Upload
others
View
6
Download
0
Embed Size (px)
Citation preview
Neophytos Neophytou
School of Engineering, University of Warwick, Coventry, U.K.
Electronic, thermal, and
thermoelectric transport in
nanostructures
WCPM Seminar Series, Feb. 12, 2015 - Warwick
Outline
Introduction – design at the nanoscale
Nanoscale thermoelectrics – design targets
Low-dimensional TEs (atomistic tight-binding + BTE)
Gated thermoelectrics: control scattering
Phonons transport for low-D (Modified Valence Force Field)
ZT figure of merit for low-D channel
Nanostructured thermoelectrics
Other studies: Nanomeshes (MC), Graphene (NEGF)
Future directions and conclusions 2
Why nano ?
3
New low-dimensional materials:
2D ultra thin layers
1D nanowires
0D quantum dots
2D graphene, 1D carbon nanotubes
Design degrees of freedom for design:
Length scale - geometry
Quantum effects (electrons behave differently)
Atomistic effects
2D graphene
thin layers Uchida et al., IEDM 03
nanowires Trivedi, 2011
nanotube quantum dots
Applications for nanodevices
4
Robert Chau, Intel, 2005
Bio-sensors
Optoelectronics Photovoltaics
Boukai et al., Nature 2008
Bio-illumination /
drug delivery
Kim et al., Nano Lett., 2011
Lu et al.,
Nano Lett., 2009
Nano-transistors
Thermoelectrics
Breus et al., Nano Lett., 2009
Ahn et al., Nano Lett., 2010
Nano-design for transistors
Length scale (the shorter, the faster)
Channel source drain
gate
ch
e
L
3D geometry (better electrostatics)
Gate
Sou
rce
Dra
in
LG
HSi
WSi
Gate
Sou
rce
Dra
in
LG
HSi
WSi
Gate
Sou
rce
Dra
in
LG
HSi
WSi
Gate
Sou
rce
Dra
in
LG
HSi
WSi
5
Appenzeller, PRL, 2004 (IBM)
60mV/dec <40mV/dec
Neophytou, Nano Lett., 10, 4913, 2010, APL 2011
experiments
[100] [110] [111]
Quantum effects (band to band tunneling) Atomistic effects (bandstructure)
Outline
Introduction – design at the nanoscale
Nanoscale thermoelectrics – design targets
Low-dimensional TEs (atomistic tight-binding + BTE)
Gated thermoelectrics
Phonons transport for low-D (Modified Valence Force Field)
ZT figure of merit for low-D channel
Nanostructured thermoelectrics
Other studies: Nanomeshes (MC), Graphene (NEGF)
Future directions and conclusions 6
Attempt similar design for thermoelectrics
7
2
e l
S TZT
Seebeck
coefficient
Lattice
thermal
conductivity
Electronic
thermal
conductivity
Electrical
conductivity
Snyder et al., Science, 2008, Nat. Mat., 2008.
15 TWatts of heat are lost, but
State of the art: ZT~1.5 (need ZT~4)
Rare earth, toxic, expensive materials
HOT COLD
e
e
heat
Abundance issues with good TE materials
8
Abundance issues for Te, toxicity for Pb
http://pubs.usgs.gov/fs/2002/fs087-02/
Design targets for nano-TE materials
Hicks and Dresselhaus -1993, Dresselhaus - 2001
)(~ EDOSdE
dSSharp peaks in DOS(E)
Low dimensionality –
improves S
le kk
TSZT
2
9
Nanostructuring -
phonon engineering
Scatter phonons only
How to proceed further ?
10
- κl reduction benefits are reaching their limits (easily)
- we need to look into σS2
Vineis et al., Adv. Mater. 22, 3790, 2010
Bulk : 140 W/mK, ZT=0.01
NWs: 1-2 W/mK, ZT~1
Case for Si:
This talk’s focus
11
Phonon properties: model and simulations
Possibility of further reduction in κl
Electronic properties: model and simulations
Interplay between σ, S at the nanoscale
(Si @ T=300K)
(2)
(1)
[100] [110] [111]
nanowires thin layers
<100> , <110>
(100) , (110), (111)
DrainChannelSource[100]
[110]
[111]
(100), (110), (112)
nanomeshes nano-
crystalline graphene
Outline
Introduction – design at the nanoscale
Nanoscale thermoelectrics – design targets
Low-dimensional TEs (atomistic tight-binding + BTE)
Gated thermoelectrics
Phonons transport for low-D (Modified Valence Force Field)
ZT figure of merit for low-D channel
Nanostructured thermoelectrics
Other studies: Nanomeshes (MC), Graphene (NEGF)
Future directions and conclusions 12
Channel description: Atomistic Tight-Binding
13
NN sp3d5s*-SO
The bulk bandstructure
[100] [110] [111]
Based on Localized Atomic Orbitals
Suitable for:
Structure deformations, strain
Material variations, heterostructures
Needs a set of fitting parameters
Computationally expensive
Compromise: between ab-initio methods and continuum methods
Able to handle 10s of thousands of atoms
Valleys-from bulk, to quantum wells, and to NWs
14
<001>
two-fold
<100>
<010>
(001)
four-fold in-plane valleys
perpendicular valleys
2D
3D Si
(001) 1D
Projection to 1D
4 X equivalent
valleys at Γ
Γ Γ
Electronic structure examples
15
NN sp3d5s*-SO
<100> , <110>
(100) , (110), (111)
DrainChannelSource
Conduction band
Valence band
[100] [110] [111]
1st Brillouin Zone
[100]
[110]
[111]
(100), (110), (112)
Length scale dependent properties
16
D=3nm D=12nm mass variation
NN, IEEE TED, 2008, Nano Lett., 2010
[100]
[111]
Electronic structure is geometry dependent
TB coupled to Linearized Boltzmann transport
At all κ-point, subbands:
velocity
density of states
2
k k kk
v v k
g v
0
( ) 2 00
BE
fR q d
k T
1
0
0
Bk RS
q R
21
22
2 0
0
Be
Rk TR
q R
0R
17
1 n
n
x
Ev E
k
1
1 1
2
n
D
n
g Ev E
Linearized Boltzmann transport: 2D
18
<100> , <110>
(100) , (110), (111)
DrainChannelSource[100]
[110]
[111]
(100), (110), (112)
Relaxation times
(of every k-state, at every subband)
phonon scattering (acoustic/optical)
surface roughness scattering
ionized impurity scattering
Basic features for TE coefficients – simple guidelines
0
0 0B F
BE
k q f ES d
k T
0
2 00
E
fq d
19
exp.
linear
Power factor maximum around Ef
0F FE E σ ~ 1/meff * exp(-ηF)
S ~ ηF
Design direction for σS2 at low dimensions
20
Change geometry at the same charge density:
σ ~ 1/meff * exp(-ηF)
S ~ ηF
From:
3D to 1D σS2
well
barrier
well
barrier
in-plane SLs cross-plane SLs core-shell NWs SL NWs
nano-dots
in latticesNanograins NW lattices/
anti-lattices (empty)
ηF =EC-EF
Neophytou and Kosina, PRB, 83, 245305, 2011
[100] [110] [111]
A thorough investigation for Si: σ determines σS2
21 Neophytou and Kosina, PRB, 83, 245305, 2011
σ ~ 1/meff * exp(-ηF)
S ~ ηF meff
S σ S σ
Neophytou and Kosina, J. Appl. Phys., 112, 024305, 2012
S σ
[100]
[110]
[111]
(100), (110), (112)
σS2
Outline
Introduction – design at the nanoscale
Nanoscale thermoelectrics – design targets
Low-dimensional TEs (atomistic tight-binding + BTE)
Gated thermoelectrics: control scattering
Phonons transport for low-D (Modified Valence Force Field)
ZT figure of merit for low-D channel
Nanostructured thermoelectrics
Other studies: Nanomeshes (MC), Graphene (NEGF)
Future directions and conclusions 22
Transport: Impurity dominated
-1-1K Wm2lk
~2-4X
reduction
gate all around
(modulation doping)
Modulation doping?
Surface charge transfer?
Gating?
23
Self-consistent computational model
24
(1)
(2)
(3)
(4)
Bandstructure(states)
Equilibrium statistics(state filling - charge)
Poisson
Charge Potential
Boltzmann transport
CHANNEL
CHANNEL
oxide
gate
EF
E(k)
Uscf
Hole dispersions under confinement
25 Low VG High VG
p-type
[110] NW
D=12nm
The effect of gating on NW mobility
26
Benefit from not using dopants
Gating seems beneficial, even with surface roughness
(accumulation is achieved with weaker fields)
Power factor improvement
27
Power factor:
Improved by ~5x
Power factor improvement versus diameter
28
Power factor improvements:
Still observed at D=20nm we were able to simulate
Might be retained up to D~40nm
Power factor - anisotropy
29
Strong anisotropy:
[111] NWs ~2x higher performance than [110]
~3x higher performance than [100]
Summary: Design strategies for low-D
30
1) Optimize the materials bandstructure:
Best choice of geometry/confinement, ηF
But in general, use of strain, alloying etc.
2) Avoid the most degrading scattering mechanisms:
Remove dopant impurities by gate field
But also modulation doping, would work
Outline
Introduction – design at the nanoscale
Nanoscale thermoelectrics – design targets
Low-dimensional TEs (atomistic tight-binding + BTE)
Gated thermoelectrics
Phonons transport for low-D (Modified Valence Force Field)
ZT figure of merit for low-D channel
Nanostructured thermoelectrics
Other studies: Nanomeshes (MC), Graphene (NEGF)
Future directions and conclusions 31
Modified Valence Force Field Method (MVFF)
32
Keating Modified
2
2 2
2
3
8
ij ijij
bs
ij
r dU
d
2
3
8
jikjik
bb
ij ik
Ud d
2 2 2 2
3
8
ij ij ik ikjik
bs bs
ij ik
r d r dU
d d
2 2
3
8
ij ij jikjik
bs bb
ij ik
r dU
d d
2
3
8
jik ikljikl
bb bb
ij ik kl
Ud d d
bond-stretching
bond-bending
cross bond
stretching
cross bond
stretching/
bending
coplanar bond
bending
Modified Valence Force Field Method (MVFF)
33
Keating Modified
, , ,
1
2A i i i
j k j k lij jik jik jik jikl
bs bb bs bs bs bb bb bb
i N j nn j k nn j k l COP
U U U U U U
2 ijij mnmn i j
m n
UD
r r
ij ij ij
xx xy xz
ij ij ij
ij yx yy yz
ij ij ij
zx zy zz
D D D
D D D D
D D D
2exp . 0l l
l
D D iq R q I
MVFF: Benchmarked to bulk Si
34
Keating Modified
MVFF: Low-dimensional phonon spectrum
35
2D ultra-thin layer 1D nanowire
acoustic
quasi-
acoustic
optical
Phonon thermal conductivity (diffusive)
36
P: specularity parameter
P=1, fully specular
P=0, fully diffusive
21( ) exp( )i
U
CB q T
T
,
,
( )1 1 ( )
( ) 1 ( )
g i
B i
v qp q
q p q W
2 2( ) exp( 4 )rmsp q q
Umklapp scattering
Boundary scattering
BTE for phonons (bulk formalism)
2
0
2
1
U
A T
Higher order scattering
ZT figure of merit
37
n-type NWs:
ZT~1.4 can be reached
(around 6-7nm)
p-type NWs:
ZT~1.4 can be reached
(around 3nm)
ZT is improved,
but still low !
(Bulk Si ZT is ~0.01)
Just low-D is not enough
Outline
Introduction – design at the nanoscale
Nanoscale thermoelectrics – design targets
Low-dimensional TEs (atomistic tight-binding + BTE)
Gated thermoelectrics
Phonons transport for low-D (Modified Valence Force Field)
ZT figure of merit for low-D channel
Nanostructured thermoelectrics
Other studies: Nanomeshes (MC), Graphene (NEGF)
Future directions and conclusions 38
Nanocomposite channels for increased Seebeck
39
S ~ ηF σ~exp(-ηF)
well barrier
superlattices
Si/SiGe
ηF
LWLB
EF
S ~ EF σ~exp(-EF)
Barriers:
Wells:
Make S and σ really independent?
How to increase both simultaneously?
Nanocrystalline Si
Collaboration: Prof. X. Zianni (Chalkida) and Prof. D. Narducci (Milano)
40
Make S and σ really independent?
How to increase both simultaneously?
charge decreases
Vb increases
WD increases
Vb
LG LGB
EF
Heavily boron doped
Annealing steps
Boron precipitates
(non-uniform distribution)
30nm
LG LGB
EF
Neophytou et al., J. Electr. Mat., 2012, ICT 2012
Nanocrystalline Si
Collaboration: Prof. X. Zianni (Chalkida) and Prof. D. Narducci (Milano)
41
Make S and σ really independent?
How to increase both simultaneously?
Vb
LG LGB
EF
3X
30nm
LG LGB
EF
Neophytou et al., J. Electr. Mat., 2012, ICT 2012, nanotechnology, 2013
Nanocrystalline Si: Simulations vs. experiments
42
Vbeff=0.06eV
Vbeff=0.09eV
Initial
Initial
Initial
Final Final
Final
Initial Final
Collaboration: Prof. X. Zianni (Chalkida) and Prof. D. Narducci (Milano)
Simultaneous enhancement in σ and S
Vb
LG LGB
EF
LG LGB
EF
Neophytou et al., J. Electr. Mat., 2012, ICT 2012, nanotechnology, 2013
Outline
Introduction – design at the nanoscale
Nanoscale thermoelectrics – design targets
Low-dimensional TEs (atomistic tight-binding + BTE)
Gated thermoelectrics
Phonons transport for low-D (Modified Valence Force Field)
ZT figure of merit for low-D channel
Nanostructured thermoelectrics
Other studies: Nanomeshes (MC), Graphene (NEGF)
Future directions and conclusions 43
Si nanomeshes
44 44
le
TSZT
2
Tang et al, Nano Lett. 2010
ZT ~ 0.4
Nanoporous membranes of single-crystalline Si (“holey” Si)
Method: Solve BTE using Monte Carlo
45 45
Boltzmann Transport Equation for phonon
Wolf, Neophytou, and Kosina, JAP, 2014
initialization
boundary scatt.
thermalization
3-phonon scatt.
Relaxation time approximation
Solve BTE using Monte-Carlo (MC)
Thermal conductivity vs porosity/roughness
46 46
[4] Randomized pores
[2,3] Ordered arrays (rectangular/hexagonal)
Phonon coherent effects are present !
random pore arrangement
Non-Equilibrium Green’s Function (NEGF)
1
2( ) [( 0 ) ]G E E i I H
1( ) ( ),
2
( - )
D E Trace G G
where i
- Density of states:
- Device Green’s function:
- Transmission:
2( ) ( )T E Trace G G
Σ1 Σ2H+U+ΣSΣ1 Σ2H+U+ΣS
Very powerful approach
Can include scattering (decoherence)
Can be computationally very expensive
For both electrons (Hamiltonian) and
phonons (dynamic matrix) 47
given n Uscf
Poisson
given Uscf n
Iterate until convergence
ELECTROSTATICS
TRANSPORT
(NEGF)
given n Uscf
Poisson
given Uscf n
Iterate until convergence
ELECTROSTATICS
TRANSPORT
(NEGF)
Graphene nano-ribbon thermoelectrics
48
(1)
Karamitaheri, Neophytou, Kosina, et al.,
JAP 111, 054501, 2012.
(2)
(3)
ZT=0 )(~ EDOSdE
dS
Outline
Introduction – design at the nanoscale
Nanoscale thermoelectrics – design targets
Low-dimensional TEs (atomistic tight-binding + BTE)
Gated thermoelectrics
Phonons transport for low-D (Modified Valence Force Field)
ZT figure of merit for low-D channel
Nanostructured thermoelectrics
Other studies: Nanomeshes (MC), Graphene (NEGF)
Future directions and conclusions 49
Hierarchy in geometry
50 50
well
barrier
Hierarchical scattering of phonons
Biswas et al. (Kanatzidis group)
Very low κl
Neophytou, Narducci, et al.,
Nanotechnology 2013,
J. Electronic Materials 2014
Very high PF:
2-phase materials: 15 mW/K2m-1
3-phase materials: 22 mW/K2m-1
(~7x compared to bulk)
larger S with 3rd phase
ZT figure of merit
51
2
l
S TZT
κl=140 W/mK (bulk)
κl=8 W/mK (our nano-grains, calculations)
5X
15X
Reduce κl
κl=1-2 W/mK (as in NWs)
Put all together:
ZT~4 ?
placement of dopants bandstructure
engineering
Transport in multi-phase materials using NEGF
52
We start with 1D
Then extend to 2D
Transport through wells and barriers:
Include acoustic and optical phonons
Energy relaxation as current flows
Include quantum effects.
Can retrieve ballistic and diffusive regimes
Red spots: defects
(here they are barriers of Vb=0.3eV)
Blue region: channel
Conclusions
Nanostructures offer the additional length scale degree of
freedom in design
Thermoelectric properties can be largely improved.
Very low thermal conductivities can be achieved
Very high power factors can be achieved
Advanced simulation techniques are required
Atomistic models for electronic and phonon bandstructure
Linearized BTE, Monte Carlo, NEGF methods for transport
Future work
Use all appropriate design guidelines to target TE
performance of nanocomposites (bandstructure, doping, κl)
Collaborate with experimentalists and material scientists to
establish technologies 53