Valence Band Energy Offset and
Effective Band Gap Extraction of
strained-Si/strained-Ge Type-II
Heterostructures on Relaxed SiGe
Jamie Teherani
5/18/2011
Motivation
2



The s-Si/s-Ge has the potential for
interesting applications due to the deep
valence band well of s-Ge and the small
effective band gap between the conduction
band of s-Si and the valence band of s-Ge.
s-Si
s-Ge
Ec
EG,eff
ΔEv
However, both the valence band offset and effective band
gap between s-Si/s-Ge is poorly known.
This work extracts these parameters from experimental MOScapacitors by fitting quantum mechanical simulations to
experimental QSCV data.
Ev
Applications
3

Group IV Tunneling Transistor

Buried Ge channel MOSFET
O. M. Nayfeh, C. N. Chleirigh, J. Hennessy, L. Gomez, J. L. Hoyt, and D. A. Antoniadis, “Design of Tunneling Field-Effect Transistors Using StrainedSilicon/Strained-Germanium Type-II Staggered Heterojunctions,” IEEE Electron Device Letters, vol. 29, no. 9, pp. 1074-1077, Sep. 2008.
Shang, H.; Frank, M. M.; Gusev, E. P.; Chu, J. O.; Bedell, S. W.; Guarini, K. W.; Ieong, M.; , "Germanium channel MOSFETs: Opportunities and challenges," IBM
Journal of Research and Development , vol.50, no.4.5, pp.377-386, July 2006.
Outline
4
Previous Work
 Valence Band Offset Extraction Method
 Experimental and Simulated CV Curves
 Parameter Sensitivity of the CV Technique
 Extracted Values Compared to Theory
 Conclusion

Outline
5
Previous Work
 Valence Band Offset Extraction Method
 Experimental and Simulated CV Curves
 Parameter Sensitivity of the CV Technique
 Extracted Values Compared to Theory
 Conclusion

Previous Work, Device Structure
Research by Cait Ni Chleirigh
6
Low-T
oxide
s-Si
s-Si1-xGex
Si1-xsGexs
Δ6
Δ4
Δ2
EG,eff
HH
ΔEv
HH & LH
LH
Red text indicates differences from current device structure.
C. N. Chleirigh, “Strained SiGe-channel p-MOSFETs : impact of heterostructure design and process technology,” Thesis.
Previous Work, Valence Band Offset
Research by Cait Ni Chleirigh
7
800
Goal: to extract valence
band offset of s-Si/s-Ge on
relaxed SiGe
700
1
C. N. Chleirigh, “Strained SiGe-channel p-MOSFETs : impact of heterostructure design and process technology,” Thesis.
This Work, Device Structure
8
1 µm Al
10 nm WN
6 nm Al2O3 high-κ dielectric
tensilely strained-Si (6 nm)
compressively strained-Ge (6 nm)
40% SiGe Relaxed Buffer (1 µm)
p- 2 to 40% SiGe Graded Buffer (4 µm)
p+ Si substrate
1 µm Al
Forming gas anneal,
450˚C for 30 min
Changes from Previous Work
9

Device Structure
 s-Si1-xGex 
s-Ge
 Larger xs (Ge fraction in relaxed Si1-xsGexs substrate)
 High-κ dielectric instead of low temperature oxide

Simulations
 Quantum
 Density
Mechanics
Gradient Model  full Schrodinger solver
 Strain
edge model  full-band quantum simulator
 Modified valence band density of states, Nv  6x6 k·p
method that accounts for nonparabolicities in valence band
 Band
C. N. Chleirigh, C. Jungemann, J. Jung, O. O. Olubuyide, and J. L. Hoyt, “Extraction of band offsets in Strained Si/Strained Si1-yGey on relaxed
Si1-xGex dual-channel enhanced mobility structures,” in Proceedings of the Electrochemical Society: SiGe: Materials, Processing and Devices, p. 99.
Outline
10
Previous Work
 Valence Band Offset Extraction Method
 Experimental and Simulated CV Curves
 Parameter Sensitivity of the CV Technique
 Extracted Values Compared to Theory
 Conclusion

Valence Band Extraction Method
Experimental Data for 40% SiGe MOS-C
Gate Lakeage per Area
(nA/cm2)
Capacitance per Area
(nF/cm2)
11
I
800
II
Cox  EOT
III IV

QSCV can be divided
into 4 regions:

Si thickness
600

ΔEv

400
1

0

-1
-2
-3
-2
-1
0
1
Gate Voltage (V)
2
3
I: hole accumulation in
the Si cap
II: hole accumulation in
the Ge well
III: hole depletion
from the Ge well
IV: electron inversion
in the Si cap
Width of II is
determined by the
valence band offset
between s-Si/s-Ge
Valence Band Extraction Method
Experimental Data for 40% SiGe MOS-C
Capacitance per Area
(nF/cm2)
12
I
II
III
IV
800
600
400
-3
I
-2
-1
II
0
Gate Voltage (V)
III
1
2
3
IV
Valence Band Extraction Method, Con’t
13


Larger the valence band offset,
the larger region II

For a larger valence band offset,
more gate voltage has to be
applied to bring holes into the s-Si

Thus, width of II is directly related to
the valence band offset
EF
Above: VG ~ 0 V
Below: VG ~ -1 V
Extraction procedure


Measure QSCV from fabricated
devices
Fit quantum mechanical QSCV
simulations to experimental data by
adjusting valence band offset
EF
Complexities of Simulation
14

Difficult Simulation Environment
 Strain
 Splits
VB and CB of s-Si and s-Ge
 Changes EG for s-Si and s-Ge
 Modifies the density of states of the different bands
 Quantum
 Thin
Mechanics
layers (~ 6 nm) for the s-Si and s-Ge
 Must properly take into account quantization effects
 Non-uniform masses, m║ ≠ m┴ because of strain warps the
valence band
 Requires use of 6x6 k·p method
6x6 k·p Method,
Top Valence Band State for Ge
15
ky (1/Å)
Energy Scale
(eV)
k·p dispersion in the direction
perpendicular to the growth
direction
Valence band is NOT parabolic!
kz (1/Å)
S. Birner et al., “Modeling of Semiconductor Nanostructures with nextnano^3,” ACTA PHYSICA POLONICA SERIES A, vol. 110, no. 2, p. 111, 2006.
Outline
16
Previous Work
 Valence Band Offset Extraction Method
 Experimental and Simulated CV Curves
 Parameter Sensitivity of the CV Technique
 Extracted Values Compared to Theory
 Conclusion

Simulation Variables
17

Dielectric (modeled as SiO2)


Thickness



Thickness
Band splitting due to strain
Band gap
Band lineup compared to
germanium (ΔEv)
Germanium




Thickness
Band splitting due to strain
Band gap
Band lineup compared to
relaxed SiGe buffer
Relaxed SiGe Buffer

Silicon





Band gap
Doping
Numerical





Effective mass versus 6x6 k.p
Number of k.p points
k-vector range for k.p analysis
Method for separation between
classical and quantum treatment
Integration method
Red indicates simulation
parameters with high sensitivity.
Experimental and Simulated QSCV
Experimental Data for 40% SiGe MOS-Capacitors
18
Capacitance per Area (nF/cm2)
800
Cox  EOT
Simulation
Experiment
700
Si thickness
600
ΔEv
500
400
-3
-2
-1
0
Gate Voltage (V)
1
2
3
Fitting Parameters, 40% SiGe Substrate
19

Dielectric (modeled as SiO2)



Silicon





EOT, 38Å
Thickness, 47Å
Band splitting due to strain, 170
meV
Band gap, 920 meV
Band lineup compared to
germanium, ΔEv = 740 meV
Germanium




Thickness, 55Å
Band splitting due to strain, 105
meV
Band gap, not sensitive, 480 meV
Band lineup compared to relaxed
SiGe buffer, 480 meV
Relaxed SiGe Buffer



Band gap, not sensitive, 970 meV
Doping, 2x1017 cm-3
Numerical





6x6 k.p
Number of k.p points, 225 pts
k-vector range for k.p analysis,
0.30 (1/Å)
Method for separation between
classical and quantum treatment,
edge separation
Integration method, simple
integration
Red indicates simulation
parameters with high sensitivity.
Band Structure for 40% SiGe Substrate
20
At VG ~ 1.8 V
4
3
38Å SiO2
Energy (eV)
2
47Å s-Si
EG = 920 meV
55Å s-Ge
500 nm 40% SiGe (p-type 2x1016 cm-3)
1
EG,eff = 180 meV
0
480 meV
ΔEv = 740 meV
X1
X2
VB1
VB2
VB3
-1
-2
-3
0
5
10
15
Position (nm)
20
25
30
Outline
21
Previous Work
 Valence Band Offset Extraction Method
 Experimental and Simulated CV Curves
 Parameter Sensitivity of the CV Technique
 Extracted Values Compared to Theory
 Conclusion

Sensitivity to ΔEv between s-Si/s-Ge
22
Simulation, ΔEv = 740 meV
Experiment
Capacitance per Area (nF/cm2)
800
ΔEv - 25 meV
700
ΔEv + 25 meV
600
500
-2.5
-2
-1.5
Gate Voltage (V)
-1
-0.5
0
Sensitivity to effective band gap, EG,eff
23
Simulation, EG,eff = 180 meV
Experiment
Capacitance per Area (nF/cm2)
800
700
600
Inversion Regime
500
Difficult experimental measurement
400
1
1.5
2
Gate Voltage (V)
2.5
3
Sensitivity to effective band gap, EG,eff
24
Simulation, EG,eff = 180 meV
Experiment
Capacitance per Area (nF/cm2)
800
700
EG,eff - 25 meV
600
EG,eff + 25 meV
500
400
1
1.5
2
Gate Voltage (V)
2.5
3
Sensitivity to effective band gap, EG,eff
25
Simulation, EG,eff = 180 ± 60 meV
Experiment
Capacitance per Area (nF/cm2)
800
700
Depletion Regime
Many parameters affect this
portion of the curve:
• Doping
• Ge thickness
• EG,eff
• Ge valence band splitting
• SiGe band lineup to Ge
• DOS integration method
Difficult to decouple
parameters for fitting.
600
500
400
1
1.5
2
Gate Voltage (V)
2.5
3
Experimental and Simulated QSCV
Experimental Data for 60% SiGe MOS-Capacitors
26
Capacitance per Area (nF/cm2)
800
Simulation, ΔEv = 680 meV, EG,eff = 190 ± 60 meV
Experiment
700
600
500
400
300
-3
-2
-1
0
Gate Voltage (V)
1
2
3
Outline
27
Previous Work
 Valence Band Offset Extraction Method
 Experimental and Simulated CV Curves
 Parameter Sensitivity of the CV Technique
 Extracted Values Compared to Theory
 Conclusion

Summary of Extracted Values
28


Extracted values given below
Substrate
ΔEv ± 30
(meV)
Si EG ± 60
(meV)
EG,eff ± 60
(meV)
40% SiGe
740
920
180
50% SiGe
760
950
185
60% SiGe
680
870
190
The values for 50% SiGe are suspect
Si EG bigger than expected
 Does not fall in line with trend
 More materials analysis will be completed to verify strain,
doping, and Ge fraction in substrate

Comparison to Theory
Suspect points for 50% SiGe, more materials analysis needed
29
0.9
1.15
Valence Band Offset Between s-Si/s-Ge (eV)
Band Gap of s-Si on relaxed Si 1-xsGexs (eV)
1.20
Theory, People and Bean
This work, extracted from CV
1.10
1.05
1.00
0.95
0.90
0.85
0.80
0.75
0.0
0.1
0.2
0.3
0.4
0.5
xs, Ge fraction of substrate
0.6
0.7
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.0
Theory, People and Bean
Theory, Van de Walle, 1986
This work, extracted from CV
0.2
0.4
0.6
0.8
1.0
xs, Ge fraction of substrate
Theory from Van de Walle and Martin using local density functional theory. Similar
theoretical calculations by Van de Walle and Martin for the GaAs/AlAs band lineup have
large discrepancies with experimental data.
R. People and J. C. Bean, “Band alignments of coherently strained GexSi1−x/Si heterostructures on 〈001〉 GeySi1−y substrates,” Applied Physics Letters, vol. 48, no. 8, p. 538,
1986.
C. G. Van de Walle and R. M. Martin, “Theoretical study of Si/Ge interfaces,” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, vol. 3, no.
4, p. 1256, Jul. 1985.
Comparison to Theory and Past Work
30
800
Valence Band Offset of s-Si/s-Si1-xGex on 40% Relaxed SiGe
700
Chleirigh's Work
This Experiment
Theory, People and Bean
600
ΔEv (meV)
500
400
300
Line drawn
only as guide
200
100
0
0
0.2
0.4
0.6
x, Ge Fraction in s-Si1-xGex Layer
0.8
1
Outline
31
Previous Work
 Valence Band Offset Extraction Method
 Experimental and Simulated CV Curves
 Parameter Sensitivity of the CV Technique
 Extracted Values Compared to Theory
 Conclusion

Conclusions
32

The valence band offset between s-Si/s-Ge is
significantly larger (+100 meV) than theory by Van de
Walle and Martin
ΔEv = 740 ± 30 meV for 40% SiGe
 Values are in good agreement with trend of Chleirigh’s
work


Determination of effective band gap less exact due to
coupling of several different materials parameters


EG,eff found to be rather constant at ~180-190 meV for 4060% SiGe substrates
More materials analysis is needed to verify strain,
doping, and Ge fraction in the samples
Back Up
33

Increase in Band Gap Due to Quantum Confinement
 X-Valley
 15
 Top
CB in Silicon
meV higher than band edge (effective mass approx.)
VB in Germanium
 30
meV below band egde (6x6 k.p method)