ECE236A Semiconductor Heterostructure Materials Basic Properties of Semiconductor Heterostructures Lectures 2 & 3 Oct. 5, 2017

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1 ECE236A Semiconductor Heterostructure Materials Basic Properties of Semiconductor Heterostructures Lectures 2 & 3 Oct. 5, 217 Basic definitions. Types of band-alignment. Determination of band-offsets: Electron affinity/anderson s rule. Common anion & common cation rules. Commutativity/transitivity rules. Interface dipoles. Midgap level alignment. Determination of energy band offsets: X-ray or UV Photo-electron Spectroscopy (XPS or UPS). Internal Photoemission. Capacitance-Voltage (C-V) Profiling. 1

2 Basic Definitions A semiconductor Heterojunction is a structure consisting of two different semiconductor materials in contact with each other that are bonded at the atomic scale. Semiconductor B Semiconductor A is conduction band offset or discontinuity of at the heterojunction interface. Heterojunction is valence band offset or discontinuity of at the heterojunction interface. The signs and magnitudes of, and E g determine to a large extent the suitability of different heterojunction material combination of specific device applications. à Spatial confinement of carriers, control over carrier injection, and almost arbitrary field and 2 potential profiles can be realized.

3 Type I: The bandgap of one material overlaps entirely that of the other. Types of Band Alignments (1) Example 1: AlGaAs/GaAs HEMT: e - s favorable holes favorable Example 2: InGaAs/InP HBT: wiki Example 3: GaN/AlGaN HEMT: Semicond. Sci. Technol. 19, , 24. Electrochem. Solid-State Lett. 5, G45- G47, 22. 3

4 Type II-staggered: Types of Band Alignments (2) Both and of one material are lower than the corresponding band-edges of the other material. Electrons are confined in one material while holes are confined in the other material. e - s favorable The 6.1 Å family (InAs, GaSb, AlSb) Example: InAs/AlSb holes favorable Γ H. Kroemer, Physica E 2, , 24 4 ß S S Krishtopenko, J. Phys.: Condens. Matter 23, 38561, 211.

5 Basic Devices that changed the World Herbert Kroemer Nobel prize in Physics 2 for basic work on information and communication technology together with: ECE13 stuff Jack S. Kilby Zhores Alferov ECE135B stuff 1959, first hybrid IC.: one BJT, 3 resistors & 1 capacitor. Texas Instruments. Proc. IRE 45, 1535, , first monolithic IC. Robert Noyce, Fairchild Semiconductor. (Cofounder of Intel). 1971, First microprocessor (Ted. Hoff et al.) 23 MOSFETs in 3 mm5x 4 mm.

6 Type II-misaligned or broken gap: Types of Band Alignments (3) Electrons are confined in one material while holes are confined in the other material. Both and in one material are lower than of the other material. The 6.1 Å family (InAs, GaSb, AlSb) e - s favorable holes favorable Example: GaSb/InAs based heterostructures. H. Kroemer, Physica E 2, , 24 M P Mikhailova, Semicond. Sci. Technol. 19, R19-R128, 24. 6

7 Type III: Formed through the combination of a semi-metal with inverted bands and a semiconductor. Types of Band Alignments (4) HgTe semi-metal band structure Δ holes e favorablee - s favorable v Example: CdTe/HgTe based heterostructures. N. F. Johnson et al., Phys. Rev. Lett. 61, 1993,

8 Determination of Bandgap Offset Values: Theory & Rules The simplest empirical rule for determining band offsets is the electron affinity rule commonly known as Anderson rule. Semiconductor A qχ A E A a Semiconductor B qχ B E a B ac χ = electron affinity. Δ = q(χ A - χ B ) Δ = ΔE g - Δ In actual semiconductor heterojunctions, band offsets are not actually predicted by the electron affinity rule. Ideal heterostructrue: qχ qχ B A E a A E a B ac What causes deviation from the electron affinity rule? à Interface dipoles and metal-induced-gap-states (MIGS). 8

9 Δ : Δ Other rules 6:4 rule Determined from measurements of Schottky contacts (Au)..51 ev.17 ev 9

10 Another Transitivity Test InP Ga.47 In.53 As Al.48 In.52 As InP åde V = = -.4 ±. 9 ev 1

11 More on the GaAs/AlGaAs System x is the Al mole fraction. For x <.45: ΔE V =.55x Al ΔE C = ΔE g ΔE V =.75x Al > ΔE C :ΔE V =6:4 Let x=.3 (Al.3 Ga.7 As) Δ =.55 x Al =.55.3 =.165eV Δ =.75 x Al =.75.3 =.225eV ΔE G =.39eV Δ : Δ =.58 :.42 11

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13 Interface Dipoles The presence of interface dipoles can alter the band-offsets at semiconductor heterojunctions. No interface dipole Interface dipole +σ -σ U The interface dipole can shift the magnitude of bandoffset from V.B. to C.B. or vice-versa. Suppose: σ=5x1 13 q/cm -2 a=5å=5x1-8 cm ε=1ε =8.85x1-13 F/cm + - a ΔU = q σ ε a =.45eV The contribution of the interface dipoles to the energy shift at the heterointerface can be 13 quite significant.

14 Alignment of midgap Energy Levels The presence of an interface can induce the formation of energy levels in the bandgap at or near the interface which can be sufficient in density to pin the Fermi level. At a heterointerface, the energies at which E F is pinned for each semiconductor should align to determine the band-offsets. This was originally developed for Schottky Barriers and sort-of works for semiconductor heterostructures but not with good quantitative accuracy. According to Tersoff, at a M-S interface, there is a continuum of states around E F because of the metal: Those states decay exponentially inside the semiconductor but still have significant amplitude a few layers from the interface. Any deviation from charge neutrality in this region results in metallic screening by the metal induced gap states or MIGS. Tersoff goes on It is therefore convenient to consider the barrier height as having two contributions a short-range part, which may be related to surface dipoles, the M-S electronegativity difference, or more subtle details of bonding, and an additional dipole from metallic screening by MIGS, which tends to pin E F so as to maintain local charge neutrality. Short range (unpinned) or screening effects (pinned) depend solely on the bulk of the semiconductor. Tersoff et al., Phys. Rev. Lett. 52,465, Tersoff goes on I therefore propose that E F must fall at or near the energy where the gap states cross over from valence-to conduction-band character. Large bandgap ionic semiconductors à short range screening à unpinned interface. Covalent semiconductors with MIGS decay length large à pinned interface. 14

15 Application to Schottky Barriers 15

16 Alignment of midgap Energy Levels at Heterinterfaces Pre-cautions: At M-S junction, defects levels may not play a role due to screening from the MIGS levels. At a semiconductor heterointerface, defect and interface state levels can be important. qφ Acceptor like Donor like qφ Acceptor like Donor like aligned qφ Despite empirical approximations, band-offsets must be determined experimentally! 16

17 Determination of Band Offsets by Experimental Methods X-ray or UV Photo-electron Spectroscopy (XPS or UPS). Internal Photoemission. Capacitance-Voltage (C-V) Profiling. 17

18 X-ray Photoelectron Spectroscopy (XPS) Is accurate for thin heterojunctions (< 2 Å). hν z 2Å A B z In XPS, the energy of an electronic state E i can be determined by measuring the kinetic energy E kin of an electron excited from E i into free space by an incident x-ray of photon energy E hν : ( ) E kin = E hυ ac E i E binding,i = ac = E hυ E kin 18

19 Valence Band States All semiconductors have tetrahedral bonds that have sp 3 hybridization. Individual atoms have outermost valence electrons in s- and p-type orbitals. ( 14 Si: 1s 2 2s 2 2p 6 3s 2 3p 2 ) s-orbital p-orbital d-orbital 19

20 X-ray Photoelectron Spectroscopy (XPS) XPS spectra of Ge XPS spectra of GaAs core-level Valence band edge As core-level Ga core-level Valence band edge Kraut et al. Phys. Rev. B 1965, XPS enables measurement of: ore for an individual semiconductor A ore B ore in a heterojunction (next page) 2

21 XPS on a Ge-GaAs Heterojunction Ge 3d Ga 3d A ore B ore ( ) + ( E B A E ) ( EvA A core core E ) core Δ = E B v E A v = E B B v ore This approach allows measurement of Δ with an accuracy of, typically, ±.5-.1 ev. Grant et al. J. Vac. Sci. Tech. B 15, 1451,

22 Internal Photoemission Measures electrical current excited over a heterojunction barrier by incident photons as a function of photon energy. Heiblum et al. Appl. Phys. Lett. 47, 53, Graded composition & doping to 5x1 16 cm -3 δ 4x1 18 cm -3 Φ T =Φ 1 +Δ qδv ξ ξ Image force lowering, negligible here. In a metal-semiconductor junction: ξ m =ξ ( x =) = 2qN D V bi =φ T δ ε AlGaAs " $ V bi kt # q % ' & 22

23 Internal Photoemission in GaAs/AlGaAs Heterojunction: The potential drop across the GaAs layer: ΔV = ε AlGaAs ε GaAs ξ m d 2 The photocurrent: Y 1/2 = I P 1/2 hυ φ T = hυ ( φ 1 +Δ qδv ) " = hυ $ φ 1 +Δ q ε 2qN AlGaAs d D $ ε 2 # GaAs ε GaAs " $ φ T δ kt # q %% '' &' & DE C =.62 DE g Heiblum et al. Appl. Phys. Lett. 47, 53,

24 Capacitance-Voltage (C-V) Profiling (1) In C-V profiling, the apparent carrier concentration profile C = dq dv C = qan D ( W ) dw dv W Q = qan D x ( ) dx N d (x)=donor concentration profile (assuming fully ionized). n(x)=electron concentration profile. n x ( ) is the apparent carrier concentration profile in a CV measurement (large Debye length on the lower doped side of the heterojunction. By measuring CV to extract n(x), we can apply: ( x ) E F = kt ln" # n x n x ( ) is the depletion layer capacitance ( ) / N ( c x ) to calculate the conduction band-edge profile. $ % is given by the following: Koremer et al. Appl. Phys. Lett. 36, 295,

25 Also, we know that dc dv = ε s A W 2 N D ( W ) = Capacitance-Voltage (C-V) Profiling (2) C = ε A s dc W dv = ε A s dw W 2 dv C 1 = C 3 qan ( D W ) qε s A 2 N ( D W ) C 3 qε s A 2 dc dv By charge neutrality: Also, d 2 φ x dx 2 n ( W ) n x = n x ( ) ( ) dx ρ x N D x ( ) dx = ρ = 1 " qn ε s ε # D x s ( ) dx = and measured apparent carrier concentration; with interface charge density ( ) dx xn x = xn x ( ) dx ( ) qn ( x ) +σ i δ( x x ) i $ % ( ) dx + n x ( ) dx Let s integrate Poisson s equation across the heterojunction: ( ) dφ x dx = 1 $ q N ε ( D x ) dx q n ( x ) dx +σ i δ( x x & % i )dx ' s & dw dv = σ i q = C qan D ( W ) W = ε A s C 25

26 Recall: Then: udv = # $ u dv% & Capacitance-Voltage (C-V) Profiling (3) x!" ρ ( x)dx # $ =! " x ρ ( x' )dx'# $ { ρ ( x' )dx'}dx xρ ( x)dx = { ρ ( x' )dx'}dx ( ) dx' { v }du dφ x' dx = 1 { ρ ( x' )dx'} dx = xρ ( x) dx ε s φ ( x = ) φ ( x = ) + 1 q Δ = 1 ( q N D ( x) n( x) ε s & ' = 1 $ & q ε s %& N D x = 1 $ & q ε s %& N D x = q $ & ε s %& N D x ( ) x dx +σ i δ x x i ( ( ) n ( x )) xdx +σ i x i ( ( ) n ( x )) x x i ( ( ) n ( x )) x x i ' ) but: () σ i = q N D x ' ( )dx) () ' ( )dx) () ( ) x dx ) + * ( ( ) n ( x )) 26 dx

27 % Δ = q2 * N D x ε s & and: n ( x ) = N ( c x ) e qφ ( x )/kt Capacitance-Voltage (C-V) Profiling (4) ( ( ) n ( x) ) x x i ( )dx q%& φ ( x = ) ' ( φ x = ( ) ' + ( Δ = q2 N ε D x s ( ( ) n ( x )) kt ln n ( )/ N c n ( ) ( ) / N ( c ) ( x x i )dx Kroemer et al. Appl. Phys. Lett. 36, 295,