Surfaces and Interfaces of III-V

Transcription

1 Surfaces and Interfaces of III-V Semiconductor Sys tems : from g row t h is s ues t o elect ronic propert ies Rita Magri CNR-Nano Istituto di Nanoscienze and Department of Physics, University of Modena and Reggio Emilia, Modena, ITALY TMCSIII: Jan 2012, Leeds

2 Acknowledgements Conor Hogan Rodolfo Del Sole CNR-Istituto di Struttura della Materia, Rome,European Theoretical Spectroscopy Facility (ETSF) and Department of Physics, University of Rome Tor Vergata, Rome, ITALY Alex Zunger NREL, USA FUNDING: Assegno della Fondazione CRM, PRIN-2005, PRIN-2007, CINECA Supercomputing Grants

3 Aim of research Understand the link between structural motifs and electronic properties (structure carrier states comparison with experiment) To optimize device design To interpret spectroscopic features when spectroscopy is used to characterize the materials

4 Outline 2D growth lattice-matched GaSb/InAs interface Empirical Pseudopotential Method Electronic properties of Abrupt vs Segregated Interfaces GaSb(001) surface Scalar and Relativistic Plane-Wave Pseudopotential Method The dilemma of the c(2x6) surface reconstruction

5 InAs/GaSb (lattice-matched system) Broken-Gap Lineup Semiconductor because of the e 1 and h 1 confinement Possibility of tuning the band gap between <0 400 mev Type II: short periods to increase the radiative ricombination efficiency

6 Structure Determination

7 Atomistic Semiempirical Pseudopotential Method Non self-consistent method V ext (r) is determined by a superposition of screened atomic potentials located at the atom equilibrium positions V V ( r) V ( r R ion, R, igr ig ion( r) e e V ( G G ) ) Spherical screened local potential We choose an appropriate functional form depending from a number of parameters

8 One possible choice v ( r) iq( r) e v ( q ) 1v q n v(q) continous function of q indicates atom type v 2 q a ( q) a0 2 a3 q a e Parameters fit to reproduce: v n ( ) a4 Tr( ) 1. Gaps E g and effective masses m * 2. Hydrostatic a g and biaxial b deformation potentials 3. Band offsets and spin-orbit splitting so 4. LDA-predicted single band edge deformation potentials a v, a c

9 Fit: results

10 Atom equilibrium positions from elastic energy minimization Valence force field method Elastic constants E, ) ( r i i is minimized with respect to the positions of all atoms (also subjected to constraints) starting from a chosen atomic configuration The minimum provides the elastic (strain) energy and the relaxed atomic positions

11 Atomistic Empirical Pseudopotential Electronic Structure Solve the Schrödinger equation: 2 v n 2m n each atom individually described not self-consistent no LDA errors r R ( r) ( r) strain minimizing atomic positions Folded spectrum method plane wave expansion of ψ(r) correct symmetry: band and valley couplings given correctly The spectrum at the left is the original spectrum of H. The spectrum at the right is the folded spectrum of (H-E_ref)^2

12 Results for the (InAs) 6 /(GaSb) m and (InAs) 8 /(GaSb) n superlattices m = 8 n = 8, 12, 16,, 40 e 1 GaSb Gap E g hh 1 InAs Gap with increasing n we expect a reduction of E g Expt. Kaspi et al., APL 76, 409 (2000)

13 Atomistic Empirical Pseudopotential Method including spin-orbit coupling Blue-shift of gap with increasing n Superlattices with abrupt interfaces

14 The reason for this behavior R. Magri and A. Zunger PHYSICAL REVIEW B 68, (2003) Electron states overlap for small values of n (thin GaSb layers) The interaction pushes down the level energy

15 So the trend is predicted but the gap values are not.. The calculated gaps are too small expecially for the thin GaSb barriers Why? n

16 The interfaces are never abrupt Sb within InAs As and In within GaInSb Normal (InAs-on-GaSb) IF rougher Interfacial broadening Steinshnider et al. PRL 85,4562 (2000)

17 The kinetic model of MBE growth Cations: Anions: b-->s E In/Ga (subsurf Ga surf In) s-->b E In/Ga (subsurf In surf Ga) b-->s E Sb/As (subsurf As surf Sb) s-->b E Sb/As (subsurf Sb surf As) Segregation Energies: s-->b b-->s In/Ga = E In/Ga - E In/Ga

18 The rate equations The rate of change of the concentration x A (t) of surface A atoms is: The rates of the exchange reactions depend on the growth temperature T g Under the conditions of the conservation of A atoms, of the total number of atoms and: ) ( ) ( ) ( ) ( ) ( ) ( / / t x t x P t x t x P t dt t dx b B s A b s B A s B b A s b B A A s A g B b s B A T k E b s B P A e / / 1 ) ( ) ( t x t x b B b A b-->s s-->b For cations: E In/Ga = 1.8 ev, E In/Ga = 2.0 ev (Dehaese et al. APL 66, 52 (95)) No values in the literature for the anions!

19 Segregated profiles r = 0.25 ML/s T g =380 C T g = 440 C b s E Sb/As = 1.68 ev s b E Sb/As = 1.75 ev Interface shift R. Magri and A. Zunger, Phys. Rev. B 64, R (2001) Anion energy barriers for subsurface surface exchange

20 Electronic consequences of interfacial segregation THEORY R. Magri and A. Zunger, Phys. Rev. B 64, R (2001) EXPT M. J. Yang, W. J. Moore, B. R. Bennett, and B. V. Shanabrook, Electron. Lett. 34, 270 (1998) (InAs) 5.5 /(In 0.28 Ga 0.72 Sb) 10 /(InAs) 5.5 /(AlSb) 14 Surprisingly, PL peak (energy gap) increases significantly with T growth above 450 C!

21 ONE REASON FOR GAP INCREASING Interface shift R. Magri and A. Zunger, Phys. Rev. B 64, R (2001) So, one reason for the increasing gap with T g is the narrowing of the InAs well the electron state goes up Interface shift

22 SECOND REASON: INTRODUCTION OF MORE Ga-As and In- Sb BONDS In a ternary system like GaAs x Sb (1-x) the number of nearest neighbor bonds is determined uniquely by x Given composition x and size of system (N total numebr of n.n. bonds): Nx Ga-As and N(1-x) Ga-Sb But InAs/GaSb is a true quaternary system Another feature of InAs/GaSb is the presence of different bonds at the interfaces even in superlattices with abrupt interfaces

23 Segregation introduces more bonding disorder at the interfaces Alloy In y Ga 1-y As x Sb 1-x N total number of n. n.bonds - + Ga As In Sb + - In As Ga Sb Only in a perfectly random alloy Nyx number of n InAs N(1-y)x number of n GaAs Ny(1-x) number of n InSb N(1-y)(1-x) number of n GaSb But if we change N i bonds of kind Ga-As and In-Sb in bonds of kind Ga-Sb and In-As the total composition (x,y) does not change Thus there are different bonding configurations corresponding to composition (x,y) To specify a given bonding configuration I need a further parameter ξ ξ = 0 random alloy ξ > 0 more Ga-Sb (In-As) bonds than Ga-As (In-Sb) ξ < 0 more Ga-As (In-Sb) bonds than Ga-Sb (In-As)

24 From the study of random In y Ga 1-y As x Sb 1-x alloys At the usual growth temperatures the alloy is not random: what bonding configurations have (InGa)/(AsSb)? Minimization of energy functional E tot ({ Si}) Echem ({ Si}) Estrain({ Si}) Monte Carlo simulation at finite Temperature Results for : at T = 600 C we find = > 0 enrichment of Ga-Sb and In-As bonds = 0 (random) E g = 0.70 = (real T = 600 C) E g = 0.67 SRO reduces gap of 30 mev

25 What we learn from the study on the quaternary alloys The introduction of disorder at the interfaces due to segregation (introducing more Ga-As and In-Sb bonds) tends to increase the band gap R. Magri, A. Zunger, and H. Kroemer J. OF APPL: PHYS. 98, (2005)

26 Final Comparison with Expt. Growth Temperature Tg = 380 C Deposition Rate 0.5 ML/s R. Magri and A. Zunger PHYS. REV. B 68, (2003)

27 Outline 2D growth lattice-matched GaSb/InAs interface Empirical Pseudopotential Method Electronic properties of Abrupt vs Segregated Interfaces GaSb(001) surface Scalar and Relativistic Plane-Wave Pseudopotential Method The dilemma of the c(2x6) surface reconstruction

28 Sb-stabilized GaSb(001) surface (1) GaSb(001) is the only one among the III-V(001) surfaces that in the V-rich regime does not form the c(4x4) reconstruction but a seemingly metallic long dimer chain reconstruction.. Why? RHEED c(2x10) c(2x6) (2) The structure of the c(2x6) reconstruction is unknown 1x3

29 Known reconstructions of Sb-rich GaSb(001) Moderately Sb-rich reconstructions The c(2x6) phase? Proposed models Long single-chains The (1x3) phase Observed by STM One lattice unit shifting of the (4x3) cells along the x4 axis

30 High Sb-rich coverage regime of GaSb(001)

31 The surface reconstructions Shown by all III-V (001) surfaces BUT GaSb (001) Satisfies the electron counting rule Shown only by GaSb (001) Violates the electron counting rule

32 Surface Energy Calculations Total energy calculations using the Quantum-Espresso Package DFT-LDA Plane-wave Pseudopotential Approach 15 Ry. cutoff Norm-Conserving Scalar and Relativistic Pseudopotentials Structure minimized with respect to the electronic degrees of freedom and the ionic degrees of freedom (using forces calculated using the Hellmann-Feynman theorem)

33 RAS Calculations Reflectance anisotropy spectroscopy (RAS) RAS R R R Surface Model: Supercells (11 layer slab, 10A vacuum) Back surface passivated with pseudo-h Optical properties: Independent particle level (DFT-RPA) Scissors shift +0.4eV Spin-orbit coupling included Many body effects tested but neglected

34 Fact: long Sb dimer chains are unstable Ab-initio calculation of the surface energy g The c(4x4) reconstruction is relatively stable, satisfies the Electron Counting Rule (ECR) and is semiconducting (like the more stable (4x3) reconstructions) Long chain c(2x10) and c(2x6) structures are unstable, do not satisfy the ECR and are metallic Surface phase diagram M. C. Righi, R. Magri,and C. M. Bertoni, PHYS. REV. B 71, (2005)

35 Fact: The Reflectance Anisotropy Spectra of c(2x6) RAS were taken on GaSb(001) surfaces with a clear c(2x6) LEED EXPT No known reconstruction model agrees with experiment!!! THEORY C. Hogan, R. Magri and R. Del Sole, Phys.Rev B 83, (2011)

36 Spin-orbit effects on RAS Spin-orbit coupling can influence optics: lifting of degeneracies of energy levels hybridization of states of different spin spin-flip processes We found no improvement

37 GaSb(001): a new structural motif? To satisfy the ECR the Sb chains have to be interrupted by missing dimers [like in c(4x4) or displaced dimers [like in (4x3)] However, also the substitution of a group V atom with a group III atom in the layer below the dimer chains can lower the surface metallicity. Excess electron = 0 if ECR is satisfied Ga substituting Sb dimer motifs

38 Ga surface antisite defects TOO FEW Metallic E F in conduction TOO MANY Metallic E F in valence RIGHT NUMBER Semiconducting

39 Thus the ECR can be satisfied in different ways by changing the different structural motifs First question: if we insert Ga substitutional defects in the right number to satisfy the ECR in the long chain reconstructions, what happens to the surface energy? We obtain stable structures? C. Hogan, R. Magri, and R. Del Sole PRL 104, (2010) The surface energy lowers considerably but these structures are still less stable than (4x3)

40 Then, why long chain reconstructions are observed instead of c(4x4) or (4x3)? Metastable phases are stabilized by the particular environmental conditions. Hypothesis: V-rich conditions stabilize Ga defects in GaSb(001) and not in other III-V(001) All the surfaces experimentally studied with RAS were prepared under very rich Sb conditions

41 Surface energy versus excess electrons We insert Ga antisite defects in these structures DFE (, ) E E H 2 Sb phasega phase bulk Sb bulk Ga f Sb

42 Results C. Hogan, R. Magri, and R. Del Sole PRL 104, (2010) Only in the case of GaSb(001) the Ga defect becomes stable when the electron excess is higher of = 0.14 the defect occurs spontaneously

43 Two strategies: missing dimers or Ga defects, what GaSb(001) prefers? both ways satisfy the ECR In GaSb(001) Ga defects are always favored over dimer removal C. Hogan, R. Magri, and R. Del Sole PRL 104, (2010)

44 Why GaSb(001) is so unique? First, we note GaSb(001) and metallic Sb are well matched. Dimer formation does not strain too much the surface Thus, it is possible to have electronic excess charge fluctuations at the surface. Sb-dimer enrichment does not increase the surface strain

45 Also Ga- Sb Bond softness Strain energy Surface structure at minimun energy without Ga Surface structure at minimum energy with Ga BUT without Ga Bonding energy Sb Ga Another possible case: Bi stabilized InSb(001) surface Also in that case a c(2x6) reconstruction is observed C. Hogan, R. Magri and R. Del Sole, Phys.Rev B 83, (2011)

46 Coming back to c(2x6) The presence of the defects decreases the positive peak between 2-3 ev and leads to a good agreement with the experimental RAS for the long chain reconstructions

47 Thank you for your attention

48 Folded spectrum method [ħ 2 /2m 2 + V ps (r) + V nl ref ] 2 i (r, ) = ( i - ref ) 2 i (r, ) ref The spectrum at the left is the original spectrum of H. The spectrum at the right is the folded spectrum of (H- E_ref)^2