electron holography in the tem

F. A. Ponce, J. Cai and M. StevensDepartment of Physics and Astronomy

Arizona State UniversityTempe, Arizona, USA

Profiling the electrostatic field and charge distributions

using electron holography

Arizona State University

Lecture 3

OutlineIntroduction to Electron holography

Principles

Applications

Topics studied in this work

Quantum wells and heterostructures in group III nitrides

Dislocation charge states in GaN under different doping conditions

Conclusions and future work

Internal Fields and Charges•The nitride semiconductors have a hexagonal wurtzite structure.•Heterojunction interfaces are typically pseudomorphic•Large strains are present Piezoelectric fields.•AlGaN/GaN interfaces present 2-dimensional electron gas•Dislocations are expected to have associated electronic charges.

•There is a need to probe and measure the internal fields and charges at dislocations and interfaces

•There has been no method to do this directly.

•In the last three years we have developed methods and demonstrated the use of electron holography for measuring the fields and charges at dislocations and interfaces in the nitridesemiconductors.

History of Electron HolographyHologram

öλος (olos)complete

γραµ (gram)message

In 1948, Gabor coined the word “hologram”.1

The complete information carried by a plane-wave (Aexp[iθ]) includes both amplitude A, and phase θ information.

Interference method is used to record complete information.

1. D. Gabor, Nature 161, 777 (1948).

Schematic of interference principle

Schematic of Electron Holography

Consider a free electron traveling through vacuum

Consider a free electron traveling through a thin foil:

Vacuum Material Vacuum

Schematic of Electron HolographyThe wavelength of the electron beam is shorter inside the material because the potential energy has changed (dropped) and therefore the kinetic energy has increased (if the total energy of the electron is to remain constant).

Vacuum Material Vacuum

The change in wavelength will cause a phase shift in the signal wave (propagating through the sample) with respect to the reference wave (traveling through vacuum only).

Achieving Electron Holograms

Coherent electron source

Ψref= Ar exp(iθr)

Interference fringes

Specimen

Objective lens

Biprism

Ψobj =Ao exp(iθo)

Philips CM-200 FEGSchematic beam path

TEM and Electron Holographic Images

I = |Ψobj+ Ψref |2 = Ao2 + Ar

2

+2AoArcos(∆θ-4παx/λ)

g

BA

DC

Specimen

Vacuum

(b)

Two-beam dark-field TEM image Electron hologram of selected area

I = |Ψg|2 = Ag2

Image Reconstruction (1)

Central band

Side band

Side band

I = |Ψobj+ Ψref |2 = Ao2 + Ar

2

+2AoArcos(∆θ - 4παx/λ)FT[I] = δ(u)⊗FT[Ao

2 + Ar2 ] +

δ(u+ 2α/λ) ⊗ FT[AoArexp(i ∆θ)] + δ(u-2α/λ) ⊗ FT[AoArexp(-i ∆θ)]

FFT

Electron hologram FFT of electron hologram

Image Reconstruction (2)

One selected side band

δ(u) ⊗ FT[AoArexp(i ∆θ)]

IFTComplex image

AoArexp(i ∆θ)

Phase Normalized amplitude

∆θ Ao/Ar

Applications of Electron HolographyTo improve spatial resolution of electron microscope.To study electromagnetic potential and magnetic fields.To obtain electrostatic potential and charge distribution in nonmagnetic materials.

)y,x(t)y,x(VC)y,x( E=θ∆

∆θ = 2π(1/λ- 1/λ’) t

Em2 o

h=λ

)VE(m2'

o +=

hλ

tΨref Ψobj

V: projected potential of specimenCE: a constant depending on the energy of the electron beam. It is

0.00728 rad/V nm at 200 keV.t: sample thickness.

At the exit plane:

Thin specimens and tilted away from strong diffraction conditions,

Electron Holography Studies on Semiconductors

Measure mean inner potentials of semiconductors 2- 4

2. M. Gajdardziska-Josifovska et al, Ultramicroscopy 50, 285 (1993).3. Y. C. Wang et al, Appl. Phys. Lett. 70, 1296 (1997).4. J. Li et al, Acta Crystall. A 55, 652 (1999).

Map potential distribution in real devices 5-7

5. S. Frabboni et al, Ultramicroscopy 23, 29 (1987).6. M. R. McCartney et al, Appl. Phys. Lett. 65, 2603 (1994).7. W. D. Rau, Phys. Rev. Lett. 82, 2614 (1999).

Study polarization fields in group III nitrides 8-11

8. D. Cherns, F. A. Ponce, et al, Sol. Stat. Comm. 111, 281 (1999).9. M. R. McCartney, F. A. Ponce, et al, Appl. Phys. Lett. 76, 305 (2000).10. J. Cai, F. A. Ponce et al, Phys. Stat. Sol. 188, 833 (2001)11. J. Cai and F. A. Ponce, J. Appl. Phys. 91, 9856 (2002).12. M. Stevens, F. A. Ponce, et al. Appl. Phys. Lett. 85, 4651 (2004)

Study of dislocations in group III nitrides 13

13. J. Cai and F. A. Ponce, Phys. Stat. Sol. 192, 407 (2002).

Blue LED, Nichia Corp.

F. A. Ponce and D. P. Bour, Nature 386, 351 (1997)

Cross-section view

GaN/GaInN/GaN/Sapphire

Using GaN buffer layers

1010 Dislocations/cm2

Columnar Model for the III-V Nitrides

F. A. Ponce, MRS Bull, 22, 51 (1997)

Low-angle domain boundaries

Tilt of the c-axis:~5 arc minX-ray rocking curves

Rotation of c-axis:~8 arc minX-ray rocking curves (assymetric reflexions)

Studies by Electron Holography Quantum wells and heterostructures

GaN/InGaN/GaN single quantum well system

GaN/AlGaN heterojunction (2DEG)

Charge distribution across dislocations in GaN

Dislocations in undoped GaN (n-type)

Dislocations in GaN:Zn (semi-insulating)

Dislocations in GaN:Mg (p-type)

Quantum Wells

They are used as active region for the purpose of carrier confinement and light emission.Spontaneous and piezoelectric polarization fields are present in the InGaN QWs.

Influence of polarization fields on optical transition in InGaN QW11, 12

E2 < E1, red-shift of band edge emissionBroaden emission peakLong carrier lifetime

11. T. Takeuchi et al. Appl. Phys. Lett, 73, 1697 (1998).12. C. Wetzel et al. J. Appl. Phys, 85, 3786 (1999).

E∆V≈ E1-E2

E2

With fields

E1

No fields

InGaN Quantum Wells

QW

16.6nm

QW

a b

(a) Phase image of QW # 4.(x=.13 d=3nm). (b) Thickness image

Thickness was measured assuming an inelastic mean free path length of 75nm. For this system the thickness was found to be ~ 220nm.

5nm 5nm

Phase Thickness

High resolution electron holography of InGaN QWs

5 10 15 20 25

14

12

10

8

6

4

2

Phas

e (r

ad)

[0001]

GaN

GaN

InGaN QW

6.106.146.186.226.266.306.346.386.426.466.506.546.586.626.666.706.746.786.826.866.90

Distance (nm)

Dis

tanc

e (n

m)

Contour Images of InGaN Quantum Well

The phase contour shows that the top GaN barrier has higher value of phase, while thickness contour shows flat plane.Phase and thickness profiles are obtained over a 2nm wide strip.

Phase contour image Thickness contour image

J. Cai and F. A. Ponce, J. Appl. Phys. 91, 9856 (2002).

5 10 15 20 25

14

12

10

8

6

4

2

[0001]

GaN

GaN

InGaN quantum well

Thic

knes

s (n

m)

Dis

tanc

e (n

m)

60.0

80.0

100.0

120.0

140.0

160.0

180.0

Distance (nm)

Energy Profile across InGaN QW

50 1000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distance (Å)

Thic

knes

s (n

m)

Phas

e (R

ad)

0

50

100

GaN InGaN GaN

[0001]

50 100-0.8

-0.6

-0.4

-0.2

0.0

Ener

gy (e

V)Distance (Å)

Observed Curve A Curve B

)y,x(t)y,x(VC)y,x( E=θ∆

The slope of energy profile indicates the electric field in the quantum well is -2.2 MV/cm. Charge distribution is analyzed following two approaches, curve A and B.

Phase and thickness profiles Energy profile

J. Cai and F. A. Ponce, J. Appl. Phys. 91, 9856 (2002)

Charge Distribution across InGaN QW

Three charge contributors: interface dipole σd, polarization charge σp and free carriers σe, h.

GaN InGaN GaN

20 40 60 80 100-10

-5

0

5

10

Distance (Å)

-5

0

5

Cha

rge

dens

ity (x

1020

cm-3)

σ3σ2

σ1σ4

(a): Curve A

(b): Curve B

σ5

σd (+)(-) (-)(+)σp (-) (+)σe, h (++) (------)Net: (+)(-) (-)(+)(-)

[0001]

(c)

Charge distribution

Charge density across InGaN QW

0 50 100 150-10

-5

0

5

10Free carriers

Interface dipole

Polarization sheet charge

Cha

rge

Den

sity

(x10

20cm

-3)

Distance (Å)

J. Cai and F. A. Ponce, J. Applied Physics 91, 9856 (2002)

The Samples

width 20Å 30Å 40Å 60Å 80Å 100Åx

0.21 100.17 90.13 3 4 5 6 7 80.09 20.05 1

GaN GaNInGaN

1. Select parameters that experimentally optimize the performanceof blue-violet laser diodes - Best light emission characteristics.

2. Vary the composition and the well widths.

-10 -5 0 5 10 15 20 25

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

distance (nm)

rel

ativ

e po

tent

ial(V

) 2nm3nm6nm8nm10nm

Well region 5.5nm

Thickness

* Denotes the ideal field

2.2MV/cm*

Electrostatic Potential Profiles

-5 0 5 10 15 20-0.2

0

0.2

0.4

0.6

0.8

1

1.2

distance along growth direction(nm)

Rela

tive

Elec

tros

tatic

Pot

entia

l (V) 2nm

3nm4nm6nm8nm10nm

2MV/cm

[0001]

Potential Profiles of InGaN quantum wells x=0.13, d=2-10nm.

2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

quantum well width(nm)

<el

ectr

osta

tic f

ield

> (

MV/

cm)Electrostatic field strengthRapid decline in field strength beyond 6nm

Electrostatic Potential Profiles

2 3 4 5 6 7 8 9 102.7

2.8

2.9

3.0

3.1

3.2

Room temperature CL peak positionfrom In0.13Ga0.87N QW

emission from 13% InGaN alloy

Emis

sion

ene

rgy

(eV)

Well width (nm)

The CL data also reflects the electron holography, with the 10nm sample exhibiting very small fields.There are two possible explanations:

1. The critical thickness has been exceeded and the layer is relaxed2. The fields have been screened due to the large well width

Cathodoluminescence of QWs

20406080100

-0.65

-0.6

-0.55

-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

Mapping the projected electrostatic potential within InGaN QWs using electron holography

support edge

capping layer interface

capping layer

distance (nm)

V

5 10 2015 3025 4035 5045

60nm GaN substrate GaN capping layer

InGaN QW

10nm

interfacial dipole field onsubstrate side

Different orientations of a 60 x 60nm projection of the electrostatic potential of In.13Ga.87N QW of width d=10nm, here we see the expected piezoelectric field is much smaller than expected (expected 2.2MV/cm, measured <0.1MV/cm). In addition to the dipole field near the substrate interface, there exist potential variations of the order of .05V/2nm in that region.

Topics Studied by Electron Holography

Quantum wells and heterostructures


GaN/AlGaN heterojunction





GaN/AlGaN Heterostructures

Sapphire

GaN

AlGaN[0001]

+ + + + + + + + + + + + +- - - - - - - - - - - - - - - -

Polarization sheet charge2-D electron gas (2DEG)

GaN/AlGaN structure is used in field-effect transistors (HFETs) due to the present of 2DEG.2DEG is caused by polarization effect.2DEG density is around 1013 cm-2.13, 14

13. E. T. Yu et al. Appl. Phys. Lett, 73, 1880 (1998).14. O. Ambacher et al. J. Appl. Phys, 85, 3222 (1999).

GaN/AlGaN HeterostructuresSpecimens

GaN (~1.5 µm)

AlxGa1-xN (65 nm)

Sample A: x = 0.19Sample B: x = 0.37

+c Orientation (Ga-polarized)n ~ 1016 cm-3

Hologram

60 nm

Vacuum

AlGaN

GaN

[0001]

J. Cai, F. A. Ponce et al, Phys. Stat. Sol. A 188, 833 (2001).

Phase and Amplitude

Amplitude

0 50 100

6

8

10

Thickness

Thickness (nm)

Phase

Phas

e (r

ad)

Distance (nm)

0

50

100

150

Phase and thickness profiles across GaN/Al0.19Ga0.81N heterostructures

∆θ(x) = CE V(x) t

[0001]

Al0.19Ga0.81N

Phase

GaN

Al0.19Ga0.81N

GaN


Energy and Charge Distribution

0 50 100

-0.5

0.0

0.5

1.0

Cha

rge

(C/c

m3 )

Distance (nm)Energy profile

Measured energy values for GaN/AlxGa1-xNCharge distribution

∆E2

∆E1 σ1

σ2

σ3

0.38 ± 0.12-0.13 ± 0.090.37

0.21 ± 0.1-0.05 ± 0.040.19∆E2∆E1x

These are average values from several measurements. The dispersion was observed to be 30-80%.

0 50 100-0.1

0.0

0.1

0.2

0.3

Etrend Emeas

Ener

gy (e

V)

Distance (nm)


Three Types of Charges at Interface

a. Free carriers and ionized donors

b. Sheet charge due to polarization

c. Interface dipole

x

ρ

Ndq

-q(n(x)-ND)

x

ρ

ρ

x

GaN AlGaN[0001]

Experimental determined σ1, σ2 and σ3 have three components:

Determination of Charge Density

σ3(-) = Nd+ σdip-≈ σdip

-σ2(+) = σpolσ1(-) = ns+ σdip

+Net Observed

-+Interface dipole (σdip)+Polarization (σpol)

+ (Depletion, Nd)- (2DEG, ns)Free carriers & ionized donors

AlGaNInterfaceGaN

Charge type and distribution

2DEG density at GaN/AlxGa1-xN

2.9 x 10120.37

1.8 x 10120.19ns (cm-2)x


Experimental Limitations

B. Radiation damage caused by high energy electron beams.

SEM image CL image at λ=358 nm

1.5 µm

A. Effect of surface depletion in TEM cross-section specimens.

Damage

Point defects are created during exposure to 200 keV electron beam.This modifies the local electronic potential.


Conclusions:2DEG Density at GaN/AlGaN

Using electron holography, we have measured the energy offset (∆E2) at GaN/AlxGa1-xN.

For x = 0.19, ∆E2 = 0.21 ± 0.1 eV;

For x = 0.37, ∆E2 = 0.38 ± 0.1 eV.

Three types of charges are present at heterostructures: free carriers, polarization sheet charge, and interface dipole.

The two dimensional electron gas density (ns) is determined from the energy profiles. It increases with aluminum concentration.

For x = 0.19, ns = 1.8 x 1012 cm-2;

For x = 0.37, ns = 2.9 x 1012 cm-2.

Surface depletion layers and radiation damage are two factors to affect electron holography measurements.


Topics Studied by Electron Holography

Quantum wells and heterostructures


GaN/AlGaN heterojunction





Dislocations in Blue LED (Nichia)

10. F. A. Ponce and D. P. Bour, Nature 386, 351 (1997).

GaN/GaInN/GaN/Sapphire

Using GaN buffer layers

1010 Dislocations/cm2

Cross-section TEM image10

Three types of DLs:Edge type, be =

Screw type, bs =

Mixed type, bm =

Threading dislocations limit the electrical and optical performance of devices.

Little is known about the electronic charge states at different type of threading DLs.

Threading Dislocations in GaN

021131

321131

0001

J. Cai and F. A. Ponce, Phys. Stat. Sol. A 192, 407 (2002).

Unit cell of wurtzite GaNbe

bsbm

GaN

F. A. Ponce et al, Appl. Phys. Lett 69, 770 (1996).

Charge states at dislocations

N-rich

Ga-rich

Defect formation energy vs. Fermi-level15

n-GaN: Negatively chargedp-GaN: Positively charged or neutralExperimental evidence 16, 17

For edge dislocations:

Deep gap states are present at full-core screw dislocation.18

No deep gap states at nanopipes.18

Experimental results show discrepancy.19

For screw dislocations:

15. A. F. Wright et al. Appl. Phys. Lett. 73, 2751 (1998).16. P. J. Hansen et al. Appl. Phys. Lett. 72, 2247 (1999).17. D. Cherns et al. Phys. Rev. Lett. 87, 205504 (2001).18. J. Elsner et al. Phys. Rev. Lett. 79, 3672 (1997).19. M. Albrecht et al. Phys. Stat. Sol. B 216, 409 (1999).

TEM and Holography of DLs in GaN

100 200 300 400 500 600

600

500

400

300

200

100

Thic

knes

s (n

m)

015.030.045.060.075.090.0105.0120.0135.0150.0165.0180.0195.0210.0225.0240.0255.0270.0285.0300.0

Distance (nm)

Dis

tanc

e (n

m)

(b) g

BA D

(a) g

A C

500 nm

A: mixed typeB: edge typeC: screw typeD: edge type

100 200 300 400 500 600

600

500

400

300

200

100Ph

ase

(rad

)

-4.0-0.62.86.29.613.016.419.823.226.630.033.436.840.243.647.050.453.857.260.664.0

Distance (nm)

Dis

tanc

e (n

m)

(c) (d)

AB

CD

Two-beam dark-field TEM images at (a) g0002 and (b) g conditions0211

Phase (c) and thickness (d) images in the region including DLsJ. Cai and F. A. Ponce, Phys. Stat. Sol. A 192, 407 (2002).

Potential and Charge Density

0 200 400 600 800-1.5

-1.0

-0.5

0.0

0.5 Measured potential Gaussian fit

Pote

ntia

l (V)

Distance (nm)

AD

C

B

(a)0 200 400 600 800 1000

-1.5

-1.0

-0.5

0.0

Charge density (x10

16cm-3)

Pote

ntia

l (V)

Distance (nm)

-15

-10

-5

0

5

10

C(b)

Potential profile across dislocations Potential and charge distribution across C

Decreased potential at DLsPotential profiles are fit by Gaussian curves, and differentiated twice to get charge densities.

DL cores are negatively charged, ~ 1017 cm-3.Positive space charge surrounds the cores.


Charge Density at Dislocations

∫−

=r

r

2 dx)xρ(xc2n π

Line charge density+++++++

+++++++

-

Ec

Ev

R

r

[0001]

Ef

Charge distribution model around the dislocations 20

r = radius of the dislocation core where electrons are trapped, R = radius of the region where free electrons are depleted.

n: The number of charges per period along the [0001] direction

c: Unit length along [0001], 5.178 Å.

r: Radius of a dislocation core.

ρ(x): Charge density determined from potential profile.

20. W. T. Read, Philos. Mag. 45, 775 (1954).J. Cai and F. A. Ponce, Phys. Stat. Sol. A 192, 407 (2002).

Charge Density at Dislocations

200.6

Mixed

r (nm)

n (e/c)

± 104015± 0.210.3

ErrorScrewEdge

Line charge density vs. tilted angle Core radii vs. tilted angle

0

0.2

0.4

0.6

0.8

1

1.2

1.4

4 6 8 10 12Tilted angle (degree)

n (e

/c)

EdgeScrewMix

0

10

20

30

40

50

60

4 6 8 10 12Tilted angle (degree)

Cor

e ra

dii (

nm)

EdgeScrewMixed


Charge States of DLs in Zn-doped GaN

A

CB

D100 nm

Phase images Amplitude images

[Zn] = 1017 cm –3; semi-insulating material, grown by HVPE, surface treated by reactive ion beam.A: Edge type (+)B and C: Mixed type (Neutral)D: Screw type (-)Positive, negative and neutral cores have been observed.

Potential and charge profiles cross A

Cathodoluminescence Analyses

2 µm

(a)

0.3 0.4 0.5 0.6 0.7 0.8 0.9

RCL

Position (µm)

CL

Inte

nsity

(a.u

. )

(b)

CL image at 359 nm

CL intensity profile across the dark spot

The dark spot diameter measured from CL image is in a range of 0.4-0.6 µm. 21

21. S. Srinivasan, J. Cai, et al, Phys. Stat. Sol., in press.

Electrostatic Potential Profile between DLs

3 2 1

K L

H

G 0211

500 nm 0 500 1000 15002.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

Pote

ntia

l (V)

Distance (nm)

K LH

TEM image of DL H, K and L Potential profile cross DL H, K and L

At positions between dislocations, the electrostatic potential fluctuates in a range of 0.6-1.2 V, with a period of 600 – 800 nm.

Surface states caused by ion beam etch are responsible for such potential variation.

Charge States of DLs in Mg-doped GaN

(a)

(b)

100 nm

A

10 20 30 40 50

10

20

30

40

50

-0.35-0.27-0.18-0.095-0.0100.0750.160.240.330.410.50

Distance (nm)

Dis

tanc

e (n

m)

10 20 30 40 50

10

20

30

40

50

70.0078.0086.0094.00102.0110.0118.0126.0134.0142.0150.0

Distance (nm)

Dis

tanc

e (n

m)

(a). Phase

(b). Thickness

A

A

Plane view TEM images. A is in contrast in (a), but out of contrast in (b)

Phase and thickness contour images around A

A: Edge type

Potential Profiles around a dislocation

10 20 30 40 50

10

20

30

40

50

-0.45-0.34-0.22-0.110.0100.120.240.350.470.580.70

Distance (nm)

Dis

tanc

e (n

m)

A

0 10 20 30 40 50 60-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Pote

ntia

l (V)

Distance (nm)

Potential contour image around A Potential profile across A

A potential peak of ~0.7 V is observed at DL A. 22

DL A is charged positively in p-GaN.

Analysis on charge states of mixed or screw type dislocation are still on going.

22. D. Cherns, J. Cai, et al, Phys. Stat. Sol., in press.

Conclusions:Charge states at threading dislocationsElectron holography was performed on threading dislocations of undoped, Zn- and Mg- doped GaN epilayers.

All dislocations are negatively charged in undoped (n-type) materials. The line charge densities of edge, screw and mixed type dislocations are 0.3, 1.0 and 0.6 ± 0.2 e/c, respectively. The corresponding core radii are around 15, 40 and 20 ± 10 nm.

Positive, negative and neutral DL cores have been identified in the Zn-doped material. Potential fluctuation between DLs were also observed. Such potential profiles are attributed to the semi-insulating nature of the material.

Edge type DLs have positively charged cores in Mg-doped GaN. Further studies are needed to identify the charge states of screw and mixed dislocations.

General ConclusionsUsing electron holography we have demonstrated that we can effectively measure the electrostatic potential at dislocations and at heterojunction interfaces.

From the potential we can determine the electrostatic charge distribution with spatial resolution down to the Angstrom level.

We have applied this technique to:

InGaN quantum wells.

AlGaN/GaN 2DEG systems.

Dislocations in GaN epilayers with different doping conditions.

Physical meaning of potential level measured by electron holography. The relationship between the potential offset at heterostructures and ∆Ecor ∆Ev.

More analyses of charge distribution across InGaN quantum wells.

Continuous study of charge states at dislocations in Mg-doped GaN.

New problems……

Toward the Future

Nucleus

1

Core levels

Ec

2 3 N

Vacuum

EvEf

Mean inner potential

Electron affinity Work function

V0

electron holography in the tem

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