Download Ionized and neutral donor bound excitons: Haynes´ rule

Ionized and neutral donor bound excitons in ZnO
B.K. Meyer1, J. Sann1, S. Lautenschläger1, M. R. Wagner2, and A. Hoffmann2
1
I. Physics Institute, Justus Liebig University, 35592 Giessen, Heinrich-Buff-Ring 16,
Germany
2
Institute of Solid State Physics, TU Berlin, 10623 Berlin, Hardenbergstr. 36, Germany
Abstract
We show for ZnO a correlation between the ionized donor bound exciton D+X recombinations
I0, I1 and I2 and the neutral donor bound exciton D0X recombinations I6a, I8 and I9,
respectively. The experimental data on the localization energies of ionized and neutral donor
bound excitons are compared to theoretical predictions and a good agreement is found. We
give an estimate of the localization energies of neutral acceptor bound excitons. One can
conclude that the localization energies of neutral donor and acceptor bound excitons in ZnO
will be very close in energy and an assignment of transition lines to donors and/or acceptors
(in the absence of decisive data from magneto-optics) will not be straight forward.
PACS: 78.55.-m, 78.55.Et, 78.20.Ls, 71.55.Gs
The complexity of excitonic recombinations in ZnO has been documented already 40 years
ago1-4, 5. More than 12 individual excitonic transitions have been reported. For only four of
them an unambiguous assignment as to the chemical nature of the defects involved could be
given6. It is, therefore, of prime interest to gain further insight into the excitonic
recombinations especially with respect to p-type doping. The identification of neutral acceptor
bound excitonic recombinations A0X will allow to control the incorporation of the acceptors
into ZnO.
From luminescence experiments on ZnO the localization energies EL are determined as the
difference between the recombination energy of the respective bound exciton lines and the
free transversal exciton line (see fig.1). In many semiconductors the localization energies EL
of excitons bound to ionized (D+) and neutral shallow donors (D0) and acceptors (A0) follow a
certain ordering e.g. EL(D+X) < EL(D0X) < EL(A0X) as found in CdS7 or EL(D0X) < EL(D+X)
< EL(A0X) as found in ZnSe8 and proposed for GaN9. This sequence can be understood as a
result of the electron to hole mass ratio =m*e/m*h which has a characteristic value for each
semiconductor. From this mass ratio one can theoretically predict the localization energies of
the bound excitons as a function of the binding energies of the shallow donors ED and
acceptors EA. In addition it also answers the question on the stability of the ionized donor
bound exciton complexes.
In this report we will show that the localization energies of the ionized and neutral donor
bound excitons scale with the respective donor binding energies (Haynes´ rule10). The
experimentally determined values of EL are in agreement with available theoretical
predictions. We suggest that localization energies of neutral acceptor bound excitons are in
the range of 16 to 25 meV for an acceptor binding energy of 165 meV.
The epitaxial films under investigation were grown by chemical vapor deposition on ZnO
substrates. In addition bulk ZnO grown from the vapor phase intentionally doped with the
group I-elements Li and Na were used. For the photoluminescence experiments the samples
2
were excited with the 325 nm line of a HeCd laser, and the emission was detected with a high
resolution monochromator. Measurement temperature was 4.2 K. The magneto-optical
investigations were performed in Voigt configurations with magnetic fields up to 5 Tesla at
1.6 K.
Fig.1 shows the photoluminescence spectra of a homoepitaxial sample with prominent I6a (Aldonor) and I8 (Ga-donor) neutral donor bound exciton recombinations. The I9 (In-donor)
recombination is rather weak. They are accompanied by high energy transitions at 3.3726 and
3.3718 eV labeled I0 and I1, respectively. Fitting the spectrum with Gaussian line shapes gives
the same intensity ratio of ~3 for I0/I1 and I6a/I8. Moreover, in samples with prominent I8
recombination as found e.g. for the samples grown on GaN-templates (interdiffusion of Ga
into the ZnO layer) the I8 and I1 lines show up almost exclusively. For samples grown on
sapphire substrates (Al2O3), Al is the dominant impurity in the ZnO films, and I6a and I0 are
observed as correlated pairs. Summarizing, it appears that I0 is related to I6a, and I1 to I8. Our
findings are in agreement with data published by Bertram et al11 and Wagner et al12.
Another correlated pair of lines exists for I2 and I9. In Na doped ZnO crystals due to
compensation the neutral donor bound exciton recombination I9 related to Indium has the
highest luminescence intensity (see fig.2.a) followed by I2. The I6a and I8 recombinations are
much lower in intensity as is the I10 line, as a result the intensities of I0 and I1 are too weak to
be resolved. A similar intensity ratio of I9 to I2 is found in a Li doped sample, here the I10
recombination is more pronounced (see fig.2.b).
As to the nature of the I0 to I2 recombinations magneto-optical experiments have shown a
conclusive picture. In fig.3 we show the magnetic field behavior of I0 and I1 (for I2/I3 see the
published data3, 13). In an applied magnetic field, both lines show the appearance of an
additional peak at the low energy side of I0 and I1 (see fig. 3). In the case of I0 this component
is superimposed by the I1 bound exciton transition. For clarification, we focus our quantitative
analysis of the magnetic field splitting on the I1 exciton line, although the same considerations
3
apply for I0. The extrapolation of the position of the low energy Zeeman component to B = 0
Tesla reveals the presence of a zero field exchange splitting. From the experimental data, the
splitting energy of the I1 complex is determined to 0.92 meV. This value is in good agreement
with the reported zero field splitting of 0.98 meV for the I2/I3 ionized donor bound exciton
complex13. Furthermore, we do not observe a linear splitting in Voigt configuration as would
be expected for a neutral bound exciton. Consequently, we attribute I0 to I2 to ionized donor
bound exciton recombinations.
Teke et al14 assigned recombination lines at 3.3686 (I2/I3) and 3.3702 eV to rotator excited
states of neutral donor bound excitons, and I0 at 3.3724 eV to a neutral donor bound exciton
with the hole from the B-valence band (DoXB). However, magneto-optical experiments3, 13
unambiguously established that I0, I1 and I2 are due to ionized donor bound excitons. Since the
A-B-splitting of the valence band is 4.7 meV15, the assignments by Teke et al14 are unlikely.
In fig.4 we show the localization energies of the ionized and neutral donor bound excitons as
a function of the donor binding energy. Two aspects are remarkable: The localization energy
EL has a linear dependence on the donor binding energy ED for both neutral and ionized
bound excitons, although with a different slope, and for donor binding energies of ED<47
meV excitons will not be bound to the ionized donors. The linear fits to our experimental data
in fig. 4 result in Eloc = 0.37·ED - 4.2 meV for neutral donors (in agreement with Meyer et al6
and Schildknecht et al16) and Eloc = 0.50·ED - 23 meV for ionized donors, with Eloc the exciton
localization energy and ED the donor binding energy.
In the following we want to put the experimental data in the context of theoretical estimates.
Table 1 summarizes the theoretical results of EL as a function of the ratio of EL to EB, and
the values EB, the impurity binding energies (ED or EA for donors or acceptors, respectively).
For ZnO the mass ratios range between 0.3 and 0.4 depending on the hole mass used. We use
the bare masses, which is m*e=0.24 in the case of the electron mass. For the hole mass two
values are available: m*h=0.59 from the calculation of the free exciton binding energy15 and
4
m*h=0.78 from the calculation of the excitonic transitions in ZnO/ZnMgO quantum well
heterostructures17. We start with the neutral impurity bound excitons. They will be stable for
all mass ratios. In the theoretical calculations of Hopfield18 and Herbert19 for D0X a ratio of
EL/ED of 0.3 for 0.3<<0.4 was obtained in perfect agreement with the experimental findings
(see table 2). Hopfield18 used a donor binding energy of 55 meV which would result in a
localization energy of 16.5 meV. From experiments on the group-III donors6 (Al, Ga, In) the
Ga-related I8 recombination comes closest with EL=16.1 meV and ED=54.6 meV. The ratio
EL/ED is only weakly dependent on  for 0.3<<0.4 as can be seen in fig.1 of Herbert19.
In the case of the ionized donor bound excitons two theoretical calculation are available (see
table 1). Skettrup et al20 used a mass ratio of 0.2 and EL=13.4 meV and obtained EL/ED=0.3
for ED=44 meV. Smith et al21 calculated for =0.46 a value of 9.4 meV for EL (with ED=59.4
meV). Changing the hole mass to 0.87 with the same electron mass Smith et al21 achieved for
EL a value of 3.3 meV for ED=55 meV (=0.275). Both results were obtained by using a
Pollmann-Büttner potential (see table 2).
Experimentally, we find for I0 and I1 localization energies of 3.4 and 4.1 meV respectively
and for I2 an energy of 8.5 meV. The localization energies of I0 and I1 are in very good
agreement with the work of Smith et al21 which would be in favor of the parameters m*e=0.24
and m*h=0.78 (=0.3). But with the same set of parameters we cannot explain the localization
energy of 8.5 meV of I2.
The theoretical results presented in table 1 base on the effective-mass-approach (EMA).
Central cell effects were not considered in the calculations of Smith et al21. While the
localization energies of neutral donor bound excitons are less sensitive to central cell effects
(see table 2) the ionized donor bound excitons are very sensitive (table 2). In our calculation
of the EMA donor binding energy ED a value of 51 meV was obtained. The I9 recombination
which is correlated to I2 is connected to a donor with a binding energy ED of 63 meV. This
difference in donor binding energies (51 vs. 63 meV) is significant and indicates the
5
remarkable influence of the core of the impurity donor on the binding energy i.e. the central
cell shift. Therefore it is not astonishing that the I2 localization energy deviates significantly
from the calculated one using a value of 0.275 for . The influence of the central cell shift on
the localization energies of ionized donor bound excitons compared to the neutral donor
bound ones has already been outlined in the publication of Merz et al8.
Another interesting point is the I10 recombination6, which from the localization energy is
explainable as a D0X recombination according to Haynes´ rule in ZnO. From fig. 4 one could
then derive the corresponding ionized donor bound exciton line. The expected line position
should be around 3.3630 eV, which interestingly is the position of the I*-recombination line
in fig. 2.b. Although the line position of I* is very close to I4, the recombination caused by
hydrogen6, 22, the evidence for hydrogen in the vapor phase grown ZnO samples is not
convincing. As one can see in fig. 2.a the I* excitonic recombination is missing, which would
not be the case if hydrogen was a ubiquitous impurity in the samples grown by vapor phase.
On the other hand the reduction of the intensity of I10 by a factor of 5 may explain the absence
of I* fig. 2.a, though we do not have enough data to make a definitive assignment.
We now turn to the interesting - but yet to be confirmed - case of the neutral acceptor bound
excitons (so far no decisive experiments on AoX have been presented). Theory23, 24 predicts
binding for 0.3<<0.4 with ratios of EL/EA between 0.10 and 0.15 (see table 1). Assuming an
acceptor binding energy of 165 meV (as found for the nitrogen acceptor25 in ZnO)
localization energies between 16 and 25 meV will result (see table 2). One can conclude that
the localization energies of neutral donor and acceptor bound excitons in ZnO will be very
close in energy, and an assignment of transition lines to donors and/or acceptors (in the
absence of decisive data from magneto-optics) will not be straight forward.
Localization energies between 60-70 meV are frequently reported26-33 for nitrogen,
phosphorous, lithium, silver and arsenic doped ZnO, and attributed to AoX recombinations (in
the spectral range from 3.31 to 3.32 eV). If the ratio of EL/EA will be between 0.10 and 0.15
6
acceptor binding energies between 400 and 600 meV result according to these large
localization energies. For acceptor binding energies around 500 meV one can already expect
substantial electron-phonon interactions leading to static or dynamic Jahn-Teller distortions.
Exciton localizations at such deep defects are not very likely processes (note the absence of
excitonic recombinations for the deep distorted Li and Na acceptors in ZnO).
In summary, we demonstrate that Haynes´ rule applies for ionized and neutral donor bound
excitons in ZnO. The localization energies for D+X and D0X are in agreement with theoretical
calculations. We predict that localization energies of neutral donor and acceptor bound
excitons in ZnO are very close in energy. And an assignment in any case needs the support of
sophisticated magneto-optical experiments.
7
Table 1: Theoretical predictions for the exciton localization energies EL, the impurity binding
energies EB and the ratio of EL to EB as a function of the electron to hole mass ratio.
exciton bound to
EL (meV)
values used in the
EB (meV)
= m*e/m*h
EL/EB
calculations
+
ionized donor D X
0
neutral donor D X
neutral acceptor A0X
a
reference
values used in
the calculations
13.4
0.2
0.3
44
20
9.4
0.46
0.15
59.4
21
3.3
0.275
0.06
55
22
-
0.3 ... 0.4
a
0.3
55
18
-
0.3 ... 0.4a
0.3
-
19
-
0.3 ... 0.4a
0.11 ... 0.13
-
23
-
0.3 ... 0.4a
0.10 ... 0.15
-
24
) based on the values of m*e = 0.24, m*h = 0.59 and m*h = 0.78, respectively.
Table 2: Experimental data on the exciton localization energies EL, the impurity binding
energies EB and the resulting ratio of EL to EB.
exciton bound to
ionized donor D+X
neutral donor D0X
0
neutral acceptor A X
EL (meV)
EL/EB
EB (meV)
3.4 (I0)
0.064
53.0 (Al)
4.1 (I1)
0.075
54.6 (Ga)
8.5 (I2)
0.134
63.2 (In)
13.1 (I*)
0.180
72.6 (X)
15.5 (I6a)
0.292
53
16.1 (I8)
0.294
54.6
19.2 (I9)
0.303
63.2
22.8 (I10)
0.314
72.6
16.5 – 24.7*
0.1 ... 0.15*
165**
* according to the estimates by Pan et al23 and Atzmüller et al24; ** binding energy of the
nitrogen acceptor (after Zeuner et al25).
8
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Fig.1: Photoluminescence spectrum of a homoepitaxial ZnO thin film taken at T = 4.2 K
showing neutral donor bound exciton recombination I6a, I8 and I9 and the corresponding
ionized donor bound exciton lines I0, I1 and I2. AT and AL are the transversal and longitudinal
free A-exciton recombinations.
I8 I6a
Intensity (arb. units)
I9
I1 I0
I2
I4
AT
3.35
3.36
3.37
Energy (eV)
11
AL
3.38
Fig. 2: Photoluminescence spectra taken at T = 4.2 K of ZnO bulk crystals grown from the
vapor phase and doped with (a) Na and (b) Li. A correlation between I9 and I2 can be derived,
as well as a tentative correlation between I10 and I*.
I10
I9
I8 I6/6a I*
I1 I0
I2
PL Intensity (arb. units)
a)
b)
3.350
3.355
3.360
3.365
Energy (eV)
12
3.370
3.375
Fig. 3: Photoluminescence measurements at T = 1.6 K on a homoepitaxial ZnO thin film
showing the behavior of the I0 and I1 recombinations in an applied magnetic field (Voigt
configuration).
PL Intensity (arb. units)
T = 1.6 K
5 Tesla
4 Tesla
3 Tesla
2 Tesla
1 Tesla
0 Tesla
3.370
I1
3.371
3.372
Energy (eV)
I0
3.373
13
Fig. 4: Localization energies of neutral D0 and ionized D+ bound excitons in ZnO as a
function of the donor binding energies ED.
Exciton localization energy (meV)
30
25
I10
20
I9
o
DX
I8/6
I*
15
10
+
I2
DX
5
0
30
I1/0
40
50
ED (meV)
14
60
70