Invited paper Review of defect investigations by means of positron ...

Appl. Phys. A 66, 599–614 (1998) 

Invited paper 

Review of defect investigations by means of positron annihilation 

in II −VI compound semiconductors 

R. Krause-Rehberg, H.S. Leipner, T. Abgarjan, A. Polity 

Fachbereich Physik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle, Germany 

(Fax: +49-345/5527160, E-mail: krause@physik.uni-halle.de) 

Received: 19 November 1997/Accepted: 20 November 1997 

Abstract. An overview is given on positron annihilation studies 

of vacancy-type defects in Cd-andZn-related II −VI compound 

semiconductors. The most noticeable results among 

the positron investigations have been obtained by the study 

of the indium- or chlorine-related A centers in as-grown cadmium 

telluride and by the study of the defect chemistry of 

the mercury vacancy in Hg1−xCdxTe after post-growth annealing. 

The experiments on defect generation and annihilation 

after low-temperature electron irradiation of II −VI compounds 

are also reviewed. The characteristic positron lifetimes 

are given for cation and anion vacancies. 

PACS: 61.70; 78.70B 

II −VI compound semiconductors are considered for applications 

in fast-particle detectors and can cover the whole 

wavelength range from the far infrared to the near ultraviolet 

in optoelectronic devices. The width of the band gap can be 

adjusted in pseudo-ternary compounds such as Hg1−xCdxTe 

by varying the composition x. TheII −VI semiconductors 

appeared promising for emitter or detector devices because 

of their excellent optical features together with the predicted 

favorable transport properties. However, no technological 

breakthrough has been achieved. This is mainly because 

no II −VI compound, except CdTe, can be amphoterically 

doped. Bulk crystals of ZnSe, CdSe, ZnS, andCdS are 

always n-type, independent of impurities [1]. ZnTe appears 

only as p-type [2]. A number of theoretical approaches for 

this behavior exists but no final experimental proofs for these 

theories have been given. The reason for the compensation 

could be the existence of extrinsic defects introduced during 

crystal growth. However, intrinsic defects or complexes of intrinsic 

defects with dopants have also been discussed. 

The research on II −VI compounds was greatly stimulated 

by the growth of nitrogen-doped, p-type ZnSe layers by molecular 

beam epitaxy (MBE) [3, 4]. p–n junctions were made, 

and first ZnSe-based blue lasers could be fabricated [5, 6]. 

Nevertheless, the doping behavior of nitrogen-doped ZnSe 

layers is also not fully understood. It is not clear why only 

Applied Physics A 

Materials 

Science & Processing 

© Springer-Verlag 1998 

the nitrogen doping during MBE works for p-type conductivity 

and why other epitaxial growth techniques provide hole 

densities of one order of magnitude lower [7]. 

Obviously, the understanding of point defects in II −VI 

semiconductors is far from being complete. Vacancy-type 

defects, for example monovacancies and complexes containing 

a vacancy, play an important role. A prominent defect 

in doped CdTe is the A center, identified by electron paramagnetic 

resonance measurements as a cadmium vacancy 

paired off with a dopant atom at the nearest neighbor site [8]. 

The dominant defect in Hg1−xCdxTe is the mercury monovacancy, 

acting as an acceptor. A high concentration of VHg 

may be the reason for the p-conductivity. These examples 

show the importance of experimental tools for the detection 

of vacancy-type defects. Such a method is positron annihilation, 

which was successfully applied for the investigation of 

the structure and the concentration of such defects in elemental 

and compound semiconductors [9–11]. Significant contributions 

have been made by positron annihilation to revealing 

the structure of such important defects in III −V compounds 

as the EL2 defect and the DX center [12–14]. 

The aim in this paper is to review available experimental 

data on defect studies in II −VI compounds by positron 

annihilation. The paper is organized as follows. The relevant 

methods of positron annihilation spectroscopy and theoretical 

calculations of the positron lifetime in II −VI compounds are 

introduced in Sect. 1. The experimental results on cadmium 

mercury telluride, cadmium telluride, and zinc-related II −VI 

compounds are reviewed in Sect. 2. Section 3 summarizes 

positron data on irradiation-induced defects. 

1 Basics of positron annihilation in semiconductors 

1.1 Positron lifetime and Doppler-broadening spectroscopy 

The detection of defects by means of positron annihilation is 

based on the capture of positrons. Comprehensive treatments 

of positron annihilation in solids can be found elsewhere [15– 

18]. Attractive potentials for positrons exist for open-volume 

defects, e.g. vacancies, and for negatively charged non-open

600 

volume defects, e.g. acceptor-type impurities. The potential 

is based in the latter case only on the Coulomb attraction between 

the positron and the negative defect [19]. The main 

reason for the binding of positrons to an open-volume defect 

is the lack of the repulsive force of the nucleus. Additional 

Coulombic contributions, which enhance or inhibit the trapping 

owing to a negative or a positive charge, respectively, 

occur for charged vacancies [18]. 

The positrons in a typical conventional positron experiment 

are generated in an isotope source. They penetrate the 

sample, thermalize and diffuse. They can be trapped in defects 

during diffusion over a mean distance of about 100 nm. 

This may result in characteristic changes of annihilation parameters. 

The positron lifetime for open-volume defects is 

increased in relation to the undisturbed bulk. This is due to 

the reduced electron densities in these defects. The clustering 

of vacancies in larger agglomerates can be observed as an increase 

in the defect-related positron lifetime. The lifetime of 

a positron is monitored in positron lifetime spectroscopy (PO- 

LIS) as the time difference between the birth of the particle 

in the radioactive source, indicated by the almost simultaneous 

emission of a 1.27-MeV γ quantum, and the annihilation 

in the sample, resulting in γ rays with an annihilation energy 

of 0.511 MeV. The lifetime spectrum is formed by the collection 

of several million annihilation events. In general, the 

spectrum consists of several exponential decay components, 

which can be numerically separated (see Sect. 1.3). 

Doppler-broadening spectroscopy (DOBS), as another 

positron technique, utilizes the conservation of momentum 

during annihilation. The total momentum of the positron 

and the electron is practically equal to the momentum of 

the annihilating electron. This momentum is transferred to 

the annihilation γ quanta. The momentum component in the 

propagation direction, pz, results in a Doppler shift of the annihilation 

energy of ∆E = pzc/2 (where c is the speed of 

light). The accumulation of several million events for a whole 

Doppler spectrum in an energy-dispersive system leads to 

the registration of a Doppler-broadened line, which is caused 

by the contributions of electron momentums in all space directions. 

The distribution of electron momentums may be 

different close to defects, and this is reflected in characteristic 

changes of the shape of the annihilation line. Annihilations 

with core electrons having higher momentums are reduced, 

for example, for a vacancy, and thus the annihilation line becomes 

narrower. The annihilation line is usually specified by 

shape parameters, such as the S parameter, which is defined as 

the area of a fixed central region of the Doppler peak normalized 

to the whole area under the peak, i.e. to the total number 

of annihilation events. Another parameter is the W parameter, 

defined in the wing parts of the annihilation line. This parameter 

is determined mainly by the annihilations of the positrons 

with core electrons. The W parameter is thus more sensitive 

to the chemical nature of the surrounding of the annihilation 

site. A plot of the W parameter versus the S parameter may be 

used for the identification of defect types [20, 21]. The slope 

of the line corresponds to the R parameter, which is characteristic 

for a certain defect type, independent of the defect 

concentration. If the pairs of (S, W) values plotted for different 

sample conditions lie on a straight line running through 

the bulk values (Sb, Wb), one has to conclude that one single 

defect type having different concentrations dominates the 

positron trapping. 

Positrons from an isotope source have a broad energy distribution 

of up to several hundred keV. This leads to a mean 

penetration depth of some 10 µm, and thin epitaxial layers 

cannot be studied. Therefore, the slow positron beam technique 

[22] was developed. It is based on the moderation of 

positrons, i.e. the generation of monoenergetic positrons with 

energies in the eV range. The energy of the positron beam can 

be adjusted in an accelerator stage. This allows the registration 

of annihilation parameters as a function of the penetration 

depth. Hence, depth profiling is possible with a variable 

information depth of up to a few µm. The basics of the defect 

profiling by slow positrons in comparison with other methods 

was presented by Dupasquier and Ottaviani [23]. 

A main result of the positron experiments is the positron 

trapping rate κ, which is proportional to the defect concentration 

C, 

κ = µC . (1) 

The proportionality constant µ is the trapping coefficient 

(specific trapping rate), which must be determined in correlation 

to an independent reference method. The determination 

of the trapping coefficient for semiconductors has been reviewed 

by Krause-Rehberg and Leipner [24]. Equation (1) 

holds strictly only in the case of a rate-limited transition of 

the positron from the delocalized bulk state into the deep 

bound state of the defect [18]. This case describes well the 

positron trapping in vacancies. The trapping coefficient for 

small vacancy clusters (n ≤ 5) increases with the number of 

incorporated vacancies n, 

µn = nµv , (2) 

where µv is the trapping coefficient of monovacancies [25]. 

1.2 Temperature dependence of positron trapping in charged 

defects 

The trapping coefficient µ in (1) is always a specific constant 

for a given temperature. The attractive potential is superimposed 

by a long-range Coulomb potential in the case 

of a charged defect. A positive charge causes a strong repulsion 

of the positron, and trapping is practically impossible. In 

contrast, a negative charge promotes positron trapping compared 

to a neutral defect by the formation of a series of 

attractive shallow Rydberg states [26]. The positron binding 

energy to the shallow Rydberg states is of the order of 

some 10 meV and, therefore, the enhancement of positron 

trapping is especially effective at low temperatures, where the 

positron may not escape by thermal activation. Thus, a distinct 

temperature-dependent trapping rate was obtained for 

negatively charged vacancies in Si [27] and in GaAs [28]. 

A detailed description of the temperature dependence of 

positron trapping in negatively charged vacancies was given 

by Le Berre et al. [28]. 

Non-open volume defects, such as acceptor-type impurities 

or negatively charged antisite defects, may also act as 

positron traps provided that they carry a negative charge. The 

extended shallow Rydberg states are exclusively responsible 

for positron trapping. The binding energy of the positron is 

small and therefore these defects are called shallow positron 

traps. The positron–position probability density at the defect

nucleus is vanishingly small because of the repulsion from 

the positive nucleus. Therefore, the positron is located and 

annihilates in the bulk surrounding the defect. The electron 

density felt by the positron equals the density in the bulk 

and hence the positron lifetime of the shallow trap is close 

to the bulk lifetime. Positron trapping to these shallow traps 

is important at low temperatures in practically all compound 

semiconductors. Manninen and Nieminen [29] calculated the 

temperature dependence of the positron detrapping rate δ: 

δ = κ 

� 

mkBT 

C 2πh2 �3/2 � 

exp − Eb 

� 

. (3) 

kBT 

Here, κ and C are the trapping rate and the concentration of 

the shallow positron traps. m is the effective positron mass, kB 

the Boltzmann constant, and Eb the positron binding energy. 

The description of the trapping in charged defects shows 

that in the presence of several charged defect types in the material 

the temperature dependence of positron trapping may 

be rather complex and a quantitative evaluation of the annihilation 

parameters as a function of the temperature T is often 

not possible. 

1.3 Trapping model 

A phenomenological description of positron trapping was 

given by Berlotaccini and Dupasquier [30] and was later generalized 

[31, 32]. The model is referred to as the “trapping 

model”. The aim is the quantitative analysis of lifetime spectra 

in order to calculate the trapping rates and the corresponding 

defect concentrations. Only one extended model that is 

sufficient for the interpretation of the experimental results is 

discussed in this paper. This model (Fig. 1) includes two different 

types of non-interacting open-volume defects and one 

shallow positron trap exhibiting thermal detrapping with the 

detrapping rate δ. The corresponding differential equations 

are 

dnb(t) 

dt =−(λb+κd1 + κd2 + κd3) nb(t) + δnd1(t), 

dnd1(t) 

dt =−(λd1 + δ) nd1(t) + κd1nb(t), 

dnd2(t) 

dt =−λd2nd2(t) + κd2nb(t), 

dnd3(t) 

dt =−λd3nd3(t) + κd3nb(t). (4) 

Defect d1 is the shallow positron trap, and d2 and d3 are 

open-volume defects, such as vacancies and vacancy agglomerates. 

b denotes the bulk state. The ni are the normalized 

numbers of positrons in the state i (i = b, d1, d2, d3) at the 

time t,andλiare the corresponding annihilation rates (inverse 

positron lifetimes). The starting conditions are nb(0) = 1and 

nd1(0) = nd2(0) = nd3(0) = 0. The solution of (4) is a sum 

of four exponential decay terms, the prefactors of which are 

the intensities I1 to I4. The lifetimes τ1 to τ4 are found in the 

exponents. The lifetimes and intensities are obtained as 

τ1 = 2 

Λ + Ξ , τ2 = 2 

Λ−Ξ , 

τ3 = 1 

, τ4 = 1 

, 

λd2 

λd3 

� b 

� d1 

Positron source 

Defect–free bulk 

Defect d1 Defect d2 Defect d3 

� d1 

� 

� d2 

� d2 

Annihilation radiation 

� d3 

� d3 

601 

Thermalization 

Trapping and 

detrapping 

Annihilation 

Fig. 1. Scheme of a trapping model including two types of open-volume 

defects, d2 and d3, and one shallow positron trap, d1. The latter exhibits 

thermally induced detrapping with the temperature-dependent detrapping 

rate δ. The individual trapping rates κd1, κd2, andκd3 and the corresponding 

annihilation rates λd1, λd2, andλd3 are drawn as arrows. λb is the bulk 

annihilation rate 

I1 = 1 − (I2 + I3 + I4), 

I2 = δ+λd1 − 1 

2 (Λ − Ξ) 

I3 = 

I4 = 

� 

× 

+ 

1 + 

� λd2 − 1 

� λd3 − 1 

Ξ 

κd1 

δ + λd1 − 1 

2 

κd3 

λd3 − 1 

2 

κd2 

+ 

(Λ − Ξ) λd2 − 1(Λ 

− Ξ) 

� 

2 

, 

(Λ − Ξ) 

κd2(δ + λd1 − λd2) 

2 (Λ + Ξ)��λd2 − 1 , 

(Λ − Ξ)� 2 

κd3(δ + λd1 − λd3) 

2 (Λ + Ξ)��λd3 − 1 . (5) 

2 (Λ − Ξ)� 

The abbreviations in (5) are 

Λ = λb + κd1 + κd2 + κd3 + λd1 + δ, 

Ξ = � (λb + κd1 + κd2 + κd3 − λd1 − δ) 2 + 4δκd1 . (6) 

The two long-lived lifetimes are equal to the defectrelated 

lifetimes: τ3 = τd2 and τ4 = τd3, and they are independent 

of the defect concentrations. The average positron 

lifetime τ for this model is given by 

τ = 

4� 

Ijτj . (7) 

j=1 

The result (5) represents the components of the lifetime spectrum. 

The experimental spectrum may be decomposed in such 

components, and the lifetimes and their intensities can be 

used to determine the corresponding trapping and detrapping 

rates. Equation (1) then provides the defect concentrations. 

Cases where the number of independent defects is smaller 

than three can easily be obtained from (5) by setting the corresponding 

trapping rates to zero.

602 

1.4 Theoretical calculation of positron lifetimes 

The positron lifetimes in the bulk and in lattice defects 

of II −VI compounds were first theoretically calculated by 

Puska [33] who used the linear muffin-tin orbital bandstructure 

method within the atomic sphere approximation. 

Monovacancies were treated in different charge states by the 

corresponding Green’s function method. More recent calculations 

from the same group [34, 35] used the superimposedatom 

model [36]. A supercell approach with periodic boundary 

conditions for the positron wave function retaining the 

three-dimensional character of the crystal was employed. The 

electron–positron correlation potential was treated with the 

local-density approximation (LDA) [37]. The results of pure 

LDA calculations provided lifetimes, which were too low 

compared to experimental values. The calculation method 

was hence modified in such a way that the d-electron enhancement 

factors for Zn, Cd, andHg were scaled to provide 

the correct lifetimes for the pure metals [34, 35]. Another approach 

used the enhancement factors for d electrons in Ag 

and Au [38]. Calculations of positron lifetimes of vacancies 

were carried out with unscaled LDA [34, 35], providing 

values that are obviously too small compared to the bulk lifetimes 

of the scaled LDA calculations. In order to compare the 

theoretical defect-related lifetimes to the experimental ones 

and to the bulk lifetimes (Table 1), the vacancy lifetimes given 

by Plazaola et al. [34, 35] were multiplied by the ratio of the 

bulk lifetimes calculated for the pure and scaled LDA, respectively. 

No relaxation effects and Jahn-Teller distortions were 

taken into account in these computations. 

Although the positron lifetimes for almost all II −VI compound 

semiconductors have been calculated, only materials 

for which experimental data exist are included in Table 1. The 

calculated bulk lifetimes agree reasonably well with the experimental 

values. However, the lifetimes calculated for the 

vacancies are always distinctly smaller than the measured 

ones. 

2 Characterization of defects in as-grown II – IV 

compounds 

2.1 Cadmium telluride 

Cadmium telluride can be amphoterically doped. However, 

the doping and compensation behavior are still not completely 

understood. Important defects for the understanding 

of the compensation are the impurity-vacancy complexes 

called “A centers” [39]. These centers consist of a group-II 

vacancy paired off with either a group-VII donor (F, Cl, 

Br, I) ontheTe site, or with a group-III donor (e.g. Ga, 

In) theCd site [40]. The ionization level of the Cl-related 

A center, (VCdClTe) −/0 , was determined by photoluminescence 

measurements to be located at 150 meV above the valence 

band [41]. The levels for the isolated monovacancies 

were also investigated experimentally. The 2−/− level of the 

Cd vacancy was found with electron paramagnetic resonance 

at Ed − Ev < 470 meV [42] and the 0/+ level of the Te vacancy 

(F center) at Ed − Ev < 200 meV (Ed defect ionization 

level, Ev position of the top of the valence band) [43]. 

2.1.1 The A center. Weakly In-doped cadmium telluride 

was studied by positron lifetime spectroscopy as a function 

of the temperature [44–46]. Distinct positron trapping 

in a monovacancy-type defect was found. The defect-related 

lifetime was given first as 330± 5ps[44], but was corrected 

later to 320± 5ps[45, 46]. The lifetime was interpreted to be 

either due to isolated Cd monovacancies in a double negative 

charge state or due to (VCdInCd) − complexes. The average 

positron lifetime exhibited a distinct decrease with decreasing 

temperature, which was attributed to the presence of shallow 

positron traps, i.e. negatively charged non-open volume 

defects. 

The compensation mechanism in iodine-doped CdTe layers 

grown by MBE was investigated by photoluminescence 

(PL), conductivity measurements, and Doppler-broadening 

Table 1. Calculated and experimental positron lifetimes for II −VI semiconductors. The bulk lifetimes were calculated using a modified semi-empirical local 

density approximation (LDA) [34, 35]. The LDA lifetimes for the vacancies given by Plazaola et al. [34, 35] are scaled by a factor to allow a more realistic 

comparison to the experiments (see text). The experimental values of the cation vacancies (vacancies of group II atoms) are related to the A centers in Inor 

Cl-doped CdTe, to the mercury vacancies in Hg1−xCdxTe, and to the Zn vacancies as part of complexes in Zn-related compounds, respectively. The only 

experimental value for anion vacancies (vacancies of group VI atoms) is that of the tellurium vacancy in Hg1−xCdxTe 

Material Bulk lifetime /ps Cation-vacancy lifetime /ps Anion-vacancy lifetime /ps 

Calculated Experimental Calculated Experimental Calculated Experimental 

CdTe 286 291 [104] 298 320 ± 5 [45, 46] 312 – 

281 [68] 330 ± 15 [44, 52, 68] 

283 ± 1 [44] 

285 ± 1 [45, 46] 

280 ± 1 [52] 

HgTe 274 274 [68] 285 – 300 – 

Hg0.8Cd0.2Te – 274 [68] – 309 [69] – 325 ± 5 [93] 

286 [69] 305 [54, 70] 

275 [54] 319 [97] 

278 [70] 

282 [97] 

ZnO – 169 ± 2 [88] – 255 ± 16 [86, 87] – – 

183 ± 4 [86, 87] 211 ± 6 [102] 

ZnS 225 230 [78, 80] 240 290 [80] 237 – 

ZnSe 240 240 [79] 253 – 260 – 

ZnTe 260 266 [78] 266 – 297 –

spectroscopy [47]. The DOBS S parameter increased distinctly 

with increasing iodine concentration, i.e. with the 

free-electron concentration. The iodine doping obviously 

induced vacancy-type defects. This result is in agreement 

with the proposed microscopic structure of the iodine-related 

A center [40]. 

Kauppinen and Baroux [48] investigated CdTe crystals 

doped with In or Cl with positron lifetime and Dopplerbroadening 

spectroscopy. The Doppler measurements were 

carried out in a background-reducing coincidence setup [49, 

50]. Vacancy-type defects were found in all samples. Defectrelated 

lifetimes of 323 and 370 ps were separated in CdTe:In 

and in CdTe:Cl, respectively. The indium- or chlorine-related 

A centers were assumed to be the positron traps responsible. 

This interpretation was supported by the Doppler measurements 

in the high-momentum range of the spectrum, where 

the annihilation with core electrons dominates. It was concluded 

that the annihilation takes place in the cadmium vacancy 

that is part of the A center. The distinct difference in 

the positron lifetime for In- andCl-related A centers was 

ascribed to different open volumes. A stronger outward lattice 

relaxation was assumed for VCdClTe. However, the observed 

longer lifetime may also be interpreted by the occurrence 

of an additional defect with larger open volume (see 

discussion of Fig. 3). 

In contrast to In doping, chlorine impurities lead to highresistance 

CdTe material. A series of CdTe samples containing 

chlorine in a concentration range from 100 to 3000 ppm 

was studied by positron lifetime measurements [51, 52]. The 

average positron lifetime measured as a function of the sample 

temperature is shown in Fig. 2. The reference sample 

exhibited a single-component spectrum with a temperatureindependent 

lifetime of 280 ± 1psthat was attributed to the 

bulk lifetime. The average lifetime increased strongly with in- 

Average lifetime [ps] 

380 

360 

340 

320 

300 

280 

300 ppm 

3000 ppm 

2000 ppm 

1000 ppm 

100 ppm 

Reference 

0 100 200 300 

Sample temperature [K] 

Fig. 2. Average positron lifetime as a function of the sample temperature 

measured in cadmium telluride with a chlorine content in a range from 100 

to 3000 ppm [52]. A nominally undoped sample is included for reference. 

The full lines are fits according to the trapping model of Fig. 1 and (5) 

Lifetime [ps] 

500 

300 

�1 

Trapping rate [s ] 

1 0 

10 

10 9 

� d2 

� d3 

603 

100 () a ( b) 

100 1000 

Cl content [ppm] 

100 1000 

Cl content [ppm] 

Fig. 3a,b. Decomposition of the positron lifetime spectra measured in 

chlorine-doped cadmium telluride at room temperature as a function of the 

chlorine content [52]. a Positron lifetime components. The two long-lived 

lifetimes ( and ◦) represent the lifetimes τd2 and τd3 related to two defects 

with different open volumes. The shortest lifetime (M) is the reduced 

positron bulk lifetime τ1, which corresponds reasonably to the lifetime (full 

line) calculated from a trapping model with two open-volume defects (obtained 

from (5) by setting κd1 = 0). b Trapping rates of the defects d2 

(A center) and d3 calculated from the decomposition of the spectra. The 

dashed lines in a and b are drawn to guide the eye 

creasing Cl content, showing that open-volume defects, probably 

in a complex with chlorine, were present. It should be 

noted that the observed change of 100 ps in τ at T ≥ 250 K is 

exceptionally large, indicating that the defect-related positron 

lifetime must be high. The open volume of the defects should 

thus be distinctly larger than that of a monovacancy. 

The lifetime spectra were decomposed at first into two 

components yielding a defect-related positron lifetime of 350 

to 395 ps, which increased with increasing Cl content [51]. 

These results correspond well to the characteristic lifetime 

of 370 ps found in CdTe:Cl by Kauppinen and Baroux [48]. 

However, the variance of the fit in the experiments by Polity 

et al. [51] was rather poor, indicating the presence of another 

unresolved lifetime component. Indeed, repeated measurements 

with a higher figure of 2 × 10 7 annihilation events 

allowed the decomposition of three components at temperatures 

above 250 K for the same samples [52]. Two lifetimes 

with τd2 = (330 ± 10) ps and τd3 = (450 ± 15) ps were separated 

(Fig. 3a). Hence, the previously obtained defect-related 

lifetime of 370 ps must be regarded as an unresolved mixture 

of τd2 and τd3. The defect d2 represents a monovacancyrelated 

defect and is attributed to the chlorine A center, 

VCdClTe. Defect d3 obviously exhibits an open volume distinctly 

larger than that of a monovacancy. The ratio τd3/τb = 

1.6 indicates that d3 comprises at least the open volume of 

a divacancy. For comparison, this ratio equals 1.34 for the 

nearest-neighbor divacancy in CdTe according to the calculations 

of Puska [38]. In contrast to the earlier results [51], the 

reduced bulk lifetimes τ1 calculated according to a trapping 

model with two open-volume defects (solid line in Fig. 3a) 

agreed reasonably well with the measured values. This trapping 

model is obtained from (5) by setting κd1 = 0, i.e. neglecting 

the shallow traps in this temperature range. 

The trapping rates κd2 and κd3 calculated from the decomposition 

of the lifetime spectra are shown in Fig. 3b. The 

trapping rates of both open-volume defects increase with the 

Cl content, leading us to the conclusion that not only d2, but

604 

also d3, represents a complex containing Cl. The concentrations 

Cd2 and Cd3 can be estimated according to (1). When the 

Cl content is increased from 100 to 3000 ppm, the d2 (A center) 

density increases from 3 × 10 16 to 4 × 10 17 cm −3 and the 

d3 density from 1 × 10 16 to 1 × 10 17 cm −3 . Hence, the total 

chlorine content in the defects d2 and d3 amounts to less than 

2% oftheCl added during crystal growth. Trapping coefficients 

of µ = 9 × 10 14 s −1 and 1.8 × 10 15 s −1 were used for 

these estimations [52]. Samples from the same set were studied 

in correlated photoluminescence measurements. The concentration 

of the A centers was determined from the shift of 

the zero-phonon line of the 1.4-eV band, which is characteristic 

for the A center. The concentrations obtained in this way 

were within the error limits of the positron measurements. 

The temperature dependence of the average lifetime 

shown in Fig. 2 exhibits a decrease towards lower T, indicating 

the presence of shallow positron traps. The trapping 

model analysis (solid line in Fig. 2) including the temperature 

dependence (3) of the detrapping rate δ revealed that 

the concentration of the shallow traps did not depend on the 

chlorine content. The shallow traps were attributed to negatively 

charged acceptor-type impurities in agreement with 

photoluminescence results [52]. 

2.1.2 Silver diffusion experiments. The diffusion of silver in 

p-type cadmium telluride results in an increase in the degree 

of compensation as detected by photoluminescence and Hall 

effect measurements [53]. This is illustrated in the upper part 

of Fig. 4, where the hole concentration is plotted against the 

time after silver was injected by dipping the crystal into an 

AgNO3 solution. 

When the silver diffusion was carried out in p-type CdTe 

crystals, the concentration of AgCd impurities increased. 

This was indicated by the enhancement of the corresponding 

(A 0 , X) bound exciton line in the PL spectra. It was supposed 

that the interstitially diffusing silver interacts with vacancies 

according to the defect reaction 

VCd + Agi → AgCd . (8) 

In order to confirm this assumption, positron lifetime measurements 

were carried out. As the native concentration of 

vacancies was too low to be detected by positron annihilation, 

post-growth annealing at 820 ◦ C under equilibrium conditions 

in a Te atmosphere was performed in a two-zone furnace 

over a period of 6 weeks. The annealing conditions were 

chosen in such a way as to increase the concentration of Cd 

vacancies to a level of several 10 16 cm −3 . An average positron 

lifetime of 294.5pswas found after this procedure [54]. The 

increase of about 10 ps in the positron lifetime compared 

to the bulk value was attributed to these cadmium vacancies. 

A silver diffusion experiment was carried out thereafter 

under conditions comparable to those used by Zimmermann 

et al. [53]. The result is shown in the lower part of Fig. 4. 

The average positron lifetime decreased markedly during the 

diffusion experiment carried out at room temperature. This 

decrease was taken as a proof of the dominance of the defect 

reaction (8), resulting in a decrease in the VCd concentration. 

A similar experiment was performed by Grillot et al. [55] in 

CdS, where cadmium vacancies were also filled by diffusing 

silver. 

However, the time constants of the diffusion process monitored 

by the change in the hole concentration and by the 

change in τ are distinctly different (Fig. 4). Although the 

electrical measurement shows the activation of the silver interstitials 

acting as donors in the bulk CdTe, the decrease in 

the average positron lifetime reflects reaction (8). Since the 

silver diffusion should be much faster than the kinetics of (8), 

it was concluded that an additional barrier has to be overcome 

for the Ag i in order for cadmium vacancy sites to become 

occupied [54]. 

2.2 Mercury cadmium telluride 

The intermixing of the semiconductor CdTe with the semimetal 

HgTe allows the adjustment of the width of the band 

gap by variation of the composition x in Hg1−xCdxTe. 

The material with a composition of about x = 0.2 becomes 

a narrow-gap semiconductor and is of interest for infrared detector 

applications in the atmospheric transmission window 

around 10 µm. TheHg vacancy is the most important point 

defect because of its electrical activity as an acceptor and 

the high diffusivity of mercury [56, 57]. Furthermore, the Hg 

partial pressure is already rather high at low temperatures. 

The stoichiometry, i.e. the content of mercury vacancies, can 

be influenced by post-growth annealing under defined vapor 

pressure conditions [58]. 

The Hg vacancy is negatively charged and is thus an interesting 

subject for the application of positron annihilation 

techniques. The first positron experiments on Hg1−xCdxTe 

were reported by Voitsekhovskii et al. [59], Dekhtyar et 

al. [60], and Andersen et al. [61]. The positron annihilation 

results of post-growth annealing and diffusion experiments 

Average hole 

�3 

density [cm ] 

Average 

lifetime [ps] 

2�10 15 

1�10 15 

295 

290 

285 

280 

CdTe 

�8 2 

DAg =10 cm/s 

0 200 400 600 

Time [h] 

Fig. 4. Hole density determined by Hall effect measurements and average 

positron lifetime as a function of the time after silver injection into a p-type 

cadmium telluride sample. The upper part of the plot was taken from Zimmermann 

et al. [53], the lower part from Krause-Rehberg et al. [54]. The 

decrease in the hole concentration corresponds to a diffusion constant DAg 

of interstitial silver of 1 × 10 −8 cm 2 /s [53]

are reviewed in this section, whereas irradiation-induced defects 

are the subject of Sect. 3.1. 

2.2.1 Post-growth annealing under defined mercury vapor 

pressure. The native point defects were investigated by 

Hall effect measurements throughout the existence region of 

Hg1−xCdxTe for x = 0.2 and 0.4 in the solid-vapor phase diagram 

[58, 62]. It was found that the double negatively charged 

mercury vacancy is the dominant point defect in the whole 

phase field. Vydyanath [62] calculated the concentration of 

VHg, assuming a generation of free carriers by band–band 

transitions and by the ionization of the VHg acceptors, 

0 ⇆ e − + h + , HgHg ⇆ V 2− 

Hg + 2h+ + Hggas . (9) 

The corresponding equilibrium constants of these reactions 

are 

� 

Ki = np, KV 2− = V 

Hg 

2− 

� 

Hg p 2 PHg , (10) 

where n and p are the concentrations of free electrons and 

holes, respectively. PHg is the Hg partial vapor pressure. The 

neutrality condition n + 2 [V 2− 

Hg ] = p can be separated into 

two regions (for low and high temperatures corresponding to 

intrinsic and extrinsic conductivity): 

� � 

n = p, 2 = p . (11) 

V 2− 

Hg 

The combination of (10) and (11) results in a third-order 

polynomial for the hole concentration, to be measured at 77 K 

after the annealing, 

p 3 77 − K 2 i PHg 

p 

2K 2− 

VHg 2 77 + 2Ki p77 − 

2K V 2− 

Hg 

PHg 

= 0 . (12) 

The equilibrium constants in (12) were determined as functions 

of the temperature by Hall effect measurements [62]. 

The iso-concentration lines of the Hg vacancies in the vapor– 

solid phase diagram calculated according to (12) are shown in 

Fig. 5 within the existence region. 

The concentration of VHg can be adjusted by the variation 

of the sample temperature (Fig. 5) by post-growth annealing 

under a given mercury vapor pressure PHg. Suchan 

annealing experiment was carried out in a two-zone furnace 

with PHg = 10 5 Pa (corresponding to a temperature of the 

Hg reservoir of 650 K) for a series of Hg0.8Cd0.2Te samples. 

The generated Hg vacancies were studied in correlated 

positron lifetime and Hall effect measurements [63, 64]. The 

average positron lifetime increased distinctly with increasing 

Hg-vacancy density, independently determined as the carrier 

density p77 (Fig. 6). The Hg-vacancy density is related to 

p77 via (11). The Hall effect measurements showed, however, 

a compensation of the acceptors by a factor of 0.5 [65], i.e. 

p77 equals the concentration of VHg. An important result of 

the combined measurement is the determination of the trapping 

coefficient as the sensitivity constant of positron trapping 

in Hg vacancies, µ = 7 × 10 −8 cm 3 s −1 , corresponding 

to 2 × 10 15 s −1 . The latter number was calculated according 

to (1) with respect to the total number of available lattice sites 

in both sublattices [24]. The straight line in the inset of Fig. 6 

is the result of the corresponding fit. The two-component 

Hg partial pressure [Pa] 

10 6 

10 4 

10 2 

10 0 

10 18 

800 

10 17 

T [K] 

700 600 

10 16 

�3 

[V Hg]/cm 

10 15 

1 1.5 

�1 

1000/ T [K ] 

500 

Hg Cd Te 

0.8 0.2 

2.0 

605 

Fig. 5. Mercury partial vapor pressure over solid Hg0.8Cd0.2Te. The straight 

lines indicate the iso-concentration lines of the mercury vacancies calculated 

according to Vydyanath [58] as a function of the sample temperature 

within the existence region of the compound (thick line) 

decomposition of the lifetime spectra provided at first a VHgrelated 

lifetime of τd = 298 ps and a bulk lifetime of 264 ps 

[64]. These values were later corrected by Krause-Rehberg et 

al. to τd = 305 ps and τb = 275 ps [54, 66, 67]. The discrepancy 

was related to problems of the source correction, being 

more difficult for materials with high atomic numbers [54]. 

Average positron lifetime [ps] 

300 

295 

290 

285 

280 

275 

�1 

� [s ] 

n–type 

10 11 

10 10 

10 9 

10 8 

p–type 

10 16 

10 �3 

17 

p 77 [cm ] 

10 18 

1.7�10 15 

10 15 

10 16 

10 17 

�3 

Carrier concentration [cm ] 

10 18 

Fig. 6. Average positron lifetime τ in Hg0.8Cd0.2Te versus the carrier 

concentration determined by Hall effect measurements at 77 K [63, 64]. 

The hole concentration corresponds to the mercury vacancy density. The 

positron trapping rate was calculated from the components of the lifetime 

spectra. It is plotted in the inset against the free-hole density p77

606 

Positron experiments were also carried out on postgrowth-annealed 

Hg1−xCdxTe samples in correlation with 

Hall effect measurements in the Laboratoire Positons CE– 

Saclay [68–70]. Positron lifetimes similar to those given 

above for the bulk and the Hg vacancy were reported (see 

Table 1). Baroux et al. [70] studied the temperature dependence 

of the hole concentration determined by Hall effect 

measurements, and the positron lifetime as a function of the 

sample temperature. The electrical measurements showed evidence 

of two ionization levels of the mercury vacancy, viz. 

the 2 − /− level located 41 ± 9meVabove the valence band 

edge and the −/0 level at 10±1meVabove Ev. These results 

were used for the interpretation of the temperature-dependent 

positron lifetime results. A maximum in the average positron 

lifetime at about 120 K was found. The decrease in the lifetime 

above this maximum was interpreted with increasing 

detrapping from the Rydberg states, which are attributed to 

thenegativechargeoftheHg vacancy. The decrease in τ below 

100 K was related to two effects: to positron trapping in 

shallow positron traps and to the two charge-state transitions 

of the Hg vacancy. A multiple-parameter fit of the τ curve was 

carried out using the detrapping rate (3) and the temperaturedependent 

trapping rate of the negatively charged mercury 

vacancies. The positron trapping in the neutral vacancies as 

well as in the shallow traps was supposed to be temperature 

independent. The concentrations of the shallow traps and the 

Hg vacancies were determined from the fit. Additionally, the 

donor concentration could be calculated in conjunction with 

the Hall measurements. 

The temperature dependence of positron trapping in 

charged Hg vacancies had already been studied prior to 

Baroux et al. [70] in Doppler-broadening measurements by 

Smith et al. [71]. The temperature dependence of the S parameter 

was similar to the course of the average lifetime 

reported by Baroux et al. The decline in the S parameter 

at high temperatures was related to peculiarities of positron 

trapping in charged vacancies as explained above. The decrease 

in the S parameter in the low-temperature range was 

exclusively related to the change of the charge state of the 

Hg vacancies, and the occurrence of shallow positron traps 

was ignored. Ionization energies of the Hg vacancy higher 

than those of Baroux et al. were found. Furthermore, the trapping 

coefficients of the vacancies were unusually high and 

had a peculiar temperature dependence, i.e. the trapping coefficient 

was higher for neutral vacancies than for negative 

vacancies at room temperature. The contradictions can be 

resolved by taking into account the occurrence of shallow 

positron traps [70]. 

However, it should be noted that the quantitative analysis 

of the temperature dependence of the positron trapping with 

the presence of differently charged vacancies and shallow 

positron traps is not straightforward. The results of the fit are 

closely related to the temperature dependencies of the trapping 

rates. It was assumed [70] that the positron trapping rates 

of the singly and doubly charged Hg vacancies were similar to 

those of charged vacancies in Si [27] or GaAs [28]. Furthermore, 

a temperature dependence of the trapping rate of shallow 

positron traps can be expected and this was neglected. 

The mutual dependence of the fitting parameters gives 

correlation coefficients very close to one. The real errors of 

calculated concentrations are much higher than the statistical 

errors and only rough estimations of the order of magnitude 

of the concentrations may be possible. The number of fit parameters 

was eight in the work of Baroux et al. [70] and 

must be drastically reduced by data to be provided from other 

techniques in order to get reliable defect concentrations and 

ionization levels. 

A systematic study of the appearance of mercury vacancies 

within the existence region of the vapor–solid phase diagram 

of Hg1−xCdxTe was carried out for x = 0.2 and 0.3 

by Krause-Rehberg et al. [65, 67]. The VHg concentration was 

adjusted during annealing in a two-zone furnace under defined 

Hg vapor pressure. The results of the positron lifetime 

measurement are shown in Fig. 7 for x = 0.2. The obtained 

vacancy concentrations are compared to the results of Vydyanath 

[58] calculated as isotherms in the plot of the vacancy 

concentration versus the vapor pressure according to the defect 

model given above. The positron lifetime spectroscopy 

was only sensitive to the Hg vacancies, whereas the Hall effect 

data [58] detected all electrically active centers. Since 

there is a good agreement between both sets of data in Fig. 7, 

the assumptions of the model (9) are fulfilled and it has to 

be concluded that the negatively charged Hg vacancies are 

indeed the dominant point defects. 

The knowledge of the positron trapping coefficient for 

Hg vacancies in Hg1−xCdxTe (Fig. 6) allowed the determination 

of vacancy profiles in the whole crystal in the as-grown 

state [64]. A travelling-heater-grown Hg0.78Cd0.22Te ingot 

was cut into slices. The positron lifetime was measured after 

standard polishing procedures at different positions by shifting 

the positron source across the wafers. The axial position 

of the wafer is indicated as the third axis in Fig. 8. This axis 

represents the growth direction. The Hg-vacancy concentration 

was calculated according to (1). A low VHg density of 

< 5 × 10 15 cm −3 was detected near the seed at the start of the 

�3 

Vacancy density [cm ] 

10 18 

10 17 

10 16 

10 15 

10 14 

10 2 

300 °C 

Area of 

existence 

10 3 

350 °C 

400 °C 

10 4 

480 °C 

10 5 

Hg vapor pressure [Pa] 

10 6 

Fig. 7. Density of mercury vacancies in Hg0.8Cd0.2Te [67] as determined 

by positron-lifetime spectroscopy (symbols). The vacancy densities were adjusted 

within the region of existence (dotted line) of the compound during 

post-growth annealing in a two-zone furnace at the given mercury vapor 

pressure and the indicated sample temperature. The full lines are the 

isotherms calculated according to (12) from the Hall effect measurements 

of Vydyanath [58]

growth. The distinct increase in the average positron lifetime 

and the vacancy concentration for wafers cut from the end 

part of the ingot is accompanied by the increase in the hole 

density p77. Both densities are of the order of 10 17 cm −3 .The 

distribution of the Hg vacancies in the ingot was related to 

the radial and longitudinal temperature variation during the 

growth. The strong increase at the end of the ingot was attributed 

to the fast cooling of this part of the crystal after 

completion of the growth [64]. The vacancy profiles observed 

after growth across the wafer can be homogenized by postgrowth 

annealing in a Hg atmosphere. It could be shown for 

samples with a pronounced U profile (for example the wafer 

at 51 mm in Fig. 8) that the vacancy density could be adjusted 

according to (12) to any desired value between 10 15 

and 10 18 cm −3 [72]. 

2.2.2 Kinetics of mercury diffusion. The mercury diffusion in 

Hg1−xCdxTe may be studied by positron annihilation spectroscopy 

via the detection of the change of the vacancy concentration. 

Figure 9 shows the result of such an experiment 

with x = 0.2 [67]. A certain Hg-vacancy concentration was 

adjusted prior to the diffusion experiment by post-growth 

annealing according to (12). The diffusion conditions are indicated 

by the arrows a, b, and c in the right-hand panel of 

Fig. 9. The starting conditions for the pre-annealing are the 

starting points of these arrows. The sample–source sandwich 

was sealed in a closed ampoule, the other end of which contained 

the mercury reservoir to control the vapor pressure. 

The positron lifetime was measured as a function of the 

diffusion time. Each positron measurement after a certain diffusion 

time was carried out after quenching the ampoule in 

water to room temperature. The measurements could not be 

carried out at elevated temperatures as originally intended, 

because of the strong dependence of the trapping coefficient 

on the temperature [72]. This dependence was related to the 

screening of the negative charge of the Hg vacancy by free 


295 

285 

275 

298 

294 

285 

280 

275 

() a 

( b) 

() c 

0 

Annealing time [s] 

10 1 

10 2 

10 3 

10 4 

Hg partial pressure [Pa] 

10 6 

10 4 

10 2 

10 0 

607 

T [K] 

800 600 

�3 

[V Hg]/cm 

1 1.5 2.0 

�1 

1000 / T [K ] 

Fig. 9. Kinetics of mercury outdiffusion monitored in a positron lifetime 

experiment. The samples were annealed at different conditions to increase 

the mercury-vacancy concentration. The positron lifetime was measured as 

a function of the annealing time. The annealing conditions of the samples 

(a), (b), and (c) are indicated in the right panel in the existence region of 

Hg1−xCdxTe (compare Fig. 5). The full lines in the left–hand panel are calculated 

according to a model of Hg diffusion via vacancies. The dashed 

line corresponds to an extended model also taking into account Hg interstitials 

[67] 

carriers in the region of intrinsic conductivity at elevated temperatures 

[24]. 

The conditions were chosen in such a way as to realize an 

outdiffusion of Hg. Correspondingly, the positron lifetime increased 

during the isothermal (Fig. 9a,b) and isobar (Fig. 9c) 

experiments. The average positron lifetime was calculated 

using a simple diffusion model supposing mercury diffusion 

via vacancies and a non-exhausting Hg source outside the 

sample (full lines in the left panel of Fig. 9). The calculation 

took into account the positron implantation profile as well as 

the Hg diffusion profile. Obviously, the observed Hg diffusion 

10 18 

10 17 

Fig. 8. Average positron lifetime 

measured as a function of the position 

in an ingot of Hg0.78Cd0.22Te 

[64]. In addition, the variation of 

the mercury-vacancy density calculated 

according to (1) is given on 

the vertical axis. The ingot grown 

by the travelling-heater method was 

sliced into wafers, which were measured 

by placing the positron source 

at various radial positions. The wafer 

location in the ingot is indicated as 

the axial position 

b 

c 

a 

10 16 

10 15

608 

cannot be described properly by the simple vacancy model 

used. The kinetics could be better understood by also taking 

into account Hg interstitials [67]. 

2.3 Zn-related II −VI compounds 

ZnSe is one of the promising materials for blue laser diodes. 

A saturation of the conductivity is not only observed for ptype 

crystals, but also for n-type material at approximately 

1 × 10 18 cm −3 for Ga doping. MBE-grown ZnSe layers doped 

with 6 × 10 15 to 2 × 10 19 cm −3 Ga were investigated with 

positron beam measurements [73]. It was found that the Znvacancy 

concentration increased with increasing Ga content. 

Figure 10 shows the relative vacancy concentration determined 

from the S parameter of the beam experiment versus 

the Ga concentration. The vacancy concentration varies 

over more than three orders of magnitude. It has been shown 

for several semiconductors that the sensitivity of various 

positron techniques for the detection of vacancies ranges from 

about 5 × 10 15 to 10 19 cm −3 [24]. One may thus conclude 

that the relative concentrations given in Fig. 10 correspond 

to that range. Miyajima et al. suggested [73] that the observed 

Zn vacancies are bound to Ga atoms. These complexes 

act as compensating centers and may limit the carrier 

concentration. 

Defects in ZnSe layers grown by metalorganic chemical 

vapor deposition (MOCVD) on GaAs substrates were investigated 

by slow-positron beam experiments. An indication 

of a high number of open-volume defects near the surface 

and at the interface to the substrate was found by Wei et 

al. [74]. Clear differences occurred between the as-grown 

layer and layers annealed under different atmospheres. It was 

concluded that heat treatment under zinc vapor is essential 

to reduce the concentration of native defects in these ZnSe 

films. Evidence for positron trapping in zinc vacancies was 

Vacancy concentration [arb. units] 

10 2 

10 1 

10 0 

10 1 � 

10 2 � 

10 15 

10 3 � 

10 16 

10 

�3 

Ga content [cm ] 

17 

10 18 1019 20 

10 

Fig. 10. Relative vacancy concentration measured by slow-positron beam 

Doppler broadening measurements as a function of the content of gallium 

dopants in ZnSe layers grown by molecular-beam epitaxy [103] 

found in heavily n-type iodine-doped ZnSe layers grown by 

MBE, but no defects were detected in undoped MOCVD and 

MBE layers [75]. It was deduced from the S and W parameter 

measurements as functions of the positron energy that there is 

a positron drift towards the GaAs substrate. The experimental 

curves could be reproduced by a simulation including an 

electric field of 1 to 3kV/cm near the interface. 

The doping of ZnSe with oxygen resulting in semiinsulating 

material was also investigated. No effect on 

positron trapping was observed for oxygen densities lower 

than 1 × 10 18 cm −3 . The measured S parameter, however, 

decreased below the bulk value to Sd/Sb = 0.987 in ZnSe 

with an O content of 1 × 10 19 cm −3 [73]. Such a behavior is 

only observed rarely, for example for oxygen clusters in silicon 

[76]. Analogously, the decrease in the S parameter in 

ZnSe:O was related to positron trapping in oxygen clusters. 

Bulk ZnSe crystals were annealed in vacuum and under 

Se atmosphere in the experimental investigations of Terashima 

et al. [77]. The authors found, by positron lifetime 

measurements, deviations from a three-state trapping model 

and supposed that a defect having a typical lifetime below 

the bulk value exists. This interpretation was supported by S 

parameter values being slightly below Sb. It was speculated 

that the effects were due to positron trapping in Se interstitial 

clusters, but further evidence with other techniques is 

required. 

There exist only a few positron studies on ZnS crystals. 

One-component lifetime spectra were obtained in asgrown 

single crystals [78–80]. The lifetime of 230 ps was 

interpreted as the bulk lifetime in accordance with the theoretical 

calculations [34, 35]. In contrast, vacancy signals 

were detected by Doppler-broadening spectroscopy in epitaxial 

layers of ZnSxSe1−x [81]. Two distinct slopes were 

found in the (S, W) plots for two types of samples, indicating 

two different vacancy-type defects. The core annihilation 

part of the annihilation line could be used for the identification 

of the sublattice of the vacancy. The annihilation 

with core electrons characterized by the W parameter carries 

information on the chemical environment of the annihilation 

site. In this way, Zn vacancies were identified in Cldoped 

and Se vacancies in N-doped material [81]. 

The sintering of ZnS polycrystals was investigated by 

Adams et al. [80]. In addition to a monovacancy-related 

lifetime component of 290 ps, a longer lifetime of 430 ps 

attributed to voids or grain boundaries was separated. The 

sintering behavior of ZnO ceramic semiconductors was also 

the subject of positron studies. Grain boundaries were considered 

as the location for point defect generation and annihilation 

[82]. Provided that the grain size is at most a few 

micrometers in diameter, a significant fraction of positrons 

annihilates near grain boundaries and provides information 

about these defects. This fraction could be calculated by 

Monte Carlo simulation as a function of grain size, shape, 

and defect concentration within the grains [83]. 

When stressed continuously by an electric field, ZnO 

varistor ceramics exhibit a degradation in the electrical 

properties. A model for the degradation mechanism involving 

the grain boundary as a source and a sink of Zn vacancies 

was proposed by Gupta and Carlson [82]. An attempt 

was made to verify this model by Doppler-broadening spectroscopy 

[84]. ZnO with a grain size of 10 µm sintered at 

1200 ◦ C was investigated. The results of annealing experi-

Fig. 11. Doppler-broadening S parameter versus the annealing temperature 

measured in zinc oxide varistor ceramics [84]. Different cooling 

regimes were applied (air and furnace cooled, respectively). The regions 

I, II, and III are explained in the text 

ments are shown in Fig. 11. The appearance of the three 

distinct regions can be well understood in the framework 

of the supposed model [82]. The formation of Zn interstitials 

accompanied by the formation of negatively charged 

Zn vacancies near grain boundaries was anticipated in region 

I (Fig. 11). The increase in the S parameter as well as 

the increase in the photocurrent was taken as a proof of the 

occurrence of both defects. The decrease in region II was 

related to the enhanced diffusivity of oxygen and to the reaction 

of oxygen with the point defects formed in region 

I. The further increase in the S parameter beyond 800 ◦ C 

(region III) was interpreted as either the thermal decomposition 

of ZnO or the generation of Frenkel pairs. The S 

parameter was a function of the cooling rate after annealing. 

The quenched air-cooled samples exhibited a lower S parameter 

than the furnace-cooled samples (Fig. 11). This fact 

was taken as a proof that indeed point defects near grain 

boundaries were examined. 

The sintering of ZnO ceramics has also been studied 

in more recent investigations [85–87] by positron annihilation 

and cathodoluminescence. No correlation could be 

established between the defects acting as positron traps and 

luminescence centers. Doping with Mn, changing the conductivity 

from n-type to semiinsulating, did not alter the 

positron trapping significantly [85]. The change in positron 

parameters was studied as a function of the sintering time 

and temperature. A defect-related lifetime of 255 ps was 

found after the ZnO was sintered at 1200 ◦ C. It was ascribed 

to defect complexes involving Zn vacancies. The 

experimentally obtained lifetime attained the bulk lifetime 

of 183 ps after the same sintering conditions. Similarly, an 

average positron lifetime of 180 ps was given by de la Cruz 

et al. [88] for untreated, high-resistivity as-grown ZnO, in 

contrast to a bulk lifetime of 169 ps reported after thermochemical 

reduction. 

3 Irradiation-induced defects 

3.1 Cd-related II −VI compounds 

609 

An early positron annihilation study on irradiation-induced 

defects in II −VI compounds was carried out by Moser et 

al. [89]. Electron irradiation experiments were performed at 

20 K with 3-MeV electrons to a dose of 1 × 10 18 cm −2 .Anannealing 

stage in the average positron lifetime was observed 

at 130 K for undoped CdTe. It was attributed to the annihilation 

of Frenkel pairs in both sublattices. Indium doping did 

not distinctly alter this annealing behavior. The same annealing 

stage was ascribed in a paper of Geffroy et al. [68] to 

the annealing of VCd. The defect-related positron lifetime was 

given as 330 ps, which is close to the value for the cadmium 

vacancy as part of the A center [52]. 

Sen-Gupta and Moser [90] performed correlated Dopplerbroadening 

and positron lifetime measurements of undoped 

and In-doped CdTe in a temperature range from 20 to 70 K 

after electron irradiation (2.5MeV, 4×10 18 cm −2 , 20 K). 

A weak annealing stage was found at 50 K in correlation with 

PL results [91] obtained on the same specimens. 

Extended positron investigations on electron-irradiationinduced 

defects in II −VI semiconductors were carried out 

by Polity et al. [92]. The annealing curve of a p-type 

CdTe sample irradiated at 4K with 2-MeV electrons (dose 

1 × 10 18 cm −2 ) is shown in Fig. 12a. The samples were kept 

at 77 K and mounted into the cryostat without intermediate 

warm-up. The positron lifetime was measured at 90 K after 

every annealing step and at 300 K after the annealing at room 

temperature. Three distinct ranges can be separated. A pronounced 

annealing stage is observed in the temperature range 

below 130 K, similar to the results of Moser et al. [89]. The 

second range comprises the increase in the average positron 

lifetime between 130 and 170 K. The lifetime reaches the 

value measured prior to irradiation in the third range up to 

600 K. 

The correlated Hall effect measurements of the investigated 

p-type CdTe sample provided a Fermi-level position at 

EF − Ev = (215 ± 25) meV, which did not change noticeably 


300 

295 

290 

285 

280 

Measurement temperature 

90 K 

300 K 

() a 

287 

285 

283 

281 

279 

277 

Annealed at 

230 K 

330 K 

450 K 

570 K 

630 K 

Reference 

0 200 400 600 0 200 400 600 

Annealing temperature [K] Sample temperature [K] 

Fig. 12a,b. Positron-lifetime measurements of p-type cadmium telluride 

irradiated with 2-MeV electrons at 4K to a dose of 1 × 1018 cm−2 [92]. 

a Average positron lifetime versus the annealing temperature. The measurement 

temperatures were 90 and 300 K, respectively. b Average positron 

lifetime as a function of the temperature after several annealing steps 

(open symbols). The curve of a non-irradiated reference sample annealed 

at 570 K is added for comparison (closed circles) 

( b)

610 

after irradiation. The electrical measurements could be carried 

out, however, only after the room-temperature annealing 

step. Thus, the position of the Fermi level in the intermediate 

temperature range from 4 to 300 K remains unknown. There 

are two cases to be discussed. In case (i), the Fermi level stays 

above the 0/+ ionization level of the Te vacancy, i.e. positron 

trapping in the neutral Te vacancies may be expected during 

the whole annealing procedure. In case (ii), the position of the 

Fermi level is temporarily shifted below the ionization level 

of the Te vacancy and moves up as a result of defect annealing 

to the value measured at room temperature, i.e. the Te vacancies 

are not detectable in this case because of their positive 

charge. 

The three annealing ranges are discussed at first under 

the assumption of the detectability of neutral Te vacancies, 

case (i). The average lifetime measured in the as-irradiated 

stage indicates the presence of vacancy-type defects. After 

room-temperature annealing, τ reaches the value measured 

before irradiation, indicating the disappearance of both the 

Te and the Cd vacancies. This annealing also becomes apparent 

in Fig. 12b, where the average positron lifetime measured 

after several annealing steps is plotted as a function of 

the sample temperature. The curves after annealing at 570 

and 630 K practically coincide with the curve of the nonirradiated 

reference sample, also annealed at 570 K. 

The recombination of Frenkel pairs in both sublattices 

is superimposed by the distinct maximum in τ at 170 K. 

This maximum might be due to the clustering of vacancies. 

It would lead to an increase in the defect-related lifetime. 

Unfortunately, the lifetime spectra could not be reliably decomposed 

to prove this fact. Under the assumption that all 

vacancies are clustered with no loss due to annealing, the 

trapping rate should remain constant according to (2) and the 

average lifetime should increase. This case is however not 

probable, because part of the vacancies are annealing. 

Thus, it is more likely that the maximum is due to the 

annealing of shallow positron traps. The average lifetime increases 

in this case, since competitive positron traps with 

a low defect-related lifetime vanish. Such shallow positron 

traps may be irradiation-induced negatively charged intrinsic 

defects, such as interstitials or antisites. 

Case (ii), i.e. the temporary appearance of positively 

charged Te vacancies, is discussed in the following. The first 

annealing stage is, under this assumption, due to the recombination 

of Frenkel pairs in the Cd sublattice. In addition to 

the explanation of the observed maximum given for case (i), 

a further possibility must be considered now. A +/0 charge 

transition of the Te vacancies may occur as a result of the shift 

of the Fermi level during annealing up to room temperature. 

The maximum may then correspond to the fact that the Te 

vacancies become visible for positrons. 

It is useful to include the results obtained in electronirradiated 

Hg1−xCdxTe with x = 0.2, 0.3, and 0.55 [92] for 

the discussion of cases (i) and (ii). The irradiation parameters 

were identical to the treatment of the CdTe sample described 

above. Only the results of the Hg0.45Cd0.55Te sample are exemplarily 

described here (Fig. 13). The other samples showed 

a similar behavior. The course of the average positron lifetime 

during the annealing experiment is plotted in Fig. 13a. 

The first annealing stage found in CdTe is also clearly visible 

in Hg1−xCdxTe for x = 0.2, but hardly detectable for x = 0.3 

and 0.55. However, the pronounced maximum at 250 K in the 

Positron lifetime [ps] 

350 

325 

300 

275 

310 

300 

290 

280 

� 2 

Sample 

temperature 

90 K 

300 K 

�− 


310 Annealing 

temperature 

300 

290 

230 K 

330 K 

450 K 

570 K 

280 

270 

() a 

270 

( b) 

100 300 500 

Annealing temperature [K] 

100 300 500 

Sample temperature [K] 

Fig. 13a,b. Positron-lifetime measurement of Hg0.45Cd0.55Te irradiated at 

4K with 2-MeV electrons to a dose of 1 × 10 18 cm −2 [92]. a Average 

positron lifetime τ and defect-related lifetime τ2 versus the annealing 

temperature. b Average positron lifetime as a function of the sample temperature 

measured after several annealing steps 

average positron lifetime occurs similar to the case of CdTe in 

all investigated Hg1−xCdxTe samples. Our favored interpretation, 

which is also supported by the results of Kiessling et al. 

[93], is the annealing of shallow positron traps in this range. 

The appearance of the maximum is thus similar to case (i) 

discussed above for CdTe. 

A two-component decomposition of the positron lifetime 

spectra was possible below 350 K annealing temperature in 

electron-irradiated Hg1−xCdxTe [92]. The second lifetime τ2 

equals 303 ps and 317 ps below and above the 200 K annealing 

temperature, respectively. This result can be understood 

under the assumption that the annealing of shallow positron 

traps is the reason for the maximum in τ . The defect-related 

lifetime is always too small in a two-component decomposition 

in the presence of shallow traps, as shown by Monte 

Carlo simulation of positron lifetime spectra [94]. 

The defect-related lifetime observed above 200 K lies in 

between those for a vacancy in the Hg/Cd sublattice and 

for a Te vacancy. The lifetime of a Hg vacancy amounts to 

305 ps, as described in Sect. 2.2. A lifetime of 323± 5pswas 

experimentally found for the Te vacancy [93]. The Fermi 

level was found to be shifted upwards after low-temperature 

electron irradiation, and the samples were heavily n-type [95]. 

It was concluded that the Te vacancies are responsible for 

the Fermi-level pinning. In this case, vacancies in both sublattices 

are detectable. This is the main difference to the 

vacancy generation in Hg1−xCdxTe during post-growth annealing 

(see Sect. 2.2.1), where the Fermi level is determined 

by the acceptor-type Hg vacancies, and Te vacancies are positively 

charged and thus invisible for positrons. 

The results of the positron lifetime measurements performed 

as a function of temperature after certain annealing 

steps are shown in Fig. 13b [92]. No influence of shallow 

positron traps is visible in the low-temperature range after 

these annealing steps. This is in accordance with the interpretation 

of the observed maximum given above as the annealing 

of shallow traps below 200 K. On the other hand, the curves 

measured after annealing at 230 K and 330 K show the typi-

cal behavior for negatively charged vacancy-type defects with 

the steep decrease in τ with increasing temperature. This behavior 

is most likely caused by the existence of negatively 

charged Hg vacancies, since the Te vacancies are neutral. 

However, average lifetimes distinctly above the defect-related 

lifetime of the Hg vacancy were reported in another annealing 

study of electron-irradiated Hg0.78Cd0.22Te by Kiessling 

et al. [93]. A defect-related lifetime of 323 ps was observed 

and was attributed to positron trapping in Te vacancies. Combining 

the results of Polity et al. [92] and Kiessling et al. [93], 

it may be concluded that actually a mixture of Hg and Te 

vacancies is observed. 

To summarize the results obtained in low-temperature 

electron-irradiated CdTe and Hg1−xCdxTe, we can say that 

the annealing behavior is very similar. The annealing of the 

irradiation-induced vacancies in both sublattices occurs in the 

range from 100 to 400 K leading to a decrease in the average 

positron lifetime. The observed maximum between 150 

and 250 K is likely to be due to the superimposed increase of 

τ as a result of the annealing of irradiation-induced shallow 

positron traps. 

There have been only two positron studies on ion implantation 

in Cd-related II −VI compounds [96, 97]. Liszkay et 

al. [96] studied Hg0.78Cd0.22Te implanted with 320 keV Al 

ions at 100 and 300 K. The defect-related Doppler parameters 

were found to be Sd/Sb = 1.05 and Wd/Wb = 0.8. A previous 

study of Hg monovacancies in this material gave a value of 

Sd/Sb = 1.02 [98]. Hence, Liszkay et al. concluded the existence 

of implantation-induced small vacancy clusters, at least 

of the size of divacancies. The formation of vacancy agglomerates 

was also reported by Voitsekhovskii et al. [97]. The divacancy 

generation reached a saturation at room temperature 

with a density of 4 × 10 16 cm −3 at a dose of 3 × 10 12 cm −2 , 

whereas after implantation at 100 K the divacancy density exceeded 

1 × 10 18 cm −3 [96]. 

3.2 Zn-related II −VI compounds 

In practically all studies of defect formation after lowtemperature 

electron irradiation in Zn-related semiconductors, 

the Zn vacancies are supposed to be single or double 

negatively charged, whereas the anion vacancies are assumed 

to be positively charged. As a consequence, only the Zn vacancies 

are detectable by positron annihilation. 

The first positron study on Zn-related II −VI compounds 

was carried out by Moser et al. [89] for ZnTe irradiated at 

20 K with 1 × 10 18 cm −2 , 3-MeV electrons. A main annealing 

stage appeared at 500 K. 

The average positron lifetime was measured in ZnSe 

electron-irradiated at 4K(2MeV,1×10 18 cm −2 ) by Abgarjan 

[99]. The results are compared to a sample irradiated 

with 200-MeV Ne ions at room temperature to a dose of 

1 × 10 14 cm −2 (Fig. 14). A continuous increase in the average 

lifetime was found in the electron-irradiated sample up 

to 300 K. The increase was discussed as resulting from either 

vacancy clustering or the annealing of shallow positron traps 

[99]. A defect-related component of 300 to 310 ps could be 

resolved. It can be concluded from the comparison with the 

theoretical calculations (Table 1) that this component may be 

due to a divacancy or a divacancy-related complex as supposed 

by Pareja et al. [79]. The case of the annealing of 

611 

shallow traps can be excluded with these results, because 

a comparable increase in τ was found both for low and high 

sample temperatures. 

The ZnSe sample irradiated at room temperature with Ne 

ions also exhibited a slight increase in the average lifetime up 

to 450 K (Fig. 14). Because the same defect-related lifetime 

of 300 to 310 ps was resolved, and the main annealing stage 

was also observed between 500 and 700 K, it was concluded 

that the same defect types dominated the positron trapping in 

the electron-irradiated and in the Ne-irradiated samples. 

In contrast to Abgarjan [99], Pareja et al. [79] found in the 

temperature range between 77 and 125 K an annealing stage 

that was interpreted as the recombination of close Frenkel 

pairs in the Zn sublattice. Another difference was the temperature 

dependence of the positron lifetime. Abgarjan measured 

an increase of about 5ps by cooling the sample from 

room temperature to 100 K. However, a distinct decrease 

was observed by Pareja et al. [79] in the same temperature 

range and was related to the charge-state transition of the 

divacancy-type defects possibly not appearing in the samples 

of a different supplier used by Abgarjan [99]. 

The positron lifetime was measured by Pareja et al. also 

in ZnS after electron irradiation at 20 and 77 K [79]. The 

initial annealing stage of close Frenkel pairs observed in 

ZnSe was not observed at the lowest measuring temperature 

of about 80 K. The average positron lifetime increased 

from 240 to 280 ps during the annealing procedure up to 

700 K. A similar annealing stage to that in ZnSe was not 


270 

260 

250 

240 

270 

260 

250 

240 

Measured at 100 K 

e � 

2 MeV 

1�10 cm 

18 2 � 

Measured at 300 K 

Ne + 

200 MeV 

1�10 cm 

14 2 � 

200 400 600 800 

Annealing temperature [K] 

Fig. 14. Annealing experiment of electron-irradiated zinc selenide (2MeV, 

1×10 18 cm −2 , 4K) compared to ZnSe crystals irradiated with neon ions 

(200 MeV, 1 × 10 14 cm −2 , 300 K). The positron lifetime was measured at 

100 K in the electron-irradiated sample and at 300 K in the Ne + -irradiated 

sample [99]

612 

found in ZnS up to this temperature. The increase in τ 

was attributed to VZn-related defects. It was observed that 

the defect-related lifetime of a sample irradiated at room 

temperature decreased with decreasing temperature below 

300 K [100]. This effect was interpreted as the change of 

the charge state of the irradiation-induced vacancy-type defects 

rather than the appearance of shallow positron traps. 

However, electrical measurements are desirable for the confirmation 

of this interpretation. 

Electron-irradiated ZnO crystals were investigated by 

Tomiyama et al. [101]. The irradiation conditions were 

28 MeV, 4 × 10 18 cm −2 ,and77 K. A clear annealing stage 

was found at 450 K. The interpretation given for this stage 

as the disappearance of irradiation-induced oxygen monovacancies 

seems to be unlikely, since these defects are expected 

to be positively charged [102]. The annealing behavior was 

found to be completely different after irradiation with 3-MeV 

protons at 223 K. A defect-related lifetime of 273 ps was 

separated after this irradiation (Fig. 15). It was attributed to 

divacancies, because the τd/τb ratio reached 1.48. In contrast, 

this ratio was 1.15 after low-temperature electron irradiation, 

corresponding to a monovacancy-related lifetime of 

211 ps. The measured average positron lifetime, as well as 

the Doppler-broadening S parameter increased during subsequent 

annealing in the temperature range of 300 to 550 ◦ C.As 

the defect-related lifetime τ2 increased in the same temperature 

range up to 378 ps, it was concluded that the divacancies 

Fig. 15. Positron-annihilation measurements of an annealing experiment of 

a zinc oxide single crystal irradiated with 3-MeV protons at 223 K [102]. 

The lifetime components τ1 (◦) andτ2 ( ) of a two-component spectra 

decomposition are shown in the upper panel. The average positron lifetime 

( ) and the Doppler-broadening S parameter (×) are plotted in the lower 

panel 

grow further to larger agglomerates. These agglomerates annealed 

during subsequent heat treatment, and the average 

positron lifetime approached the bulk lifetime at 1100 ◦ C. 

4 Summary 

Vacancy-related defects may play an important role for many 

of the electrical and optical properties of II −VI compound 

semiconductors. Positron annihilation is a specific method for 

the investigation of the concentration and the kind of these 

defects. The defect-related positron lifetime especially provides 

information on the size of the open-volume defect, i.e. 

it can be distinguished between monovacancies, divacancies, 

and larger agglomerates. Furthermore, the temperature dependence 

of the positron trapping may give indications on the 

charge state of the vacancies. The comparison of Dopplerbroadening 

measurements with theoretical calculations in the 

high-momentum part may allow in the future the identification 

of the chemical surrounding of the vacancy, and hence 

the identification of the corresponding sublattice of the defect. 

However, it is still rather difficult to analyze whether the 

vacancy is isolated or part of a complex with an impurity or 

another intrinsic defect. 

The positron studies of defects in II −VI compounds have 

been reviewed in this paper. Defects in the as-grown state, 

after heat treatment, and after low-temperature irradiation 

have been dealt with. The main emphasis of the investigations 

was put on the characterization of Cd-related compounds. Important 

results were obtained from the investigation of the 

A centers in indium- and chlorine-doped cadmium telluride 

and from the quantitative analysis of the defect chemistry in 

Hg1−xCdxTe crystals related to the mercury vacancy. 

As the positrons are very sensitive to the charge state of 

the detected vacancy, a reliable interpretation of the data requires 

the knowledge of the position of the Fermi level to be 

determined from electrical measurements. Furthermore, such 

positron experiments were especially successful with respect 

to the defect identification, when other defect-sensitive techniques 

were applied to the same samples. Future progress 

can also be expected from the improvement of the theoretical 

calculations of the ionization levels of the defects and the 

determination of defect-related positron lifetimes, taking into 

account the lattice relaxation. 

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