1. Theory

Definition: A photoluminescence spectrometer excites a semiconductor with light above its band gap and measures the spectrum of light emitted as electrons and holes recombine (HORIBA OSD-104).
Information: Peak energies give the band gap, excitons, impurities and defects; peak width and symmetry indicate composition and crystal quality (HORIBA OSD-104; HORIBA low-temperature note).
Temperature: The gap shrinks and lines broaden with temperature, described by the Varshni relation (Nepal et al.; Herr et al.).
Alloys: For alloys such as AlGaN, the gap and its temperature dependence vary with composition through bowing parameters (Nepal et al.).

2. Working Principle

Excitation: A laser with photon energy above the gap, often chopped for lock-in detection (HORIBA OSD-104).
Collection and dispersion: Emitted light is collected, dispersed in a monochromator and detected by a CCD, photomultiplier or InGaAs detector (HORIBA notes).
Cryostats: Liquid-nitrogen, liquid-helium or closed-cycle cryostats from about 4 $K$ , with heating stages to 800 $K$ or more (HORIBA low-temperature note; Nepal et al.).
Mapping: x-y stages give maps of peak energy and intensity across wafers (HORIBA OSD-104).

3. Applications

Band gap and composition: Alloy fraction in AlGaN, InGaN, InGaAs and SiGe (Nepal et al.; background knowledge).
Impurities and defects: Dopant identification in Si and III-V materials at low temperature (HORIBA notes).
Wafer quality: Maps of uniformity and defects in epitaxial wafers (HORIBA OSD-104).
Optoelectronic devices: Emission wavelength of LED and laser structures before processing (background knowledge).

Emission Physics

Name	Formula	Related Formulae	Variables/Constants
Photon energy and wavelength	$E = h ν = \frac{h c}{λ}, E [eV] = \frac{1239.84}{λ [ nm ]}$	$Δ E = \frac{1239.84 Δ λ}{λ ^{2}}$	$E : p h o t o n e n er g y$ $h : P l an c k co n s t an t$ $ν : f r e q u e n cy$ $c : s p ee d o f l i g h t$ $λ : w a v e l e n g t h$ $Δ E, Δ λ : l in e w i d t h in e n er g y an d w a v e l e n g t h; co n v er s i o n (ba c k g r o u n d k n o w l e d g e); H O R I B A O S D - 104 : e mi tt e d p h o t o n l o w er in e n er g y t han t h e e x c i t a t i o n an d cor r es p o n d in g t o t h e ban d se p a r a t i o n, 500 t o 2000 nm o p er a t i o n; H O R I B A l o w - t e m p er a t u r e n o t e : r oo m - t e m p er a t u r e P L u p t o 100 nm w i d e$ $(co m p u t e d : 3.4175 eV i s 362.8 nm, 1.12 eV i s 1107 nm; a 100 nm w i d t h a t 1300 nm i s 73 meV)$
Band-to-band line shape	$I (E) \propto E^{2} E - E_{g} exp (- \frac{E - E _{g}}{k _{B} T})$	$E_{p e ak} \approx E_{g} + \frac{k _{B} T}{2}, F W H M \approx 1.8 k_{B} T$	$I (E) : e mi ss i o n in t e n s i t y$ $E_{g} : ban d g a p$ $k_{B} : B o l t z mann co n s t an t$ $T : t e m p er a t u r e$ $F W H M : f u l l w i d t h a t ha l f ma x im u m; f r ee - c a r r i er r eco mbina t i o n f or m (ba c k g r o u n d k n o w l e d g e, P ank o v e); H O R I B A : ban d g a p f r o m P L, p e ak p os i t i o n, sy mm e t r y an d F W H M in d i c a t in g s t r u c t u r e an d co m p os i t i o n$ $(co m p u t e d : k_{B} T /2 = 12.9 meV a t 300 K an d F W H M ab o u t 47 meV)$
Excitons and donor-acceptor pairs	$E_{F X} = E_{g} - E_{x}, E_{B X} = E_{F X} - E_{l oc}$	$E_{D A P} = E_{g} - (E_{A} + E_{D}) + \frac{q ^{2}}{4 π ε r}$	$E_{F X} : f r ee - e x c i t o n l in e$ $E_{x} : e x c i t o n bin d in g e n er g y$ $E_{B X} : b o u n d or l oc a l i z e d e x c i t o n$ $E_{l oc} : l oc a l i z a t i o n e n er g y$ $E_{A}, E_{D} : a cce pt or an d d o n or i o ni z a t i o n e n er g i es$ $ε : p er mi tt i v i t y$ $r : p ai r se p a r a t i o n; f or m s (ba c k g r o u n d k n o w l e d g e, P ank o v e); H er r e t a l . : f r ee - e x c i t o n r eco mbina t i o n d o minan t ab o v e 200 K in G a N; N e p a l e t a l . : l oc a l i z e d - e x c i t o n l in es d o minan t a t l o w t e m p er a t u r e in A l G a N$ $(a ss u m e d : E_{x} = 25 meV f or G a N; co m p u t e d : t h e f r ee e x c i t o n l i es 25 meV b e l o w t h e g a p)$

Temperature and Composition

Name	Formula	Related Formulae	Variables/Constants
Varshni temperature dependence	$E_{g} (T) = E_{g 0} - \frac{α T ^{2}}{T + β}$	$GaN: E_{g 0} = 3.495 eV, α = 0.94 meV/K, β = 791 K or α = 0.73 meV/K, β = 594 K$	$E_{g 0} : g a p a t 0 K$ $α, β : e m p i r i c a l co n s t an t s (β r e l a t e d t o t h e D e b y e t e m p er a t u r e); N e p a l e t a l . : G a N 3.495 eV, 0.94 meV/K, 791 K, A l N 6.064 eV, 2.63 meV/K, 2082 K, f i t ab o v e 200 K w h er e l oc a l i z a t i o n i s n e g l i g ib l e, 10 t o 800 K; H er r e t a l . : (7.3 pl u s or min u s 0.3) e - 4 e V / K an d 594 pl u s or min u s 54 K f r o m 2 t o 1200 K (see t h e Q / A); H O R I B A : p e ak s b r o a d e n an d s hi f t t o l o w er e n er g y a s t e m p er a t u r e r i ses$ $(co m p u t e d : t h e 300 K s hi f t i s 77.5 meV w i t h N e p a l^{'} s p a r am e t er s an d 73.5 meV w i t h H er r^{'} s; a t 800 K i t i s 378 a g ain s t 335 meV)$
Alloy composition from the gap	$E_{g} (x, 0) = (1 - x) E_{G a N} + x E_{A l N} - b x (1 - x)$	$α (x) = (1 - x) α_{G a N} + x α_{A l N} - c x (1 - x), β (x) = (1 - x) β_{G a N} + x β_{A l N} - d x (1 - x)$	$x : A l N f r a c t i o n$ $b : b o w in g p a r am e t er$ $c, d : b o w in g o f t h e V a r s hni co n s t an t s; N e p a l e t a l . : b = 1 eV w i t h E_{G a N} = 3.5 an d E_{A l N} = 6.1 eV, c = 2.15 meV/K, d = 1561 K, f i tt e d E_{g 0} o f 4.311 eV a t x = 0.38, P L p e ak s o f 4.27 eV a t 10 K an d 3.92 eV a t 800 K f or x = 0.38$ $(co m p u t e d : x = 0.38 g i v es 4.252 eV f r o m t h e b o w in g f or m u l a, 59 meV b e l o w t h e f i tt e d 4.311; x = 0.5 g i v es 4.55 eV)$
Thermal quenching	$I (T) = \frac{I _{0}}{1 + C e x p ( - E _{a} / k _{B} T )}$	$ln (\frac{I _{0}}{I} - 1) = ln C - \frac{E _{a}}{k _{B} T}$	$I_{0} : l o w - t e m p er a t u r e in t e n s i t y$ $C : r a t i o o f n o n r a d ia t i v e t o r a d ia t i v e r a t es$ $E_{a} : a c t i v a t i o n e n er g y o f t h e q u e n c hin g c hann e l; A r r h e ni u s f or m (ba c k g r o u n d k n o w l e d g e); H O R I B A l o w - t e m p er a t u r e n o t e : in t e n s i t y f a l l s w i t h t e m p er a t u r e a s c a r r i er s esc a p e t h r o ug h n o n r a d ia t i v e p r ocesses$ $(a ss u m e d : E_{a} = 50 meV, C = 100; co m p u t e d : I = 0.999 I_{0} a t 50 K an d 0.065 I_{0} a t 300 K)$

Excitation Conditions

Name	Formula	Related Formulae	Variables/Constants
Excitation-power dependence	$I \propto P^{k}$	$k \approx 1 to 2 (excitons, band edge), k < 1 (defect and DAP bands)$	$P : e x c i t a t i o n p o w er$ $k : p o w er e x p o n e n t; b e ha v i o u r (ba c k g r o u n d k n o w l e d g e); D A P l in es a l so s hi f t t o hi g h er e n er g y w i t h p o w er a s c l oser p ai r s s a t u r a t e (ba c k g r o u n d k n o w l e d g e)$ $(co m p u t e d : k = 1.5 m e an s a t e n f o l d p o w er in cr e a se r ai ses t h e ban d - e d g e s i g na l 31.6 t im es)$
Excitation depth and source choice	$δ = \frac{1}{α ( λ _{e x c} )}, E_{e x c} > E_{g}$	$E_{e x c} = 6.28 eV (197 nm) for AlGaN up to AlN$	$δ : e x c i t a t i o n d e pt h, α (λ_{e x c}) : ab sor pt i o n coe f f i c i e n t a t t h e l a ser w a v e l e n g t h; r e l a t i o n (ba c k g r o u n d k n o w l e d g e); N e p a l e t a l . : f r e q u e n cy - q u a d r u pl e d 100 fs T i : s a pp hi r e a t 6.28 eV, 3 mW, 76 MHz, 1.3 m m o n oc h r o ma t or, c l ose d - cy c l e h e l i u m cr y os t a t; H O R I B A O S D - 104 : A r + l a ser, c h o pp er an d l oc k - in, l i q u i d - ni t r o g e n - coo l e d I n G a A s d e t ec t or, ma pp in g s t a g e; H O R I B A l o w - t e m p er a t u r e n o t e : 10 mW H e N e a t 632.8 nm, t h er m oe l ec t r i c I n G a A s, 1 m m o n oc h r o ma t or, 4.5 K$ $(a ss u m e d : α = 1 \times 1 0^{4} c m^{- 1} f or S i a t 532 nm; co m p u t e d : δ = 1 μ m; 1239.84/6.28 = 197 nm, ab o v e t h e 6.06 eV A l N g a p)$

Important Questions

Ques: What does a photoluminescence spectrometer measure?

The light a semiconductor emits after being excited above its band gap. Absorbed photons create electron-hole pairs that relax to the band edges or to defect levels and recombine, emitting photons with less energy than the excitation (HORIBA OSD-104). HORIBA’s system uses an Ar+ laser, chopped for lock-in detection, a fibre-coupled illuminator, a monochromator and a liquid-nitrogen-cooled InGaAs detector for 500 to 2000 $nm$ , with a mapping stage and cryostat. The emission energy follows from $E = 1239.84/ λ$ : GaN at 3.42 $eV$ emits near 362.8 $nm$ and silicon’s 1.12 $eV$ gap corresponds to 1107 $nm$ (computed). Peak position, width and symmetry reveal band gap, composition, impurities and growth quality. Reference: HORIBA Scientific, ‘Photoluminescence of Semiconductors’, application note OSD-104 (2014) (fetch-tool summary); J. I. Pankove, Optical Processes in Semiconductors, Dover 1971 (background knowledge; not opened).

Ques: Why is photoluminescence often measured at low temperature?

Because lines become sharp enough to identify. HORIBA’s low-temperature note describes room-temperature PL as broad, up to 100 $nm$ wide, 73 $meV$ at 1300 $nm$ (computed), while at 4.5 $K$ in a closed-cycle cryostat the peaks are sharp; as temperature rises, the peak broadens, shifts to lower energy as the gap shrinks, and weakens as carriers escape through nonradiative paths. Thermal broadening alone gives a band-to-band width of about $1.8 k_{B} T$ , 47 $meV$ at 300 $K$ (background knowledge; computed). At low temperature, free and bound exciton lines separate, so donors and acceptors can be identified by their binding energies. A long monochromator, 1 $m$ in HORIBA’s system, resolves lines that a 0.32 $m$ instrument blurs. Reference: HORIBA Scientific, ‘High Resolution Low Temperature PL of Semiconductors’, application note (fetch-tool summary); J. I. Pankove, Optical Processes in Semiconductors, Dover 1971 (background knowledge; not opened).

Ques: How is the band gap read from a PL spectrum?

From the band-edge peak, corrected for its line shape and for excitons. Free-carrier emission rises as $E - E_{g}$ above the gap and falls exponentially, so its peak sits at about $E_{g} + k_{B} T /2$ , 12.9 $meV$ above the gap at 300 $K$ (background knowledge; computed). In materials with strong excitons, the dominant line is the free exciton, below the gap by the exciton binding energy, about 25 $meV$ in GaN (assumed value), and at low temperature bound or localized excitons lie lower still (background knowledge). Nepal et al. attribute low-temperature AlGaN lines to localized excitons and fit the gap only above 200 $K$ ; Herr et al. use free-exciton line-shape fits above 200 $K$ for GaN. The PL peak is therefore close to, but not exactly, the gap. Reference: N. Nepal, J. Li, M. L. Nakarmi, J. Y. Lin and H. X. Jiang, ‘Temperature and compositional dependence of the energy band gap of AlGaN alloys’, Appl. Phys. Lett. 87, 242104 (2005) (symbols partly lost in extraction) (fetch-tool summary); H. Herr, V. Alex and J. Weber, ‘Temperature Dependence of the Fundamental Band Gap in Hexagonal GaN’, MRS Proc. 482, 719 (1997) (abstract) (fetch-tool summary); J. I. Pankove, Optical Processes in Semiconductors, Dover 1971 (background knowledge; not opened).

Ques: Which Varshni parameters describe GaN, 0.94 meV/K and 791 K or 0.73 meV/K and 594 K?

Both come from PL fits: Nepal et al. give 0.94 $meV/K$ and 791 $K$ over 10 to 800 $K$ , and Herr et al. give 0.73 plus or minus 0.03 $meV/K$ and 594 plus or minus 54 $K$ over 2 to 1200 $K$ . The two constants are strongly correlated, so the curves agree better than the numbers suggest: the gap shift at 300 $K$ is 77.5 $meV$ with Nepal’s set and 73.5 $meV$ with Herr’s, only 4 $meV$ apart, but 378 against 335 $meV$ at 800 $K$ (computed). Herr et al. also note that the gap depends on the substrate through strain. For room-temperature work either set is adequate; for high temperatures, Herr’s, fitted to 1200 $K$ , is the more likely reliable one (my reading). Reference: N. Nepal, J. Li, M. L. Nakarmi, J. Y. Lin and H. X. Jiang, ‘Temperature and compositional dependence of the energy band gap of AlGaN alloys’, Appl. Phys. Lett. 87, 242104 (2005) (symbols partly lost in extraction) (fetch-tool summary); H. Herr, V. Alex and J. Weber, ‘Temperature Dependence of the Fundamental Band Gap in Hexagonal GaN’, MRS Proc. 482, 719 (1997) (abstract) (fetch-tool summary).

Ques: How does PL give the composition of an alloy?

By inverting the composition dependence of the gap. For AlGaN, Nepal et al. use $E_{g} (x, 0) = (1 - x) E_{G a N} + x E_{A l N} - b x (1 - x)$ with 3.5 and 6.1 $eV$ and a bowing parameter of 1 $eV$ ; x = 0.5 gives 4.55 $eV$ (computed). The Varshni constants also bow, with c = 2.15 $meV/K$ and d = 1561 $K$ . For x = 0.38, the formula gives 4.252 $eV$ , 59 $meV$ below the fitted 4.311 $eV$ for that sample (computed), showing that individual samples scatter around the trend and that strain and localization shift peaks. The 10 $K$ peak of 4.27 $eV$ falls to 3.92 $eV$ at 800 $K$ . Composition from PL is therefore typically checked against X-ray diffraction (background knowledge). Reference: N. Nepal, J. Li, M. L. Nakarmi, J. Y. Lin and H. X. Jiang, ‘Temperature and compositional dependence of the energy band gap of AlGaN alloys’, Appl. Phys. Lett. 87, 242104 (2005) (symbols partly lost in extraction) (fetch-tool summary).

Ques: What do excitation-power and temperature dependences reveal?

The type of recombination and the quenching channels. Intensity scales as $P^{k}$ : band-edge and excitonic emission give k between about 1 and 2, while defect and donor-acceptor-pair bands saturate with k below 1, and donor-acceptor-pair lines also shift to higher energy with power as close pairs dominate (background knowledge); with k = 1.5, ten times more power gives 31.6 times more signal (computed). Against temperature, intensity follows $I_{0} / [1 + C exp (- E_{a} / k_{B} T)]$ , whose Arrhenius slope gives the activation energy of the escape path (background knowledge). With an assumed 50 $meV$ and C = 100, the signal falls to 6.5 per cent of its low-temperature value at 300 $K$ (computed). HORIBA attributes this drop to nonradiative escape. Reference: J. I. Pankove, Optical Processes in Semiconductors, Dover 1971 (background knowledge; not opened); HORIBA Scientific, ‘High Resolution Low Temperature PL of Semiconductors’, application note (fetch-tool summary).

Ques: How is the excitation laser chosen?

Its photon energy must exceed the gap, and its absorption depth sets which layer is probed. The light penetrates about $1/ α$ : silicon at 532 $nm$ , with an assumed $1 \times 1 0^{4}$ $c m^{- 1}$ , is excited over about 1 $μ m$ (computed), while shorter wavelengths probe nearer the surface. Wide-gap materials need ultraviolet: Nepal et al. used a frequency-quadrupled 100 $fs$ Ti:sapphire laser at 6.28 $eV$ , 197 $nm$ , above AlN’s 6.06 $eV$ gap (computed), with 3 $mW$ at 76 $MHz$ and a 1.3 $m$ monochromator. HORIBA’s low-temperature system uses a 10 $mW$ HeNe at 632.8 $nm$ for infrared-emitting materials, and its other system an Ar+ laser. Pulsed lasers also allow time-resolved PL, whose decay gives carrier lifetimes (background knowledge; Lifetime Testers page). Reference: N. Nepal, J. Li, M. L. Nakarmi, J. Y. Lin and H. X. Jiang, ‘Temperature and compositional dependence of the energy band gap of AlGaN alloys’, Appl. Phys. Lett. 87, 242104 (2005) (symbols partly lost in extraction) (fetch-tool summary); HORIBA Scientific, ‘High Resolution Low Temperature PL of Semiconductors’, application note (fetch-tool summary); HORIBA Scientific, ‘Photoluminescence of Semiconductors’, application note OSD-104 (2014) (fetch-tool summary).

References

HORIBA Scientific, “Photoluminescence of Semiconductors,” application note OSD-104, 2014. Available: https://static.horiba.com/fileadmin/Horiba/Application/Materials/Photovoltaics/Photoluminescence_of_Semiconductors.pdf
J. I. Pankove, Optical Processes in Semiconductors. New York: Dover, 1971 (cited from background knowledge).
HORIBA Scientific, “High Resolution Low Temperature PL of Semiconductors,” application note. Available: https://static.horiba.com/fileadmin/Horiba/Application/Materials/Photovoltaics/High_Resolution_Low_Temperature_PL_of_Semiconductors.pdf
N. Nepal, J. Li, M. L. Nakarmi, J. Y. Lin and H. X. Jiang, “Temperature and compositional dependence of the energy band gap of AlGaN alloys,” Applied Physics Letters, vol. 87, 242104, 2005, doi: 10.1063/1.2142333.
H. Herr, V. Alex and J. Weber, “Temperature Dependence of the Fundamental Band Gap in Hexagonal GaN,” MRS Online Proceedings Library, vol. 482, p. 719, 1997, doi: 10.1557/PROC-482-719.

Quartz 5

Explorer

Photoluminescence Spectrometer