Effects of impurity band in heavily doped
ZnO:HCl
G. V Colibaba, A. Avdonin, Ivan Shtepliuk, M. Caraman, J. Domagala and I. Inculet
The self-archived postprint version of this journal article is available at Linköping
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Colibaba, G. V, Avdonin, A., Shtepliuk, I., Caraman, M., Domagala, J., Inculet, I., (2019), Effects of impurity band in heavily doped ZnO:HCl, Physica. B, Condensed matter, 553, 174-181.
https://doi.org/10.1016/j.physb.2018.10.031
Original publication available at:
https://doi.org/10.1016/j.physb.2018.10.031
Copyright: Elsevier
Effects of impurity band in heavily doped ZnO:HCl
G.V. Colibaba1*, A. Avdonin2, I. Shtepliuk3, M. Caraman1, J. Domagała2, I. Inculet1
1Moldova State University, Chisinau, Moldova
2Institute of Physics, Polish Academy of Sciences, Warsaw, Poland 3Linkoping University, Linkoping, Sweden
*Moldova State University, str. A. Mateevici 60, MD-2009, Chisinau, Moldova, phone: +(373) 69
784311, e-mail: Gkolibaba@yandex.ru
A comparative study of properties of ZnO:HCl single crystals obtained by various methods is presented. Characterization by photoluminescence, optical and electrical measurements in the wide temperature range has allowed to analyze the energy spectra of Cl-containing stable defects in ZnO. Presence of shallow Cl donors, deeper donor complexes, incorporating several Cl atoms or stable H-Cl pairs and presence of compensating deep acceptors, attributed to VZnClO centers, are demonstrated. The presence of shallow donor impurity band, as
well as strong dependence of its activation energy on the doping level is shown. The controversy of various models for estimation of this dependence is discussed. It is demonstrated, that 90% of this dependence is caused by feature of temperature dependence of Hall coefficient related to conductive impurity band, and a more correct equation for activation energy is suggested. An abnormally low efficiency of neutral impurity scattering of charge carriers and strong optical absorption in the near-IR spectral range are demonstrated and attributed to upper conductive impurity band of negatively charged donors with an extra electron.
Keywords: Halide vapor transport; Zinc Oxide; Impurity band; Donor activation energy; Carrier transport phenomena
1. Introduction
Zinc oxide (ZnO) crystals have drawn the attention of scientific community due to their possible applications in various fields [1−4]. Doping of ZnO by transitional metals and rare-earth elements is a promising approach for obtaining novel high-performance light-emitting materials. Nanoporous matrices (nanotemplates) fabricated on homogeneously doped substrates with controllable conductivity can be used to make nanowires
and nanotubes of various materials which are promising structures for optoelectronics and photonics [5−7]. One of the most suitable methods for synthesis of ZnO crystals with controllable electrical parameters and controllable impurity composition is the chemical vapor transport (CVT) in sealed chambers.
The dense HCl medium used as a chemical vapor transport agent (TA) favors the formation of void-free n-ZnO single crystals. However, a very low growth rate, which is limited by the weak temperature dependence of the pressures for the main CVT gaseous species, is inherent for this method [8]. The development of technology for the simultaneous use of HCl, used to generate a dense growth medium, and other TAs, causing a stronger temperature dependence of pressures of the chemical interaction species, can promise the increase of the growth rate of ZnO. Recently new methods using HCl+H2, HCl+CO and HCl+C TA mixtures were suggested for ZnO
single crystal growth [9−11]. In particular, the increase of the growth rate up to 1−1.5 mm per day has been achieved. Due to this reason, aforementioned method offers an alternative route for obtaining ZnO with controllable electrical parameters.
The exact nature of the centers containing Cl impurity in ZnO and their activation energy are still poorly studied, and the corresponding published data are inconsistent. The theoretical research of Cl donors predicting high value of the activation energy of over 550 meV is shown in Ref. [12]. The resistivity > 108 Ω⋅cm of ZnO
crystals grown in the media of NH4Cl decomposition products, was specified in Ref. [13]. At the same time, the
high concentration of free electrons of up to 3⋅1019 cm-3 is shown for ZnO:Cl:C single crystals [14]. The
chlorine impurity in ZnO thin films and nanowires was suggested to cause the low resistivity of about 3⋅10−3
Ω⋅cm and high free electron concentrations over 1020 cm−3 [15, 16].
The electrical measurements in a wide temperature range revealed the low activation energy for Cl donors of 23 meV in ZnO:Cl:C single crystals [14]. The same measurements revealed two donor centers with the activation energy of 30 and 65 meV in ZnO:Cl films; strong dependence of these activation energies on the doping level was also found [17]. The dependence of donor activation energy on doping level is very controversial in ZnO [18, 19]. The suggested magnitudes of this dependence differ from each other by several times. In the majority of the cited publications, the effect of the conductive impurity band formation and the corresponding correction of the ionization energy were not discussed.
The present investigation is a comparative study of properties of CVT ZnO:HCl single crystals obtained by using various TAs. The energy spectrum of Cl impurity is investigated, considering effects related to conductive impurity band.
2. Experiment
The source material used for crystal growth was ZnO powder with initial purity of 99.99%. The growth of crystals was carried out in the sealed quartz ampoules, preliminarily evacuated down to 10−4 Torr. HCl, HCl+H
2,
HCl+CO/C mixtures were used as TAs [8−11]. The loaded pressure of HCl, corresponding to the growth temperature (HClo), was varied in the 0.7−4 atm range. The growth temperature (T
gr) was maintained at 1050
°С. Thermal annealing of ZnO:HCl samples was carried out in air at 1060 °С during 36 hours, to eliminate the stoichiometric deviation and the residual hydrogen impurity. Several procedures of annealing in air or in oxygen atmosphere at different temperatures were also carried out.
The transmission spectra (Tr) of the samples with thickness of 0.8 mm were measured in the 200−2500 nm spectral range. The photoluminescence (PL) spectra were excited by a nitrogen laser (3.68 eV, ~10 mW/mm2,
103 Hz, 10 ns pulse width) and collected at 110 and 300 K in the 350−2500 nm spectral range using a monochromator with 1.4 nm/mm reciprocal dispersion. Conductivity (σ), Hall coefficient (RH) and Hall
mobility (µH ≡ RHσ) were calculated from the Hall effect measurements in the 19−300 K temperature range, in
magnetic field of 1.4 T, using six-probe method. The indium droplets fused with samples were used as electrical contacts. Before PL and Hall measurements, the samples were preliminarily polished and etched for several minutes in HCl aqueous solution. The crystallinity of ZnO crystals was determined by probing their rocking curves, using CuKα radiation, and a double crystal X-ray spectrometer. The etch pit density has been estimated
on [0001]Zn surface after the treatment in HCl aqueous solution.
3. Experimental results
3.1. Structural quality
CVT growth of ZnO crystals in a medium with a low pressure of loaded HCl (HClo < 1 atm) is accompanied
by appearance of angle boundaries defects. Full width at half maximum of rocking curves (FWHM RC) for such samples is about 500 arcsec. A denser HCl medium decreases the density of these defects (FWHM RC is about 200−300 arcsec); however, it strongly reduces the growth rate [8]. HCl+H2 gas mixture with ratio ~1:1 mol can
be successfully used for the increase of the growth rate up to 1.5 mm per day at Tgr of 1050 °C and for rising the
crystalline quality up to 100−200 arcsec [9]. The best results were achieved with HCl+CO and HCl+C TA mixture. The unseeded ZnO crystals with growth rate of about 1 mm per day at Tgr = 1050 °C (FWHM RC of
c and a are 5.2078 and 3.2500 Å, respectively, for crystals grown at pure HCl pressure of 4 atm and annealed in air. The relatively large crystal lattice parameters are explained by the presence of Cl impurity, since ionic radius of Cl1− (1.81 Å) is larger than that of O2− (1.36 Å).
3.2. PL properties
PL properties of ZnO crystals grown using various TAs based on HCl are similar, and they depend on Cl impurity. Spectra measured at 110−300 K consist of an intensive near band-gap emission band localized at 3.34 eV (371.3 nm) and a much weaker emission peak at about 2.5 eV (496 nm). This long wavelength emission is caused by oxygen vacancies (VO) [20]; thus, Cl impurity does not generate low energy emission, which is in
accordance with previous studies [16, 17, 21]. The near band-gap PL spectrum decomposed by means of Alentsev method, using varied excitation levels, is shown in Fig. 1(a, b) [22, 23]. The short-wavelength band FXA at 3.366 eV (368.4 nm) almost coincides with the free exciton band [1]. Exciton band I2s (3.354 eV, 369.7
nm) and I2d (3.326 eV, 372.8 nm) can be ascribed to donors, which, in accordance with Haynes rule [24, 25],
have the activation energy of 38±6 meV and 121±10 meV, respectively. I1s component (3.306 eV; 375.1 nm) is
attributed to excitons bound with acceptors having the activation energy of 600±50 meV. Some deeper acceptors with the activation energy of 810±50 meV can cause the I1d band (3.285 eV, 377.5 nm).
The dominating I2s and I2d bands are observed at any doping levels and after any post-growth treatment. The
I2d band slightly lowers at the decrease of doping level of Cl. While I2s can be associated with simple isolated Cl
donors, I2d can be caused by Cl-related complexes, including several Cl atoms or stable H-Cl pairs. Similar
dominating I2s band was observed earlier in PL spectra of ZnO:HCl films grown at lower temperatures (800 °C)
[21]. The important feature is that the doping level has no essential influence on the localization of these emission bands in the investigated range of impurity concentration of about (1÷20)⋅1018 cm−3. The I
1sband can
be attributed to the associative centers of Cl impurity atoms and intrinsic defects, for example, zinc vacancies (VZnClO), which were predicted in [26]. A surplus of Zn in the investigated material suppresses the intensity of
this band (Fig. 1(c)). 3.3. Transmission spectra
The transmission spectra of the as-grown ZnO:HCl crystals obtained in gaseous mediums containing high Zn vapor pressure (HCl+H2, HCl+CO/C TAs) are characterized by a high optical density in the 2−3 eV spectral
annealing in air. Annealing at about 1050−1080 °C for 36 h is enough for reaching the highest transparency in a visible spectral range (Fig. 2(a)).
The weak optical absorption in the 2.5−3.2 eV spectral range cannot be suppressed by annealing in air and it is absent in the crystals non-doped by Cl. Intensity of this absorption increases with the increase of the doping level of Cl (Fig. 2(a)). Similar absorption was observed earlier in heavily doped ZnO:Cl nanowires [16]. In a case when optical absorption (α) is caused by electron transitions from deep acceptors to conductance band (CB), (αE)2 obeys a linear dependence on photon energy (E), allowing to estimate the activation energy of corresponding acceptors [28]. The described calculation gives a value of about 0.5 eV (Fig. 2(b)). These acceptors can be recognized as the VZnClO defects predicted in the Ref. [26]. Similar activation energy was
found for zinc vacancy−donor defects in other II−VI semiconductor materials [25, 29]. Longer wavelength absorption can be related to deeper acceptors, having the activation energy of 0.68 eV or to optical transitions from VZnClO acceptors to empty levels of Cl donors.
Annealed ZnO:HCl crystals have absorption in the near-IR spectral range at 1.5−0.5 eV (800−2500 nm) (Fig. 3(a, b)). This absorption increases with the increase of HClo, but this can be partially suppressed by the
presence of Zn vapor in the growth medium (Section 3.4). This spectral range usually corresponds to the optical absorption by free electrons in the CB. However, there are two important discrepancies with the theory. The coefficient of such optical absorption (αIR) should have the following dependence [30]:
, (1)
δ CB IR=const n λ
α ⋅ ⋅
where nCB is the charge carrier concentration in CB, λ is the wavelength, δ parameter is equal to 3.5 and 2.5 in
the case of scattering of free electrons by impurity ions and by polar-optical phonons, respectively. The observed near-IR absorption follows the law const⋅nCB2⋅λ3.5 (Fig. 3(c)). Since scattering of carriers by
polar-optical phonons is one of the main scattering mechanisms for all investigated samples, at the typical measurement temperature (300 K), the value of δ is expected to be 2.5. Similar near-IR absorption was observed in high conductive ZnO:Cl thin films obtained by metal-organic chemical vapor deposition [15]. However, the authors of this work did not obtained strong evidence for relation between this absorption and free charge carriers.
3.4. Electrical properties
ZnO crystals, grown in media containing HCl, have high conductivity which is attributed to shallow Cl donors [8]. The concentration of free electrons in CB (nCB estimated as 1/qRH, where q is the elementary charge)
at constant HClo pressure has a certain dependence on the composition of CVT medium (Table 1). By
comparing the density of various gaseous species, one can hypothesize that the efficiency of Cl doping is lower at higher Zn pressure. This hypothesis is confirmed by electrical measurements, higher transparency in the ultraviolet-blue (Cl-related acceptors, Section 3.3) and in the near-IR (free electron absorption) spectral ranges. This effect can be attributed to the increase in concentration of intrinsic donor-like defects, such as interstitial zinc and oxygen vacancy [31]. The concentration of neutral Cl impurity atoms (Clo) depends on the density of
Cl-containing species (ZnCl2) in the growth medium. The total concentration of Cl donors (Cl) at growth
temperature can be calculated by means of Boltzmann statistics as follows:
, (2) ) kT ΔE F E ( Cl = Cl + Cl = Cl C D o o + − − exp 2
where Cl+ is the concentration of ionized Cl donors, E
C is the energy of CB bottom, F is Fermi energy, ∆ED is
the activation energy of donors, k is Boltzmann constant, T is absolute temperature. For a high growth temperature regime, Cl+ >> Clo. The increase in density of other donors, raising the position of Fermi level,
should decrease Cl+ concentration (Eq. 2), thereby lowering the efficiency of Cl doping.
The concentration of non-compensated donors (ND−NA) in the obtained crystals has a linear dependence on
HClo pressure at constant growth conditions and TAs ratio (Fig. 4(a)). Additional annealing in air or oxygen
atmosphere decreases the concentration of intrinsic donors, promotes the fast out-diffusion of the hydrogen donor-like impurity, and should enhance the density of compensating acceptors, such as VZnClO. At the same
time, such annealing has no strong influence on nCB values (Fig. 4(b)). It means that Cl-containing defects are
the main stable donors, while the compensation degree of these donors is characterized by a weak dependence on pressure of oxygen in the annealing medium.
3.4.1. Model of one conductive band
An increase in the doping level leads to the increase in conductivity and free electron concentration, but it decreases the mobility due to the increase in impurity scattering (Fig. 5). The concentration of donors (ND) and
of the compensating acceptors (NA), as well as the activation energy of donors (∆ED), can be estimated by using
, (3) D D A CB+N =N n n − , (4) 1 exp 2 1 + ) kT ΔE F E ( N = n D C D D − −
where nCB and nD are electron concentrations in the CB and on the donor levels, respectively. For case of
nondegenerate electronic gas in CB, Eq. 4 can be rewritten as follows:
, , (5)
1
*+
n
N
N
=
n
CB C D D ) kT ΔE ( N N C D C ≡ exp − 2 *where NC is the density of the state in the CB. As a consequence, Eq. 3 can be simplified in this case to a
square-law equation: . (6) * C CB A D A CB CB =N n N N ) N + (n n − − ⋅
The obtained experimental data can be described by a wide range of fitting parameters of Eq. 6, corresponding to the compensation degree (NA/ND) in the range from 0 up to 40%. However, for each set of fitting parameters,
ND−NA values are almost constant and are useful for characterization of samples (Fig. 6).
With increasing doping level the obtained ∆ED drops to 1−2 meV (Fig. 6). Value of ∆ED can essentially
differ from the activation energy of the isolated donor centers (∆EDo), which corresponds to a case of a very low
doping level. There are several models proposed for explication of the decrease in the activation energy: (i) the impurity band formation and its thickening with the increase of the impurity concentration, (ii) the lowering of the CB bottom due to Coulomb interactions between free electrons and ionized donors and due to appearance of conductive upper Hubbard impurity band overlapping with the CB bottom, (iii) screening of the impurity ions by free charge carriers [32−37]. Usually, the observed dependences of ∆ED are not in the good agreement with
any of the mentioned models. The following empirical dependence of the ∆ED is often proposed for
semiconductors: . (7) 3 / 1 N β ΔE = ΔED Do − ⋅
Value of β parameter is controversial. It is usually equal to approximately (4.5±0.5)⋅10−5 meV⋅cm for semiconductors having a static relative dielectric constant in the range of 7−9, which is valid for ZnO [1]. As was proposed in [18], for ZnO β is equal to 5⋅10−5meV⋅cm, while in some reports β ≈ 2⋅10−5meV⋅cm was used [19]. The physical meaning of parameter N is also controversial. The authors of [18] and [19] attribute it to the
full donor and acceptor concentration, respectively, while in some Refs., N is regarded as the concentration of ionized impurity centers (Nii), both donors and acceptors; Nii = 2NA + nCB [8, 33].
Equation 7 and the calculated concentrations of defects (Eq. 6) allow to estimate ∆EDo. This energy has
strong dependence on the doping level at β = 5⋅10−5meV⋅cm and N = N
D (Fig. 6). The mean deviation of ∆EDo is
lowest in the case of β = 4⋅10−5meV⋅cm, N = N
ii and for compensation degree close to zero. The average value
of ∆EDo in this case is equal to 61±2 meV at 300 K, which is in good accordance with the activation energy
predicted for hydrogen-like donors in ZnO [38] (Fig. 6). At the same time, the observed strong dependence of the activation energy on the doping level is in conflict with PL results (Section 3.2, I2s band). Moreover, the
energy of about 60 meV is not the lowest in undoped materials; ∆ED ~ 30 meV is often observed [38, 39].
3.4.2. The model of two conductive bands
A well-conducting impurity band (IB) is believed to exist when the following Mott criterion is satisfied:
, (8) 3 / 0.54 0.62 0 3 / 1 ≤ − m ε N = a a = γ D o
where a is the average distance between the impurity atoms (numerator of Eq. 8), ao is Bohr radius of a
hydrogen-like impurity atom, ε0 is static relative dielectric constant, m* is the effective electron mass [34]. Value
of γ for lowest (ND ≈ 1018 cm−3) and highest (ND ≈ 20⋅1018 cm−3) doping levels in the investigated crystals is
about 4 and 1.5, respectively. In the case of a low compensation, the center of IB should be localized at the energy level of the isolated donors (ED). The width of impurity band (W) can be estimated as follows [34]:
, (9)
γ) ( ΔE
W ≈ HLDexp −
where ∆EHLD is the activation energy of hydrogen-like donors. W equals to about 1 meV and 14 meV for
samples with lowest and highest doping levels, respectively, if ∆EHLD = 60 meV.
For the present study, a constant density of donor states is assumed in the ED±W/2 range. In this approach,
Eq. 5 should be rewritten after integration over energy of donor states as follows:
. (10) ) kT) W ( n N + kT) (W n N + W kT ( N = n CB C CB C D D 2 / exp 1 2 / exp 1 ln 1 * * − −
. (11) ) n N n N n N ) kT W ( ( + n N N = n CB C CB C CB C CB C D D 2 * * * 2 * ) 1 ( ) 1 ( 24 1 1 1 + − −
Corresponding calculation, based on Eq. 10 shows that widening of the impurity band should reduce ∆ED (i.e.
fitting parameter of Eq. 6) by 0.1 and 2 meV for ZnO:HCl samples with ND ≈ 1⋅1018 and 20⋅1018 cm−3 ,
respectively, if ∆EDo = 60 meV. These are by one order of magnitude smaller in comparison with the results
from Fig. 6 (Section 3.4.1). Thus, estimation based on the Mott criterion shows the presence of conductive impurity bands in all investigated samples; however, their expansion is insignificant. In the following analysis, the effect related to the IB conduction is taken into account for the explication of observed dependence of the donor activation energy on doping level.
In the case when carriers participating in the conductivity belong to two energy bands, Hall coefficient and Hall mobility can be written as follows [30, 40]:
, (12) 2 2 1 1 2 2 2 2 1 1 1 ) μ n + μ q(n μ n r + μ n r = R 2 2 H , (13) 2 1 1 2 2 2 2 1 1 1 μ n + μ n μ n r + μ n r = σ R 2 2 H
where r, n and µ are corresponding Hall factor, concentration of charge carriers and their mobility, respectively. Eqs. 12, 13 can be rewritten as follows:
, (14a) 2 1 1 xb) + ( ) xb + x)(r + ( = )R N q(N 2 H A D− . (15) xb + xb + r μ = σ R 2 1 H 1
r2(rIB) can be assumed to be equal to unity, r1(rCB) ≡ r, x ≡ n2/n1 = nIB/nCB, b ≡ µ2/µ1 = µIB/µCB. For the Eq. 14a,
the constancy of full concentration of mobile electrons (nCB+nIB = ND−NA) is assumed for entire investigated
temperature range, hence 1/qRH → ND−NA at 1/T → 0 and 1/T → ∞. Temperature dependence of RH (Eqs. 12,
14a) should have a maximum at some THmax. Usually, db/dT << dx/dT. For this case, maximum of RH(T)
corresponds to approximate equality of conductivities: qn1µ1 ≈ qn2µ2 or xb ≈ 1 at T = THmax. As a consequence,
the equation for maximal value of RH (Eq. 14a) can be written as follows:
, (16a) ) b + )(r b + ( = )R N
q(ND A Hmax 1 1/ max max max
where RHmax , bmax and rmax correspond to T = THmax. As usually bmax << 1: . (17a) max max max 4q(ND NA)RH r b − ≈
Equation 14a can be simplified into a square-law equation with respect to x, considering b ≈ const = bmax and r
≈ const, for investigated temperature range. The maximum of RH(1/T) dependence is observed at T of about 50−100 K in some highly conductive semiconductor materials [41], but this is absent in highly compensated semiconductors if T ≥ 50 K [42].
Wider temperature dependences of 1/qRH for some ZnO:HCl samples are shown in Fig. 7(a). These
dependences have minimums (maximums of RH) in the 50−75 K range. Temperature dependence of Hall
mobility for wider temperature range is presented in Fig. 7(b). Strong exponential dependence of mobility at T < 70 K is attributed to hoppingconductivity of IB [41]. The decrease of activation energy of hoppingconductivity at the increase in doping level is attributed to the increase in overlapping of wave functions of impurity centers.
The fitting curve of RH (ZnO:HCl, ND = 3⋅1018 cm−3), calculated using Eq. 6 for the model of one conductive
band is shown in Fig. 8(a) as curve 1. The example of fitting curve for the model of two conductive bands, calculated using Eq. 14a, is shown in Fig. 8(a), as curve 2. During fitting procedure we have used: (i) choice of ND−NA; for first iteration ND−NA = 1/qRH at 1/T → 0; (ii) value of bmax can be obtained from Eqs. 16a or 17a,
assuming rmax ≈ 1 (Section 3.4.3); (iii) x (n
IB/nCB) is calculation from Eq. 14a using experimental values of RH at
b = bmax = 5⋅10−3 and r = 1; (iv) n
IB = nCB⋅x = ND−NA−nCB; as a consequence, nCB⋅(1+ x) = ND−NA; (v) nCB is
calculated from Eq. 6 at fitting NA and ∆ED, W(ND) dependence was neglected; (vi) the calculated nCB (Eq. 6) is
compared with values obtained from stage (iv).
The mentioned above model, in which n2 ≡ nIB and 1/qRH → ND−NA at 1/T → ∞, is widely used for highly
compensated materials. For ZnO:HCl, the compensation degree is relatively low (Section 3.4.1). As a consequence, an alternative approach is used in the present work [41]: conductivity of IB is considered to be proportional to concentration of empty donor states, n2 = NA+n1(nCB) instead of ND−NA−n1(nCB), 1/qRH is closeto
NA at the lowest temperatures. For this model Eq. 15 is true, Eqs. 14a, 16a and 17a must be rewritten as follows:
, (14b) 2 1 1 xb) + ( ) xb + )(r (x = R qN 2 H A − , (16b) ) b + )(r b ( = R
qNA Hmax 1/ max 1 max max
. (17b) max max max 4qNARH r b ≈
Optimal fitting curve for this model has a better agreement with the experiment at the lowest temperatures (Fig. 8(a), curve 3). This fitting procedure includes the following: (i) choice of ND−NA and NA; ND−NA ≈ 1/qRH at 1/T
→ 0, NA ≈ 1/qRHmin, where RHmin isminimal value at the lowest temperatures; (ii) bmax (Eq. 16b or 17b), at rmax ≈
1; (iii) x is calculation from Eq. 14b at b = bmax = 6⋅10−2, r = 1; (iv) n
2 = nCB⋅x = NA+nCB, nCB⋅(x−1) = NA; (v) nCB
is calculated from Eq. 6 at fitting ∆ED; (vi) the calculated nCB (Eq. 6) is compared with values obtained from
stage (iv).
Finally, direct fitting, using Eqs. 6 and 12 gives an unessential correction for RH(1/T) at T < THmax (Fig. 8(a),
curve 4). For the direct fitting r1(rCB)(T) and µ1(µCB)(T) were obtained from temperature dependence of total
mobility (Section 3.4.3), r2(rIB) was set to 1 and µ2(µIB)(T) was estimated as 1/µIB = 1/µIB(lT)+1/µint (using
Matthiessen’s rule [43]), where µIB(lT) is an exponential temperature dependence at the lowest temperatures, and
µint is mobility limited by intrinsic-phonon scattering mechanisms (Section 3.4.3).
The distribution of electrons between the CB and IB, estimated by means of Eqs. 14b, 16b for two ZnO samples is shown in Fig. 7(a). The most important result of the described fitting procedure is the following: when two channels of conductivity are taken into account, the value of 1/qRH can be essentially higher than nCB
(Fig. 7(a)) at a high doping level, and the slope of 1/qRH vs (1/T) (T > THmax) dependence can mismatch the
activation energy of impurity centers. As a consequence, the real influence of doping level on the activation energy of donors is one order of magnitude smaller in comparison with the model of one conductive band. Value of parameter ∆ED obtained duringthis fitting procedureis 22 and 19 meV, for samples with ND ≈ 3⋅1018
and 17⋅1018 cm−3, respectively; while the observed slope of 1/qR
H (1/T) dependence decreases by about 20 meV
at such increase of ND (Section 3.4.1, Fig. 6). Thus, real dependence of the activation energy is only 10−20% of
observed dependence of the slope of 1/qRH (1/T) dependence. The compensation degree is about 0.07. Suitable
β parameter (Eq. 7) is relatively low of about 6⋅10−6 meV⋅cm, N ≡ N
ii, and value of the activation energy
approximated to a case of a very low doping level (∆ED0) is about 29 meV.
3.4.3. Features of carrier transport phenomena
There are several carrier scattering mechanisms that play a major role in carrier transport in ZnO crystals: polar-optical phonon scattering (po), acoustic phonon scattering via the piezoelectric potential (pe) and via the
deformation potential (dp), as well as ionized (ii) and neutral impurity (ni) scattering [18, 43, 44]. Common formula for mobility associated with i-th scattering mechanism (µi), can be written as follows [44]:
, (18) pi i i 0 i i T N f(T) μ = μ
where i = dp, ni, po, pe and ii, µi0 depends on the material parameters, f(T) is a function of temperature for some
scattering channels, Ni is concentration of corresponding scattering centers (Table 2). Parameters of ZnO used in
calculations (including electron polaron mass m*=0.29m
e and effective polar-optical phonon temperature Tpo =
750 K) were obtained from [18]. The Matthiessen’s rule (1/µ = ∑1/µi) is the simplest and most widely used
method for the evaluation of the total mobility; however, the error of this method can exceed 40% [44]. The recently proposed modified equation having a 99% accuracy of calculation was used for ZnO:HCl:
, (19)
∑
∑
∑
× = i i i i i i i i i X X Xµ
µ
µ
µ
1 1where Xi parameters (Colibaba’s potentials) are related to the energy dependence of relaxation times of the
corresponding scattering mechanisms [44] (Table 2). A similar equation having a 98−99% accuracy of calculation has been proposed for total Hall factor r [44]; however, as the ni scattering (rni = 1) dominates in
heavily doped ZnO:HCl with a low compensation degree, r is close to 1 in a wide range of temperatures and doping levels.
In accordance with Eq. 15:
. (20) 2 H CB xb + r xb + σ R = μ 1
For wide range of ND, NA and∆ED, b<<1; xb = 1 at T = THmaxand xb << 1 at higher temperatures (Section 3.4.2).
As a consequence, µCB ≈ 2⋅RHσ/r at T = THmax, and µCB → RHσ/r for higher temperatures. The example of
experimental µCB(T) and µCB(T) calculated with this correction, is shown in Fig. 8(b). The concentration of
donors and acceptors used in Eqs. 18 and 19 have been obtained from the fitting of RH(T) dependence (Section
3.4.2). A satisfactory accordance between the calculated result and the experimental data cannot be obtained for ZnO:HCl, at any doping level (Fig. 8(b), curve 1) with the use of Erginsoy model for ni scattering (the most important scattering channel): Ani factor = 1 (Table 2, [45]). The model of Meyer and Bartoly, considering the
discrepancy of calculated curve, based on Meyer and Bartoly model, is significantly higher (Fig. 8(b), curve 2). The best result has been obtained by assuming that Ani ≤ 1 and has considerable temperature dependence (Fig.
8(b), curve 3 and inset). Ani decreases with the decrease of temperature and with the increase of doping level. It
is noteworthy, that efficiency of ni scattering (value of Ani factor) is controversial, according to many reports.
For example, Ani ≈ 3 was observed for hydrothermal ZnO crystals. Such value has been attributed to deep donors
which do not influence the RH [18].
4. Discussion
In accordance with Fig. 7(a), the estimation of the activation energy of impurity for 75−300 K range can be essentially erroneous for heavily doped samples, because of the effects related to the IB conduction. At the increase of doping level, the shift of the maximum of RH(T) dependence to higher temperatures takes place,
decreasing the effective activation energy (the slope of ln(1/qRH) vs (1/T) dependence). 80−90% of this
dependence is caused by this effect. Considering conductivity of IB, the corrected dependence of the activation energy on the doping level for shallow donors in ZnO:HCl crystals can be proposed as follows: ∆ED =
29−6⋅10−6N
ii1/3(cm−1) meV. Smaller values of the activation energy of the isolated donors (∆EDo = 29 meV) and
d(∆ED)/dND are in a better accordance with PL results, in contrast with the predictions of the model of one
conductive band (Section 3.2, 3.4.1, 3.4.2).
At the same time, there are two important discrepancies of the obtained results with the theory: (i) the features of near-IR absorption spectra (Section 3.3), and (ii) the low efficiency of ni scattering (Section 3.4.3). At high doping levels, the sublattice of neutral donors can cause appearance of upper Hubbard IB, with the activation energy of about 0.1∆ED. The states of this shallow upper IB are usually more extended than those of
the lower IB. The electrons participating in total conductivity use empty states in CB, in the usually referred lower IB (the band of neutral donors) and in the upper IB (negatively charged donors with an extra electron, the so called D− states), which can partially overlap with the bottom of the CB. The model of upper IB has been
investigated for classical semiconductors [36, 37]. Perhaps high temperature conductivity of ZnO:HCl (T > THmax) is caused by charge carriers in both the CB and the upper IB. The mobility of charge carriers in upper IB
is not limited by ni scattering. As a consequence, the total efficiency of this scattering channel depends on distribution of electrons between CB and upper Hubbard IB. At relatively low temperatures, close to THmax, the
concentration of charge carriers in upper impurity band dominates; Ani factor is close to 0 (Fig. 8(b), inset). At
Experimental αIR has square-law dependence on nCB (Fig. 3(c)), but it is proportional to ND−NA and
concentration of electrons on donor levels in a wide spectral range. The experimentally observed δ = 3.5 (Section 3.3, Eq. 1) is more appropriate for electrons of IB, for a wide temperature range, including room temperature. Thus, it can be suggested, that the observed near-IR absorption is related to charge carriers of upper IB, overlapping with the CB bottom. This sets the background for further investigation of D− impurity
band in ZnO.
5. Conclusions
The characteristics of ZnO:HCl crystals basically depend on the centers caused by the chlorine impurities, which are stable against any post-growth treatments. Investigation of the transmittance spectra, of the photoluminescence and of the electrical properties shows the presence of shallow Cl donors with controversial value of the activation energy. Deeper donor complexes, incorporating several Cl atoms or stable H−Cl pairs, have the activation energy of 121±10 meV, and the compensating deep acceptors, attributed to VZnClO centers,
have the activation energy of 600±50 meV.
The presence of a shallow donor impurity band with a low compensation degree (≤7 %), as well as the strong dependence of its activation energy on the doping level is demonstrated. The controversy of various models for estimation of this dependence is shown. It is calculated, that the thickening of the impurity band at the increase of impurity concentration is very weak and cannot account for the observed decrease of activation energy. The effect of impurity band conduction is studied. It is demonstrated that 80−90% of the observed dependence of the effective activation energy on impurity concentration is caused by temperature dependence of Hall coefficient corresponding to conductance via the impurity band. A better formula for the activation energy is suggested as ∆ED = 29−6⋅10−6(2NA+nCB)1/3(cm−1) meV.
An abnormally low efficiency of neutral impurity scattering of charge carriers and strong optical absorption in the near-IR spectral range, which cannot be attributed to free electrons in conductance band, are observed in heavily doped ZnO:HCl crystals. For explication of these effects, the model of upper high-conductance impurity band of negatively charged donors has been discussed.
Acknowledgements
This work was supported by the Supreme Council for Science and Technological Development of the Academy of Sciences of Moldova under the project No. 15.817.02.34A.
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Figure captions
Fig.1. The normalized near-edge PL spectra of ZnO crystals grown with HClo = 2 atm. (a) The influence of
excitation level (%) on the spectrum of sample annealed in air; (b) the deconvolution of spectrum of the same sample; (c) the influence of annealing in various media at excitation level of 17 %. T = 110 K.
Fig.2. Transmission spectra for the visible spectral range of ZnO crystals grown at HClo (2 atm) + H
2 (2 atm)
and annealed in air at various temperatures (°C) (a). The dotted line shows the spectrum of crystal grown at HClo (0.7 atm) + H
2 (0.7 atm) and annealed at 1080 °C. The edge optical absorption spectrum of sample
Fig.3. Near−IR transmission spectra of ZnO crystals annealed in air (1060 °C) with indicated free electron
concentration (1018 cm−3) (a). The near−IR optical absorption coefficient vs wavelength (b). Values of
αIR(1.5µm) vs free electron concentration (c). T = 300 K.
Fig.4. The influence of HClo pressure in the growth medium on n
CB and ND−NA for ZnO crystals grown with the
use of pure HCl (a). The influence of O2 pressure in annealing medium on free electron concentration (b). T =
300 K.
Fig.5. Temperature dependence of conductivity (a), of 1/qRH (b) and Hall mobility (c) for ZnO crystals after
annealing in air, with indicated concentrations of non−compensated donors (1018 cm−3).
Fig.6. Dependence of donor concentration (ND), activation energy of donors (∆ED) and activation energy of
isolated donors (∆EDo)on the concentration of non−compensated donors. A range of possible fitting values is
shown for each parameter. White circles show ∆EDo for β = 5·10−5 meV⋅cm, N = ND. Gray circles show ∆EDo for
β = 4·10−5 meV⋅cm, N = N
ii. Underlined symbols correspond to a case when compensation degree is equal to 0.
Fig.7. Temperature dependence of calculated electron concentrations in the CB and IB and 1/qRH values for
sample with ND = 3⋅1018 cm−3 (dotted lines) and ND = 17⋅1018 cm−3 (solid lines) (a). Temperature dependence of
Hall mobilities for samples with indicated ND (1018 cm−3).
Fig.8. The experimental temperature dependence of RH (a) and mobility in CB (b). Open symbols for µ(T)
correspond to corrected data. Solid lines show fitting curves obtained using various models. ND = 3⋅1018 cm−3.
Part (b) illustrates the components of optimal fitting mobility, related to ni, ii and intrinsic-phonon (int ≡ po+pe+dp) scattering channels. Inset illustrates Ani(T) dependence.
Table 1. The influence of TA composition on the free electron concentration (300 K, 1018 cm−3) and on the
pressure of the main gaseous species of CVT systems. All pressures are expressed in atm.
Table 2. For the calculation of mobility associated with various scattering mechanism in ZnO (cm2/Vs)
a) µi0 depend on: the relative electron polaron mass (m=m*/me), the static (ε0) and high-frequancy (ε∞) dielectric
constants, the effective polar-optical phonon temperature (Tpo (K)), the deformation potential (E1 (J)), the
piezoelectric coefficient (P⊥) and the longitudinal elastic constant (cL (Pa)) [18, 43]; the second line is for
ZnO
c) χ = 0.1(Tpo/T)2 + 0.8(Tpo/T) + 0.1 (1.2 ≤ Tpo/T ≤ 5), χ = (Tpo/T)1/2−0.8 (2.5 ≤ Tpo/T ≤ 5) [44]; for Tpo/T>5,
f(T)po = (eTpo/T−1)⋅(kTpo)1/2 [43]
d) y = 1.29⋅1014mε
0T2/nCB [43, 44]; for ZnO: y = 2.92⋅1014T2/nCB
e) for n-type materials; if donors and acceptors can be only single ionized; concentration of donors (ND),
acceptors (NA) and charge carriers (nCB) must be expressed in cm−3 [18, 43]
HClo = 2 HCl o = 2 H2 o = 2 HClo = 2 Co = 1 nCB 3.1 1.6 1.0 ZnCl2 0.87 0.87 0.94 H2O 0.89 1.01 0.17 HCl 0.24 0.25 0.11 Zn 2⋅10−6 0.14 0.34
dp ni po pe ii 1 2 / 5 2 1 42 10 8.15 − − ⋅ L c m E 1 0 22 10 1.44 ε m− ⋅ ) ε (ε m Tpo 3/2 1 01 25.4 − − ∞ − 1 0 2 / 3 2 25.4 − ε m P 2 0 2 / 1 15 10 3.29 − ⋅ ε m µ0 a 1.12⋅10−42 8.80⋅104 3.38⋅10−2 1.17⋅10−23 2.65⋅1035 f(T) − Ani−1b χ(e ) c T Tpo/ 1 − − (ln(1+y)−y/(1+y))−1d N e − N D−NA−nCB − − 2NA+nCB p −1.5 0 0.5 (0 f) − 0.5 1.5 X 0.59 1 1.60 (1 f) 1.60 3.53−3.2/lny
