Transcript
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Fizyka przyrzadów ˛ spintronicznych z nanodrutów półprzewodnikowych Janusz Adamowski Paweł Wójcik, Maciej Wołoszyn, and Bartłomiej Spisak Wykład wygłoszony na konferencji ”From Spins to Cooper Pairs”, Zakopane, 22-26 wrze´snia 2014
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
The spintronics is based on the spin-polarized currents that are generated by spin filters, modified/controlled by spin transistors.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
The spintronics is based on the spin-polarized currents that are generated by spin filters, modified/controlled by spin transistors.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
The spintronics is based on the spin-polarized currents that are generated by spin filters, modified/controlled by spin transistors.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
These spintronics devices can be fabricated in: planar (mesa-type) geometry, vertical (nanowire-type) geometry.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
These spintronics devices can be fabricated in: planar (mesa-type) geometry, vertical (nanowire-type) geometry.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
These spintronics devices can be fabricated in: planar (mesa-type) geometry, vertical (nanowire-type) geometry.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
In my lecture, I will mainly focus on the nanowire-based spintronics devices. I will introduce the physical background of the operation of spin filters and spin transistors.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
In my lecture, I will mainly focus on the nanowire-based spintronics devices. I will introduce the physical background of the operation of spin filters and spin transistors.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Vapor-liquid-solid (VLS) growth mechanism of Si semiconductor nanowire.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
”Forest” of GaAs nanowires.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
SEM image and (inset) schematic of a back-gated InSb nanowire field-effect transistor with Ni metal contacts. M. Fang et al., J. Nanomaterials (2014).
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Cross section of the hexagonal InGaAs core-shell nanowire. K. Tomioka et al., Nature 488 (2012) 189.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Transistor based on p-type Si Gate-All-Around (GAA) nanowires. G. Larrieu and X.-L. Han, Nanoscale 5 (2013) 2437. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Typical size of semiconductor nanowires: length L ∼ 1µm diameter D ' 10 ÷ 100 nm =⇒ quasi-one dimensional structures
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Typical size of semiconductor nanowires: length L ∼ 1µm diameter D ' 10 ÷ 100 nm =⇒ quasi-one dimensional structures
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Typical size of semiconductor nanowires: length L ∼ 1µm diameter D ' 10 ÷ 100 nm =⇒ quasi-one dimensional structures
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Typical size of semiconductor nanowires: length L ∼ 1µm diameter D ' 10 ÷ 100 nm =⇒ quasi-one dimensional structures
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Outline
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Outline
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Outline
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Outline
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Outline
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
I. Physical background of spintronics
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The operation of spintronics devices is based on the interaction between the electron spin magnetic moment and effective magnetic field. This interaction is of relativistic origin and can be derived from either the classical electrodynamics or quantum relativistic theory (Dirac equation).
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The operation of spintronics devices is based on the interaction between the electron spin magnetic moment and effective magnetic field. This interaction is of relativistic origin and can be derived from either the classical electrodynamics or quantum relativistic theory (Dirac equation).
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
In my lecture, I will consider only the spin-polarized electrons in semiconductors. These considerations can also be applied to the holes in semiconductors if – in the following formulas – we replace the electron charge q = −e, band mass me , etc., by the corresponding quantities characterizing the hole, i.e., q = +e, mh , etc.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
In my lecture, I will consider only the spin-polarized electrons in semiconductors. These considerations can also be applied to the holes in semiconductors if – in the following formulas – we replace the electron charge q = −e, band mass me , etc., by the corresponding quantities characterizing the hole, i.e., q = +e, mh , etc.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
In my lecture, I will consider only the spin-polarized electrons in semiconductors. These considerations can also be applied to the holes in semiconductors if – in the following formulas – we replace the electron charge q = −e, band mass me , etc., by the corresponding quantities characterizing the hole, i.e., q = +e, mh , etc.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Classical electrodynamics
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
If the electron with charge q = −e (e is the elementary charge) and rest mass me0 moves with velocity v in external magnetic (B) and electric (F) fields (measured in the laboratory frame), then – in the reference frame moving together with the electron – the electron experiences the magnetic field Beff = B + BSO , where BSO = −
1 v×F. c2
(1)
(2)
Eq. (2) results from the Lorentz transformation of the electromagnetic field and is valid with the accuracy of (v/c)2 , where c = velocity of light in vacuum. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
If the electron with charge q = −e (e is the elementary charge) and rest mass me0 moves with velocity v in external magnetic (B) and electric (F) fields (measured in the laboratory frame), then – in the reference frame moving together with the electron – the electron experiences the magnetic field Beff = B + BSO , where BSO = −
1 v×F. c2
(1)
(2)
Eq. (2) results from the Lorentz transformation of the electromagnetic field and is valid with the accuracy of (v/c)2 , where c = velocity of light in vacuum. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
If the electron with charge q = −e (e is the elementary charge) and rest mass me0 moves with velocity v in external magnetic (B) and electric (F) fields (measured in the laboratory frame), then – in the reference frame moving together with the electron – the electron experiences the magnetic field Beff = B + BSO , where BSO = −
1 v×F. c2
(1)
(2)
Eq. (2) results from the Lorentz transformation of the electromagnetic field and is valid with the accuracy of (v/c)2 , where c = velocity of light in vacuum. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
If the electron with charge q = −e (e is the elementary charge) and rest mass me0 moves with velocity v in external magnetic (B) and electric (F) fields (measured in the laboratory frame), then – in the reference frame moving together with the electron – the electron experiences the magnetic field Beff = B + BSO , where BSO = −
1 v×F. c2
(1)
(2)
Eq. (2) results from the Lorentz transformation of the electromagnetic field and is valid with the accuracy of (v/c)2 , where c = velocity of light in vacuum. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
If the electron with charge q = −e (e is the elementary charge) and rest mass me0 moves with velocity v in external magnetic (B) and electric (F) fields (measured in the laboratory frame), then – in the reference frame moving together with the electron – the electron experiences the magnetic field Beff = B + BSO , where BSO = −
1 v×F. c2
(1)
(2)
Eq. (2) results from the Lorentz transformation of the electromagnetic field and is valid with the accuracy of (v/c)2 , where c = velocity of light in vacuum. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The electron with spin s possesses the spin magnetic moment µs = −
gµB s. ~
µB = e~/(2me0 ) = Bohr magneton g = Lande factor In vacuum g = 2 (with accuracy of 10−3 ).
Janusz Adamowski
Physics of nanowire spintronic devices
(3)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The electron with spin s possesses the spin magnetic moment µs = −
gµB s. ~
µB = e~/(2me0 ) = Bohr magneton g = Lande factor In vacuum g = 2 (with accuracy of 10−3 ).
Janusz Adamowski
Physics of nanowire spintronic devices
(3)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The electron with spin s possesses the spin magnetic moment µs = −
gµB s. ~
µB = e~/(2me0 ) = Bohr magneton g = Lande factor In vacuum g = 2 (with accuracy of 10−3 ).
Janusz Adamowski
Physics of nanowire spintronic devices
(3)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Electron interacts with magnetic field Beff via the dipol-field interaction. The energy of this interaction is given by Espin = EZ + ESO ,
(4)
EZ = −µs · B
(5)
where is the spin Zeeman interaction energy and ESO =
1 µs · (F × v) c2
is the spin-orbit interaction energy.
Janusz Adamowski
Physics of nanowire spintronic devices
(6)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Electron interacts with magnetic field Beff via the dipol-field interaction. The energy of this interaction is given by Espin = EZ + ESO ,
(4)
EZ = −µs · B
(5)
where is the spin Zeeman interaction energy and ESO =
1 µs · (F × v) c2
is the spin-orbit interaction energy.
Janusz Adamowski
Physics of nanowire spintronic devices
(6)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Electron interacts with magnetic field Beff via the dipol-field interaction. The energy of this interaction is given by Espin = EZ + ESO ,
(4)
EZ = −µs · B
(5)
where is the spin Zeeman interaction energy and ESO =
1 µs · (F × v) c2
is the spin-orbit interaction energy.
Janusz Adamowski
Physics of nanowire spintronic devices
(6)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Electron interacts with magnetic field Beff via the dipol-field interaction. The energy of this interaction is given by Espin = EZ + ESO ,
(4)
EZ = −µs · B
(5)
where is the spin Zeeman interaction energy and ESO =
1 µs · (F × v) c2
is the spin-orbit interaction energy.
Janusz Adamowski
Physics of nanowire spintronic devices
(6)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Electron interacts with magnetic field Beff via the dipol-field interaction. The energy of this interaction is given by Espin = EZ + ESO ,
(4)
EZ = −µs · B
(5)
where is the spin Zeeman interaction energy and ESO =
1 µs · (F × v) c2
is the spin-orbit interaction energy.
Janusz Adamowski
Physics of nanowire spintronic devices
(6)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Introducing the linear momentum of electron p = me0 v we obtain ESO =
1 µs · (F × p) . me0 c2
Janusz Adamowski
Physics of nanowire spintronic devices
(7)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Introducing the linear momentum of electron p = me0 v we obtain ESO =
1 µs · (F × p) . me0 c2
Janusz Adamowski
Physics of nanowire spintronic devices
(7)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Remark If the electric field is central, i.e., F(r) = Fr (r)(r/r), then Eq. (7) transforms into e~Fr ESO = − 2 2 s · l , (8) 2me0 c r s = electron spin l = r × p = orbital angular momentum =⇒ ESO in form (8) explains the name: spin-orbit interaction.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Remark If the electric field is central, i.e., F(r) = Fr (r)(r/r), then Eq. (7) transforms into e~Fr ESO = − 2 2 s · l , (8) 2me0 c r s = electron spin l = r × p = orbital angular momentum =⇒ ESO in form (8) explains the name: spin-orbit interaction.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Remark If the electric field is central, i.e., F(r) = Fr (r)(r/r), then Eq. (7) transforms into e~Fr ESO = − 2 2 s · l , (8) 2me0 c r s = electron spin l = r × p = orbital angular momentum =⇒ ESO in form (8) explains the name: spin-orbit interaction.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Remark If the electric field is central, i.e., F(r) = Fr (r)(r/r), then Eq. (7) transforms into e~Fr ESO = − 2 2 s · l , (8) 2me0 c r s = electron spin l = r × p = orbital angular momentum =⇒ ESO in form (8) explains the name: spin-orbit interaction.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Remark If the electric field is central, i.e., F(r) = Fr (r)(r/r), then Eq. (7) transforms into e~Fr ESO = − 2 2 s · l , (8) 2me0 c r s = electron spin l = r × p = orbital angular momentum =⇒ ESO in form (8) explains the name: spin-orbit interaction.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Relativistic quantum mechanics The previous results can also be obtained from the relativistic quantum mechanics (Dirac equation). The spin Zeeman energy EZ [Eq. (5)] and SO energy ESO [Eq. (7)] are calculated as expectation values of the corresponding terms in the Dirac Hamiltonian.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Relativistic quantum mechanics The previous results can also be obtained from the relativistic quantum mechanics (Dirac equation). The spin Zeeman energy EZ [Eq. (5)] and SO energy ESO [Eq. (7)] are calculated as expectation values of the corresponding terms in the Dirac Hamiltonian.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Relativistic quantum mechanics The previous results can also be obtained from the relativistic quantum mechanics (Dirac equation). The spin Zeeman energy EZ [Eq. (5)] and SO energy ESO [Eq. (7)] are calculated as expectation values of the corresponding terms in the Dirac Hamiltonian.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Spin interactions in semiconductors
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The conduction-band electron in a semiconductor is described within the effective mass approximation (EMA). According to the EMA we make the following replacements: me0 =⇒ me = conduction-band effective mass, g =⇒ g? = effective Lande factor
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The conduction-band electron in a semiconductor is described within the effective mass approximation (EMA). According to the EMA we make the following replacements: me0 =⇒ me = conduction-band effective mass, g =⇒ g? = effective Lande factor
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The conduction-band electron in a semiconductor is described within the effective mass approximation (EMA). According to the EMA we make the following replacements: me0 =⇒ me = conduction-band effective mass, g =⇒ g? = effective Lande factor
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The conduction-band electron in a semiconductor is described within the effective mass approximation (EMA). According to the EMA we make the following replacements: me0 =⇒ me = conduction-band effective mass, g =⇒ g? = effective Lande factor
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
In vacuum g? = g = 2. In semiconductors, g? takes on different values: g? > 2, g? < 2, and even g? < 0. E.g., for GaAs: g? = −0.44, while for magnetic semiconductors, e.g., CdMnTe, g? can reach ' 500, =⇒ the giant Zeeman splitting in magnetic semiconductors.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
In vacuum g? = g = 2. In semiconductors, g? takes on different values: g? > 2, g? < 2, and even g? < 0. E.g., for GaAs: g? = −0.44, while for magnetic semiconductors, e.g., CdMnTe, g? can reach ' 500, =⇒ the giant Zeeman splitting in magnetic semiconductors.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
In vacuum g? = g = 2. In semiconductors, g? takes on different values: g? > 2, g? < 2, and even g? < 0. E.g., for GaAs: g? = −0.44, while for magnetic semiconductors, e.g., CdMnTe, g? can reach ' 500, =⇒ the giant Zeeman splitting in magnetic semiconductors.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
In vacuum g? = g = 2. In semiconductors, g? takes on different values: g? > 2, g? < 2, and even g? < 0. E.g., for GaAs: g? = −0.44, while for magnetic semiconductors, e.g., CdMnTe, g? can reach ' 500, =⇒ the giant Zeeman splitting in magnetic semiconductors.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The spin-orbit (SO) coupling in semiconductor can be obtained from Eq. (7) if we replace electron-positron creation energy =⇒ electron-hole creation energy (semiconductor energy gap) 2me0 c2 ' 1 MeV =⇒ Eg ' 1 eV =⇒ SO interaction in semiconductor would be ∼ 106 times stronger than in vacuum ??? However, the experiments show that the SO interaction in semiconductors is not so strong.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The spin-orbit (SO) coupling in semiconductor can be obtained from Eq. (7) if we replace electron-positron creation energy =⇒ electron-hole creation energy (semiconductor energy gap) 2me0 c2 ' 1 MeV =⇒ Eg ' 1 eV =⇒ SO interaction in semiconductor would be ∼ 106 times stronger than in vacuum ??? However, the experiments show that the SO interaction in semiconductors is not so strong.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The spin-orbit (SO) coupling in semiconductor can be obtained from Eq. (7) if we replace electron-positron creation energy =⇒ electron-hole creation energy (semiconductor energy gap) 2me0 c2 ' 1 MeV =⇒ Eg ' 1 eV =⇒ SO interaction in semiconductor would be ∼ 106 times stronger than in vacuum ??? However, the experiments show that the SO interaction in semiconductors is not so strong.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The spin-orbit (SO) coupling in semiconductor can be obtained from Eq. (7) if we replace electron-positron creation energy =⇒ electron-hole creation energy (semiconductor energy gap) 2me0 c2 ' 1 MeV =⇒ Eg ' 1 eV =⇒ SO interaction in semiconductor would be ∼ 106 times stronger than in vacuum ??? However, the experiments show that the SO interaction in semiconductors is not so strong.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The spin-orbit (SO) coupling in semiconductor can be obtained from Eq. (7) if we replace electron-positron creation energy =⇒ electron-hole creation energy (semiconductor energy gap) 2me0 c2 ' 1 MeV =⇒ Eg ' 1 eV =⇒ SO interaction in semiconductor would be ∼ 106 times stronger than in vacuum ??? However, the experiments show that the SO interaction in semiconductors is not so strong.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
For the semiconductor in external magnetic field F the spin-orbit interaction is described by the Rashba Hamiltonian ˆ , HSO,R = eαˆ σ · (F × k) ˆ = −i∇. where α is the Rashba coupling constant and k For InAs: me = 0.026 me0 and α = 1.17 nm2 .
Janusz Adamowski
Physics of nanowire spintronic devices
(9)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
For the semiconductor in external magnetic field F the spin-orbit interaction is described by the Rashba Hamiltonian ˆ , HSO,R = eαˆ σ · (F × k) ˆ = −i∇. where α is the Rashba coupling constant and k For InAs: me = 0.026 me0 and α = 1.17 nm2 .
Janusz Adamowski
Physics of nanowire spintronic devices
(9)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
For the semiconductor in external magnetic field F the spin-orbit interaction is described by the Rashba Hamiltonian ˆ , HSO,R = eαˆ σ · (F × k) ˆ = −i∇. where α is the Rashba coupling constant and k For InAs: me = 0.026 me0 and α = 1.17 nm2 .
Janusz Adamowski
Physics of nanowire spintronic devices
(9)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
For the semiconductor in external magnetic field F the spin-orbit interaction is described by the Rashba Hamiltonian ˆ , HSO,R = eαˆ σ · (F × k) ˆ = −i∇. where α is the Rashba coupling constant and k For InAs: me = 0.026 me0 and α = 1.17 nm2 .
Janusz Adamowski
Physics of nanowire spintronic devices
(9)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The Rashba interaction results from the motion of the electron in the external electric field (generated by the external electrodes). The electrons in solids also experience the internal electric field generated by the atomic cores. This field also leads to the SO interaction (called the Dresselhaus interaction). This interaction depends on crystal structure, size of the nanostructure, and doping, but is independent of the external electric field F. =⇒ For sufficiently high F the Rashba interaction dominates. In the following, I will consider the Rashba interaction only.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The Rashba interaction results from the motion of the electron in the external electric field (generated by the external electrodes). The electrons in solids also experience the internal electric field generated by the atomic cores. This field also leads to the SO interaction (called the Dresselhaus interaction). This interaction depends on crystal structure, size of the nanostructure, and doping, but is independent of the external electric field F. =⇒ For sufficiently high F the Rashba interaction dominates. In the following, I will consider the Rashba interaction only.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The Rashba interaction results from the motion of the electron in the external electric field (generated by the external electrodes). The electrons in solids also experience the internal electric field generated by the atomic cores. This field also leads to the SO interaction (called the Dresselhaus interaction). This interaction depends on crystal structure, size of the nanostructure, and doping, but is independent of the external electric field F. =⇒ For sufficiently high F the Rashba interaction dominates. In the following, I will consider the Rashba interaction only.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The Rashba interaction results from the motion of the electron in the external electric field (generated by the external electrodes). The electrons in solids also experience the internal electric field generated by the atomic cores. This field also leads to the SO interaction (called the Dresselhaus interaction). This interaction depends on crystal structure, size of the nanostructure, and doping, but is independent of the external electric field F. =⇒ For sufficiently high F the Rashba interaction dominates. In the following, I will consider the Rashba interaction only.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The Rashba interaction results from the motion of the electron in the external electric field (generated by the external electrodes). The electrons in solids also experience the internal electric field generated by the atomic cores. This field also leads to the SO interaction (called the Dresselhaus interaction). This interaction depends on crystal structure, size of the nanostructure, and doping, but is independent of the external electric field F. =⇒ For sufficiently high F the Rashba interaction dominates. In the following, I will consider the Rashba interaction only.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
The Rashba interaction results from the motion of the electron in the external electric field (generated by the external electrodes). The electrons in solids also experience the internal electric field generated by the atomic cores. This field also leads to the SO interaction (called the Dresselhaus interaction). This interaction depends on crystal structure, size of the nanostructure, and doping, but is independent of the external electric field F. =⇒ For sufficiently high F the Rashba interaction dominates. In the following, I will consider the Rashba interaction only.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
Model of nanowire
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
We assume that the electron motion is quasi-free in the growth direction (z) and confined in the transverse (x, y) directions. The transverse confinement potential can be taken in the form of deep potential well. For the infinitely deep potential well we get the transverse energy levels En⊥ =
~2 π 2 n⊥ 2 , me D
where n⊥ = 1, 2, . . . and D is the diameter of the nanowire.
Janusz Adamowski
Physics of nanowire spintronic devices
(10)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
We assume that the electron motion is quasi-free in the growth direction (z) and confined in the transverse (x, y) directions. The transverse confinement potential can be taken in the form of deep potential well. For the infinitely deep potential well we get the transverse energy levels En⊥ =
~2 π 2 n⊥ 2 , me D
where n⊥ = 1, 2, . . . and D is the diameter of the nanowire.
Janusz Adamowski
Physics of nanowire spintronic devices
(10)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
We assume that the electron motion is quasi-free in the growth direction (z) and confined in the transverse (x, y) directions. The transverse confinement potential can be taken in the form of deep potential well. For the infinitely deep potential well we get the transverse energy levels En⊥ =
~2 π 2 n⊥ 2 , me D
where n⊥ = 1, 2, . . . and D is the diameter of the nanowire.
Janusz Adamowski
Physics of nanowire spintronic devices
(10)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
We assume that the electron motion is quasi-free in the growth direction (z) and confined in the transverse (x, y) directions. The transverse confinement potential can be taken in the form of deep potential well. For the infinitely deep potential well we get the transverse energy levels En⊥ =
~2 π 2 n⊥ 2 , me D
where n⊥ = 1, 2, . . . and D is the diameter of the nanowire.
Janusz Adamowski
Physics of nanowire spintronic devices
(10)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
We assume that the electron motion is quasi-free in the growth direction (z) and confined in the transverse (x, y) directions. The transverse confinement potential can be taken in the form of deep potential well. For the infinitely deep potential well we get the transverse energy levels En⊥ =
~2 π 2 n⊥ 2 , me D
where n⊥ = 1, 2, . . . and D is the diameter of the nanowire.
Janusz Adamowski
Physics of nanowire spintronic devices
(10)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
In numerical calculations, the transverse potential well can be taken finite, but sufficiently deep. In the electron transport through the nanowire, the quantum states with different n⊥ (transverse modes, transverse subbands) form the different conduction channels.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Classical electrodynamics Relativistic quantum mechanics Spin interactions in semiconductors Model of nanowire
In numerical calculations, the transverse potential well can be taken finite, but sufficiently deep. In the electron transport through the nanowire, the quantum states with different n⊥ (transverse modes, transverse subbands) form the different conduction channels.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
II. Spin filter
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
Results for mesa-type (planar) GaN/GaMnN resonant tunneling diode
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
Summary of the results for spin filter
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
Summary of the results for spin filter
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
Summary of the results for spin filter
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
spin polarization of the current =
j↑ − j↓ , j↑ + j↓
jσ = current density for σ =↑, ↓.
Janusz Adamowski
Physics of nanowire spintronic devices
(11)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
Summary of the results for spin filter
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
Results for the resonant tunneling diode made from GaN/GaMnN nanowire
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
D E=2 meVD E=2 meV
U EN
EQW
z
Schematic of the resonant tunneling diode (RTD) based on the ferromagnetic semiconductor nanowire. Emitter (left contact) and quantum well are fabricated from ferromagnetic GaMnN, collector (right contact) – GaN, barriers – AlGaN, ∆E = spin splitting of the conduction band in GaMnN, ∆E ∼ EZ . Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
0 .4 ( b ) a n tip a r a lle l, T = 4 .2 K ∆E ∆E ∆E ∆E ∆E ∆E ∆E ∆E
0 .3
c u r r e n t d e n s ity [1 0
-3
a .u ]
( a ) p a r a lle l, T = 4 .2 K
0 .2
0 .1
= 2 m = 2 m = 5 m = 5 m = 1 0 = 1 0 = 1 5 = 1 5
e V , e V , e V , e V , m e V m e V m e V m e V
0 .0 0 .0 6
0 .0 9
0 .1 2 V
b
0 .1 5
0 .1 0
0 .1 5 V
[V ]
b
0 .2 0
[V ]
Current-voltage characteristics of the nanowire RTD with ferromagnetic contacts at 4.2K. The magnetization of the source and QW regions is (a) parallel (b) antiparallel. Janusz Adamowski
Physics of nanowire spintronic devices
s p in s p in s p in s p in , s p , s p , s p , s p
u p d o w u p d o w in u p in d o in u p in d o
n n w n w n
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
1 .0
( a ) p a r a lle l, T = 4 .2 K
p o la r iz a tio n
0 .5
E = 2 E = 5 E = 1 E = 1 E = 2
1 .0
( b ) a n tip a r a lle l, T = 4 .2 K
m e V m e V 0 m e V 5 m e V 0 m e V
0 .5
0 .0
0 .0
-0 .5
-0 .5
-1 .0 0 .1 0
p o la r iz a tio n
∆ ∆ ∆ ∆ ∆
Summary of the results for spin filter
-1 .0 0 .1 1
0 .1 2 V b[V ]
0 .1 3
0 .1 2
0 .1 4
0 .1 6
V b[V ]
Spin polarization of the current at 4.2K. The magnetization of the source and QW regions is (a) parallel (b) antiparallel.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
0 .0
Summary of the results for spin filter
( b ) a n tip a r a lle l, T = 3 0 0 K
( a ) p a r a lle l, T = 3 0 0 K
0 .0 -0 .2
∆E ∆E ∆E ∆E ∆E ∆E ∆E
-0 .4 -0 .6 -0 .8
= 2 m = 5 m = 1 0 = 1 5 = 2 0 = 3 0 = 4 0
e V
-0 .4
e V m e V m e V m e V m e V m e V
p o la r iz a tio n
p o la r iz a tio n
-0 .2
-0 .6 -0 .8
-1 .0
-1 .0 0 .0 5
0 .1 0
0 .1 5 V b[V ]
0 .2 0
0 .0 5
0 .1 0
0 .1 5
0 .2 0
V b[V ]
Spin polarization of the current at 300K. The magnetization of the source and QW regions is (a) parallel (b) antiparallel. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
Electron spin transitions in the nanowire with the parallel and antiparallel magnetization of the source and QW regions. The source-drain voltage increases from the top to bottom panel. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
Summary of the results for spin filter Antiparallel magnetization configuration is preferred for efficient spin polarization. Spin current polarization can reach |P| = 1 at zero temperature and |P| = 0.75 at room temperature. The spin filter is an analog of the polarizer (analyzer) of photons.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
Summary of the results for spin filter Antiparallel magnetization configuration is preferred for efficient spin polarization. Spin current polarization can reach |P| = 1 at zero temperature and |P| = 0.75 at room temperature. The spin filter is an analog of the polarizer (analyzer) of photons.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
Summary of the results for spin filter Antiparallel magnetization configuration is preferred for efficient spin polarization. Spin current polarization can reach |P| = 1 at zero temperature and |P| = 0.75 at room temperature. The spin filter is an analog of the polarizer (analyzer) of photons.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Summary of the results for spin filter
Summary of the results for spin filter Antiparallel magnetization configuration is preferred for efficient spin polarization. Spin current polarization can reach |P| = 1 at zero temperature and |P| = 0.75 at room temperature. The spin filter is an analog of the polarizer (analyzer) of photons.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
III. Spin transistor
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
III.A. Idea of spin transistor
Analogy between the operation of electro-optic modulator and spin transistor.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
III.A. Idea of spin transistor
Analogy between the operation of electro-optic modulator and spin transistor.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Janusz Adamowski
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
(b) gate
(a) source - gate E
(c) gate - drain
E
E
k
k
k
(d) x
gate drain
source
Fx
NW
z
Lg y
L t substrate
Schematic of the spin transistor based on the nanowire with the side gate. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
III.B. Ideal operation mode
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We assume: full spin polarization of electrons in source and drain contacts zero temperature ballistic transport (no scattering) conduction via one transverse subband
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We assume: full spin polarization of electrons in source and drain contacts zero temperature ballistic transport (no scattering) conduction via one transverse subband
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We assume: full spin polarization of electrons in source and drain contacts zero temperature ballistic transport (no scattering) conduction via one transverse subband
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We assume: full spin polarization of electrons in source and drain contacts zero temperature ballistic transport (no scattering) conduction via one transverse subband
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We assume: full spin polarization of electrons in source and drain contacts zero temperature ballistic transport (no scattering) conduction via one transverse subband
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
(a) No-spin-flip and (b) spin-flip transmission as a function of gate voltage Vg and energy E of the injected electron.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
(a )
I /I0
0 .4
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
V g = 1 . 5 5 V , I t o t a l = I
0 .2
V g = 2 . 3 4 V , I t o t a l = I
0 .0 0 .0
0 .3
0 .6 V
d s
0 .9
(V )
Current-voltage characteristics of the gated nanowire at 0K.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
0 .6
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
I = I t o
(b )
I
ta l
I (I0)
0 .4
0 .2
0 .0 0
1
2 V g(V )
3
4
Current I as a function of gate voltage Vg at 0K.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
4
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
(a ) 1 .0
s p in d e n s ity
0 .5
3
0 .0 s
-0 .5
x
s y
s z
(b )
O
-1 .0 0
L g / λS
2
5 0
1 0 0
1 5 0 z (n m )
2 0 0
2 5 0 1 .0
s p in d e n s ity
0 .0 s x
-0 .5 s
y
s
-1 .0
z
0
(a ) V
0
(b ) V
g
g
= 1 .5 5
1
= 2 .3 4
0 .5
0
2
5 0
4
1 0 0
1 5 0 z (n m )
2 0 0
2 5 0
6
V g(V )
λSO = characteristic length for the spin-orbit coupling, Lg = gate length, Vg = gate voltage. After passing length λSO , the rotating electron spin turns back to its initial state. (a) Integer (b) half-integer number of sz spin rotations. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We have found that ratio Lg /λSO is the linear function of gate voltage. Lg = aVg , λSO where a = 0.65 V−1 .
Janusz Adamowski
Physics of nanowire spintronic devices
(12)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We have found that ratio Lg /λSO is the linear function of gate voltage. Lg = aVg , λSO where a = 0.65 V−1 .
Janusz Adamowski
Physics of nanowire spintronic devices
(12)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We have found that ratio Lg /λSO is the linear function of gate voltage. Lg = aVg , λSO where a = 0.65 V−1 .
Janusz Adamowski
Physics of nanowire spintronic devices
(12)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
III.C. Realistic operation mode
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Spin polarization of electrons in the contacts P=
n↑ − n↓ n↑ + n↓
nσ = electron density for spin σ =↑, ↓
Janusz Adamowski
Physics of nanowire spintronic devices
(13)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Spin polarization of electrons in the contacts P=
n↑ − n↓ n↑ + n↓
nσ = electron density for spin σ =↑, ↓
Janusz Adamowski
Physics of nanowire spintronic devices
(13)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Spin polarization of electrons in the contacts P=
n↑ − n↓ n↑ + n↓
nσ = electron density for spin σ =↑, ↓
Janusz Adamowski
Physics of nanowire spintronic devices
(13)
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We assume: partial spin polarization of electrons in contacts (P < 1) room temperature conduction via many transverse subbands
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We assume: partial spin polarization of electrons in contacts (P < 1) room temperature conduction via many transverse subbands
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We assume: partial spin polarization of electrons in contacts (P < 1) room temperature conduction via many transverse subbands
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
We assume: partial spin polarization of electrons in contacts (P < 1) room temperature conduction via many transverse subbands
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
(b ) P = 0 .4
1 2
V g= 0 V V g= -0 .1 V
9
I/I0
V g= -0 .2 V 6
V g= -0 .3 V V g= -0 .4 V 3
V g= -0 .5 V 0 0 .0
0 .5
1 .0 V
d s
1 .5
2 .0
(V )
Current-voltage characteristics for the partial spin polarization (P = 0.4) at 300 K.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
3 0 0 P = 1 .0 P = 0 .4
I/I0
2 0 0
1 0 0
0 0
2
4
6
8
1 0
V g (V )
Current I as a function of gate voltage Vg for the full (P = 1) and partial (P = 0.4) spin polarization at 300 K. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
III.D. Comparison with experiment
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
An InAs Nanowire Spin Transistor with Subthreshold Slope of 20mV/dec Kanji Yoh1), Z. Cui1), K. Konishi1), M.Ohno2), K.Blekker3), W.Prost3), F.-J. Tegude3), J.-C. Harmand4) 1) Research
Center for Integrated Quantum Electronics , Hokkaido University, 060-6828 Sapporo, Japan School of Engineering, Hokkaido University, 060-6828 Sapporo, Japan and Information Engineering , University of Duisburg-Essen, 47057 Duisburg, Germany 4) CNRS-Laboratory of Photonic and Nanostructures , F-91460 Marcoussis, France phone: +81 11 706-6872, fax: +81 11 716-6004, email:
[email protected] 2) Graduate
3) Semiconductor
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Current-voltage characteristics of nanowire spin transistor for P = 0.4 and temperature T = 300K. Symbols correspond to experimental data of Yoh et al., curves – calculation results. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Current I as a function of gate voltage Vg for T = 300K. Upper panel: calculation results for the full (P = 1, red solid curve) and partial (P = 0.4, blue broken curve) spin polarization. Lower panel: experimental data of Yoh et al. Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Period of current oscillations as a function of gate voltage: ∆Vgexpt = ∆Vgcalc = 60mV .
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
III.A. Idea of spin transistor III.B. Ideal operation mode III.C. Realistic operation mode III.D. Comparison with experiment
Period of current oscillations as a function of gate voltage: ∆Vgexpt = ∆Vgcalc = 60mV .
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
IV. Summary
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
In the gated nanowire, the gate voltage modulates the spin-orbit interaction, which changes the electron spins without the external magnetic field. =⇒ All-electric operation. =⇒ Current oscillations as a function of gate voltage. =⇒ The current can be switched on/off by tuning the gate voltage (separately for each spin polarization). The efficient operation of the spin transistor strongly depends on the spin polarization of electrons in the source and drain contacts. =⇒ Gate-controlled InAs nanowire can operate as the spin transistor.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
In the gated nanowire, the gate voltage modulates the spin-orbit interaction, which changes the electron spins without the external magnetic field. =⇒ All-electric operation. =⇒ Current oscillations as a function of gate voltage. =⇒ The current can be switched on/off by tuning the gate voltage (separately for each spin polarization). The efficient operation of the spin transistor strongly depends on the spin polarization of electrons in the source and drain contacts. =⇒ Gate-controlled InAs nanowire can operate as the spin transistor.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
In the gated nanowire, the gate voltage modulates the spin-orbit interaction, which changes the electron spins without the external magnetic field. =⇒ All-electric operation. =⇒ Current oscillations as a function of gate voltage. =⇒ The current can be switched on/off by tuning the gate voltage (separately for each spin polarization). The efficient operation of the spin transistor strongly depends on the spin polarization of electrons in the source and drain contacts. =⇒ Gate-controlled InAs nanowire can operate as the spin transistor.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
In the gated nanowire, the gate voltage modulates the spin-orbit interaction, which changes the electron spins without the external magnetic field. =⇒ All-electric operation. =⇒ Current oscillations as a function of gate voltage. =⇒ The current can be switched on/off by tuning the gate voltage (separately for each spin polarization). The efficient operation of the spin transistor strongly depends on the spin polarization of electrons in the source and drain contacts. =⇒ Gate-controlled InAs nanowire can operate as the spin transistor.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
In the gated nanowire, the gate voltage modulates the spin-orbit interaction, which changes the electron spins without the external magnetic field. =⇒ All-electric operation. =⇒ Current oscillations as a function of gate voltage. =⇒ The current can be switched on/off by tuning the gate voltage (separately for each spin polarization). The efficient operation of the spin transistor strongly depends on the spin polarization of electrons in the source and drain contacts. =⇒ Gate-controlled InAs nanowire can operate as the spin transistor.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
In the gated nanowire, the gate voltage modulates the spin-orbit interaction, which changes the electron spins without the external magnetic field. =⇒ All-electric operation. =⇒ Current oscillations as a function of gate voltage. =⇒ The current can be switched on/off by tuning the gate voltage (separately for each spin polarization). The efficient operation of the spin transistor strongly depends on the spin polarization of electrons in the source and drain contacts. =⇒ Gate-controlled InAs nanowire can operate as the spin transistor.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Main goal of spintronics: Perfect operation of the spin transistor for each spin polarization.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Main goal of spintronics: Perfect operation of the spin transistor for each spin polarization.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Perfect operation of the conventional field-effect transistor. I. Ferain et al., Nature 479 (2011) 310.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Badania finansowane przez Narodowe Centrum Nauki w ramach grantu DEC-2011/03/B/ST3/00240.
Janusz Adamowski
Physics of nanowire spintronic devices
I. Physical background of spintronics II. Spin filter III. Spin transistor IV. Summary
Dzi˛ekuj˛e Panstwu ´ za uwag˛e.
Janusz Adamowski
Physics of nanowire spintronic devices
