Quantum Transport Simula0on: A few case studies where it is necessary

Transcription

1 Quantum Transport Simula0on: A few case studies where it is necessary Sayeef Salahuddin Laboratory for Emerging and Exploratory Devices (LEED) EECS, UC Berkeley sayeef@eecs.berkeley.edu

2 The celebrated Moore s Law Low power Architectures;Lecture #1:IntroducKon, Dr. Avi Mendelson Source: New Microarchitecture Challenges in the Coming GeneraKons o fcmos Process Technologies Fred Pollack, Intel Corp. Micro32 conference key note

3 The celebrated Moore s Law Quantum Transport Boltzmann Transport Equa0on Dri<- Diffusion Hydrodynamic model

4 A few numbers to remember M: number of current carrying modes l: length of the conductor λ: mean free path λ: nm in Si nm in III- V materials We are approaching an era where quantum transport simulakon is necessary!

5 A Few Examples Conven0onal Device geometry source drain Direct Source to Drain tunneling source drain Off- State leakage through band- to- band tunneling Novel Devices Non- Semiconductor quantum devices Band- to- band tunneling transistor (presentakon by Dr. Luisier this morning)

6 Spin Transfer Torque Devices Top Electrode! CoFeB (3)! MgO (0.85)! Insulator! CoFeB (3)! Ru (0.85)! CoFe (2.5)! Bottom Electrode! So< layer Pinned layer Slonczewski, JMMM, 96 Berger, PRB,96 KaKne, PRL 2000 R 0 Pinned layer Oxide So< layer Kubota et. al., JJAP, 44, 0 40, 1237,2005 Current

7 Why STT Devices?

8 Key challenges for device simulakon Kubota et. al., JJAP, 44, 40, 1237,2005 Can we explain the (i) Amplitude of the switching current (ii)resistance With the same set of device parameters?

9 Self Consistent solu0on of the transport and magne0za0on dynamics NEGF (Non Equilibrium Green s Function) Voltage Electron Transport: NEGF Equations Current Magnetization Spin Dynamics Torque LLG S. Salahuddin and S. Daga: IEDM (2006)

10 Torque from conserva0on of angular momentum Fixed magnet oxide So< ferromagnet The difference of spin currents is absorbed by the so< magnet

11 Effec0ve mass treatment of the transport Band structure dependent parameters Fixed magnet oxide So< ferromagnet Band spliing Fermi level Barrier Height EffecKve mass in barrier E f K up K down W. H. Butler et al, PRB, 2001 S0les Group, PRL, 2008, Macdonald Group, PRL, 2008

12 Incorpora0ng transverse modes/k sampling Oxide z x y Cross seckon is typically larger than 50 nm X 50 nm Fixed magnet So< ferromagnet E K x >0 k z >0 k x =0 k z =0 E f k y K x >0 k z =0

13 Effect of the transverse modes Pure 1D 10 modes Pure 1D 100 modes

14 Physics of Spin Torque Top Electrode! CoFeB (3)! MgO (0.85)! Insulator! CoFeB (3)! Ru (0.85)! CoFe (2.5)! Bottom Electrode! Fixed magnet Oxide So< ferromagnet z x y Non Equilibrium distribu0on for the right magnet + Torque Torque felt by the selectrons = Torque felt by the delectrons Calculated from NEGF CalculaKons Known from band spliing MagneKzaKon of The magnet Can be calculated from the other three

15 Experimental Benchmark Experiment Theory 32 Fuchs et. al., PRL 96, , 2006 TMR (%) Current (ma)

16 Experimental Benchmark Experiment Theory: Salahuddin group and Daea Group TMR (%) Current( µ A) Voltage (V) T. Kawahara et. al., ISSCC, 2007

17 Experimental Benchmark PRL 99, (2007) Theory: UCB and Purdue Ef = 2.25 V = 2.15 ev m* = 0.2 m0 m* FM = m0 U b = 1.4 V

18 A typical hysteresis from self consistent NEGF- LLG simulakon

19 Typical contour of voltage induced switching

20 Experimental Benchmark Nat. Phys. 4, (2008) Theory: UCB and Purdue

21 Experimental Benchmark PRB 79, (2009) Theory: UCB and Purdue Perpendicular Component Perpendicular Component E f = 2.25 V = 2.15 V m * = 0.32 m0 m FM* = 0.73 m0 U b = 0.9 V

22 Experimental Benchmark Nature Physics, 4, 37, 2008 Theory: UCB and Purdue

23 Nature Physics, 4, 37, 2008 Experimental Benchmark Theory: UCB and Purdue E f = 2.25 V = 2.15 V m * = 0.18 m0 m FM* = 0.73 m0 U b = 0.77 V

24 Band spliing Fermi level Barrier Height E f EffecKve mass in barrier K up K down

25 Integrated system V H Quantum Device Simulator I R Circuit Simulator

26 Puing it with circuit First Device Circuit Simula0on Device and magnekzakon dynamics Circuit Variability Op0mal opera0ng point from device circuit co- simula0on Li, Augus0ne, SS, Roy, DAC, 2008, pp

27 Conclusion Quantum Transport SimulaKon is going to be necessary for many devices in the nano scale regime! Acknowledgement: NSF/NRI