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Network for Computational Nanotechnology (NCN)UC Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP
Homo-junction InGaAs Band-to-band Tunneling Diodes
Cho, Woo-Suhl
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Moore’s law and MOSFET scaling
• Transistor dimensions scale to improve performance, and reduce cost per transistor
• Increased packing density followed by Moore’s law
Moore’s law* Downscaling of Transistors**
Motivation
* http://en.wikipedia.org/wiki/Moore's_law/ ** http://www.intel.com/technology/mooreslaw/
2
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Dramatic Increase of Power Consumption
• CMOS microprocessors have reached the maximum power dissipation level that BJT based chips had
Motivation
* R. R. Schmidt, and B. D. Notohardjono, “High-End Server Low-Temperature Cooling”, IBM J. Res. & Dev., vol.46, No. 6, p. 739, 2002
3
• New device concept or idea required
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Power consumption in MOSFETs
P IOFF VDD
Motivation
* S. Borkar, “Getting Gigascale Chips: Challenges and Opportunities in Continuing Moore’s Law”, ACM Queue, vol. 1, No. 7, p. 26, 2003
4
• Downscaling of MOSFETs
- Leakage current usually fixed at IOFF=0.1μA/ μm- Increased transistor density per chip (>1 billion)
• Increase of power consumption & heat generation
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Limitations of MOSFET ScalingMotivation
log(Id)
Vg
VDD
5
• Device with SS ≤ 60mV/dec is highly desired
VDD
ION ∝ (VDD −VT )η
(1≤η < 2)
• Limitations of scaling- Almost non-scalable supply voltage VDD
- Physical limit of Sub-threshold Swing (SS)
SS ≥2.3kTq;60mV
dec
ION
ION
IOFF
IOFF
VT`
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New Device Candidate: BTBT FETsMotivation
S
D
EF
EF
+Vg
BTBT FETs
• Majority carrier transport through the barrier
• Band-to-band tunneling of cold electrons
• Boltzmann tails are ignored
MOSFETs
• Minority carrier transport over the barrier
• Diffusion of hot electrons• Depends on the thermal
distribution of carriers• SS ≥ 60mV/dec limit
S
D
+Vg
6
• SS ≤ 60mV/dec possible
Possible candidate to replace MOSFETs
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BTBT FET BTBT Diode
P+ drain
N+ source
Substrate
• Vertical structure- Sharp p-n interface can be more
easily fabricated
• Experimental data exist
2
No Gate Bias: OFF STATE
Source
Drain
Positive gate bias: ON STATE
BTBT
+Vg
Study of BTBT DiodesMotivation
Buried Oxide
P+ N+
Gate oxide
S DI
Gate
7
• Horizontal structure- Difficult to get sharp interface- Need excellent channel control
through gate contact
• Low on current
• Learn about the tunneling properties
• Test the potential of a given material as a TFET
• Test simulation model to design BTBT
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Outline
8
• Approach• Basic Physics of Tunneling Diodes
- Band-to-band Tunneling- I-V Characteristic of BTBT Diodes
• InGaAs Diodes- Junction Modeling and Effects of Junction Abruptness- Solution to Increase Tunneling Currents
• Band Gap Narrowing Effect and Modeling
- Solution to Shift the Onset of Thermionic Current• Effects of Doping Variation• Excess Current• Temperature Dependence
• Summary and Future Work
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Outline
9
• Approach• Basic Physics of Tunneling Diodes
- Band-to-band Tunneling- I-V Characteristic of BTBT Diodes
• InGaAs Diodes- Junction Modeling and Effects of Junction Abruptness- Solution to Increase Tunneling Currents
• Band Gap Narrowing Effect and Modeling
- Solution to Shift the Onset of Thermionic Current• Effects of Doping Variation• Excess Current• Temperature Dependence
• Summary and Future Work
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• Use full-band and atomistic quantum transport simulator based on the tight-binding model (OMEN) to model TDs- Ballistic transport using NEGF
• Reproduce and understand experimental data- Homogeneous InGaAS tunneling diodes (TDs) fabricated and
measured at Penn State, a partner in the MIND center
Simulation Approach and Objective
3
10 Approach
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Outline
11
• Approach• Basic Physics of Tunneling Diodes
- Band-to-band Tunneling- I-V Characteristic of BTBT Diodes
• InGaAs Diodes- Junction Modeling and Effects of Junction Abruptness- Solution to Increase Tunneling Currents
• Band Gap Narrowing Effect and Modeling
- Solution to Shift the Onset of Thermionic Current• Effects of Doping Variation• Excess Current• Temperature Dependence
• Summary and Future Work
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Band-to-band Tunneling
Pt =exp −4 2m* Eg
32
3qhε⎛
⎝⎜⎜
⎞
⎠⎟⎟
Basic Physics12
• Narrow band gap- Increase tunneling probability- Material property
P+
N+
EFPEFNW
• High doping density- More degeneracy- High electric field- Small width barrier- Increase tunneling current
P+
N+
EFN
EFP
W
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Use of InGaAsBasic Physics
MaterialsEg (eV) at 300K
m*/m0
Si 1.12 1.08
Ge 0.67 0.55
InAs 0.35 0.013
In0.53Ga0.47As 0.75 0.038
• Small band gap material: Si Ge III-V (InAs)
• Indirect semiconductor Direct semiconductor
• In0.53Ga0.47As: Lattice matched to InP
13
Indirect
Direct
Eg
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I-V Characteristics of BTBT DiodesBasic Physics
I
V
14
IV
VV
P+
N+
EFNEFP
EV
EC
P+
N+
EFN
EFP
EV
EC
Tunneling current
IP
VP
P+
N+EFN
EFP
EV
EC
Excess current(Gap state current)
P+
N+
EFN
EFP
EV EC
Thermionic current
P+
N+
EFN
EFP
EVEC
Zenercurrent
NDR
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Outline
15
• Approach• Basic Physics of Tunneling Diodes
- Band-to-band Tunneling- I-V Characteristic of BTBT Diodes
• InGaAs Diodes- Junction Modeling and Effects of Junction Abruptness- Solution to Increase Tunneling Currents
• Band Gap Narrowing Effect and Modeling
- Solution to Shift the Onset of Thermionic Current• Effects of Doping Variation• Excess Current• Temperature Dependence
• Summary and Future Work
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Fabricated device Simulated device
Device Structure and Doping ProfilePenn State: InGaAs Diode
• A InGaAs lattice matched to InP BTBT Diode
• NA=1020/cm3, ND=5×1019/cm3
16
10nm
20nm
N+
x
In0.53Ga0.47As
P+
3nm
NA=8×1019
ND=4×1019
I
Measured I-V
• I-V chracteristics of BTBT diodes
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Abrupt doping Linear doping
20nm10nm
3nm
D (N+)S (P+)
NA=8×1019/cm3
ND=4×1019/cm3
x
20nm10nm
3nm
D (N+)S (P+)
ND=4×1019/cm3
x
Doping Profiles at the Junction
17
NA=8×1019/cm3
0 0
Junction Modeling
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• Only Zener tunneling branch is shown
• Step junction uses Rs closer to the estimated value (20Ω)
Effect of Junction Abruptness
18 Junction Modeling
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I-V Characteristics: Experiment vs Simulation
• Step junction is used
• Zener current matched- Too low series resistance: RS=13.5Ω
vs. Estimated value: RS=20Ω
7
I-V Characteristics: Experiment vs Simulation
19
• Poor reproduction of forward-biased region- Low peak and valley currents- Thermionic current turns on at large
bias
• Investigate potential explanations for the observed disagreements
Junction Modeling
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Outline
20
• Approach• Basic Physics of Tunneling Diodes
- Band-to-band Tunneling- I-V Characteristic of BTBT Diodes
• InGaAs Diodes- Junction Modeling and Effects of Junction Abruptness- Solution to Increase Tunneling Currents
• Band Gap Narrowing Effect and Modeling
- Solution to Shift the Onset of Thermionic Current• Effects of Doping Variation• Excess Current• Temperature Dependence
• Summary and Future Work
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Causes of BGN: High Doping Effects
• High doping level ≥ 1018/cm3
- D.O.S depends on the impurity concentration- Overlapping impurity states form an impurity band
~200meV BGN
Band Gap Narrowing21
Impurity Bands
EC
EV
ΔED
Donor Impurity Band
ΔED
E
EC
ρDOS(E)
• Random distribution of impurities- Potential fluctuation of the band edges- Impurity states tails into the forbidden gap
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BGN Calculation ModelJain-Roulston model*
Band Gap Narrowing22
• AdvantagesAdvantages1.Compact model calculated based on many-body theory2.Compute BGN as function of doping concentrations (N), and material parameters (A, B, C)3.Compute band shifts in major and minor bands separately for all materials4.No need for experimental fitting parameters
•S. C. Jain, and D. J. Roulston, Solid-State Electronics, vol. 34, No. 5, p. 453, 1990
S (P+) D (N+)
Before BGN
Eg
After BGN
Eg1 Eg2S (P+) D (N+)
ΔEV(min)
ΔEC(min)
ΔEV(maj)
ΔEC(maj)P+
N+
EF
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BGN calculation for In0.53Ga0.47As
Band Gap Narrowing23
p-In0.53Ga0.47As
ΔEg
ΔEc
ΔEV
n-In0.53Ga0.47As
ΔEg
ΔEcΔEV
NA=8e19/cm-3 ND=4e19/cm-3
• Most shift occurs at conduction band
• Not negligible shift in minor band
• Less BGN than n-type material
* S. C. Jain, J. M. McGregor, and D. J. Roulston, and P.Balk, Solid-State Electronics, vol. 35, No. 5, p. 639, 1992.* James C. Li, Marko Sokolich, Tahir Hussain, and Peter M. Asbeck, Solid-State Electronics, vol. 50, p. 1440, 2006.
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Inclusion of BGN in Tight-Binding
Band Gap Narrowing
S (P+) D (N+)
In0.53Ga0.47As before BGN
0.75eV
In1-x1Gax1As-In1-x2Gax2As after BGN
Eg1 Eg2
In1-x1Gax1AsIn1-x2Gax2As
S (P+) D (N+)
11
1. Calculate new compositions of In and Ga from the reduced band gaps
•
2. Calculate tight-binding parameters from the empirical parameters of InAs and GaAs, and Bowing parameters
3. Shift band edges
Eg(300K ) =0.43x2 + 0.63x+ 0.36
CIn1−xGaxAs =(1−x)CInAs + xCGaAs + x(1−x)BIn1−xGaxAs
24
23nm10nm
S (P+) D (N+)0.6450eV0.5804eV
In0.64Ga0.36As In0.71Ga0.29As
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1
Penn State: InGaAs DiodeThe effect of BGN
25
• Closer to the experimental data: Effect of BGNCloser to the experimental data: Effect of BGN1.An increase of the series resistance2.An increase of tunneling current including the peak current3.An earlier turn-on of the thermionic current
2.2.3.3.
2.2.
1.1.
1.1.
• Discrepancies:Discrepancies:1.Mismatch in NDR region, and low valley current2.A shift of the thermionic current
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Outline
26
• Approach• Basic Physics of Tunneling Diodes
- Band-to-band Tunneling- I-V Characteristic of BTBT Diodes
• InGaAs Diodes- Junction Modeling and Effects of Junction Abruptness- Solution to Increase Tunneling Currents
• Band Gap Narrowing Effect and Modeling
- Solution to Shift the Onset of Thermionic Current• Effects of Doping Variation• Excess Current• Temperature Dependence
• Summary and Future Work
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What can shift the thermionic current?
* Effect of doping variation
1. Influence of the donor concentration2. Influence of the acceptor concentration
27
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(1) Variation of the donor concentration ND
• Higher tunneling current for higher ND
- Increase in tunneling window ( )
• No shift of the thermionic current onset- No variation of potential barrier ( )
8
P+
N+
EF
28 Effect of Doping Variation
P+
N+
EF
P+
N+
EF
NA=8e19/cm3Experiment dataND=8e19/cm3
ND=4e19/cm3
ND=2e19/cm3
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P+
N+
EF
(2) Variation of the acceptor concentration NA
9
29 Effect of Doping Variation
P+
N+
EF
P+
N+
EF
• Small increase in tunneling current for higher NA
- Increase in tunneling window ( )
• Earlier turn-on of the thermionic current for lower NA
- Lowered potential barrier ( )- No strong influence 8
ND=4e19/cm3Experiment dataNA=4e19/cm3
NA=8e19/cm3
NA=1.2e20/cm3
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What can increase the valley current?
30
* Excess current
1. Existence of excess current via gap states2. Influence of excess current
I
V
IV
VV
Excess current(Gap state current)
Thermionic current
Zener
NDR
Tunneling current
IP
VP
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Source of Excess Current (Ix) Excess Current
P+
N+
EFN
EFP
A
B
C
V Eg
qV
EV
EC E
Tail states
EC
EV
Conduction band
Valence band
ρDOS(E)
E
x
• Tunneling + Energy loss mechanism through gap states*• Gap States are mostly originated from the band edge tails
- A: Tails of acceptor levels extending to the forbidden gap- B: Tails of donor levels extending to the forbidden gap
* A. G. Chynoweth, W. L. Feldmann, and R. A. logan, Phys. Rev, vol. 121, p. 684, 1961
31
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(1) Existence of Ix: Intrinsic I-V dataExcess Current
q
kTq
3kTσ
32
• No series resistance is included• Purely thermionic current beyond the valley in the simulation data• Lower slope of the experiment data (σ≈⅓ of q/kT) at the valley confirms
the existence of Ix
• Assume that there is a dominant Ix around the valley
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Excess Current CalculationExcess Current
• Exponential nature of the excess current*
Linear increase of the currents beyond the valley
* D. K. Roy, Solid-State Electron., vol. 14, p.520, 1971
I x ≈IV exp(σ(V −VV )m−IR)
33
IV =4.1×105[A / cm2 ]VV =0.765[V]
R=20(600 ×10−7 )2π[Ω⋅cm2 ]
σ =13×
qkT
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(2) The Effect of Excess Current Excess Current
* Effects of excess current (BGN is included)of excess current (BGN is included)
1. Increased current around and beyond the valley2. Closer match to the experiment results
34
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Effect of BGNPenn State: InGaAs Diode
V=0.95V
Efl
Efr
VP=0.35V
Efl Efr
V=-0.4V
Efl Efr
Efl
Efr
VV=0.64V
35
(Ix included)
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(3) The Effect of TemperatureTemperature Dependence
* Effects of temperatureof temperature
1. 20meV more BGN occurs at room temperature2. Increase of peak and NDR region currents
36
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Outline
37
• Approach• Basic Physics of Tunneling Diodes
- Band-to-band Tunneling- I-V Characteristic of BTBT Diodes
• InGaAs Diodes- Junction Modeling and Effects of Junction Abruptness- Solution to Increase Tunneling Currents
• Band Gap Narrowing Effect and Modeling
- Solution to Shift the Onset of Thermionic Current• Effects of Doping Variation• Excess Current• Temperature Dependence
• Summary and Future Work
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• Investigate the performances of homogeneous InGaAs III-V band-to-band-tunneling (BTBT) diodes
• Study the tunneling properties of a given material and its potential as a BTBT Field-Effect Transistors (TFETs)
• Use full-band and atomistic quantum transport solver based on tight-binding to simulate BTBT diodes
• Coherent tunneling (no e-ph)
• Compare the simulation results to experimental data from Penn State
• BGN provides good agreement with experimental data for tunneling currents: Zener and peak currents
• Excess current increase current around and beyond valley
• Current in NDR region is not well captured
• Solution: T-dependence, e-ph scattering
OBJECTIVE RESULTS
APPROACH
Summary
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Conclusion & Future works
• To investigate tunneling device, high doping effects such as BGN, and current via gap states should be considered
39
• Electron-phonon scattering should be included to examine the effect on the increase of the current in the NDR region
• The approach can be applied to the analysis of other tunneling devices, such as the broken gap heterostructure diodes, and TFETs
• Need the verification of the approach by analyzing another fabricated device
• Exploring some other scattering mechanisms that may explain the mismatches between the experiments and simulation results
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40 Acknowledgement
Prof. Klimeck
Prof. Lundstrom and Prof. Garcia
Dr. Mathieu Luisier
All NCN Students and Group Members
Thank you!