1. COULOMB INTERACTION OF He -like IMPURITY IN SEMIMAGNETIC QUANTUM DOT
P.Kalpana, P.Nithiananthi and K.Jayakumar*
Nanostructure lab, Department of Physics, Gandhigram Rural University, Gandhigram, Tamilnadu, India

2. Spintronics
A new class of device based on the Quantum of electron spin, rather than on charge, may yield next generation of microelectronics

3. SPINTRONICS – Interplay of the Spin / Charge / Photon creates a better world than with the today’s microelectronic devices
Spin
Transport
Photon
(Magnetism)
Charge
(Electronics)
Magneto Optical IC
Spin -LED
Quantum Computer
MRAM
Spin - FET

4. Why Spin? Connection between spin and magnetism
Intrinsic connection between spin and quantum mechanics
Short range spin – dependent exchange interactions
Speed and Power Dissipation
Long coherence or relaxation

5. Giant Magneto Resistance
To some people, years = a decade.
To IBM Research, years = a revolution.
a very large change in electrical
resistance in a ferro magnet / para
magnet multi layer structure. – Makes it’s mass market debut in IBM’s record breaking 16.8 gigabyte hard disk for desktop computers

6. Spins and Scattering
An electron moving into a magnetized region will exhibit spin-dependent scattering
Electrons with spins in the direction of the magnetic field will scatter less than electrons with spins opposite the direction of the magnetic field
Magnetization

7. GMR in Magnetic Layered structures – without magnetic field
Alternate layers of ferromagnetic material will naturally align with opposite magnetization
All electrons coming in will scatter since they’ll have opposite spin from magnetization in some region
Ferromagnetic material with magnetization in direction of turquoise arrow
Non-ferromagnetic material spacer

8. GMR in Magnetic Layered structures – with magnetic field
If an external field is present, ferromagnetic layers will all align with external field
Only half of the electrons coming in will scatter maximally, those with spin opposite external field
Ferromagnetic material with magnetization in direction of turquoise arrow
Non-ferromagnetic material spacer
Externally applied magnetic field

9. Datta – Das Spin Transistor – First spintronic device

10. Why Diluted magnetic semiconductors (DMS)?
Crucial element for the success of spintronics – To find a proper material that combines the desirable properties of ferromagnetism and semiconductors
Role of the interface separating different materials and how to create and measure spin polarization
Spin Injection
Spin Transport
Spin Detection
Normal metal –Semiconductor contacts
Directly injecting spins from Ferro magnet into a nonmagnetic semiconductor
Obtained spin polarization substantially smaller
Do not amplify signals
Complete picture of transport across the interface is not yet available

11. Reduces the significant material differences
Advantages:
Reduces the significant material differences
Provides Spin Polarized Carriers
Diluted Magnetic Semiconductors –Magnetic ions partially substitutes the Cations in the host lattice and become diluted semiconductors , where x – Magnetic ion concentration
Eg: CdTe/Cd1-xMnxTe, GaAs/Ga1-xMnxAs
Concentrated Diluted Non - magnetic
Magnetic Semiconductor Magnetic Semiconductor Semiconductor
Magnetic ion
Cation
Anion

12. INTRODUCTION: DILUTED MAGNETIC SEMICONDUCTORS
Magnetic Semiconductors basically a Semiconductor with filled Valance Band and empty Conduction Band.
Energy bands can be described by band theory similar to ordinary Semiconductors.
Wavefunctions are Bloch functions – not localized at a particular atom but extending over the entire crystal.

13. Mn as an impurity: II-VI vs III-V
II III IV V VI Si P Sn Se Zn Hg Cd B C Al N O S Ga Ge In As Sb Te Mn
(III, Mn)-V
(Ga,Mn)-As
(In,Mn)-As
(II,Mn)-VI
(Cd,Mn)-Te
Mn in III-V semiconductors: acceptor level below VB top (hole picture!) → hydrogenic acceptor level
Mn3+ becomes Mn2+ (spin 5/2) + weakly bound hole
Mn in II-VI semiconductors: no levels in gap, stable Mn2+ (half filled) → only introduces spin 5/2, no carriers

14. IMPORTANCE OF (II,VI)Mn DMS
Smaller Defect Concentrations and easier to dope with shallow impurities
Tunability of their lattice parameters and their energy gaps Preparation of quantum wells, superlattices, bandgap engineering
Why CdTe, Particular?
Direct band gap
Crystal structure – Zinc Blende
Bandwidth intermediate between narrow
and high

15. Electronic configuration for
Cd – 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2
Te - 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2 5p4
Mn - 1s2 2s2 2p6 3s2 3p6 3d5
Exciting combination of both magnetic and Semimagnetic properties.
Exhibit magnetic hysteresis effect
Magnetic Compounds – in general contain transition metal atom with partially filled d – shells
Electronic states are derived from 3d – orbitals
e- s in these d – state are more localized which are responsible for localized magnetic moment in Magnetic Semiconductor.

16. Exchange Interaction between Charge Carrier and localized
Ferro magnet has spontaneous magnetic moment i.e e- spin and magnetic moment arranged in regular manner and there is an internal interaction tending to line up the magnetic moment parallel to each other – exchange field
This exchange interaction orient magnetic moment leading to net magnetization below Tc.
Exchange Interaction between Charge Carrier and localized
magnetic moment
g = Lande Splitting Factor
B = Bohr Magneton
 = g B Sn
Magnetic atom Sn S Rn
Conduction e- r

17. The Hamiltonian for conduction electron interacting
with magnetic atom is given by
Unperturbed Interaction between Interaction between
Hamiltonian conduction e- & localized moments
magnetic moment

18. Giant Zeeman Splitting

19. BOUND MAGNETIC POLARONS IN SEMICONDUCTOR LATTICE
Because of polarization of the spin system there is a possibility of charge carrier might be self trapped – Magnetic Polaron
These electrons lie in their hydrogenic orbital with characteristic Bohr radii
As their concentration increases , their individual orbits extends out into narrow impurity bands
The electron interacts with all the magnetic ions that lied within that orbit.
Each electron has an exchange interaction with all the magnetic ions lying within it’s orbital or ‘Sphere of influence’
If there are large enough number of magnetic spins within the orbital , the electron is completely spin polarized
The atomic magnetic moments have an indirect exchange interaction mediated by the carriers, that results in ferromagnetic ordering
BOUND MAGNETIC POLARONS IN SEMICONDUCTOR LATTICE

20. IMPURITY DOPING OF CdTe AND CdMnTe
Un intentional Or
Intentional
Donors
Acceptors
Shallow
Deep
Indium Dopants, Halogen Atoms n-type CdTe
P, As and Sb Dopants p-type CdTe
Impurities
Doping Not only Provides free carriers but undesired formation of deep defects

21. He – like IMPURITY In CdTe/Cd1-xMnxTe
Quantum Dot Z
Energy
Conduction band
Cd1-xMnxTe
CdTe EB
Esub
<H>min

22. Quantum Mechanical Tunneling
Classical electrodynamics - forbids flow of current through an insulating barrier M
Sc / I M e-
Application – has voltage –
non vanishing probabaility for
an e- to tunnel through I – barrier giving rise to flow of current
Quantum Mechanics

23. Single electron Transistor
The single-electron tunneling transistor - a device that exploits the quantum effect of tunneling to control and measure the movement of single electrons was devised. Experiments have shown that charge does not flow continuously in these devices but in a quantized way.

24. Coulomb Blockade
a) When a capacitor is charged through a resistor, the charge on the capacitor is proportional to the applied voltage and shows no sign of quantization. (b) When a tunnel junction replaces the resistor, a conducting island is formed between the junction and the capacitor plate. In this case the average charge on the island increases in steps as the voltage is increased (c). The steps are sharper for more resistive barriers and at lower temperatures.

25. Coulomb Interaction and the Binding of He like impurity in Semimagnetic Cubical Quantum Dot (CQD) Under Square Confinement

26. THEORETICAL FRAMEWORK
Methods used
EFFECTIVE MASS APPROXIMATION
VARIATIONAL PROCEDURE GROUND STATE IMPURITY ENERGY

27. barrier model) in the effective mass approximation is given by
The Hamiltonian of the two donor electrons in a CdTe/Cd1-xMnxTe QD (in the finite
barrier model) in the effective mass approximation is given by
where, g = ħwc/2R* (wc – cyclotron frequency) is the parameter of the strength of the magnetic field and (g =1 corresponding to Tesla).
The effective confinement potential for the cubical QD is given as,
where, L = size of the CQD and V0=70%DEgB.

28. The external applied magnetic field strongly changes the difference in the band gap between Cd1-xMnxTe and CdTe by[1]
- Band gap difference between Cd1-xMnxTe/CdTe without magnetic field.
- is chosen with  as a parameter(=0.5) and 0 as the critical
magnetic field which depends upon the value of the composition ‘x’
Eg (Cd1-xMnxTe) = x (meV). The critical field (in Tesla) for other
values of composition (x) is given as B0 = A2exp[nx], where, A2 = and n=
The trial wavefunction for the singlet ground state is chosen as

29. evaluate the electron – electron interaction energy.
Where, a=(2m*E/3)1/2, b=(2m*(V0-E)/3)1/2 and  is the variational parameter and Cee is obtained from the continuity condition
The minimum of the Hamiltonian is evaluated and the variational parameter λ
is fixed in the wave function ψ1s (r1, r2) and this wavefunction is used to
evaluate the electron – electron interaction energy.
The lowest energy (E) without the donor impurity is obtained by using the transcendental equation
The binding energy of double donors in the presence of magnetic field is found by solving the Schrödinger equation variationally, and is given by

30. Electron-Electron interaction energy against Dot size for x=0
Electron-Electron interaction energy against Dot size for x=0.3 for various magnetic fields.
On CentreIE > On EdgeIE
For Narrow Dot size, There is no appreciable difference between OC and OE Interaction energy because of the behaviour of the wavefunction.
For L < 90Å, IE as the magnetic field
Turnover occurs at higher magnetic field B

31. (W a 1/L2), W = Effective confinement frequency
(VCoulomb a 1/L), Vcoulomb = Interaction energy between donor electrons, L = Dot Size
Decreasing Dot Size Increasing Dot Size

32. Attributing the turnover feature to the interplay between three forces
At lower QD radius the repulsive force gain in strength and causes tunneling which in turn reduces the IE
Attractive Force due to the confining potential in a dot that tends to confine the electrons together
Repulsive force due to the Coulomb interaction between the electrons themselves
Magnetic field which reduces the confinement and aids the repulsive forces.
First B
Second
Third

33. electron-electron interaction energy against Dot size for x=0
electron-electron interaction energy against Dot size for x=0.3 for various magnetic fields.
A shallow to deep transition of the Binding Energy (BE) as the dot size reduced, since the < Potential > seen by the electrons becomes more negative (Attractive) as Dot size (L) reduces
When g = critical field, BE decreases because of the reduced barrier height
BE for OC impurity than OE impurity because of the delocalization of the e- wavefunction towards the Cd1-xMnxTe barrier since the barrier potential increases (Interaction of Mn2+ in the barrier and the external magnetic field) .
But for g = 5, No appreciable difference in BE When impurity is at zi=0 and zi= L/2, because the amount of increase of KE and PE for OC and OE impurity is of the same order

34. Drastic difference in Potential Energy of Mn2+ on the carriers and low expectation value of PE even though the KE increases, upto 100Å
Beyond 100Å, the OE binding energy for g=0 << both OC and OE binding energy for g=5 only because of the predominance of potential energy
Variation of potential energy of Mn2+ on the carriers (meV) against dot size for with and without magnetic field
Dot Size (Å)
g=0
zi=L/2
g=5 50 70 90
0.0927
100
200
250
350

35. Conclusions
Both BE and IE is larger only when the impurity is at on center of the well
This behaviour is slightly changed in the narrower dot region when the magnetic field is applied externally.
This work will be very useful for understanding the Coulomb blockade in Nanostructured systems and to understand the two particle spectra also.

36. References
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Pandey R K, Manoj K Harbola and Vijay A Singh, J.Phys.:Condens.Matter 2004, 16:
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Bastard G, Brum J.A. and R.Ferreira: Solid State Physics 1991, 44: 229.
Falicov L. M, Physics Today 1992, 45:46
Von Ortenberg M, Phys.Rev. Lett. 1982, 49:104

37. Thanks For Your Kind Attention