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Phys. Status Solidi RRL 7, No. 9, 647–650 (2013) / DOI 10.1002/pssr.201307217
Time-resolved free carrier lifetime
microscopy in bulk GaN
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Patrik Ščajev*, Saulius Nargelas, and Kęstutis Jarašiūnas
Institute of Applied Research, Vilnius University, Saulėtekio ave. 9-III, Vilnius 10222, Lithuania
Received 20 May 2013, revised 28 June 2013, accepted 16 July 2013
Published online 23 July 2013
Keywords GaN, free-carrier absorption, carrier lifetime microscopy, recombination, grain boundaries
*
Corresponding author: e-mail patrik.scajev@ff.vu.lt, Phone: +370 5 2366036, Fax: +370 5 2366037
A novel setup for lifetime microscopy measurements was designed and applied for carrier lifetime mapping in a bulk
GaN. Photoexcitation by a picosecond UV pump and detection of time-resolved free carrier absorption (FCA) images on
a CCD camera enabled the mapping of carrier lifetime distribution with a spatial resolution of 5 μm. The spatial variation
of lifetime in the bulk HVPE-grown GaN revealed the presence of different-size crystalline grains, with lifetime peaking
up to 70 ns in the centers of the largest grains (~ 20 μm in di-
ameter) and dropping to 10 ns in the small ones, while the
spatially averaged lifetime was 40 ns. The inhomogeneity
was ascribed to the interplay of nonradiative diffusion-limited
recombination at grain boundaries and a bulk lifetime in
the crystallite centers. The numerical solution of spatiallyresolved carrier decay rate in the crystallite centers at high injection levels and comparison with experimental data provided a bulk nonradiative recombination time of ~ 70 ns.
© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction The carrier lifetime is an important
parameter in semiconductor technology as it affects the
performance of many devices, their speed, power losses,
and electrical/optical efficiency [1]. Lifetime control
allows evaluating the material structural quality and its suitability for these devices. The commonly used optical techniques for point-by-point lifetime mapping, such as timeresolved photoluminescence (TRPL) [2, 3], free carrier
absorption [3, 4], and microwave photoconductivity decay
[3, 5] provide high temporal resolution (~ns) but have limited spatial resolution (~10 μm) and are time consuming [4].
CCD camera-based photoluminescence lifetime mapping
[6, 7] has much higher spatial resolution (~μm) and fast data
acquisition, but the carrier lifetime is determined indirectly
from the PL signal intensity proportionality to the lifetime.
Besides that, the relationship of TRPL signal with free carrier lifetime in direct bandgap semiconductors is encumbered by in-depth carrier redistribution (diffusion from the
excited region or bleaching) and reabsorption of emission of
the carriers diffused far enough from the surface (e.g. in bulk
GaN [8, 9]). Therefore, much faster PL decay does not necessarily represent the actual carrier lifetime.
On the other hand, free carrier absorption and transient
grating techniques are more advantageous for carrier life-
time measurements (as provide the depth-integrated carrier
density [8, 9]) but still have limited spatial resolution. They
have the potential for a simultaneous monitoring both of
spatial and temporal features, what is very important for
hydride vapour phase epitaxy (HVPE) grown GaN, as the
material inhomogeneities, such as dislocations and point
defects, are detrimental to the fabrication of reproducible
high-power Schottky diodes [10].
We report on a fast time-resolved free carrier lifetime
microscopy setup with high spatial (~5 μm) and temporal
(~2 ns) resolutions. The setup was constructed using a picosecond pump and delayed nanosecond probe laser pulses
to provide nonequilibrium carrier absorption signals on a
CCD camera at different delay times after photoexcitation.
Processing of FCA decays in each camera pixel provided
the carrier lifetime mapping over a few hundred micrometer large area.
The setup was proved for mapping of carrier lifetimes
in a high-quality bulk GaN, which exhibited extremaly
long spatially-averaged carrier lifetimes of 40 ns [9]. The
investigated spatial variation of lifetime in the bulk HVPEgrown GaN revealed the presence of different size crystalline grains with lifetime peaking at 70 ns in the centers of
the largest grains and as low as 10 ns in the vicinity of
© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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P. Ščajev et al: Time-resolved free carrier lifetime microscopy in bulk GaN
small grains. Such large inhomogeneity was ascribed to the
interplay of nonradiative diffusion-limited recombination
at the grain boundaries and bulk lifetime in the crystallite
centers, as confirmed by numerical modeling. The novel
technique opened a possibility for direct monitoring of
long nonradiative recombination features in a high density
plasma in the “defect free“ crystallite centers.
(shutter opened, pixel average is Ii,wex(Δt)) and off (shutter
closed, pixel average is Ii,woex(Δt)) at varying probe delay.
The time dependent differential absorption (DA) signal on
each pixel was calculated according to the relation
DAi(Δt) = ln [Ii,woex(Δt)/Ii,wex(Δt)] = σeh ΔNs(Δt) .
Here σeh = 2.2 × 10
–17
(1)
2
cm [11] is the FCA cross section of
d
2 The technique The experimental setup for timeresolved free carrier lifetime microscopy, based on differential absorption (DA), is provided in Fig. 1a. The picosecond Nd :YAG Ekspla PL2143 (τ L = 25 ps) laser 3rd
harmonic at 355 nm (pump) generates carriers in the sample, while the 1st harmonic of a nanosecond single mode
Ekspla NL303G laser at 1064 nm probes the generated
FCA decay. The external synchronization pulse from an
electronic delay generator (Highland Technology P400)
triggers the picosecond laser, while the same but electronically delayed pulse triggers the nanonsecond laser. A
photodetector, PD, controls the average excitation energy
in 1% interval. The DA data are recorded on a CCD camera (12 bit Thorlabs BC106-UV with 6.5 μm pixel size) at
different probe delay times, Δt. For probe beam attenuation,
a λ/2 plate and a polarizer were used. The used lenses of
F1 = 100 mm and F2 = 250 mm focal lengths magnify the
sample image on the CCD camera by 2.5 times, thus one
pixel can provide a 2.6 μm spatial resolution. The actual
resolution of 5 μm was determined by measuring two-fold
drop of transmitted probe intensity near a thin foil edge.
The setup successfully operated at ambient light conditions
as 20 dB infrared filter was used on the camera.
For carrier lifetime mapping, 200 probe pulses were
measured and averaged in each pixel with excitation on
Figure 1 (a) Free carrier lifetime microscopy setup and (b) images of differential absorption signal in GaN, i.e. DA(Δt) at different relative pump and probe delays, Δt.
© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
GaN, ΔNs(Δt) = Ú Δ N(z, Δt) dz is the integrated over depth
0
injected carrier density (in cm–2); ΔN(z, Δt) is the spatiotemporal carrier density profile (in cm–3). The DA images
for bulk GaN are shown on Fig. 1b at three fixed delay
times. At small delay (2 ns), the signal spatial distribution
is quite homogeneous due to position independent carrier
generation and relatively weak impact of speckles and
probe inhomogeneity, while at longer delays the ongoing
recombination discloses the carrier lifetime inhomogeneity.
The inhomogeneity factor (i.e. a ratio of spatially-averaged
standard deviation to an average signal) increases with
time and equals to 0.1, 0.3 and 1.0 at 2, 30 and 70 ns delay
times, respectively. The carrier lifetime τ was determined
for each pixel assuming the exponential decay of the DA
signal (DAi(Δt) ~exp (–Δt/τ)) and taking the time interval
Δt = τ. About 40 seconds were needed to obtain the DA
image at a fixed delay, and 10 minutes per full carrier lifetime image, with good spatial (5 μm) and temporal (~2 ns)
resolution.
3 Measurement results on GaN and discussion
We investigated spatially-resolved carrier dynamics in
200 μm thick HVPE-grown GaN (electron concentration,
mobility, and dislocation density are n0 = 1.3 × 1016 cm–3,
μn = 1200 cm2/Vs [12], and 5 × 105 cm–2 [9], respectively).
The measurements of DA images at various delay times
provided the lifetime mapping (Fig. 2a) with τ values varying in a wide range (from 10 to 70 ns). Moreover, the spatial distribution of lifetimes resembled islands of long lifetime (50–70 ns), surrounded by regions of reduced lifetime
(20–40 ns). In some areas, the lifetime dropped to 10 ns
(see enlarged view in Fig. 2a with points 1–3). Lifetime
maps did not depend significantly (±20%) on the excitation fluence in a range from 1.0 to 6.4 mJ/cm2.
In Fig. 2b, we compared the spatially-resolved FCA
decays for selected pixels. We found that the decay rate
varies with time in areas of lifetime maxima (point 1) and
surrounding regions (point 2). In the maxima, the initial
decay is slow (~70 ns) but becomes twice faster at longer
delays, while in the surrounding minima the opposite tendency was observed (it increases from 20 to 40 ns). We
note that in the regions with the shortest lifetime the decay
is almost exponential (point 3). On the other hand, spatially-averaged lifetime over the full area (85 × 70 pixels,
Fig. 2c) has shown very similar lifetime value of 40 ns, as
those in the decay tails of points 1 and 2.
To explain the FCA decay rate peculiarities, we used a
model of diffusion-limited recombination on grain boundawww.pss-rapid.com
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Phys. Status Solidi RRL 7, No. 9 (2013)
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via an interface recombination velocity S, being proportional to the point defect density Ndef.
In order to calculate the carrier diffusion governed
nonradiative recombination decay rate at various lateral
positions, we solved a balance equation in cylindrical coordinates (ρ, z). The hexagonal columns were converted to
cylinders to simplify the calculations
∂ ΔN ( ρ , z , Δt ) 1 ∂ Ê
∂ ΔN ˆ
=
Da (ΔN ) ρ
Á
∂ Δt
ρ ∂ρË
∂ ρ ˜¯
+
Figure 2 FCA carrier lifetime map at I0 = 6.4 mJ/cm2 (a), decays
at selected points (b) as well as spatially averaged decays over the
whole investigated area (c). In (d) and (e) the modelled depthaveraged lateral and depth-resolved carrier profiles are shown.
The modelling provided fits (solid lines) for the experimental
curves (b, c), while the dashed curves in (b) do not take into account the contribution of τRBULK.
ries [13]. The validity of the model was previously confirmed by an inverse correlation between the temperature
dependences of the carrier diffusivity, D(T), and the nonradiative recombination time, τnRad(T), which linearly increased with temperature. The wurtzite GaN is known to
grow as a microcrystalline material, when hexagonal crystallites continuously enlarge during the growth [14]. In the
vicinity of crystallite boundaries, the crystalline quality is
reduced due to presence of structural defects and strain
[15], leading to the accumulation of point defects at grain
boundaries [16–18]. In our case, for the estimation of lifetime spatial variation, we assumed that impact of point defects in the vicinity of grain boundaries can be evaluated
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∂ Ê
∂ ΔN ˆ
ΔN
D (ΔN )
+
.
∂ z ÁË
∂ z ˜¯ τ RBULK
(2)
Here, the boundary conditions are defined in the cylinder
center (with radius rcyl) and its interface, respectively:
∂ ΔN (0, t ) ∂ ρ = 0, ∂ ΔN (rcyl , t ) ∂ ρ = -ΔN (rcyl , t ) S /Da .
The photogenerated carrier density in-depth
profile is described by the relation ΔN(z, t = 0)
= α(z) I(z)/hν, where α(z) = α0/(1 + bI(z)) is the absorption
coefficient: α0 = 105 cm–1 at 355 nm with a factor
b = 1.82 cm2/mJ, which accounts for absorption bleaching
[11]. I0 = I(z = 0) is the excitation fluence in mJ/cm2 and
τRBULK is the bulk lifetime. We also took into account
the injection dependent carrier diffusivity D(ΔN)
= (1.5 + ΔN/2.2 × 1019) cm2/s [19].
The numerical solution of Eq. (2) provided dynamics
of spatial carrier redistribution within the grains and decay
on grain boundaries, governed by the S value on the
boundary (τnRad ∝ 1/S) and the time required for carriers to
reach the boundary by diffusion from the grain center
(τnRad ∝ rcyl2/D). In addition to these nonradiative processes,
we added a term τRBULK, which accounts for the local recombination in the defect-free central areas of grains. Consequently, the total lifetime is an average of all contributing processes: 1/τR = 1/τnRad + 1/τRBULK.
The numerical modeling confirmed that the decay time
increase in point 1 is due to the fact that the carriers must
be delivered to the grain boundaries (point 2) by diffusion
from more distant and less defective regions. To simulate
the recombination processes in these areas, we solved the
Eq. (2) for a 18 μm large grain (rcyl = 9 μm). The calculated lateral carrier profiles are shown in Fig. 2d for various times after injection, while the corresponding carrier
in-depth profiles are given in Fig. 2e. Using the carrier
density profiles, the decay kinetics in the near grain
boundary (point 2) and defect free area (point 1) were calculated by Eq. (1) neglecting the bulk term and using large
interface recombination velocity, S = 4 × 104 cm/s (Fig. 2b,
dashed curves). In such a case, the calculated curves are
slower than the experimental ones: the initial part of the
measured decay of 58 ns (in point 1) does not correspond
to the solely diffusion-limited 300 ns time. Therefore, in
order to obtain a good fit to the experimental data in the
central part of the grain, the impact of bulk recombination
(τRBULK = 70 ns) in the crystallites was added, in addition
to the diffusion-limited recombination on the grain
© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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P. Ščajev et al: Time-resolved free carrier lifetime microscopy in bulk GaN
boundaries, and the latter calculations (see solid curves in
Fig. 2b) fitted well the experimental data. The fast exponential decay of τnRad ~ 12 ns (in the point 3) was attributed
to ~6 μm grain size (the same S value was used).
Spatially-averaged FCA decays were simulated
(Fig. 2c), and their decay tails of 40 ns provided an average
effective grain size of about 15 μm (the grain coalescence
probably leads to different interface trap densities on different grain edges, thus randomizing the lifetime pattern).
We note that the latter decay time remains constant at
Δt > 30 ns, in spite of that the carrier density in this time
interval varies in the 1018–1019 cm–3 range (according to
Fig. 2e). Therefore, not dependent on excitation, the total
lifetime τR points to constant values of diffusion-limited
recombination time (τnRad = const) and bulk recombination
time (τRBULK = const).
The τRBULK lifetime is probably related to the intragrain
nonradiative traps, as photon emission to the air does not
effectively contribute to the carrier density reduction.
This peculiarity can be explained by large minimal effective radiative recombination time according [20]:
τ *rad = τsatφreabsφextrφenh, where τsat ~ 30 ns is the saturated
radiative lifetime (τsat = 1/[B(ΔN) ΔN] ~ const at ~1019 cm–3
injections as the bimolecular recombination coefficient
B ~ 1/ΔN at ΔN > ~2 × 1018 cm–3 [21]; at lower injections
in GaN B = 2 × 10–11 cm3/s [8]), φreabs is the reabsorption
factor (φreabs = dph/d* × [1 – exp (–d*/dph)], dph = 2 μm [8]
is the photon mean free path, d* is the carrier distribution
thickness), φextr = 1/(4nGaN2) = 0.037 is the light extraction
efficiency factor [21] from GaN to air (nGaN = 2.6 is the
refractive index for 3.4 eV GaN PL peak [21]), and
φenh ~ 1/(1 + τsat/τnRad) is the inverse number of time the
photon reabsorption process occurs. Finally, the calculations led to a value of τ *rad > ~400 ns, being much larger
than the determined experimentally. Indeed, in thin InGaN
quantum wells the above mentioned factors can be suppressed to reach radiative efficiency close to unity [21, 22].
In confirmation to the above explanation, ~40 ns injection
independent (in 1016–1017 cm–3 range) average lifetime was
observed in the sample at two photon excitation conditions
[9]. Therefore, recombination rate on the nonradiative traps
in the bulk and on the edges of the grains is injection independent in the 1016–1019 cm–3 range.
4 Conclusions The setup for lifetime microscopy
with high spatial (~5 μm) and temporal (~2 ns) resolution
provided free carrier lifetime mapping in the bulk HVPE
grown GaN. Spatially inhomogeneous lifetime distribution
resembled the grain structure, thus, the model of diffusionlimited nonradiative recombination on grain boundary defects was used. For fitting the measured spatially resolved
FCA decays, the model required the inclusion of a bulk recombination rate, especially in large crystallites. The latter
© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
rate was ascribed to bulk nonradiative traps. In this way,
a novel time-resolved free carrier lifetime microscopy
setup was verified as a useful tool for monitoring of nonradiative recombination processes in highly excited nitride
materials.
Acknowledgements The research was sponsored by the
European Community’s social foundation under Grant Agreement No. VP1-3.1-ŠMM-08-K-01-004/KS-120000-1756. We acknowledge H. Morkoç for sharing the bulk GaN sample.
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