unneling transport Courtesy Prof. S. Sawyer, RPI Also Davies Ch. 5
Electron transport properties l e : electronic mean free path l φ : phase coherence length λ F : Fermi wavelength
ecture Outline Important Concepts for Resonant unneling Diodes RDs RD Physics and Phenomena RD Equations and Parameters RDs vs. unnel Diodes Advantages and Disadvantages of RDs Applications Summary
RD Concepts: Why unneling Devices? Advantage of this quantum effect device Wors at room temperature High switching speed ow power consumption Differing operating principles Quantization Quantum tunneling Negative Differential Resistance NDR http://www.cse.unsw.edu.au/~cs411/projects/ presentations/james-pp.ppt#66,9,resonant unnelling Diodes
RD Concepts: unneling unneling Quantum mechanical phenomenon Calculate tunneling probability with Schrödinger s equation Complex barrier shapes Requires finite barrier height and thin barrier width
RD Concepts: unneling unneling Majority carrier effect Not governed by conventional time transit concept W Governed by quantum transition probability per unit time proportional to exp[-<0>w] <0> is the average value of momentum encountered in the tunneling path..
unneling transport: single barrier I Davies Ch. 5
Current in one-dimension U U U d f h e hv d v f e I d v d d d d d v f e I ], [ ], [ 1 ], [ : transmission coefficient
U d f h e I ], [ U R R R d f h e I ], [ U R R d f f h e I I I ],, [ otal current in one-dimension
ow bias limit,,,, f ev f ev f f R d f h e G V I G d f h V e I U U / h e G f U R R d f f h e I I I ],, [ : conductance at low temperatures
unneling probability o determine tunneling probability d dx m* E U x 0 Wavefunction for simple rectangular barrier height of U 0 and width W is m* E U ψ =exp±ix where 0
unneling probability Solution to tunneling probability t B A 1 U 0 sinh W 4E U 0 E 1 ~ 16 16 E U 0 E U 0 exp m* U 0 E W Using WKB for other barrier shapes where wavefunction is x exp i x dx t B exp A x x 1 m* Ux E dx
ransmission coefficient for single barrier Potential barrier of 0.3 ev and thicness of a = 10 nm in GaAs
Current in and 3 dimensions ],, [, exp 0, z z z z z z z f d v d e I m m U z u r i z z U D z B B D de E E n h e I m U m n / exp ln1 D n :wave function :energy
U R D D U D z de E E n E n h e J de E E n h e J m U E ] [ U de E E m h e J arge bias and low temperature limit otal resonant tunneling current
unneling vs. Resonant unneling
unneling vs. Resonant unneling http://w3.ualg.pt/~jlongras/oic-ndrd.pdf
RD consists of RD concepts Emitter region: source of electrons E Double barrier structure: inside is the quantum well, with discrete energy levels Collector region: collect electrons tunneling through the barrier C
RD concepts Double barriers formed Quantum well quantizes energy h n E n E Cw 8m* W Assumes infinite barrier height Actual barrier height ΔE c ~0.-0.5eV giving quantized levels of ~0.1eV
A bound state vs. a resonant state
RD concepts Carriers tunnel from one electrode to the other via energy states within the well Wavefunctions of Schrodinger equation must be solved for emitter, well, and collector unneling probability exhibits peas where the energy of the incoming particle coincides with quantized levels
Profile through a three-dimensional resonant tunneling diode Profile through a three-dimensional resonant-tunnelling diode. he bias increases from a to d, giving rise to the IV characteristic shown in e. he shaded areas on the left and right are the Fermi seas of electrons.
Resonant unneling Diode c Negative Differential Resistance Animation courtesy of the group of Prof. G Klimec and the NanoHub
RD Concepts: NDR Negative Differential Resistance r dv di DC biasing in the NDR region can be used for Oscillation Amplification High speed switching http://www.answers.com/topic/gunn-diode?cat=technology
ransmission coefficient for resonant tunneling / 1 R p p a v E E E 4 R R p 1 E p If = R
ransmission coefficient of a resonant-tunneling structure
RD parameters Probability of tunneling when electron energy does not align with quantized state Probability of tunneling when electron energy does align with quantized state E E R E n Resonant tunneling current is given by 4 R R J q NE E de m* N E ln 1 exp E F E
Characteristics of real resonant tunneling diodes
RD Research 010
AlGaN/GaN resonant tunneling diodes 4 4 6 6 30 30 8 8 Structure: low Al-composition 18% barriers RMS roughness of 8 Å Devices: 4 4 to 30 30 µm D. i et al., Appl. Phys. ett. 100, 5105 01.
RDs vs. unnel Diodes unnel Diodes were discovered by Esai in 1958 Studied heavily degenerately doped germanium p-n junctions Depletion layer width is narrow Found NDR over part of forward characteristics
RDs vs. unnel Diodes a Fermi level is constant across the junction Net tunneling current zero applied voltage is zero Voltage applied: tunneling occurs Under what conditions? b Maximum tunneling current c unneling current ceases No filled states opposite of unoccupied states d Normal diffusion and excess current dominates High doping arge capacitance Difficult device growth
RDs vs. unnel Diodes unneling Probability for tunnel diodes triangular barrier t exp 4 m * E g 3q Both effective mass and bandgap should be small Electric field should be large 3
RDs vs. unnel Diodes Comparison of typical current voltage characteristics Ip/Iv ratios 8:1 for Ge 1:1 GaSb 8:1 for GaAs 4:1 for Si imitation on ratio Pea current doping, effective tunneling mass, bandgap Valley current distribution of energy levels in forbidden gap defect densities
RDs vs. unnel Diodes Advantages of RDs Not transit time limited No minority carrier charge storage Maximum operational oscillation projected in the Hz range at room temperature Better leaage current can be used as a rectifier ower doping than p-n reduced capacitance Easier to fabricate and design than tunnel diodes Multiple NDR peas multivalue logic and memory Disadvantages of RDs Does not supply enough current for high power oscillations
Nine-State Resonant unneling Diode Memory Eight double barriers Al/In 0.53 Ga 0.47 As/InAs grown by MBE Applications A.C. Seabaugh et al., IEEE Electron Dev. ett., ED-13, 479, 199
High frequency, low power dissipation rigger circuits AlAs/GaAs RDs 110 GHz Pulse Generator 1.7 ps switching transition times with InAs/AlSb RDs Oscillators 71 GHz with InAs/Alsb Applications.C. Sollner, GaAs IC Symposium, 15, 1990
wo paths to Hz ight/optics photonics Radio/microwave electronics
Emerging technologies
Why Resonant unnelling Devices? Wors at room temperature! Extremely high switching speed Hz ow power consumption Well demonstrated uses ogic gates, fast adders, ADC etc. Can be integrated on existing processes In one word: Feasible
Summary unneling and negative differential resistance are ey characteristics of RDs hese devices are used for amplification, oscillation, and high speed switching RDs are not transit time limited no minority carrier storage charge unneling occurs when incoming energy of electrons coincide with quantized states in quantum wells resonance Diminished current due to lac of available electrons in line with quantized states causes NDR hermionic emission dominates in the valley