Spring 2009 EE 710: Nanoscience and Engineering

Transcription

1 Spring 009 EE 710: Nanoscience and Engineering Part 8: Sprintronics Images and figures supplied from Goddard, et.al, Handbook of Nanoscience, Engineering, and Technology, CRC Press, 004 and other refereed sources as indicated d Instructor: John D. Williams, Ph.D. Assistant Professor of Electrical and Computer Engineering Associate Director of the Nano and Micro Devices Center University of Alabama in Huntsville 406 Optics Building Huntsville, AL Phone: (56) Fax: (56) williams@eng.uah.edu 1

2 Spintronics: Electronic Devices Based on Control of an Electron s Spin Goal: Overcome the heat dependence generated and limiting processor speed inherent in MOSFETs. This is achieved by measuring the spin pseudo-vector without requiring large bias voltages that consume power. However the designs shown will not provide a significant power or heat reduction. A different architecture is required JDW, UAHuntsville ECE, Spring 009

3 The Spin Field Effect Transistor Identical transistor design to a MOSFET except that the source and grain contacts are ferromagnetic Assume the channel is a quantum wire with the lowest transverse subband occupied carriers Two ferromagnetic contacts are magnetized along the direction of the channel. JDW, UAHuntsville ECE, Spring 009 3

4 The Spin Field Effect Transistor Source, injects electrons into the channel with spins aligned along the direction of the source s magnetization If as assumed, the spin injection efficiency is 100%, then every carrier has its spin aligned toward the direction of the drain If there is no spin precession in the channel b/c of spin orbit interaction, and no spin-flip interactions occur then 100% of the proper spin injected electrons are collected by the drain This of course is NOT always the case The drain (also ferromagnetic) is a spin selective transmitter. Assume that it is a 100% effective spin filter that passes only carriers whose spins are aligned parallel to its magnetization. For high field saturated materials, this is indeed a proper assumption JDW, UAHuntsville ECE, Spring 009 4

5 Lorentz Force and the Gate Field The assumptions listed here hold true for systems with two large magnetic structures in close proximity and with a small electric field between them. Remember the Lorentz force F=q(E-vxB), which yield cyclotron resonance of charged particles traveling at a velocity v along a particular direction when both E and B are applied. Particles will precess in a helical path that can be controlled by the application of E and B to yield spins oriented along the proper direction when they meet the drain electrode. However, transistors require the application of an electrostatic potential across the gate. The potential is realized in the form of an electric field alters the precession of electrons between the source and drain. The spin interaction due to the gate is called a Rashba spin-orbit interaction It acts like an effective magnetic field that is oriented in a direction mutually perpendicular to the direction of the curent flow and that of the gate electric field IE OUT OF THE BOARD!!!! Strength of the Rashba field is: ( m*) a ( v ) = Ey v eh 46 BRashba 5 JDW, UAHuntsville ECE, Spring 009

6 Effects of the Gate Field Strength of the Rashba field is: ( m*) a46 BRashba( v) = E v y eh Spins injected from the source precess about the additional electric field with an additional Larmor frequency term: Ω( v) = ebrashba( v) ( m*) a = m * h Note that the new precession takes place on the xy plane, b/c the additional field is along the z-direction (out of the board) The rate of precession can be derived d as: dφ dφ dx dφ ( m*) a46 Ω( v) = = = v = E dt dx dt dx h d φ ( m *) a46 = E y dx h Where φ is the angle of spin precession JDW, UAHuntsville ECE, Spring E y v y v 6

7 Effects of an Gate Field The spatial rate of spin precession is independent of the carrier velocity (the speed of the injection from source to drain). This means that every electron in the circuit precesses at exactly the same angle as it traverses the distance between source and drain Think of the gate electrode as a spin angle orientation guide. The gate in essence (and independent of any scattering of electrons between magnets) sets the angle of spin precession for ALL electrons traveling between the two magnets. The spin angle therefore derived for electrons in the system is therefore solved direct integration of: dφ = dx ( m*) a h 46 E y To obtain: Φ = ( m*) a h Rashba 46 E y L where L is the source to drain separation 7 JDW, UAHuntsville ECE, Spring 009

8 Gate Bias Operatoin If the Electric field is such that Φ Rashba ( v) = (n + 1)π where n is an integer, then the carriers arriving aat the drain have their spins antiparallel to the drain s magnetization. Under this condition the carriers are blocked and no current flows. Thus by altering the gate potential, one can modulate the source-to-drain current and realize the field effect transistor 8 JDW, UAHuntsville ECE, Spring 009

9 Temperature Effects Note that because the gate bias is the driving force for the device, scattering losses at high temperatures become independent of transistor performance. However: Magnetic materials do not maintain large degrees of magnetization over large temperature regimes and are known to produce only partial magetic moments at elevated temperatures. Thus the transistor will be governed by the ability to control field properties as well as gate material performance at the desired d operating temperature. 9 JDW, UAHuntsville ECE, Spring 009

10 Dresselhaus SPINFET Occurs when the semiconductor lacks the crystallographic inversion symmetry Results in an effective magnetic field just like the Rashba interaction Let us assume that the transistor channel is in the [100] direction. The effective magnetic field due to a Dresselhaus interaction will be directed along the x axis and is strength given by ( m*) a B s v 4 π π Dresselhaus( ) = v e h W W z z where W z and W y are the transverse dimensions of the quantum wire channel (of rectangular cross section). Spins injected along either y or z will then precess along the x-axis as derived by the Lorentz force with a Dresselhaus magnetic field strength The angel by which the spin precesses in traveling a distance L between source and drain is therefore Φ Dresselhaus m * a 4 π π = W z W h z JDW, UAHuntsville ECE, Spring 009 L 10

11 Dresselhaus SPINFET Dresselhaus SPINFET Again the angle is independent of the carrier velocity, and therefore not subject to thermal averaging (the same as the Rashba circuit). Thus we can change the Dresselhaus spin injection angle by varying Wz with a split gate potential. This will also realize a transitor action. A li ti f l t i fi ld i l ith th f t th idth Application of an electric field in plane with the ferromagnets across the width of the of the circuit alters W z controls the drain current. *) ( v W W e a m v B y z Dresselhaus = 4 *) ( ) ( π π h L W W a m y z Dresselhaus = Φ 4 * π π h JDW, UAHuntsville ECE, Spring

12 Combination Devices If both Rashba and Dresselhaus interaction are present, then v Btotal = BDresselhaus xˆ + BRashba zˆ Yielding an extra rotation angle θ along the x direction given by: BRashba a E 46 y tan( θ ) = = B Dresselhaus a4 π π Thus the total precession angle is governed by: W z Wy Φ = m * L h ( a4e y ) + a4 π Wz π Wy Note: Ferromagnetic contacts can also induce a real magnetic field into the contact. This field is NOT proportional to the carrier velocity but is constant over time. Thus the angle by which the carrier precesses about the static bias field will be velocity dependent leading to thermal shifts in the performance of the overall circuit. External magnetic fields can also promote spin-flip events that lead to additional scattering in these circuits. THE PROBLEM IS NOT AS SIMPLE as the authors would have you believe. JDW, UAHuntsville ECE, Spring 009 1

13 Quantum Designed SPINFETS where B B nkv n=v Two spin-split subbands that generate a theta wavevector dependence If n=v then both wave vectors are dependent with θ=π/8, if not then dependence on θ is lost JDW, UAHuntsville ECE, Spring

14 High Spin Efficiency Two know routes: Using highly spin-polarized half metals as ferromagnetic spin injectors Unfortunately there are no half metals with 100% spin polarization at any temperature above absolute zero Using spin-selective barriers that inject spins of a particular polarzation only At best can transmit one kind of spin at one specfic injection energy The best spin-selective barrier uses resonant tunneling Near room temperatures, spin injection efficiency is approx. 90% using tunneling (ie nanofabrication to generate a gap less than a few nm) As of 006 there have been no devices capable of competing with Si The best candidate JDW, to UAHuntsville date is ECE, graphene Spring

15 Spin Injection from Ferromagnets Tunneling Calculations Temperature, T in units of k b =1 Layer thickness l, and width w Acceptor Concentration DonerConcentration Tunneling Current, J Spin based electron Density 15 JDW, UAHuntsville ECE, Spring 009 JDW UAH t ill ECE S i 009

16 Spin Injection from Ferromagnets Spin based electron density in the carrier Yields spin based current density r= 1 to 3 Yields, the spin factor JDW, UAHuntsville ECE, Spring 009 Polarized electron vel Tunneling Velocity 16 thermal electron vel

17 Polarization by Spin Injection Consider a spin injection that occurs at reverse bias, V<0 For The value of leading to spin polarization of the current as: 17 JDW, UAHuntsville ECE, Spring 009

18 Accumulated Current Density The Degree of spin polarized nonequilibrium electron polarization in at the surface of the semiconductor can be equated as: Leading to a total current density of spin up carriers: Where μ is the carrier mobility, and τ s is the scattering time constant of spin oriented electrons in the semiconductor measured from the characteristic current density of the circuit, J s : J s = qn D τ s 18 JDW, UAHuntsville ECE, Spring 009

19 Accumulated Current Density One can also now obtain a purely physical equation for the interfacial spin accumulation as We can now find the total current by applying the above equation to general equation for electron spin And a saturation current when qv/t> 3 JDW, UAHuntsville ECE, Spring

20 Spin Injection Efficiency Spin injection efficiency can now be determined by the ratio of updown over down-up carrier densities 0 JDW, UAHuntsville ECE, Spring 009

21 At equilibrium With applied bias voltage V 1 JDW, UAHuntsville ECE, Spring 009