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
cho68@purdue.edu
Motivation
2
Moore’s law and MOSFET scaling
Moore’s law*
Downscaling of Transistors**
• Transistor dimensions scale to improve performance, and
reduce cost per transistor
• Increased packing density followed by Moore’s law
* http://en.wikipedia.org/wiki/Moore's_law/
** http://www.intel.com/technology/mooreslaw/
3
Motivation
Dramatic Increase of Power Consumption
• CMOS microprocessors have reached the maximum
power dissipation level that BJT based chips had
• New device concept or idea required
* R. R. Schmidt, and B. D. Notohardjono, “High-End Server Low-Temperature Cooling”, IBM J. Res. &
Dev., vol.46, No. 6, p. 739, 2002
Motivation
4
Power consumption in MOSFETs
P  I OFF VDD
• 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
* S. Borkar, “Getting Gigascale Chips: Challenges and Opportunities in Continuing Moore’s Law”, ACM
Queue, vol. 1, No. 7, p. 26, 2003
Motivation
5
Limitations of MOSFET Scaling
log(Id)
ION  (VDD  VT )
(1    2)
ION
ION
IOFF
 d log I d 
1
SS 

slope  dVg 
1
kT 60mV
SS  2.3 ;
dec
q
IOFF
Vg
VT`
VDD
VDD
• Limitations of scaling
- Almost non-scalable supply voltage VDD
- Physical limit of Sub-threshold Swing (SS)
• Device with SS ≤ 60mV/dec is highly desired
Motivation
6
New Device Candidate: BTBT FETs
MOSFETs
BTBT FETs
+Vg
S
EF
S
Possible
candidate
to replace MOSFETs
EF
D
D
•
•
•
•
Minority carrier transport over
the barrier
Diffusion of hot electrons
Depends on the thermal
distribution of carriers
SS ≥ 60mV/dec limit
+Vg
•
•
•
•
Majority carrier transport
through the barrier
Band-to-band tunneling of cold
electrons
Boltzmann tails are ignored
SS ≤ 60mV/dec possible
Motivation
7
Study of BTBT Diodes
BTBT Diode
BTBT FET
No Gate Bias: OFF STATE
Positive gate
bias: ON STATE
Gate
• Learn about the
Gate oxide
tunneling
properties
Source
S
+Vg
P+BTBT
D
N+
I
• Test the potential
of a
Buried
Oxide
given
material
as a
Drain
TFET
• Horizontal
structure model
• Test simulation
- Difficult
to getBTBT
sharp interface
to design
- Need excellent channel control
through gate contact
N+ source
P+ drain
Substrate
• Vertical structure
- Sharp p-n interface can be more
easily fabricated
• Experimental data exist
• Low on current
2
8
Outline
• 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
9
Outline
• 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
Approach
10
Simulation Approach and Objective
• 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
3
11
Outline
• 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
Basic Physics
12
Band-to-band Tunneling
P++
P
EFP
EFP
• High doping density
EFN
EFN
W
W
N+
N+
 4 2m* E 3 2 
g
Pt  exp  

3qh 

-
More degeneracy
High electric field
Small width barrier
Increase tunneling current
• Narrow band gap
- Increase tunneling probability
- Material property
Basic Physics
13
Use of InGaAs
Indirect
Direct
Materials
Eg (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
Eg
• Small band gap material: Si  Ge  III-V (InAs)
• Indirect semiconductor  Direct semiconductor
• In0.53Ga0.47As: Lattice matched to InP
Basic Physics
14
I-V Characteristics of BTBT Diodes
I
Thermionic current
Tunneling
current
IP
Excess current
(Gap state current)
NDR
IV
VP
Zener
current
EV
EFP
P+
EFN
EC
N+
EV
EFP
P+
V
VV
EC
EFN EV
+ EC EFP
N
N+
P+
N
EFN
EC EV
EFP
+
P+
EFN
EC
N+
15
Outline
• 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
Penn State: InGaAs Diode
16
Device Structure and Doping Profile
Fabricated device
Simulated
Measured I-V
device
10nm
P+
NA=8×1019
I
3nm
N+
• A InGaAs lattice matched to InP
BTBT Diode
20nm
x
ND=4×1019
• I-V chracteristics of BTBT diodes
• NA=1020/cm3, ND=5×1019/cm3
In0.53Ga0.47As
Junction Modeling
17
Doping Profiles at the Junction
Abrupt doping
Linear doping
S (P+)
S (P+)
D (N+)
3nm
x
D (N+)
3nm
ND=4×1019/cm3
0
20nm
10nm
20nm
10nm
ND=4×1019/cm3
0
NA=8×1019/cm3
NA=8×1019/cm3
x
18
Junction Modeling
Effect of Junction Abruptness
• Only Zener tunneling branch is shown
• Step junction uses Rs closer to the estimated value (20Ω)
19
Junction Modeling
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
• Poor reproduction of forwardbiased region
- Low peak and valley currents
- Thermionic current turns on at large
bias
• Investigate potential
explanations for the observed
disagreements
7
20
Outline
• 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
Band Gap Narrowing
21
Causes of BGN: High Doping Effects
Impurity Bands
E
Donor Impurity Band
EC
ΔED
EC
ΔED
EV
ρDOS(E)
• High doping level ≥ 1018/cm3
- D.O.S depends on the impurity concentration
- Overlapping impurity states form an impurity band
• Random distribution of impurities
- Potential fluctuation of the band edges
- Impurity states tails into the forbidden gap
~200meV
BGN
Band Gap Narrowing
22
BGN Calculation Model
Jain-Roulston model*
•S. C. Jain, and D. J. Roulston, Solid-State Electronics, vol. 34, No. 5, p. 453, 1990
1
3
1
4
Eg  Ec  Ev  AN  BN  CN
Before BGN
ΔEC(min)+
After BGN
P
S (P+)
D (N+)
Eg
Eg1
S (P+)
ΔEV(maj)
1
2
ΔEC(maj)
D (N+)
EFEg2
+ V(min)
ΔE
N
• Advantages
1.Compact model calculated based on many-body theory
2.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
materials
4.No need for experimental fitting parameters
Band Gap Narrowing
23
BGN calculation for In0.53Ga0.47As
p-In0.53Ga0.47As
n-In0.53Ga0.47As
ND=4e19/cm-3
NA=8e19/cm-3
ΔEg
ΔEg
ΔEV
ΔEc
• Not negligible shift in minor band
• Less BGN than n-type material
ΔEc
ΔEV
• Most shift occurs at conduction
band
* 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.
Band Gap Narrowing
24
Inclusion of BGN in Tight-Binding
In0.53Ga0.47As before BGN
In1-x1InGa
As-In
Ga
As
after BGN
Ga
In
Ga
0.64x1
0.36As1-x2
0.71x2
0.29As
In1-x1Gax1As
S
(P+)
D
(N+)
0.75eV
0.6450eV
Eg1
S (P+)
S
(P+)
10nm
In1-x2Gax2As
D (N+)
D (N+)
0.5804e
E
V g2
23nm
1. Calculate new compositions of In and Ga from the reduced
band gaps
• Eg(300K )  0.43x 2  0.63x  0.36
2. Calculate tight-binding parameters from the empirical
parameters of InAs and GaAs, and Bowing parameters
CIn1 xGax As  (1 x)CInAs  xCGaAs  x(1 x)BIn1 xGax As
3. Shift band edges
11
Penn State: InGaAs Diode
25
The effect of BGN
1.
2.
3.
2.
1.
• Closer to the experimental data: Effect of BGN
1.An increase of the series resistance
2.An increase of tunneling current including the peak current
3.An earlier turn-on of the thermionic current
• Discrepancies:
1.Mismatch in NDR region, and low valley current
2.A shift of the thermionic current
1
26
Outline
• 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
27
What can shift the thermionic current?
* Effect of doping variation
1. Influence of the donor concentration
2. Influence of the acceptor concentration
28
Effect of Doping Variation
(1) Variation of the donor concentration ND
NA=8e19/cm3
Experiment data
ND=8e19/cm3
ND=4e19/cm3
ND=2e19/cm3
P+
EF
N+
• Higher tunneling current for higher ND
- Increase in tunneling window (
)
• No shift of the thermionic current onset
- No variation of potential barrier (
)
8
Effect of Doping Variation
29
(2) Variation of the acceptor concentration NA
ND=4e19/cm3
Experiment data
NA=4e19/cm3
NA=8e19/cm3
NA=1.2e20/cm3
+
+
P
P
P+
EF
E
EFF
N+++
N
N
• 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
)
9
8
30
What can increase the valley current?
I
IP
Tunneling
current
Thermionic current
NDR
Excess current
(Gap state current)
IV
Zener
VP
VV
* Excess current
1. Existence of excess current via gap states
2. Influence of excess current
V
Excess Current
31
Source of Excess Current (Ix)
EC
E
P+
A
qV
EFP
Conduction
band
EFN
C
EC
V
B
N+
Eg
EV
E
E
Valence
band
x
Tail
states
V
ρDOS(E)
• 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
32
Excess Current
(1) Existence of Ix: Intrinsic I-V data
q
σ
3kT
q
kT
• 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
33
Excess Current
Excess Current Calculation
* D. K. Roy, Solid-State Electron., vol. 14, p.520, 1971
I x  IV exp( (V  VV )m  IR)
IV  4.1  10 5 [A / cm 2 ]
VV  0.765[V ]
R  20(600  10 7 )2  [  cm 2 ]

1 q

3 kT
• Exponential nature of the excess current*
Linear increase of the currents beyond the valley
34
Excess Current
(2) The Effect of Excess Current
* Effects of excess current (BGN is included)
1. Increased current around and beyond the valley
2. Closer match to the experiment results
Penn State: InGaAs Diode
35
Effect of BGN
V=-0.4V
Efl
Efr
(Ix included)
V=0.95V
VV=0.64V
VP=0.35V
Efr
Efr
Efl
Efr
Efl
Efl
36
Temperature Dependence
(3) The Effect of Temperature
* Effects of temperature
1. 20meV more BGN occurs at room temperature
2. Increase of peak and NDR region currents
37
Outline
• 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
Summary
OBJECTIVE
•
•
Investigate the performances of
homogeneous InGaAs III-V band-toband-tunneling (BTBT) diodes
Study the tunneling properties of a
given material and its potential as a
BTBT Field-Effect Transistors (TFETs)
APPROACH
•
•
•
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
RESULTS
• 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
39
Conclusion & Future works
• To investigate tunneling device, high doping effects such
as BGN, and current via gap states should be considered
• Electron-phonon scattering should be included to examine
the effect on the increase of the current in the NDR region
• Exploring some other scattering mechanisms that may
explain the mismatches between the experiments and
simulation results
• Need the verification of the approach by analyzing another
fabricated device
• The approach can be applied to the analysis of other
tunneling devices, such as the broken gap heterostructure
diodes, and TFETs
40
Acknowledgement
Prof. Klimeck
Prof. Lundstrom and Prof. Garcia
Dr. Mathieu Luisier
All NCN Students and Group Members
Thank you!