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10p PhD Course 18 Lectures Nov-Dec 2011 and Jan – Feb 2012 Literature Semiconductor Physics – K. Seeger The Physics of Semiconductors – Grundmann Basic Semiconductors Physics - Hamaguchi Electronic and Optoelectronic Properties of Semiconductors - Singh Quantum Well Wires and Dots – Hartmann Wave Mechanics Applied to Semiconductor Heterostructures - Bastard Fundamentals of Semiconductor Physics and Devices – Enderlein & Horing Examination Homework Problems (6p) Written Exam (4p) Additionally Your own research area. Background courses (Solid State Physics, SC Physics, Sc Devices)
Semiconductor Physics
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1. Introduction 2. Crystal and Energy Band structure 3. Semiconductor Statistics 4. Defects and Impurities 5. Optical Properties I : Absorption and Reflection 6. Optical Properties II : Recombinations 7. Carrier Diffusion 8. Scattering Processes 9. Charge Transport 10. Surface Properties 11. Low Dimensional Structures 12. Heterostructures 13. Quantum Wells/Dots 14. Organic Semiconductors 15. Graphene 16. Reserve and Summary
Course Layout
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Based on : The Physics of Semiconductors, Grundmann, Chapter 9. Semiconductor Optics, C.F. Klingshirn, Ch. 9-14 Lecture Anne Henry, IFM Lecture Ivan Ivanov, IFM Lecture Micheal Reshchikov, Virgina Commonwelth University, Richmond, USA
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Lecture Layout Optical Techniques Photoluminscence Optical Recombinations Band-to-Band DAP Free Exciton Bound Exciton Temperature Dependence Internal Transitions Recombination Processes Time Resolved Photolumnscence
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Optical techniques
LUMINESCENCE: spontaneous emission of light in solids • Fluorescence: fast luminescence (electric-dipole allowed) • Phosphorescence: slow luminescence (electric-dipole forbidden) • Photo-luminescence (optical excitation) • Cathodo-luminescence (cathode ray (e-beam) excitation) • Electro-luminescence (electrical excitation) • Thermo-luminescence (heating) • Chemo-luminescence (chemical reaction)
FTIR
• Fourier Transform Infrared Reflectivity RAMAN
• Phonon Scattering
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PL : Photoluminscence
Laser Excitation above bandgap, creates electrons and holes. Cryostat Normally Liquid He, < 2 K Detector PMT Photomultipliertube, scanning of monochromator CCD
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FTIR – Fourier Transform Infrared Spectroscopy
Michelson Interferometer Interference from fixed and moving mirror
is converted by Fourir Transform to intensity spectrum
Advantages: Improved Signal/Noise Improved resolution Disadvantages Requires internal light source to monitor
mirror movement. Cannot use sensitive detectors in visible
range. Mainly used for absorption and luminscence
in the infrared. λ < 1 µm.
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Recombination
BB FE BE DAP IBE FB
Excited electrons
Created holes
Excitation ħν
D
A
R
D
A A
IT
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Recombination
Energy and Momentum must be conserved
Direct In-direct
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Band-to-Band
Spontaneous recombination rate dependent on electron and hole occupancy in each band
PL Intensity
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GaN From M. Reshchikov Virgina Commonwelyh Univ, Richmond USA
Free-to-Bound
Free-to-Bound (FB) recombinations dominates at higher temperatures, when Donors and Acceptors are ionized.
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Free-to-Bound : Spectral Broadening
At higher temperatures carriers are distributed in energy in the conduction band.
Involvment of phonons in the recombination..
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DAP : Donor-Acceptor-Pairs
R a∼DA
D
A
Remote pairs
Close pairs
VALENCE BAND
CONDUCTION BAND
R
D
A
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DAP : Donor-Acceptor-Pairs
Under certain conditions sharp lines related to specific Donor-Acceptor pair distance.
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DAP : Donor-Acceptor-Pairs
From Ivan Ivanov, IFM
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DAP : Donor-Acceptor-Pairs
Possible DAP arrangments:
• Dh-Ah (hh set)
• Dh-Ak (hk set)
• Dk-Ah (kh set)
• Dk-Ak (kk set)
} equivalent structure
In SiC two different donor and Acceptor positions Hexagonal (h) Cubic (k)
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DAP : Donor-Acceptor-Pairs
For deep donors and acceptors – involvment of phonons. For direct bandgap semiconductors mainly LO-phonons. Broadening dependent of number of involved phonons, N. S : Huang-Rhys factor (average number of involved phonons)
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DAP : Donor-Acceptor-Pairs
Huang Rhys Factor: Dependent on the displacement, q, in the configuration coordinate (CC) scheme. S << 1 Weak coupling No-phonon line dominates. S > 1 Strong coupling Broadening and shift toeards lower energies.
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FE : Free Excitons
Electron – hole pair. Free to move in the lattice. Requires high purity material, and low temperatures. Binding energies ~5 – 50 meV
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BE : Bound Excitons :
The mechanism of binding exciton
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Bound Excitons : Haynes Rules
The empirical Haynes’ rule: The binding energy of an exciton to a shallow donor (acceptor) is proportional to some degree of the ground-state energy of this donor (acceptor).
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Free Excitons : Direct Bandgap
FE present in high quality materials. No-phonon line dominates. Weak coupling to optical phonons, LO
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Excitons : Fine Structure
In p-type layer relative intensity between Donor and Acceptor BE changes
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Excitons : Fine Structure In HVP GaN Two different Donors. Splitting of valence band gives three different free excitons. XA, XB and XC Excited free exciton states XA
n=2
Two-electron transitions ( )2e Electron-hole recombination leaves remaining electron in excited state
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Excitons : Fine Structure
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2250230023502400
PL In
tens
ity (a
.u)
NP
TA
LA LO
TO
305031003150320032503300
Photon Energy (meV)
2.3 1014 cm-3
1.8 1015 cm-3
6.5 1017 cm-3
P0
Q0 P76
I76
NP
TA
LA
LOTO
3C 4H 6H
SiC:N 1 NP 2 NP 3 NP + phonon replicas + phonon replicas + phonon replicas
2850290029503000
P0
R I76
NP
TA
LA LO
TO
S0
1.5 1015 cm-3
3C 4H 6H
SiC:N 1 NP 2 NP 3 NP + phonon replicas + phonon replicas + phonon replicas
Bound Excitons : Indirect Bandgap
BE: ħω = Eg – EFE – EBE - Ephonon
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BE : Local phonon spectrum
DI and DII is a common but not identified defect in SiC:4H DI one defct in as-grown material. Local phonon replicas related to the defect distortion dependent of defect symmetri. DII several (?) defects in irradiated material with excited states and local phon replicas.
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305031003150320032503300
Photon Energy (meV)
2.3 1014 cm-3
1.8 1015 cm-3
6.5 1017 cm-3
P0
Q0 P76
I76
NP
TA
LA
LOTO
Bound Excitons : Relative Intensities
Relative intensities between free exciton and bound exciton changes with donor doping. Lower doping gives increased FE recombination Can be used to determine doping level.
SiC:4H T = 2K
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Multiple Bound Excitons
PNP
BNP AsNP
BTO
PTO
BTA
FETO
FELO
NP TA TO LO LA
P2 P3
B2
B3
BMEC
Si
Multiple Bound Exciton Complexes: Multiple electron-hole pairs bound at neutral donor, seen in Si, GaP, CdSe and SiC
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3880 3884 3888
PL in
tensit
y (a
rb. u
nits) a) 4H-SiC: n = 8.1 1015 cm-3
fitspectrumcomposing lines
I76.4
P68
Q51
++
Wavelength (Å)3880 3884 3888
Wavelength (Å)
b) 4H-SiC: n = 2.3 1014 cm-3
fitspectrumcomposing lines
I76.4
P68Q
51
+ +
0.1
1
10
100
1E+14 1E+15 1E+16 1E+17
Net carrier concentration (cm-3)
R =
BE
/FE
4H-SiCn = 5.2x1014 R (cm-3)
1014 1015 1016 1017
Q0
I76.4
(CV measurement)
Bound Excitons : Doping Dependence
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Bound Excitons : Doping Dependence
At higher doping the BE line broadens and shift to lower energies due to bandgap narrowing. PL position used to determine doping.
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PL : Temperature Dependence
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PL : Temperature Dependence
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PL : Temperature Dependence Spectra dominated by BE at low temperatures. These ionize and the FE intensity increases. Increased spectral broadening with temperature. Red-shift due to reduced bandgap with temperature. At room-temperature difficult to distinguish between FE and FB and BB recombinations.
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Internal Transitions
Transitions between different electronic states of impurities. Mostlt related to deep defects. Excitations seen in absorbtion. Relaxations seen in photoluminscence. Transitions at relatively low energies, as compared to bandgap.
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spin degeneracy of the state (2S+1=2)
notation of atomic d-state, n=3, l=2, 2l+1 = 5-fold degeneracy.
Internal Transitions : V in SiC V, Vanadium substitutional on Si-site [Ar] 3d3 4s2 (5 valence electrons) 4 for bonds, 1 remaining 3d1 strongly bound to the impurity. 5-fold degnerate (10 including spin) energy levels
In tetrahedral symmetry the state splits in a doubly and triply degenerate states (disregarding spin).
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When the symmetry is reduced to trigonal, further splitting occurs.
Internal Transitions : V in SiC
Finally, when the spin-orbit interaction is included.
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Source: Kaufmann & Dörnen, Phys. Rev. B 55, 13009 (1997)
Internal Transitions : V in SiC
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Recombination Mechanisms Excited States decays to equilibrium by different mechanisms
• Radiative • Non-radiative • Auger Recombination • Surface recombination • Tunneling processes • Thermal Ionisation • Diffusion
The total decay rate is a sum of all recombination mechanisms, w
w = wr + wnr + ws + wt + wTh + wD + ……
BB FB DAP FE BE
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TRPL - Time Resolved PL
Excitons in direct bandgap materials Radiative recombinations Exponential decay timescale ~< nsec Excitons in indirect bandgap materials Non-radiative Auger recombinations Exponential decay timescale ~nsec DAP Radiative recombination Non-exponential decay timescale ~µsec IBE Radiative recombination Exponential decay timescale ~ µsec-msec
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TRPL – Temperature Dependence
At higher temperatures when exciton or donor/acceptor ionize, the decaytime decreases. Additional recombination path for the recombination. Can be used to determine activation energies. Example: DAP band in GaN gives donor energy. Isoelectronic bound exciton gives activation energies and recombination times for excited states.
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Carrier Kinetics
Carrier relaxation in CB and VB timescale ~1ps Faster for LO emission and slower for LA and TA. Capture to Donors and Acceptors timescale ~100ps
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PL : Full Spectral Range
GaN
Free Excitons Bound Excitons DA-pairs FB
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Extended defects: Stacking faults, optical properties
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Stacking faults, optical properties
periodic crystal potential
perturbation from the stacking fault
always capable of binding one carrier => binding exciton is always possible! (Free, but confined in 2D).
Extended defects: an example
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Stacking faults, optical properties Optical signature: Free-exciton-like emission (but at odd energy position)
Source: J. Hassan et al., J. Appl. Phys. 105, 123513 2009
Extended defects: an example