Lecture 3. Profiling the electrostatic field and charge distributions using electron holography. F. A. Ponce, J. Cai and M.

Transcription

1 Lecture 3 Profiling the electrostatic field and charge distributions using electron holography F. A. Ponce, J. Cai and M. Stevens Department of Physics and Astronomy Arizona State University Tempe, Arizona, USA Arizona State University

2 Outline Introduction 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

3 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 nitride semiconductors.

4 History of Electron Holography In 1948, Gabor coined the word hologram. 1 Hologram öλος (olos) complete γραµ (gram) message 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. Schematic of interference principle 1. D. Gabor, Nature 161, 777 (1948).

5 Schematic of Electron Holography Consider a free electron traveling through vacuum Consider a free electron traveling through a thin foil: Vacuum Material Vacuum

6 Schematic of Electron Holography The 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).

7 Achieving Electron Holograms Coherent electron source Ψ ref = A r exp(iθ r ) Ψ obj =A o exp(iθ o ) Specimen Objective lens Biprism Interference fringes Schematic beam path Philips CM-200 FEG

8 TEM and Electron Holographic Images g (b) A B C D Vacuum Specimen Two-beam dark-field TEM image Electron hologram of selected area I = Ψ g 2 = A g 2 I = Ψ obj + Ψ ref 2 = A o2 + A r 2 +2A o A r cos( θ-4παx/λ)

9 Image Reconstruction (1) Side band FFT Central band Side band Electron hologram I = Ψ obj + Ψ ref 2 = A o2 + A r 2 +2A o A r cos( θ -4παx/λ) FFT of electron hologram FT[I] = δ(u) FT[A o2 + A r2 ] + δ(u+ 2α/λ) FT[A o A r exp(i θ)] + δ(u-2α/λ) FT[A o A r exp(-i θ)]

10 Image Reconstruction (2) IFT Complex image A o A r exp(i θ) One selected side band δ(u) FT[A o A r exp(i θ)] Phase θ Normalized amplitude A o /A r

11 Applications of Electron Holography To improve spatial resolution of electron microscope. To study electromagnetic potential and magnetic fields. To obtain electrostatic potential and charge distribution in nonmagnetic materials. Thin specimens and tilted away from strong diffraction conditions, At the exit plane: Ψ ref Ψ obj t θ = 2π(1/λ- 1/λ ) t λ = h 2m o E λ' = h 2m ( E V ) o + θ x,y ) = C V( x,y )t( x,y ) ( E V: projected potential of specimen C E : a constant depending on the energy of the electron beam. It is rad/v nm at 200 kev. t: sample thickness.

12 Electron Holography Studies on Semiconductors Measure mean inner potentials of semiconductors 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 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 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 J. Cai and F. A. Ponce, Phys. Stat. Sol. 192, 407 (2002).

13 Blue LED, Nichia Corp. Cross-section view GaN/GaInN/GaN/Sapphire Using GaN buffer layers Dislocations/cm 2 F. A. Ponce and D. P. Bour, Nature 386, 351 (1997)

14 Columnar Model for the III-V Nitrides Low-angle domain boundaries Tilt of the c-axis: ~5 arc min X-ray rocking curves Rotation of c-axis: ~8 arc min X-ray rocking curves (assymetric reflexions) F. A. Ponce, MRS Bull, 22, 51 (1997)

15 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)

16 Quantum Wells

17 InGaN Quantum Wells E V E 1 -E 2 E 1 E 2 No fields 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. 11. T. Takeuchi et al. Appl. Phys. Lett, 73, 1697 (1998). 12. C. Wetzel et al. J. Appl. Phys, 85, 3786 (1999). With fields Influence of polarization fields on optical transition in InGaN QW11, 12 E 2 < E 1, red-shift of band edge emission Broaden emission peak Long carrier lifetime

18 High resolution electron holography of InGaN QWs QW 5nm 5nm QW 16.6nm Phase Thickness 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.

19 Distance (nm) Contour Images of InGaN Quantum [0001] GaN InGaN QW GaN Well Phase (rad) Distance (nm) [0001] GaN InGaN quantum well GaN Thickness (nm) Distance (nm) Phase contour image Distance (nm) Thickness contour image 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. J. Cai and F. A. Ponce, J. Appl. Phys. 91, 9856 (2002).

20 Phase (Rad) Energy Profile across InGaN QW GaN InGaN GaN 50 [0001] Distance (Å) Phase and thickness profiles 100 Thickness (nm) Energy (ev) θ( x,y ) = CEV( x,y )t( x,y ) Energy profile Distance (Å) The slope of energy profile indicates the electric field in the quantum well is -2.2 MV/cm. Observed Curve A Curve B Charge distribution is analyzed following two approaches, curve A and B. J. Cai and F. A. Ponce, J. Appl. Phys. 91, 9856 (2002)

21 Charge density (x10 20 cm -3 ) Charge Distribution across InGaN (a): Curve A (b): Curve B σ σ 4 1 σ 2 σ Distance (Å) σ 5 (c) GaN InGaN GaN σ d (+)(-) (-)(+) σ p (-) (+) σ e, h (++) (------) Net: (+)(-) (-)(+)(-) [0001] Charge distribution QW Charge Density (x10 20 cm -3 ) Polarization sheet charge Free carriers Interface dipole Distance (Å) Charge density across InGaN QW Three charge contributors: interface dipole σ d, polarization charge σ p and free carriers σ e, h. J. Cai and F. A. Ponce, J. Applied Physics 91, 9856 (2002)

22 The Samples 1. Select parameters that experimentally optimize the performance of blue-violet laser diodes - Best light emission characteristics. 2. Vary the composition and the well widths. GaN InGaN GaN width 20Å 30Å 40Å 60Å 80Å 100Å x

23 Electrostatic Potential Profiles relative potential(v) Thickness Well region 5.5nm 2.2MV/cm* * Denotes the ideal field 2nm 3nm 6nm 8nm 10nm distance (nm)

24 Electrostatic Potential Profiles Relative Electrostatic Potential (V) MV/cm [0001] 2nm 3nm 4nm 6nm 8nm 10nm distance along growth direction(nm) Potential Profiles of InGaN quantum wells x=0.13, d=2-10nm. <electrostatic field> (MV/cm) quantum well width(nm) Electrostatic field strength Rapid decline in field strength beyond 6nm

25 Cathodoluminescence of QWs Room temperature CL peak position from In 0.13 Ga 0.87 N QW 3.2 Emission energy (ev) emission from 13% InGaN alloy 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 relaxed 2. The fields have been screened due to the large well width

26 Mapping the projected electrostatic potential within InGaN QWs using electron holography capping layer InGaN QW V nm GaN substrate GaN capping layer capping layer interface support edge distance (nm) nm interfacial dipole field on substrate side Different orientations of a 60 x 60nm projection of the electrostatic potential of In.13 Ga.87 N 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.

27 Topics Studied by Electron Holography Quantum wells and heterostructures GaN/InGaN/GaN single quantum well system GaN/AlGaN heterojunction Charge distribution across dislocations in GaN Dislocations in undoped GaN (n-type) Dislocations in GaN:Zn (semi-insulating) Dislocations in GaN:Mg (p-type)

28 GaN/AlGaN Heterostructures [0001] AlGaN Polarization sheet charge 2-D electron gas (2DEG) GaN Sapphire 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 cm , E. T. Yu et al. Appl. Phys. Lett, 73, 1880 (1998). 14. O. Ambacher et al. J. Appl. Phys, 85, 3222 (1999).

29 GaN/AlGaN Heterostructures Specimens Hologram Al x Ga 1-x N (65 nm) [0001] Vacuum GaN (~1.5 µm) AlGaN Sample A: x = 0.19 Sample B: x = 0.37 GaN +c Orientation (Ga-polarized) n ~ cm nm J. Cai, F. A. Ponce et al, Phys. Stat. Sol. A 188, 833 (2001).

30 Al 0.19 Ga 0.81 N Phase and Amplitude GaN Phase Phase (rad) 8 6 Phase Thickness [0001] Thickness (nm) Al 0.19 Ga 0.81 N Distance (nm) 0 GaN Amplitude Phase and thickness profiles across GaN/Al 0.19 Ga 0.81 N heterostructures θ(x) = C E V(x) t J. Cai, F. A. Ponce et al, Phys. Stat. Sol. A 188, 833 (2001).

31 Energy and Charge Distribution Energy (ev) E trend E meas E 2 Charge (C/cm 3 ) E 1 σ 1 σ Distance (nm) Distance (nm) Energy profile Charge distribution Measured energy values for GaN/Al x Ga 1-x N x E 1 E ± ± ± ± 0.12 These are average values from several measurements. The dispersion was observed to be 30-80%. J. Cai, F. A. Ponce et al, Phys. Stat. Sol. A 188, 833 (2001). σ 3

32 Three Types of Charges at Interface Experimental determined σ 1, σ 2 and σ 3 have three components: GaN AlGaN [0001] a. Free carriers and ionized donors ρ N d q b. Sheet charge due to polarization -q(n(x)-n D ) ρ x c. Interface dipole ρ x x

33 Determination of Charge Density Charge type and distribution GaN Interface AlGaN Free carriers & ionized donors -(2DEG, n s ) + (Depletion, N d ) Polarization (σ pol ) + Interface dipole (σ dip ) + - Net Observed σ 1 (-) = n s + σ dip + σ 2 (+) = σ pol σ 3 (-) = N d + σ dip - σ dip - 2DEG density at GaN/Al x Ga 1-x N x n s (cm -2 ) x x J. Cai, F. A. Ponce et al, Phys. Stat. Sol. A 188, 833 (2001).

34 Experimental Limitations A. Effect of surface depletion in TEM cross-section specimens. B. Radiation damage caused by high energy electron beams. 1.5 µm Damage SEM image CL image at λ=358 nm Point defects are created during exposure to 200 kev electron beam. This modifies the local electronic potential. J. Cai, F. A. Ponce et al, Phys. Stat. Sol. A 188, 833 (2001).

35 Conclusions: 2DEG Density at GaN/AlGaN Using electron holography, we have measured the energy offset ( E 2 ) at GaN/Al x Ga 1-x N. For x = 0.19, E 2 = 0.21 ± 0.1 ev; For x = 0.37, E 2 = 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 (n s ) is determined from the energy profiles. It increases with aluminum concentration. For x = 0.19, n s = 1.8 x cm -2 ; For x = 0.37, n s = 2.9 x cm -2. Surface depletion layers and radiation damage are two factors to affect electron holography measurements. J. Cai, F. A. Ponce et al, Phys. Stat. Sol. A 188, 833 (2001).

36 Topics Studied by Electron Holography Quantum wells and heterostructures GaN/InGaN/GaN single quantum well system GaN/AlGaN heterojunction Charge distribution across dislocations in GaN Dislocations in undoped GaN (n-type) Dislocations in GaN:Zn (semi-insulating) Dislocations in GaN:Mg (p-type)

37 Dislocations in Blue LED (Nichia) GaN/GaInN/GaN/Sapphire Using GaN buffer layers Dislocations/cm 2 Cross-section TEM image F. A. Ponce and D. P. Bour, Nature 386, 351 (1997).

38 Threading Dislocations in GaN Three types of DLs: 1 Edge type, b e = Ga N Screw type, b s = 0001 b m b s Mixed type, b m = F. A. Ponce et al, Appl. Phys. Lett 69, 770 (1996). b e Unit cell of wurtzite GaN Threading dislocations limit the electrical and optical performance of devices. Little is known about the electronic charge states at different type of threading DLs. J. Cai and F. A. Ponce, Phys. Stat. Sol. A 192, 407 (2002).

39 Charge states at dislocations For edge dislocations: n-gan: Negatively charged p-gan: Positively charged or neutral Experimental evidence 16, 17 N-rich For screw dislocations: Deep gap states are present at fullcore screw dislocation. 18 No deep gap states at nanopipes. 18 Experimental results show discrepancy. 19 Ga-rich Defect formation energy vs. Fermi-level 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, (2001). 18. J. Elsner et al. Phys. Rev. Lett. 79, 3672 (1997). 19. M. Albrecht et al. Phys. Stat. Sol. B 216, 409 (1999).

40 TEM and Holography of DLs in GaN (a) A C g (b) A B D g A: mixed type B: edge type C: screw type D: edge type 500 nm Distance (nm) Two-beam dark-field TEM images at (a) g 0002 and (b) g conditions 1120 (c) D A B C Distance (nm) Phase (rad) Distance (nm) (d) Distance (nm) Phase (c) and thickness (d) images in the region including DLs J. Cai and F. A. Ponce, Phys. Stat. Sol. A 192, 407 (2002) Thickness (nm)

41 Potential (V) (a) A Potential and Charge Density Measured potential Gaussian fit B C D Distance (nm) Potential profile across dislocations Potential (V) (b) C Distance (nm) 5 0 Charge density (x10 16 cm -3 ) Potential and charge distribution across C Decreased potential at DLs Potential profiles are fit by Gaussian curves, and differentiated twice to get charge densities. DL cores are negatively charged, ~ cm -3. Positive space charge surrounds the cores. J. Cai and F. A. Ponce, Phys. Stat. Sol. A 192, 407 (2002).

42 [0001] Charge Density at Dislocations R r Line charge density n = 2π c r r x 2 ρ( x )dx n: The number of charges per period along the [0001] direction c: Unit length along [0001], Å. r: Radius of a dislocation core. E c E f - ρ(x): Charge density determined from potential profile. E v 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. 20. W. T. Read, Philos. Mag. 45, 775 (1954). J. Cai and F. A. Ponce, Phys. Stat. Sol. A 192, 407 (2002).

43 Charge Density at Dislocations n (e/c) Edge Screw Mix Core radii (nm) Edge Screw Mixed Tilted angle (degree) Tilted angle (degree) Line charge density vs. tilted angle Core radii vs. tilted angle Edge Screw Mixed Error n (e/c) ± 0.2 r (nm) ± 10 J. Cai and F. A. Ponce, Phys. Stat. Sol. A 192, 407 (2002).

44 Charge States of DLs in Zn-doped GaN A B C Potential and charge profiles cross A 100 nm Phase images Amplitude images D [Zn] = 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.

45 Cathodoluminescence Analyses (a) (b) CL Intensity (a.u.) R CL 2 µm CL image at 359 nm Position (µm) CL intensity profile across the dark spot The dark spot diameter measured from CL image is in a range of µm S. Srinivasan, J. Cai, et al, Phys. Stat. Sol., in press.

46 Electrostatic Potential Profile H G K between DLs L TEM image of DL H, K and L Potential (V) nm H K Distance (nm) Potential profile cross DL H, K and L At positions between dislocations, the electrostatic potential fluctuates in a range of V, with a period of nm. Surface states caused by ion beam etch are responsible for such potential variation. L

47 A: Edge type (a) Charge States of DLs in Mgdoped GaN (a). Phase 50 A 100 nm Distance (nm) Distance (nm) Distance (nm) (b). Thickness A A (b) Plane view TEM images. A is in contrast in (a), but out of contrast in (b) Distance (nm) Phase and thickness contour images around A

48 Potential Profiles around a dislocation 0.8 Distance (nm) A Potential (V) Distance (nm) Potential contour image around A Distance (nm) 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.

49 Conclusions: Charge states at threading dislocations Electron 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 Zndoped 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.

50 General Conclusions Using 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.

51 Toward the Future Physical meaning of potential level measured by electron holography. The relationship between the potential offset at heterostructures and E c or E v. Vacuum Electron affinity Work function Mean inner potential E c E v V 0 E f Core levels Nucleus N More analyses of charge distribution across InGaN quantum wells. Continuous study of charge states at dislocations in Mg-doped GaN. New problems