tunneling transport
TRANSCRIPT
Tunneling transport
Courtesy Prof. S. Sawyer, RPIAlso Davies Ch. 5
Electron transport properties
le: electronic mean free path
lφ: phase coherence length
λF: Fermi wavelength
Lecture Outline• Important Concepts for Resonant Tunneling
Diodes (RTDs)• RTD Physics and Phenomena• RTD Equations and Parameters• RTDs vs. Tunnel Diodes
– Advantages and Disadvantages of RTDs
• Applications• Summary
RTD Concepts: Why Tunneling Devices?
• Advantage of this quantum effect device– Works at room temperature– High switching speed – Low power consumption
• Differing operating principles– Quantization– Quantum tunneling– Negative Differential Resistance
(NDR) http://www.cse.unsw.edu.au/~cs4211/projects/presentations/james-pp.ppt#266,9,Resonant Tunnelling Diodes
RTD Concepts: Tunneling• Tunneling
– Quantum mechanical phenomenon
• Calculate tunneling probability with Schrödinger’s equation
• Complex barrier shapes
– Requires finite barrier height and thin barrier width
RTD Concepts: Tunneling• Tunneling
– Majority carrier effect – Not governed by
conventional time transit concept
– Governed by quantum transition probability per unit time proportional to exp[-2<k(0)>W]
W
<k(0)> is the average value of momentum encountered in the tunneling path…..
Tunneling transport: single barrier
I L
Davies Ch. 5
Current in one-dimension
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T(k): transmission coefficient
LU
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Total current in one-dimension
Low bias limit
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: conductance
at low temperatures
Tunneling probability
d2
dx2
2 m*
2E U x( )( ) 0
k2m* E U 0
• To determine tunneling probability
• Wavefunction for simple rectangular barrier height of U0 and width W isψ =exp(±ikx) where
Tunneling probability
• Solution to tunneling probability
• Using WKB for other barrier shapes where wavefunction is
T t B 2
A 21
U 02 sinh2 k W( )
4E U 0 E
1
~16E U 0 E
U 02
exp 22 m* U 0 E
2 W
x( ) exp xik x( )
d
T t B 2
A 2exp 2
x 1
x 2x
2 m*
2U x( ) E( )
d
16
Transmission coefficient for single barrier
Potential barrier of 0.3 eV and thickness of a = 10 nm in GaAs
Current in 2 and 3 dimensions
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2
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Large bias and low temperature limit
Total resonant tunneling current
Tunneling vs. Resonant Tunneling
Tunneling vs. Resonant Tunneling
http://w3.ualg.pt/~jlongras/OIC-NDRd.pdf
RTD concepts• RTD consists of
– Emitter region: source of electrons T(E)
– Double barrier structure: inside is the quantum well, with discrete energy levels
– Collector region: collect electrons tunneling through the barrier T(C)
RTD concepts• Double barriers formed• Quantum well quantizes
energy
– Assumes infinite barrier height
• Actual barrier height (ΔEc) ~0.2-0.5eV giving quantized levels of ~0.1eV
E n E Cwh2 n2
8 m* W2
A bound state vs. a resonant state
RTD 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
• Tunneling probability exhibits peaks where the energy of the incoming particle coincides with quantized levels
Profile through a three-dimensional resonant-tunnelling diode. The bias increases from (a) to (d), giving rise to the I(V) characteristic shown in (e). The shaded areas on the left and right are the Fermi seas of electrons.
Profile through a three-dimensional resonant tunneling diode
L
Resonant Tunneling Diode
Negative Differential Resistance
(c)
Animation courtesy of the group of Prof. G Klimeckand the NanoHub
RTD Concepts: NDR• Negative Differential
Resistance
• DC biasing in the NDR region can be used for– Oscillation– Amplification– High speed switching
rdVdI
http://www.answers.com/topic/gunn-diode?cat=technology
Transmission coefficient for resonant tunneling
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(1)(
2
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pk
pk
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ET
2)(4
RL
RLpk TT
TTT
1)( pkET
If TL=TR
Transmission coefficient of a resonant-tunneling structure
RTD parameters• Probability of tunneling when electron energy
does not align with quantized state
• Probability of tunneling when electron energy does align with quantized state
• Resonant tunneling current is given by
Jq
2 EN E( ) T E( )
d N EkT m*
2ln 1 exp
E F E
kT
T E( ) T L T R
T E E n 4 T L T R
T L T R 2
Characteristics of real resonant tunneling diodes
RTD Research (2010)
Devices: 4 × 4 to 30 × 30 µm2
Structure: low Al-composition (18%) barriers RMS roughness of 8 Å
6×6
8×8
4×4
30×30
AlGaN/GaN resonant tunneling diodes
D. Li et al., Appl. Phys. Lett. 100, 252105 (2012).
RTDs vs. Tunnel Diodes• Tunnel Diodes were
discovered by Esaki in 1958– Studied heavily
(degenerately) doped germanium p-n junctions
– Depletion layer width is narrow
– Found NDR over part of forward characteristics
RTDs vs. Tunnel 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) Tunneling current ceases
– No filled states opposite of unoccupied states
• (d) Normal diffusion and excess current dominates
High dopingLarge capacitanceDifficult device growth
RTDs vs. Tunnel Diodes• Tunneling Probability for
tunnel diodes (triangular barrier)
• Both effective mass and bandgap should be small
• Electric field should be large
T t exp4 2 m*
E g
3
2
3 q
RTDs vs. Tunnel Diodes• Comparison of typical current
voltage characteristics• Ip/Iv ratios
– 8:1 for Ge– 12:1 GaSb– 28:1 for GaAs– 4:1 for Si
• Limitation on ratio– Peak current (doping, effective
tunneling mass, bandgap)– Valley current (distribution of energy
levels in forbidden gap (defect densities)
RTDs vs. Tunnel Diodes• Advantages of RTDs
– Not transit time limited• No minority carrier charge storage • Maximum operational oscillation projected in the THz range (at
room temperature)• Better leakage current (can be used as a rectifier)
– Lower doping than p-n (reduced capacitance)– Easier to fabricate and design than tunnel diodes– Multiple NDR peaks (multivalue logic and memory)
• Disadvantages of RTDs– Does not supply enough current for high power oscillations
Applications• Nine-State Resonant
Tunneling Diode Memory– Eight double barriers
Al/In0.53Ga0.47As/InAs grown by MBE
A.C. Seabaugh et al., IEEE Electron Dev. Lett., EDL-13, 479, (1992)
Applications• High frequency, low
power dissipation– Trigger circuits
• AlAs/GaAs RTDs 110 GHz
– Pulse Generator • 1.7 ps switching transition
times with InAs/AlSb RTDs
– Oscillators• 712 GHz with InAs/Alsb
T.C. Sollner, GaAs IC Symposium, 15, (1990)
• Two paths to THz– Light/optics
(photonics)– Radio/microwave
(electronics)
Emerging technologies
Why Resonant Tunnelling Devices?
• Works at room temperature!• Extremely high switching speed (THz)• Low power consumption• Well demonstrated uses
– Logic gates, fast adders, ADC etc.• Can be integrated on existing processes• In one word: Feasible
Summary• Tunneling and negative differential resistance are key
characteristics of RTDs• These devices are used for amplification, oscillation, and
high speed switching• RTDs are not transit time limited (no minority carrier storage
charge)• Tunneling occurs when incoming energy of electrons
coincide with quantized states in quantum wells (resonance)• Diminished current due to lack of available electrons in line
with quantized states causes NDR• Thermionic emission dominates in the valley