Effects of Crystal Orientation on the Optical Properties...

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Effects of Crystal Orientation on the Optical Properties of GaN based Devices

Transcript of Effects of Crystal Orientation on the Optical Properties...

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Effects of Crystal Orientation on

the Optical Properties of GaN

based Devices

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Outline

Crystal orientation and polarization

k.p method for QW of arbitrary

orientation

Results for InGaN/GaN QW

LD performance

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Spontaneous Polarization

Cubic

zero net polarization

Hexagoanl

Non-zero net

polarization

N. G. Thillosen (PhD thesis: Spin-Bahn-

Wechselwirkung in niedrigdimensionalen

AlxGa1−xN/GaN-Elektronengasen)

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Piezoelectric polarization

Cubic Hexagonal

No strain Bi-axial

strainNo strain

Bi-axial

strain

N. G. Thillosen (PhD thesis: Spin-Bahn-

Wechselwirkung in niedrigdimensionalen

AlxGa1−xN/GaN-Elektronengasen)

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Alternative growth orientations

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Band structure

Conduction band is treated by

parabolic model

SzeV

kz n

rki

t

c

ntt |)(

1),(

S is spherical wavefunction, η is spin,φn(z) is

the envelope function of nth subband

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Valence band

Valence band is treated by 6x6 k.pmethod, including top three valence bands

6

1

),(1

),(i

i

t

i

m

rki

t

v

m UkzgeV

kz tt

gm is the envelope function of the mth subband

Ui are basis functions

)()(),( DkHkH

|)(|),( kEkH

For quantum well

strain

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Rotation

JQE, v43,p1175,2007

)(kHHamiltonian for arbitrary rotation

can be obtained by rotation matrix

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Strain tensor for arbitrary crystal

orientation Strain coefficients for arbitrary crystal

orientation are calculated by

minimizing the elastic energy under

the conditions for pseudo-morphic

growth.

PRB, v59, 4725, 1999

6

1

6

12

1

i j

jiij dVCW

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Anisotropic band structure

c-plane: isotropic

m-plane: anisotropic

band structure.

Smaller effective

mass in y-direction

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Optical momentum matrix

2

22

||||

||||

v

m

c

n pe

MeMnm

Optical momentum matrix elements

for transition between conduction

band n and valence band m are

defined as

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Optical matrix elements: c-plane

A,B,C are for transitions from conduction band to top

three valence bands. Integrating over (kx-ky) plane,

optical matrix elements are NOT dependent on E-field

polarization on x-y plane.

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Optical matrix elements: m-plane

A,B,C are for transitions from conduction band to top

three valence bands. Optical matrix elements are

dependent on polarization.

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Optical gain

Optical gain is calculated by

,,

2

2

00

2

)(][||)(mn

v

m

c

nnmt

r

LffMkddmcn

qg

L(ω) is broadening function. Note 2D integration is

necessary except for c-plane QWs, where the band

structure is isotropic. Similar 2D integration for

spontaneous rates as well.

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Optical gain for different

orientations

30nm-In15Ga85N/GaN

Quantum well at

carrier density of

6.67e25/m3

No polarization

charge in all cases

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Effects of crystal orientation:

from c-plane to m-plane No polarization charge

Optical gain: polarization dependent,

enhanced in y-polarization

Transport: effective mass is reduced

How do these affect the

laser performance?

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Laser performance:

finite-element simulation

Edge-emitting laser active region:

30-nm In15Ga85N/GaN QW (x3)

No polarization charges in all cases

Band diagram

L-I curve