Dynamical effect of laser bumped electron- hole semiconductor By - PowerPoint PPT Presentation

5 th SPSP 5 th Spring Plasma School at Port Said 1- 5 March 2020 Dynamical effect of laser bumped electron- hole semiconductor By Amany Zakaria Elgarawany Assistant Lecturer of Mathematics, Department of Basic Sciences, - Modern Academy for computer sciences 3/5/2020 Amany Elgarawany PHD Researcher 1

I’ m Mathematician not Physicist 3/5/2020 Amany Elgarawany PHD Researcher 2

Introduction Outline Electromagnetic wave effect Objective of the Paper The wave Equation Dispersion Relation Sagdeev Potential Modified NLSE Appendix 3/5/2020 Amany Elgarawany PHD Researcher 3

Introduction An Electron is defined as a negative charge or negative atomic particle. A Hole as a vacancy left in the valence band because of the lifting of an electron from the valence band to a conduction band. Amany Elgarawany PHD Researcher 3/5/2020 4

Introduction  Hole is a positive-charge, positive-mass quasiparticle.  Holes can move from atom to atom in semiconducting materials as electrons leave their positions .  The mobility of electrons is higher than that of the holes, because the effective mass of electron is less than a hole. An electron-hole pair For every electron raised to the conduction band by external energy, there is one hole left in the valence band, creating what is called an electron-hole pair . 3/5/2020 Amany Elgarawany PHD Researcher 5

Introduction Recombination Occurs when a conduction-band electron loses energy and falls back into a hole in the valence band.  Recombination rate is controlled by the minority carrier lifetime.  Recombination mechanisms for materials is highly important for the optimization of semiconductor devices such as solar cells and light emitting diodes. 3/5/2020 Amany Elgarawany PHD Researcher 6

Introduction  Semiconductors are the materials which have a conductivity between conductors (generally metals) and non-conductors or insulators (such ceramics). 3/5/2020 Amany Elgarawany PHD Researcher 7

Introduction  Types of Semiconductors  Intrinsic Semiconductor ( holes = electrons )  Extrinsic Semiconductor ( excess or shortage of electrons )  N-Type Semiconductor ( Mainly due to electrons)  P-Type Semiconductor ( Mainly due to holes ) 3/5/2020 Amany Elgarawany PHD Researcher 8

Semi-conductor materials Material Symbol Usage Germanium Ge radar detection diodes - first transistors Silicon S integrated circuits -insulation layers Gallium arsenide GaAs high performance RF devices Silicon carbide SiC yellow and blue LEDs. 3/5/2020 Amany Elgarawany PHD Researcher 9

Semi-conductor materials Material Symbol Usage Gallium Nitride GeN microwave transistors -microwave ICs-blue LEDs Gallium phosphide GaP produce a green light-(+N ) yellow- green- (+ZnO) red. Cadmium sulphide CdS photoresistors - solar cells 3/5/2020 Amany Elgarawany PHD Researcher 10

• Recombination Process • Increase in current flow • Diffusion of charges • Decrease the energy gap EMW effect on • Decrease the mobility of Semi-Conductor carriers E-H particles • Increase the collision rate • Increase the conductivity (Intrinsic) • Decrease the conductivity ( Extrinsic) 3/5/2020 Amany Elgarawany PHD Researcher 11

Objectives • This study introduce the mathematical model of the interaction between electromagnetic field and electron hole particles. • Using Maxwell’s equations along with e-h fluid equations that contain laser field effect, we derive an evolution wave equation describing the system, which called a modified nonlinear Schrödinger equation (mNLSE). • The mNLSE is reduced to an energy equation containing the Sagdeev potential describing the localized propagating pulses in semiconductor. 3/5/2020 Amany Elgarawany PHD Researcher 12

The wave equation for homogeneous plasma • From Maxwell's Eqs. , we can extract the wave equation , which describe the propagation of laser field in the plasma.   2 1 A 4 J    A (1)  2 2 c t c       2 4 (2) e when          J en v q n v , and en q n (3) e e k k k e e k k k k 3/5/2020 Amany Elgarawany PHD Researcher 13

Laser - Electron – Hole Interaction 3/5/2020 Amany Elgarawany PHD Researcher 14

Laser - Electron – Hole Interaction • We can extract the wave equation , which describe the propagation of laser field in the electron-hole plasma.  2 1 A 4 π e   2 - A = - (n v n v ) (4) h h e e  2 2 c t c • And the Poisson eq.  2  = - 4 π e(n - n ) e h (5) • Where the velocity with relativistic effect e A e A v = , v = - e h m c γ m c γ (6) e e h h 3/5/2020 Amany Elgarawany PHD Researcher 15

Laser - Electron – Hole Interaction • Also from the relativistic fluid equation   V B  1        p ( . ) v p e E P   t e c n   (7) e at    p e A c / ( momentum ) , P n kT ( pressure ) (8) e e ,we derive the densities   2 m c q (a) for electron (9)  n = n exp - e (γ - 1) + e   e e0 e T T   e e   2 m c q  n = n exp - h (γ - 1) + h   (b) for hole (10) h h0 h T T   h h 3/5/2020 Amany Elgarawany PHD Researcher 16

Laser - Electron – Hole Interaction • The vector potential of the light takes the form 1 (11)   2  A = (r, t) (x + i y)exp i k.r - i ω t • The differential equation after substituting in eq. (4) takes the form      2   2 2 N N c k c          pe  2 e h i + i + 1 - + M 1 - = 0         t 2 2 2 2   (12) 2 1 + a 1 + M a     3/5/2020 Amany Elgarawany PHD Researcher 17

Laser - Electron – Hole Interaction • The resulting form from the wave equation after the scaling, the nondimensional form can be reduced to a modified NLSE      a 1 1 N N     (13)  2 i + a + 1 - e + M 1 - h a = 0      τ 2 2  2 2  2 1 + a 1 + M a     • Where 2 m c a         2 0 , t / , 0 pe (14) e            r c u / , u c k g pe g pe 3/5/2020 Amany Elgarawany PHD Researcher 18

Modified NLSE Modified NLSE • NL dispersion • Instability • The Sagdeev relation of system potential. • The modulat- • Solution of • The light ional instability NLSE by amplitude. growth rate HPM 3/5/2020 Amany Elgarawany PHD Researcher 19

The nonlinear dispersion relation - Growth rate • At the potential takes the form   (15)    a = ( a a )exp i , where a  a 0 1 0 1 Substituting in the differential eq.,      a 1 1 N N      2 e h i + a + 1 - + M 1 - a = 0 (16)      τ 2 2 2 2   2 1 + a 1 + M a     • The nonlinear frequency shift take the form     1 N ( a ) N ( a )       e 0 h 0 1 - + M 1 - (17)     2 2 2   2 1 + a 1 + M a       0 0 3/5/2020 Amany Elgarawany PHD Researcher 20

The nonlinear dispersion relation - Growth rate • We linearize the differential eq. (16) At   a      with respect to where � � a 1 = ( X iY )exp i . k i 1 is the frequancy of the low frequancy modulations , and X , Y are real constants. • After Tayler series , and linearization N ( ) a N ( ) a           * * * * e h ( a a ) , ( a a ) (18) 1 1 1 1 2 2 2 1 + a 1 + M a 3/5/2020 Amany Elgarawany PHD Researcher 21

The nonlinear dispersion relation - Growth rate • After substituting in Eq. (16) with respect to , the a 1 differential eq. takes the form  a a 1   (19)       2 * * 1 0 i + a M ( a a ) = 0  1 1 1 τ 2 2 • Let      * a U i V a U i V 1 1 • Assume the plane wave (20)           i k . i i k . i U u e , and V v e 0 0 3/5/2020 Amany Elgarawany PHD Researcher 22

The nonlinear dispersion relation - Growth rate • The nonlinear dispersion relation is   2 2 k k       2 * a 0 ( M )   (21) 2 2   • The modulational instability growth rate   2 k k          * i a 0 ( M )   (22) 2 2   3/5/2020 Amany Elgarawany PHD Researcher 23

The Sagdeev potential • The nonlinear system at   (23)     a( , z ) = w z ( )exp i Substituting in the differential eq.,      a 1 1 N N      2 i + a + 1 - e + M 1 - h a = 0      τ 2 2  2 2  2 1 + a 1 + M a     • The integration of a modified NLSE gives this form 1   2     w ( z ) ( w ) 0 (24) 2 3/5/2020 Amany Elgarawany PHD Researcher 24