlattice) knowing the magnitude of the intensity I0. In the
case s[c = 0 we have
u.= MS0(I0)n2__(cosу/ — сот sin^^_
a(l + а>2т2) J0(x0)Jl(xw)(sin^) + J0(xw)Jl(x0)(cos^) ,
где x0 = x(I = /0), xw = xi(I = /0). CONCLUSION
Calculations show that when CO2 is illuminated by a laser with an intensity of I= 0.1 MW / cm2, a wavelength of 10.6 ^m (at which ют=32) and for a semiconductor (with a mobility of |=104cm2/(Vs)) with a superlattice with a period of =10-6 cm, we get the value Sz(L) =106 V/cm, and the value Sz(L) =106 V/cm.
From the latest analysis of the electric field strength, even in the semiclassical approximation, there is a linear-circular dichroism of the current of the photon drag effect in semiconductor superstructures.
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