Resonant tunneling
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Izaro Laresgoiti Low dimensional systems Quantum tunneling Resonant tunneling RTD Structure How does it work? Materials Applications Conclusions TC ∝ e −2 k 2 L α decay: Polonium -212 (alpha particle 8,78MeV) 0.287eV 0.0807eV 0.287eV 0.0807eV TLTR T= (1 − RL RR ) 2 + 4 RR RL sin 2 χ = 2π n 1 χ χ = 2ka + ρ + ρ L R 2 TL=TR=0.8 The condition for resonant states! Assuming that TL and TR are small: T = TPK TL=TR=0.2 TLTR 4TLTR = ≈ 2 (1 − RR RL ) 2 (TL + TR ) Near the resonance (TL and TR<<1) T Tpk €€€€€€€€€€ Er 1 ⎡ ⎛ ⎢ ⎜E−E pk T ( E ) = Tpk ⎢1 + ⎜ ⎢ ⎜⎜ 1 Γ ⎢⎣ ⎝ 2 ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ 2 ⎤ ⎥ ⎥ ⎥ ⎥⎦ −1 0.8 Breit-Wigner 0.6 Γ 0.4 Scape rate 0.2 ã 1 2 3 4 I II III IV V Regions (12-25nm) I-V: Emitter/collector(heavily doped(~108cm-3) small bandgap, GaAs) II-IV: Q barrier(~0.23eV):larger bangap (AlGaAs). III : QW: smaller bandgap jp NDR jv Important performance parameter: 1.Peak current density (Jp) 2.Valley current density (Jv) 3.Peak to valley ratio (PVR): Jp/Jv 1. 2. 3. 4. 5. E1: Resonant energy E2: phonon absorption E3: phonon emission E4:Thermoionic emission Non resonant tunneling Valley current To obtain the better performance 1. Maximize Ip Æ high frequency (>104 A/cm 2) 2. Minimize Iv Æ reduce lekege current and hence the power consumtion. 3. Maximize PVR Æallow an appropriate memory with a reasonable noise margin 4. Minimize RCt NDR Real current curve To increase Ip: (increases f) 1. Decrease the thickness of the barrier 2. Increase the doping in the emitters However: Increases also the IV Decreases the PVR Trade off between high speed and power consumption!! Small device (12-25nm/conventional device ~100nm) Extremely high switching speed (e.g., 1 ps switch, fmax~1 THz/215GHz conventional) Low power consumption Work at room temperature Flexible design NDR characteristics(Intrinsic bistability , incfrease functionality) Type Good PVR and current densityÆIp~500kA/cm2 PVR ~52 Good for high frequency switching applications CMOS incompatible and high cost Si III-V (Eg. GaAs, InP) based CMOS compatible RTDÆNot good properties (NDR at low temp, PVR ~1.2-2.4) RITD RITD type III-V RITD based in Si Compatible with CMOS NDR at room T PVR~4 Ip~2kA/cm2 Microwave oscillators NDRÆ compensate the R Ideal oscillator Real oscillator RTD Æavoid the amplitude decay Novel digital logic circuits.(PVR=10 enough) Static memory (computer) | | RTD more stable (NDR), bistability. Reduced the number of devices The simplest configuration Due to the continuous development of computer industry is inevitable the use of quantum based devices because they provide: Low footprint and high device density. High switching speed(high computation capacity) Low power consumption Due to their high switching velocity and the NDR RTDs are very useful for very high frequency oscillator circuits. Books: “The Physics and Applications of Resonant Tunnelling Diodes”. by Hiroshi Mizuta, Tomonori Tanoue. (Cambridge Studies in Semiconductor Physics and Microelectronic Engineering). “Nanoelectronics and Information Technology: Advanced Electronic Materials and Novel Devices” by Rainer Waser “The Physics of Low-dimensional Semiconductors: An Introduction” by John H. Davies Papers and talks: L.L. Chang, L. Esaki, and R. Tsu. “Resonant tunneling in semiconductor double barriers”, Appl. Phys. Lett. 24, 593 (1974). S.L. Rommel, T.E. Dillon, M.W. Dashiell, H. Feng, J. Kolodzey, P.R. Berger, P.E. Thompson, K.D. Hobart, R. Lake, A.C. Seabaugh, G. Klimeck, and D.K. Blanks, “Room Temperature Operation of Epitaxially Grown Si/Si0.5Ge0.5/Si Resonant Interband Tunneling Diodes “, Appl. Phy. Lett, 73, 2191 (1998). “Resonant Tunneling Diodes: Theory of Operation and Applications”. Johnny Ling, University of Rochester, Rochester , NY 14627 “Brief overview of nanoelectronic devices”, James C. Ellenbogen. Government Microelectronics Applications Conference (GOMAC98). “Resonant Tunneling Transistor Characteristics Using a Fabry-Pariot Resonator”. Chomsik Lee. Journ. Korean Physic. Soc, vol 31 “Long journey into tunneling”. Leo Esaki. Nobel Lecture, December 12, 1973 “Confined Electrons and Photons. New Physics and Application”. Elias Burstein and Claude weisbuch “Extending CMOS: Quantum functional Circuits Using Si-Based Resonant Interband Tunneling Diodes”. Paul R. Berger. March 11, 2005 “Resonant Tunneling Diodes”. Ni, Man. Advanced Electronic Devices. April 26. 2005 “ Quantum Wells, Wires, Dots; Quantum Coherent Devices”, Stephen Goodnick. IEEE Nanotechnology Conference in 2003 nanoHUB: online simulations and more: https://www.nanohub.org/tools/rtd/ (Simulate 1D resonant tunneling devices and other heterostructures via ballistic quantum transport)
