Phương trình động lượng tử cho điện tử giam cầm trong siêu mạng hợp phần và hệ số hấp thụ sóng điện từ yếu bởi điện tử giam cầm trong siêu mạng hợp phần khi có mặt trương laser[r]
Trang 1Influence of Laser radiation on the absorption
of a weak electronmagnetic wave by confined electrons in compositional superlatices (case of
electron - acoustic phonons interaction)
Ngo Thi Ha
Hanoi University of Science, VNU; Faculty of Physics
Major:The theoretical physics and mathematical physics
Code: 60 44 01 Supervisors: PhD Dinh Quoc Vuong Date of Presenting Thesis: 2011
Abstract Giới thiệu tổng quan về siêu mạng hợp phần, và đưa ra biểu thức giải tích về
hệ số hấp thụ phi tuyến sóng điện từ yếu bởi điện tử giam cầm trong bán dẫn khối khi chịu ảnh hưởng của trường bức xạ laser bằng phương pháp phương trình động lượng tử Phương trình động lượng tử cho điện tử giam cầm trong siêu mạng hợp phần và hệ số hấp thụ sóng điện từ yếu bởi điện tử giam cầm trong siêu mạng hợp phần khi có mặt trương laser (trường hợp tán xạ điện tử-phonon âm) Tính số và bàn luận
Keywords Vật lý lý thuyết; Vật lý toán; Trường bức xạ laser; Sóng điện từ
Content
Survey interacting electron-phonon system in the compositional superlattices are present in the case of two electromagnetic waves is described
( ) sin sin
as the electric field intensity vectorE01
and 1 corresponds with the wall amplitude and frequency of electromagnetic waves has from the weak, and the corresponding amplitude and frequency of the laser radiation, t is time The corresponding vector of the form 01 02
( ) E c os E c os
Hamiltonian of the electron-phonon system in the compositional superlattices is written as:
0
,
( )
e
Trang 2' ', ,
, ,
n p
n p q
z
q n n p
,
n k
a
,
,
n k
a
is the operator of birth, destruction of electronic state n p,
; b q, b q is the
operator of birth, destruction of phonon state q
with wave vector q
, qqqz; p
is the electron momentum vector in the plane perpendicular to the z-axis of compositional superlattices;
q
is the phonon frequency; ' ,
.
I q z z e dz is in super form factor compositional superlattices; n p,
is the energy of electrons in compositional superlattices; C q is constant interaction depends on the mechanism of electron scattering - phonon; c is the speed of light; plank constant; e is the electron charge Using the transformation operator has obtained the quantum equation for the electron-phonon system:
' '
,
, , , ,
( )
n k
q n n
l s m f
n q
n t
D I q J a q J a q J a q J a q t
t
i
i
', ( )2 q n k, ( )2 q 1
n k q
i
n k q
n t N n t N
i
Here, the symbol x t is understood as the statistical average operator x; n n p,( )t is the
a eE m a eE m J( )z is the Bessel functions of real numbers;
N b b
is the particle number operator of electrons;
Trang 3, ( ) , ,
n t aa is the particle number operator of electrons; is parameters included the assumption of adiabatic interaction
From the quantum equation (4), Bessel functions and developed using Fourier transfer spectrum obtained analytic expressions for the absorption coefficient near
q
s m where the different scattering cases
The scattering electron - acoustic phonons:
2
z q
s O
q q C
v V
which VO is the normalized volume (selected V O 1); is the electric constant strain,
is crystal density; v s is sound velocity
'
3 2
2
2
, 0 02
B
n n
32 H H 16 H H H H 64 H G G G
(6)
in which:
7
4
4 3
a os2 exp
2
s m
s m
m
B a
exp exp
s m
5
4
4
2
s m
s m
m
B a
s m
3
4
4 exp
2
s m
s m
m
s m
Trang 4 '
0
B
1
m n
L
the first mini n, d is the super-cycle superlattices; n the energy levels in the isolated pits; m the effective mass of electrons; L z the width of the isolated holes; k B is the
Boltzmann constant; T is the absolute temperature;
3/ 2 3 0
n e n
V m k T
, n0 is the carrier
concentration; K( )z the second modified Bessel functions; is the angle between two vectors of electromagnetic waves; n n, ' is the Kronecker symbol
Survey of the compositional superlattices GaAs - Al0.3Ga0.7As Observed in the temperature region from 320K to 365K strongest dependence, the absorption coefficient decreased rapidly with the energy of electromagnetic waves with the same key and value temperature absorption coefficient value as positive, negative, even is zero This means that the absorption coefficient in the coefficient was converted to increase and it shows the difference compared with conventional semiconductors
From the Hamiltonian equations of electron-phonon system, has developed the quantum equations and get the expression for the coefficient absorption of weak electromagnetic waves by confined electron in the compositional superlattices in the presence of laser radiation field In the case of near threshold to get analytical expressions for the absorption coefficient for the mechanism of electron- acoustic phonons interaction The results showed that the absorption coefficient depends on the complexity of the system temperature, amplitude and frequency of the weak and electromagnetic wave laser radiation Also depends strongly on the parameters characteristic of the superlattice The numerical results for GaAs compositional superlattice GaAs - Al0.3Ga0.7As evidence for the results obtained by theory The new result is that in determining the conditions (temperature, wave energy .) with each other scattering mechanisms underlying the absorption coefficient can be negative means that the absorption coefficient into the coefficient to increase In limited cases while ignoring the nonlinear terms return results corresponding to the case of linear absorption
Trang 5References
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