Calculation of minibandstructure balanced type II GaAsBi...

Calculation of miniband structurein strain‐balanced type‐II GaAsBi/GaAsN superlattice

Jinyoung Hwang and Jamie Phillips*Jinyoung Hwang and Jamie PhillipsSolid State Electronics LaboratoryDepartment of Electrical Engineering and Computer ScienceUniversity of Michigan, Ann Arbor, MI, United States*j hilli@ i h d*[email protected]

University of MichiganElectrical Engineering and Computer Science

OutlineOutline

Motivations for GaAsBi/GaAsN Type‐II SLS/ yp

Study Objectives

Calculation Methodology Strain‐Balanced Criteria

Band alignment and Strain effect

Schrödinger Poisson Self Consistent Equation Schrödinger – Poisson Self‐Consistent Equation

Results

Future worku u e o

Conclusion

July 16th, 2010 2University of MichiganElectrical Engineering and Computer Science

Motivations for GaAsBi/GaAsNMotivations for GaAsBi/GaAsN

Desire narrow bandgap material with effective lattice match g pto GaAs Key for low‐cost GaAs

technologytechnology

Particularly important for optoelectronic devices such as detectors wheresuch as detectors where thick active regions required

Lasers?

GaAs

GaAsN GaAsBi

GaAs

Lasers

Photodetectors

Solar Cells

July 16th, 2010University of MichiganElectrical Engineering and Computer Science 3

Motivations for Type‐II SLSMotivations for Type II SLS

Advantages of superlattices – ee Enhance

Bandstructure engineering Effective bandgap Electronic transport Effective

ee EnhanceCarrier transport(barrier tunneling)(miniband conduction)

Electronic transport Controlled by layer thickness

Advantages of GaAsBi/GaAsN

Effective bandgap Increase

g /Type‐II superlattice Effective lattice match to GaAs Minibands in conduction/valence Effective

Minibande

Radiativetransition can

GaAsBi

Minibands in conduction/valence band can be independently controlled

Radiative transitions (lifetime, absorption) can be controlled

bandgap

h

Radiativetransition

Miniband

transition can be controlled by overlap of the minibands


p )GaAsN

Study ObjectivesStudy Objectives

Develop method for calculating electronic structurep g

Determine range of transition energies for SLS Strain balanced structures

“Reasonable” Bi and N content (up to 5% Bi and N composition)

Varying thickness for GaAsBi GaAsN layers Varying thickness for GaAsBi, GaAsN layers

Initial objective to determine criteria to achieve “1 eV” material for photovoltaics


Simulation MethodologySimulation Methodology

1 Determine precondition of concentrations of Bi and N using the strain‐balanced criteria on a GaAs substrate

Strain‐balanced Criteria1

Obtain band edge discontinuity of the heterostructure based on GaAsBi and GaAsN band alignment

Band alignment of GaAsBi/GaAsN superlattice2

Consider strain effect due to lattice mismatch

Mi ib d l l i i S h ödi P i i3 Simulate energy states in the superlattice using self consistent Schrödinger – Poisson equation Transfer matrix algorithm used to solve Schrödinger equation

Miniband calculation using Schrödinger – Poisson equation3


Strain‐Balanced SLSStrain Balanced SLS

Strain ‐ balanced criteria on GaAs substrate Balancing compressive strain (GaAsBi) and tensile strain (GaAsN)

Condition of zero average in‐plane stress[1]

Results: GaAs1‐xBix / GaAs1‐yNy

t1 (GaAsBi)= t2 (GaAsN)

Bi (x) N (y)

0.01 0.006

0.02 0.011

0.03 0.017

0.04 0.022

0.05 0.028


[1] N. J. Ekins‐Daukes, K. Kawaguchi, and J. Zhang, Crystal Growth & Design 2, 287 (2002)

Strain‐Balanced SLSStrain Balanced SLS

Critical thickness of GaAsBi and GaAsN on GaAs substrate

2000

GaAsBiGaAsN | |

1000

1500

GaAsN

knes

s (Å

)

| |

500

1000

Crit

ical

thic

k

100 Å

0 0.01 0.02 0.03 0.04 0.050

Composition of Bi and N


Band alignment – Bi N alloysBand alignment Bi, N alloys

GaAsBi GaAsN

Conduction and Valence band alignment[2] Conduction and Valence band alignment[3]

GaAsBi GaAsN

Conduction band of GaAs Conduction band of GaAsConduction band of GaAs Conduction band of GaAs

HH/LH bands of GaAs HH/LH band of GaAs1‐yNy

July 16th, 2010 9University of MichiganElectrical Engineering and Computer Science

[2] K. Alberi, J. Wu, W. Walukiewicz, K. M. Yu, O. D. Dubon, S. P. Watkins, C. X. Wang, X. Liu, Y. –J. Cho, and J. Furdyna, Phys. Rev. B. 75, 45203 (2007)[3] W. Shan, W. Walukiewicz, K. M. Yu, J. W. Ager III, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson, S. R. Kurtz, H. P. Xin, and C. W. Tu, Phys. Stat. Sol 223, 75 (2001)

Band alignment‐ Bi N AlloysBand alignment Bi, N Alloys

General Band alignment of GaAs1‐xBix (x=0~0.05) , GaAs1‐yNy (y=0~0.05), y yand GaAs

E (GaAs) = 1 424 eVGaAs BiGaAs NGaAs GaAs Eg(GaAs) = 1.424 eVGaAs1‐xBixGaAs1‐yNyGaAs GaAs

July 16th, 2010University of Michigan Electrical Engineering and Computer Science 10

Band alignment ‐ Strain effectBand alignment Strain effect

Strain effect on band alignment

⁄

g GaAsBi: Compressive strain / GaAsN: Tensile strain

Pseudomorphically grown on a (100)‐oriented substrate

⁄

CB moving upward

Eg(GaAs) = 1.424 eVGaAsBi

GaAsNGaAs GaAs

CB moving downward

Heavy hole band

Light hole bandLight hole band

y


Heavy hole bandHH and LH separated

Electronic Structure CalculationElectronic Structure Calculation

Coupled Schrödinger – Poisson Equation[4]p g q

Generate V(x) and ρ(x) Solve the Schrödinger equation for Ei and Ψi

Compute N(Ei) assuming Fermi distribution

Calculate charge density

Generate band profile from the charge

density

Compare with V(x)

DONE

Solving Schrödinger equationC l l bb d i h l i Calculate subband structure in the superlattice

Transfer matrix approach[5] used


[4] C. H. Fischer IV, Ph.D. dissertation. University of Michigan (2004)[5] E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, IEEE Journal of Quantum Electronics 29, 2731 (1993)

Miniband structure of SLSMiniband structure of SLS

Miniband of GaAs0 96Bi0 04 / GaAs0 979N0 0210.96 0.04 / 0.979 0.021

Layer thicknessGaAs0.96Bi0.04GaAs0.979N0.021

40 Å40 Å

# f l 25# of layers 25

Total thickness of SLS 100nm

Effective

GaA

s

GaA

s

band gap 1.0011 eV


Transition energy of SLS

Transition energy range for different Bi composition


gy g pComposition of Bi and N: 0 ~ 5%

12

1.3

1.4

1.5

rgy

(eV

)

Bi(1%): 1.40 ~ 1.20eV

0.9

1

1.1

1.2

Tran

sitio

n E

ner

Bi(2%): 1.37 ~ 1.01eVBi(3%): 1.33 ~ 0.88eVBi(4%): 1.30 ~ 0.80eV

020

4060

80100

020

4060

80100

0.7

0.8

T

Bi(5%): 1.26 ~ 0.72eV

100



Transition energy range for different Bi composition


1.6

gy g p

1

1.2

1.4

n E

nerg

y (e

V)

GaAs

0

500

50

0.8

Tran

sitio

n

GaAsBi/GaAsN SLS

100100


ResultsResults

Thickness of individual layer vs. transition energy with

1.6

0.8

y gydifferent N and Bi composition (t1,GaAsBi = t2,GaAsN)

1.2

1.4

rgy

(eV

)

1

0.9

h(um

)Bi: 1%

1

1.2

rans

ition

Ene

r

1 41.31.2

1.1

Wav

elen

gth

1eVBi: 2%

Bi: 3%

Bi: 4%

Bi 5%

20 0 60 80 1000.6

0.8

Tr

2

1.61.51.4Bi: 5%

20 40 60 80 1000.6

Thickness (A)


Future workFuture work

Carrier transport simulationp Tunneling probability

Carrier scattering probability via Monte‐Carlo simulation

D i l i i l d l l di i Determine electron transport in vertical and lateral directions

Radiative transitions Wavefunction overlap Wavefunction overlap

Optical absorption/recombination lifetimes

Compare with experimental data Material parameters, band offsets, etc, used in simulation

Experimental SLS structures


ConlclusionsConlclusions

Electronic structure of GaAsBi/GaAsN superlattices were calculated for varying layer thickness and alloy composition

GaAsBi/GaAsN superlattices offer a wide range of effective bandgap( 0 7 1 4 V) f i b l d G Aenergy (~0.7 – 1.4 eV) for strain‐balanced structures on GaAs

Attractive for variety of optoelectronic devices, and need further experimental and theoretical research effortsexperimental and theoretical research efforts

This work is supported by the Center for Solar and Thermal Energy Conversion, an Energy Frontier Research Center funded by the Department of Energy Office of Basic Energy Sciences


Frontier Research Center funded by the Department of Energy Office of Basic Energy Sciences

Calculation of minibandstructure balanced type II GaAsBi...

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