Extraction of Large Valence Band Offsets in Strained-Si ...teherani.ee.columbia.edu/uploads/2/3/7/2/23722259/valence_band_offsets_04.pdf · Type II Heterostructures on Relaxed SiGe

Extraction of Large Valence Band

Offsets in Strained-Si/Strained-Ge

Type II Heterostructures on

Relaxed SiGe Substrates

Jamie Teherani, Dimitri Antoniadis, and Judy Hoyt

2/2/2012

Motivation

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.

2

EG,eff

s-Si s-Ge

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 MOS-

capacitors by fitting quantum mechanical simulations to

experimental QSCV data.

Ev

Ec

Direct Applications3

Group IV Tunneling Transistor Buried s-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 Strained-

Silicon/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.

𝑽𝒈

Bulk Ge: 𝜇ℎ ≤ 1900, 𝜇𝑒 ≤ 3900 cm2/V*s

Bulk Si: 𝜇ℎ ≤ 450, 𝜇𝑒 ≤ 1400 cm2/V*s

Source: http://www.ioffe.ru/SVA/NSM/Semicond/

Applications to Type-II TFET Structure4

Material AMaterial B

Insulating dielectric

Insulating substrate

Gate DrainSource

EG,eff

Different material systems can be used

(Mat. A/Mat. B) can be (InAs/GaSb) or (Si/Ge)

Si/Ge is investigated in current work

Tunneling current is exponentially dependent on 𝐸𝐺,𝑒𝑓𝑓 SS also depends on the electrostatics and Dit at the

oxide/semiconductor interface

Both band alignment and Dit can be explored with MOS-C structure

Mat.

A

Mat.

B

dielectric

Type-II Band

Alignment

Outline

Previous Work

Valence Band Offset Extraction Method

Experimental and Simulated CV Curves

Parameter Sensitivity of the CV Technique

Extracted Values Compared to Theory

Conclusion

5

Outline

Previous Work





Conclusion

6

Previous Work, Device Structure

Research by Cait Ni Chleirigh

Δ2

Δ4

EG,eff

s-Si Si1-xsGexss-Si1-xGex

LH

HH

HH & LHΔEv

Low-T oxide

Δ6

Red text indicates differences from current device structure.

C. N. Chleirigh, “Strained SiGe-channel p-MOSFETs : impact of heterostructure design and process technology,” Thesis.

7

Previous Work, Valence Band Offset

Research by Cait Ni Chleirigh8

C. N. Chleirigh, “Strained SiGe-channel p-MOSFETs : impact of heterostructure design and process technology,” Thesis.

Goal: to extract valence

band offset of s-Si/s-Ge on

relaxed SiGe

1

800

700

x

xs

Fabricated MOS-capacitor Structure9

1 µm Al

6 nm Al2O3 high-κ dielectric

tensilely strained-Si (6 nm)

40% SiGe Relaxed Buffer (1 µm)p- 2 to 40% SiGe Graded Buffer (4

µm)

10 nm WN

compressively strained-Ge (6 nm)

p+ Si substrate

1 µm Al

Forming gas anneal,

450˚C for 30 min

Strained-Si/Strained-Ge pseudomorphic to relaxed SiGe layer

varied Ge content to vary the strain

MOS-C structure used to extract valence band offset, DEv and

effective bandgap, EG,eff

Detailed Valence Band Structure10

s-Si Si1-xsGexss-Ge

Sihh

Gehh

Δ𝐸𝑣

1st sub-bandΔ𝐸 = 45 meV

Silh

Gelh

SiGehh & lh

Band splitting due to strain in the s-Si and s-Ge layers

Quantization included in simulation but not reflected in quoted value

Δ𝐸𝑣 value quoted in this work corresponds to the difference between

the Gehh valence band edge and the Silh valence band edge

Changes from Previous Work

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 Mechanics Density Gradient Model full Schrodinger solver

Strain Band edge model full-band quantum simulator

Modified valence band density of states, Nv 6x6 k·pmethod that accounts for nonparabolicities in valence 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.

11

Outline

Previous Work





Conclusion

12

Valence Band Offset ExtractionSimulation for 35% SiGe MOS-C13

400

500

600

700

800

900

-3 -2 -1 0 1 2 3Cap

acit

ance

pe

r A

rea

(nF/

cm2)

Gate Voltage (V)

Simulation

I II III IV

Si Ge SiGe

I II III IV

Si Ge SiGe Si Ge SiGe Si Ge SiGe

Extracting Key Parameters

400

500

600

700

800

900

-3 -2 -1 0 1 2 3

Cap

acit

ance

pe

r A

rea

(nF/

cm2)

Gate Voltage (V)

Experimental Data (Quasistatic CV) for 35% SiGe MOS-C14

EG,eff

(EG,s-Si)

Si thickness

ΔEv

EOT

I II III IV

Complexities of Simulation

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 Mechanics

Thin 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

15

6x6 k·p Method,

Top Valence Band State for s-Ge

k y(1

/Å)

kz (1/Å)

Energy Scale

(eV)

k·p dispersion in the direction

perpendicular to the growth

direction

Valence band is NOT parabolic!

S. Birner et al., “Modeling of Semiconductor Nanostructures with nextnano^3,” ACTA PHYSICA POLONICA SERIES A, vol. 110, no. 2, p. 111, 2006.

16

Energy-momentum (E-k) dispersion

kx

ky

kz

Outline

Previous Work





Conclusion

17

Simulation Variables

Dielectric (modeled as SiO2)

Thickness

Silicon

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

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.

18

400

500

600

700

800

900

-3 -2 -1 0 1 2 3

Cap

acit

ance

pe

r A

rea

(nF/

cm2)

Gate Voltage (V)

SimulationExperiment

Fitting Parameters:𝛥𝐸_𝑣 = 770 meV𝐸_(𝐺,𝑒𝑓𝑓) = 190 meV𝐸_(𝐺,𝑆𝑖) = 960 meVs-Si cap thickness = 49 ÅAl2O3 thickness = 58 Å (38 Å EOT)

Comparison of Best Fit Simulation and

Measurement19

Si thickness

EOT

Sensitivity to ΔEv between s-Si/s-Ge20

500

600

700

800

-2.5 -2 -1.5 -1 -0.5 0

Cap

acit

ance

pe

r A

rea

(nF/

cm2)

Gate Voltage (V)

Simulation, ΔEv = 770 meV

Δ𝐸𝑣 + 25 meV

Δ𝐸𝑣 - 25 meV

CV technique is very sensitive to Δ𝐸𝑣!

400

500

600

700

800

1 1.5 2 2.5 3Cap

acit

ance

pe

r A

rea

(nF/

cm2)

Gate Voltage (V)

Simulation,Experiment

EG,eff + 25 meV

EG,eff - 25 meV

EG,eff = 190 meV

Sensitivity to effective band gap, EG,eff21

400

500

600

700

800

1 1.5 2 2.5 3Cap

acit

ance

pe

r A

rea

(nF/

cm2)

Gate Voltage (V)

Simulation,Experiment

EG,eff = 190 meV

Sensitivity to effective band gap, EG,eff

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.

22

Outline

Previous Work





Conclusion

23

Summary of Extracted Values

Extracted values given below

24

Substrate ΔEv (meV) EG,eff (meV) Si EG (meV)S-Si cap

thickness (Å)

35% SiGe 770 ± 25 190 ± 50 960 ± 50 49 ± 2

42% SiGe 760 ± 25 185 ± 50 950 ± 50 45 ± 2

52% SiGe 670 ± 25 190 ± 50 870 ± 50 43 ± 2

EG,eff

s-Si s-Ge

ΔEvEG,Si

Extracted Values Compared to Theory25

s-Si Band Gap as a Function of Strain Δ𝐸𝑣 as a Function of Strain

We find that Δ𝐸𝑣 is ~100 meV larger than theoretically predicted

∴ EG,eff between s-Si/s-Ge is 100 meV smaller than previously thought

~100 meV𝐸𝐺,𝑆𝑖

Si Ge SiGe

0.0 0.2 0.4 0.6 0.8 1.0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Vale

nce B

and O

ffset

Betw

een s

-Si/s-G

e (

eV

)

xs, Ge fraction of substrate

Calculation, People and Bean

Calculation, Van de Walle, 1986

This work, extracted from CV

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.8

0.9

1.0

1.1

1.2

Band G

ap o

f s-S

i on r

ela

xed S

i 1-x

sGe

xs (

eV

)

xs, Ge fraction of substrate

Calculation, People and Bean

Experimental Data, Welser

This work, extracted from CV

Valence Band Offset of s-Si/s-Si1-xGex

on ~40% Relaxed SiGe26

0

100

200

300

400

500

600

700

800

0 0.2 0.4 0.6 0.8 1

ΔE

v(m

eV

)

x, Ge Fraction in s-Si1-xGex Layer

Ni Chleirigh's WorkThis ExperimentTheory, People and Bean

Line drawn only as guide

Our extracted Δ𝐸𝑣 is inline with previous experimental work.

Updated deformation potentials are required to correct theory.

s-Si

relaxed

Si0.6Ge0.4s-Si1-xGexdielectric

Δ𝐸𝑣

x is varied

Summary of Extracted Values

Extracted values given below

27

Substrate ΔEv (meV) EG,eff (meV) Si EG (meV)S-Si cap

thickness (Å)

35% SiGe 770 ± 25 190 ± 50 960 ± 50 49 ± 2

42% SiGe 760 ± 25 185 ± 50 950 ± 50 45 ± 2

52% SiGe 670 ± 25 190 ± 50 870 ± 50 43 ± 2

Explanation of Relatively Constant EG,eff

with Changing Substrate Ge Fraction28

s-SiSi1-xsGexsSubstrate

s-Ge

Band movement

as xs increases

increasingstrain

decreasing strain

As the Ge fraction of the relaxed SiGe substrate increases, strain

in the s-Si layer increases and strain in the s-Ge layer decreases.

The net result is that the Si CB and Ge VB (orange lines) end up

moving in the same direction as strain is changed.

Outline

Previous Work





Conclusion

29

Conclusions30

MOS-C structure emulates channel region of TFETs

MOS-C analysis is a viable technique to extract band

alignments in the Si-Ge system

Extracted EG,eff is ~100 meV smaller than predicted by theory

Same band alignment information is required in III-V

TFET heterostructures

Technique still needs to be demonstrated in more difficult

material systems

Currently pursing MOS-C structures in the InAs/GaSb system

Important to extract Dit

Acknowledgements31

Winston Chern, MIT

MOS-capacitor analysis

Liliana Ruiz, UT Brownsville

MOS-capacitor analysis

Jose Menendez, ASU

Deformation potential theory and analysis

Christian Poweleit, ASU

Raman analysis

Backup Slides32

Decoupling of Fitting Parameters33

400

500

600

700

800

-3 -2 -1 0 1 2 3

Cap

acit

ance

pe

r A

rea

(nF/

cm2)

Gate Voltage (V)

ExperimentSimulation, 47 Å Si capSimulation, 49 Å Si capSimulation, 51 Å Si cap

High sensitivity to extraction of EOT and s-Si cap thickness.

Valence Band Extraction Method

400

600

800

Cap

acit

ance

pe

r A

rea

(nF/

cm2)

-2

-1

0

1

-3 -2 -1 0 1 2 3Gat

e L

ake

age

pe

r A

rea

(nA

/cm

2)

Gate Voltage (V)

I II III IV QSCV can be divided into 4 regions:

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

Experimental Data for 35% SiGe MOS-C34

Si thickness

ΔEv

Cox EOT

Small gate leakage

Conclusions

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’swork

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 40-60% SiGe substrates

More materials analysis is needed to verify strain, doping, and Ge fraction in the samples

35

Back Up36

Increase in Band Gap Due to Quantum Confinement

X-Valley CB in Silicon

15 meV higher than band edge (effective mass approx.)

Top VB in Germanium

30 meV below band edge (6x6 k.p method)

Extraction of Large Valence Band Offsets in Strained-Si ...teherani.ee.columbia.edu/uploads/2/3/7/2/23722259/valence_band_offsets_04.pdf · Type II Heterostructures on Relaxed SiGe

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