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

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

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

Lecture Layout Optical Techniques Photoluminscence Optical Recombinations Band-to-Band DAP Free Exciton Bound Exciton Temperature Dependence Internal Transitions Recombination Processes Time Resolved Photolumnscence

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

PL : Photoluminscence

Laser Excitation above bandgap, creates electrons and holes. Cryostat Normally Liquid He, < 2 K Detector PMT Photomultipliertube, scanning of monochromator CCD

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.

Recombination

BB FE BE DAP IBE FB

Excited electrons

Created holes

Excitation ħν

D

A

R

D

A A

IT

Recombination

Energy and Momentum must be conserved

Direct In-direct

Band-to-Band

Spontaneous recombination rate dependent on electron and hole occupancy in each band

PL Intensity

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.

Free-to-Bound : Spectral Broadening

At higher temperatures carriers are distributed in energy in the conduction band.

Involvment of phonons in the recombination..

DAP : Donor-Acceptor-Pairs

R a∼DA

D

A

Remote pairs

Close pairs

VALENCE BAND

CONDUCTION BAND

R

D

A

DAP : Donor-Acceptor-Pairs

Under certain conditions sharp lines related to specific Donor-Acceptor pair distance.

DAP : Donor-Acceptor-Pairs

From Ivan Ivanov, IFM

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)

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)

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.

FE : Free Excitons

Electron – hole pair. Free to move in the lattice. Requires high purity material, and low temperatures. Binding energies ~5 – 50 meV

BE : Bound Excitons :

The mechanism of binding exciton

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).

Free Excitons : Direct Bandgap

FE present in high quality materials. No-phonon line dominates. Weak coupling to optical phonons, LO

Excitons : Fine Structure

In p-type layer relative intensity between Donor and Acceptor BE changes

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

Excitons : Fine Structure

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

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.

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

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

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

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.

PL : Temperature Dependence

PL : Temperature Dependence

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.

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.

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).

When the symmetry is reduced to trigonal, further splitting occurs.

Internal Transitions : V in SiC

Finally, when the spin-orbit interaction is included.

Source: Kaufmann & Dörnen, Phys. Rev. B 55, 13009 (1997)

Internal Transitions : V in SiC

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

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

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.

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

PL : Full Spectral Range

GaN

Free Excitons Bound Excitons DA-pairs FB

Extended defects: Stacking faults, optical properties

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

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