Time-resolved and excitation-dependent photoluminescence study of CdTe/MgCdTe
double heterostructures grown by molecular beam epitaxy
Xin-Hao Zhao, Michael J. DiNezza, Shi Liu, Su Lin, Yuan Zhao, and Yong-Hang Zhang
Citation: Journal of Vacuum Science & Technology B 32, 040601 (2014); doi: 10.1116/1.4878317
View online: http://dx.doi.org/10.1116/1.4878317
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LETTERS

Time-resolved and excitation-dependent photoluminescence study of
CdTe/MgCdTe double heterostructures grown by molecular beam epitaxy
Xin-Hao Zhao
Center for Photonics Innovation and School for Engineering of Matter, Transport, and Energy,
Arizona State University, Tempe, Arizona 85287

Michael J. DiNezza and Shi Liu
Center for Photonics Innovation and School of Electrical, Computer, and Energy Engineering,
Arizona State University, Tempe, Arizona 85287

Su Lin
Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287

Yuan Zhao and Yong-Hang Zhanga)
Center for Photonics Innovation and School of Electrical, Computer, and Energy Engineering,
Arizona State University, Tempe, Arizona 85287

(Received 26 March 2014; accepted 6 May 2014; published 19 May 2014)
This Letter reports the optical properties of CdTe/MgCdTe double heterostructures grown by
molecular beam epitaxy. Low-temperature photoluminescence shows strong band-to-band
emission and very weak defect related peaks, indicating low defect densities. The measured
Shockley–Read–Hall lifetimes range from 57 to 86 ns at room temperature for samples grown
under different conditions. The material radiative recombination coefficient B in the recombination
rate defined as R ¼ ADn þ ð1  cÞBDn2 þ CDn3 [Wang et al., Phys. Status Solidi B 244, 2740
(2007)] is evaluated to be 4.3 6 0.5  109 cm3s1 with a photon recycling factor c of 0.85
C 2014 American Vacuum Society.
calculated based on the geometric structure of the samples. V
[http://dx.doi.org/10.1116/1.4878317]

I. INTRODUCTION
Recently, there has been growing interest in the study of
CdTe and related heterostructures with the goal of improving
CdTe thin-film solar cells. CdTe has a nearly ideal bandgap
(1.5 eV) and large absorption coefficient, which make it
suitable for solar cell applications. Extensive studies were
carried out on CdTe heterojunction solar cells,1,2 and nowadays, polycrystalline p-type CdTe absorber and n-type CdS
window layers grown on glass superstrate structures are used
for thin-film cells with a record efficiency of 19.6%.3 This
efficiency is still much lower than the Shockley–Queisser
limit (32%) predicted by the detailed balanced model.4 It
is expected that monocrystalline CdTe enables higher efficiency solar cells due to much lower defect density. It can
also be used as a model system to study not only novel highefficiency cell designs but also various defects and grain
boundaries in a controlled manner. With these motivations
in mind, we recently demonstrated the molecular-beamepitaxy (MBE) grown CdTe/MgCdTe double heterostructure
(DH) with excellent structural and optical properties.5
Furthermore, despite the extensive research on CdTe solar
cells, the radiative recombination coefficient (B) is not well
investigated. In this Letter, the optical properties, including

a)

Electronic mail: yhzhang@asu.edu

040601-1 J. Vac. Sci. Technol. B 32(4), Jul/Aug 2014

the radiative recombination coefficient, of multiple
CdTe/MgCdTe DHs are further investigated using low temperature photoluminescence (PL), time-resolved PL (TRPL),
and excitation-dependent PL measurements.
II. EXPERIMENT
CdTe/MgCdTe DHs are grown on lattice matched (001)
InSb substrates using a dual-chamber MBE system as
reported previously.5 The DHs consist of a 1 lm thick CdTe
layer sandwiched by 30 nm thick MgCdTe barrier layers. All
of the epilayers are undoped. It is found that MgCdTe
provides sufficient carrier confinement for the CdTe layer,
which enables PL measurements without significant surface
recombination losses.5
PL measurements are carried out using a spectrometer
equipped with a photomultiplier tube (PMT). The excitation
source is a 532 nm laser diode. During excitation-dependent
PL measurements, the laser power density is varied from
0.51 W/cm2 to 118 W/cm2 using a neutral density filter. The
samples are mounted on the cold finger of a closed-cycle
helium cryostat for temperature dependent measurements.
TRPL is measured using a time-correlated single photon
counting (TCSPC) system. The excitation source is an ultrafast titanium-sapphire laser with a 130 fs pulse duration. The
laser output at a wavelength of 750 nm is sent through a
pulse selector to obtain pulses at a 0.8 MHz repetition rate. A

2166-2746/2014/32(4)/040601/4/$30.00

C 2014 American Vacuum Society
V

040601-1

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040601-2 Zhao et al.: Time-resolved and excitation-dependent photoluminescence study

040601-2

spectrometer equipped with a high speed microchannel plate
PMT detector is used for single photon counting. The detection wavelength is set to 820 nm, which is the PL peak position of CdTe at room temperature. Data acquisition are done
using a single photon counting card.
III. RESULTS AND DISCUSSION
At room temperature, all of the studied CdTe/MgCdTe
DH samples show very strong PL intensity comparable to
that of a MBE-grown GaAs/AlGaAs DH sample.5
Temperature-dependent PL measurements are conducted
under low laser power density (0.023 W/cm2) for a
CdTe/MgCdTe DH sample grown at 280  C with Cd/Te flux
ratio of 1.5. As shown in Fig. 1, the band edge emission
peak shifts to higher energy as the temperature decreases.
The slope of high energy side (the Planck tail) varies with
temperature and is proportional to 1=kT, as expected. The
PL intensity is much stronger at lower temperatures due to
weaker Shockley–Read–Hall (SRH) recombination. When
the temperature reaches below 100 K, a broad peak in the
range of 820–890 nm appears, which is believed to be related
to defect states.6 At higher temperatures, these defect states
are more likely to recombine nonradiatively due to the interaction with phonons. Thus, this broad peak only shows up at
very low temperatures. The intensity of the broad peak is
more than two orders of magnitude weaker than that of the
band edge emission, indicating low defect density in the
CdTe layer and at the CdTe/MgCdTe interfaces.
Figure 2 shows the TRPL measurements of three CdTe/
MgCdTe DH samples grown under different conditions.
Samples A1561, A1564, and A1566 are grown with a Cd/Te
flux ratio of 1.5 and substrate temperatures of 265  C,
250  C, and 295  C, respectively. The initial photon excited
carrier density in the CdTe layer is estimated to be less than
1015 cm3. The carrier decay dynamics can be modeled
using the function, Dn ¼ Dn0 expðt=sÞ, where Dn0 is the
initial excited carrier density and s is the minority carrier

FIG. 1. (Color online) PL spectra of a CdTe/MgCdTe double heterostructure
measured at different temperatures using the same excitation power density
(0.023 W/cm2). The band edge emission peak shifts to higher energy as temperature decreases. The PL intensity becomes stronger at lower temperatures
indicating higher radiative recombination efficiency. The broad peak in the
range of 820–890 nm at 20 K and 100 K is related to defect states.

FIG. 2. (Color online) Time-resolved photoluminescence of CdTe/MgCdTe
double heterostructures. Shockley–Read–Hall lifetime is extracted from the
slope at the tail of the decay curve.

lifetime. For undoped epilayers, the measured lifetime is
related to different recombination processes in the form of

1
s ¼ 1=sSRH þ 1=sRad þ 1=sAug
¼ ðA þ ð1  cÞBðn0 þ DnÞ þ Cðn0 þ DnÞ2 Þ1 ;

(1)

where A, B, and C are the SRH, radiative, and Auger recombination coefficients, respectively. n0 is the unintentionally
doped carrier concentration. It is assumed that A is independent of the excess carrier densities. The radiative recombination coefficient B defined here is only dependent on the
material properties such as the density of states and the optical transition matrix elements. c is the photon recycling factor, which is the percentage of spontaneously generated
photons reabsorbed by the CdTe layer.7 Considering negligible effect of n0 on the total lifetime, when Dn becomes sufficiently small, s is approximately equal to the SRH lifetime.
As shown in Fig. 2, the TRPL curves decay singleexponentially after 140 ns, and the SRH recombination lifetimes are extracted by fitting the single exponential decay
part of the curves. The lifetime of the monocrystalline CdTe
epilayers is much longer than that of typical polycrystalline
CdTe films whose lifetime is only a few nanoseconds,8 indicating that monocrystalline CdTe has much superior material
properties. The longest lifetime of 86 ns is also longer than a
recently reported 66 ns lifetime for a bulk monocrystalline
CdTe measured by sub-bandgap two photon excitation
method.9
Excitation-dependent PL measurements are conducted to
analyze different recombination processes at different excitation levels and to extract the radiative recombination
coefficient B. During steady-state PL measurements, the generation rate (G) is equal to the recombination rate (R) inside
the CdTe layer as described by7
G ¼ R ¼ ADn þ ð1  cÞBDn2 þ CDn3 :

(2)

In semiconductors, the large index of refraction results in a
small escape cone for luminescence, and the large absorption
coefficient near the bandedge (2  104 cm1)10 results in a

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040601-3 Zhao et al.: Time-resolved and excitation-dependent photoluminescence study

short mean free path for photons created by radiative recombination inside the semiconductor. Consequently, the photons will either be recycled multiple times before escaping
the sample (when the internal quantum efficiency is high) or
will become heat through nonradiative recombination. It is
therefore necessary to include the photon recycling effect,
since it substantially affects the measured net radiative
recombination rate when the internal quantum efficiency is
relatively high. The photon recycling factor c is calculated to
be 0.85 for the 1 lm thick CdTe using the method introduced
by Steiner et al.11 The generation rate (G) is estimated based
on the absorption of pump laser in the 1 lm CdTe layers,
taking into account the reflection loss and loss in the front
cap and barrier layers. The reflection loss is calculated based
on the incident angle of laser and the refractive index of
CdTe. No surface scattering is considered since the surface
of the sample is specular. The relation in Eq. (2) is valid
when photogenerated carrier density Dn is much larger than
the equilibrium carrier density n0 . It is also assumed that
recombination at the CdTe/MgCdTe interfaces is sufficiently
small, and that carriers distribute uniformly in the CdTe
layer. These assumptions are reasonable due to the fact that
CdTe is undoped, has long carrier lifetime, and thus long diffusion length is expected. The measured PL intensity (I) is
proportional to the net radiative recombination rate and can
be expressed as
I ¼ gð1  cÞBDn2 ;

(3)

where g is a proportionality factor, which is affected by the
collection efficiency of the spontaneous emission from the
sample surface by the PL system. From Eqs. (2) and (3), the
power law relation between the PL intensity (I) and generation rate (G) is given by7
G ¼ A0 I0:5 þ B0 I þ C0 I1:5 ;

(4)

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
where A0 ¼ A= gð1  cÞB, B0 ¼ 1=g, and C0 ¼ C=
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð gð1  cÞBÞ3 . The excitation-dependent PL results of the
above three CdTe samples are shown in Fig. 3. The generation rate (G) is plotted as a function of the PL intensity (I)
using a log–log scale. As shown in the figure, the sample
with the longer SRH lifetime has a stronger PL intensity and
therefore higher internal quantum efficiency compared to
others at the same excitation density. For sample A1561, the
slope of the curve is 0.52 at the low excitation range, which
indicates that SRH recombination dominates at low injection
according to the power law relation between G and I. This
further confirms that the lifetime extracted from TRPL measurement at low excitation densities is the SRH lifetime. It
also confirms that the equilibrium carrier density n0 should
be very low (estimated to be at least lower than 1015 cm3);
otherwise, radiative recombination will contribute even
under low excitation. As the generation rate becomes
greater, the slope increases to 0.96, indicating that radiative
recombination becomes dominant. No feature of Auger
recombination was observed, which is expected since a relatively moderate PL pump density is used. All other CdTe

040601-3

FIG. 3. (Color online) Excitation-dependent PL measurements of samples
with different SRH lifetimes. At the same excitation rate, the sample with
longer SRH lifetime shows stronger PL intensity. The slope of the curve for
sample A1561 is 0.52 at lower excitation range meaning that SRH recombination dominates, whereas at higher excitation range the slope becomes
0.96, meaning that radiative recombination dominates.

samples demonstrated a similar behavior. Values of A0 and
B0 are obtained by fitting the excitation-dependent PL curves
with Eq. (4). The SRH recombination coefficient A is the
inverse of the measured SRH lifetime, i.e., A ¼ 1=sSRH .
Therefore, the radiative recombination coefficient (B) can be
calculated using the relationship
B¼

A2 B0
;
 cÞ

A20 ð1

(5)

which comes from Eqs. (3) and (4).
The published experimental values of the radiative recombination coefficient (B) are scattered according to the literature.
Two references reported the values of B (2  109 cm3s1
and 3  109 cm3s1) extracted from experimental results,
without considering the photon recycling effect.8,12 Thus, their
reported B values are also related to the sample structure and
may vary from sample to sample. In our work, the radiative
recombination coefficient is defined as a material parameter,
which is independent of sample geometry, since the geometry
is accounted for by the photon recycling factor c as defined
above. Table I summarizes the fitting results for six CdTe DH
samples grown under different conditions. The optimal growth
temperature and CdTe flux ratio are 265  C and 1.5, respectively, as determined by TRPL. As expected, similar values for
material radiative recombination coefficient B are obtained despite different material qualities (i.e., different SRH lifetimes).
The average radiative recombination coefficient of all the studied samples is then determined to be 4.3 6 0.5  109 cm3s1
for the MBE grown CdTe epilayers. It is worth of mentioning
that accurate radiative recombination coefficient and the inclusion of photon recycling effect are critically needed for the
modeling of CdTe solar cells.
IV. SUMMARY
In summary, the optical properties of six CdTe/MgCdTe
double heterostructures grown under different conditions on

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040601-4 Zhao et al.: Time-resolved and excitation-dependent photoluminescence study

040601-4

TABLE I. Summary of radiative recombination coefficient (B) of CdTe extracted from experimental results. A0 and B0 are obtained by fitting the
excitation-dependent photoluminescence curves to Eq. (4) and B is calculated using Eq. (5) based on the measured SRH lifetime, A0, B0, and c.
Sample #
A1561
A1571
A1566
A1567
A1568
A1564

Growth temperature (  C)

Flux ratio (Cd/Te)

SRH lifetime (ns)

A0 (cm3s1)

B0 (cm3s1)

B (cm3s1)

265
280
295
265
265
250

1.5
1.5
1.5
1.2
1.8
1.5

86
83
74
64
58
57

8.78  1020
8.69  1020
1.12  1021
1.32  1021
1.45  1021
1.39  1021

3.74  1018
3.99  1018
4.63  1018
4.12  1018
3.95  1018
4.24  1018

4.3  109
5.1  109
4.5  109
3.8  109
3.7  109
4.5  109

lattice matched InSb substrates are studied with low temperature PL, time-resolved PL, and excitation-dependent PL
measurements. SRH lifetimes ranging from 57 ns to 86 ns
are measured at room temperature for these samples. Low
temperature PL measurements show a strong band-to-band
emission peak and a broad and much weaker defect related
peak, indicating low defect density. With excitationdependent PL measurements, it is found that SRH recombination dominates at low generation rate (1022 cm3s1)
and radiative recombination dominates at high generation
rate (1024 cm3s1). The sample geometry independent,
material radiative recombination coefficient of CdTe is estimated to be 4.3 6 0.5  109 cm3s1, after corrected by the
photon recycling effect. This parameter is needed for the
modeling of CdTe solar cells.
ACKNOWLEDGMENTS
The authors gratefully thank A. P. Kirk for helpful discussions on this Letter. This work was partially supported by
AFOSR (Grant No. FA9550-12-1-0444), Science
Foundation Arizona (Grant No. SRG 0339-08), and NSF
(Grant No. 1002114). This material is also based upon work

supported by the National Science Foundation Graduate
Research Fellowship (Grant No. DGE-0802261).
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