P Fochuk - The nature of point defects in cdte - страница 1
Journal of ELECTRONIC MATERIALS, Vol. 35, No. 6, 2006
Special Issue Paper
The Nature of Point Defects in CdTe
P. FOCHUK,1'3 R. GRILL,2 and O. PANCHUK1
1. —Chernivtsi NationalUniversity, 2vul. Kotsiubinskoho, Chernivtsi, 58012 Ukraine.
2. —Charles University, Faculty of Mathematics and Physics,Institute of Physics, Ke Karlovu 5, CZ-121 16, Prague 2, Czech Republic. 3.—E-mail: firstname.lastname@example.org
High temperature in-situ Hall effect measurements in CdTe single crystals grown by different techniques at 500-1,200 Kunder well-definedCdand Te vaporpressure weremade. It was established that native pointdefects (PD) Cdf+ and are dominantatT > 770 KinCd-rich CdTe. Theirformation enthalpies weredetermined (AHvTe = 1.3 eV; AHCdf+ = 2.5 eV).Itwas shown that VT^e dominate at lowtemperaturesand Cdf+ begintoprevail at T > 930K. In Te-saturated CdTe at heating up to ~ 800 K, the hole density was Te vapor pressure independent. At highertemperatures(HT), the conductivity changed to intrinsic type, turning then into n-type. The resultswereexplained in the framework of Kroger's quasichemical formalism assuming the presence of an electrically active foreign point defect, the oxygen acceptor. The PD structure modeling demonstrated satisfactory agreementwithexperimentalresultsboth fortemperature andcomponent vaporpressuredependencies.
Key words: CdTe, point defects, high temperature, modeling, Hall effect
Aperfect knowledge ofsemiconductor point defect structure is the foundation of high-quality x-ray detector-grade material production.1Only then is it possible to achieve the best resolution and sensitivity. Up to now, different opinions concerningthe nature of intrinsic point defects (PD) have not permitted the correct background to be chosenfor both technology processes and interpretation of experimental results.
and Cdf+ are usually mentioned as dominant native species in theCdsaturation region,2-7 althoughCd;+ and even CdTe are sometimesmen-tioned.8'9 Many PDs areconsidered to be primary in the Te saturation region. In chronological order, the first were Cd vacancies (VCd)proposed by De Nobel.2 Wienecke and Glazovalso concurred.10'11 Using in situ Hall-effect measurements, Smith,4 Zanio,7 and Jasinskaite12 considered that impurities determined the hole concentration in this part of the phase diagram. Later, the antisitedefect TeCd was proposed by Van Vechten, Maksimovskii, and Martynov.13,14 In reality, however,wide acceptance of this suggestion began after Berding's ab initio calculation. Sheshowed that the formation energy of TeCd can be less than thatofVCd.15,16 This theory was maintained by Chen,8Brebrick,17 Fiederle,18
(Received October 17, 2005; accepted December 22, 2005)
Krsmanovic,19 Babentsov,20 and Grill,21,22 all of whom based their PD modelsonBerding's calculated results.
Experimentally, the PD that could be antisite TeCd was found by Bardeleben,23 Verstraeten,24 and Awadalla.25 In the first case, it was revealed in the EPR spectra of CdTe and CdTe<V> single crystals. In the second, thermo-electrical effect spec-troscopy and first-principlesband-structure calculations were used. This PD withionization energy E = 0.18 ± 0.01 eV25 was later identifiedasthe isoelec-tronic oxygen-cadmium vacancy pair (OTe-VCd)~/2~.
In summary, in the Cd-rich part of Cd-Te phase diagram the situation is clearer:the dominant PDs at high temperature are presumably Cdf+ and but their "areas of existence'' are still unknown. According to Chern,3 is the main donor PD at T < 1070 K. In Te-saturated CdTe, the situation is more complicated. Nearly 8to10different PDs (VCd, VCd,Ter,TeCd,Si, (OTe-VCdr/2~and other possible impurities)could be responsible for the charge carrier content.
Therefore, the purposes of this workare (a) to investigate the CdTe galvanomagnetic properties in situ at high-temperaturedefect equilibrium (HTDE)under well-definedCd/Te vapor pressure and (b) to build up computed PD structure models at HTDEinthe wide rangeofcomponent pressures and temperature.
CdTe crystals were grown from 6N-purity Cd and Te by different growthtechniques: THM, classic Bridgman technique, vaporphase,and HPB. Thecon-centrationsofthe main residual impurities (at./cm3), [Cu, Fe] < 1 X 1016 and [Si] < 2 X 1016,were established by atomic absorption analysis. The samples (2.5 mm X 2.5 mm X 15 mm) were cutfrom the bottom and middle ofthe ingots. They were ground, polished, and etched. High-temperature Hall-effect measurements under well-definedCd(PCd)orTe vapor pressure (PTe2)inthe 500-1200 Ktempera-ture range werecarriedout. The Hall scattering factor was takenas1.The samples were placed in sealed quartz ampouleswithsix clamped graphite (or welded tungsten) contacts.
RESULTS AND DISCUSSION
Usually,from 570 up to 770 K, samples exhibit p-type conductivity(Fig.1). Subsequent heating converts them to n-type, and after long-term meas-urementsathigher temperaturesand Cd vapor pressures, such material no longer changes its con-ductivitytype backtop-type. The electron mobility values obtained are similar to Smith'sdata.4
The dependency of the electron density([e ]) on Cd vapor pressure had aslope у = 1/3, which was observed at temperatures, higherthan 770 K(Fig. 2). This fact is in agreement withthe quasichemical defect reaction (QCDR)theory, proposed by Kroger26 for the case when dominantnativedonor point defects are doubly charged. Therefore,one can conclude, thatunder these conditions only and Cdf+areresponsible for electron concentration in undoped CdTe, but notCd;+ or CdTe,whichgive -y values of +1/2 and +1, respectively. Chern,using his self-diffusion data, assumed Cdf+to be the main intrinsic PD at T >~ 1,070 K.3 To check this, we carried out annealingat970-1,170 Katmaximal PCd and followed the anneal withacold water
200 400 600 800 1000
Fig. 1. Temperature dependence of charge carrier mobility under PCd in undoped CdTe.
-3.5 -2.0 -0.5 1.0
Fig. 2. Electron concentration dependenceonPCd in undoped CdTe at high-temperature defect equilibrium.
quench (Table I). As one can see, the electron concentration, whichispresent at high temperatures in CdTe, is reduced even more after quenching, by 20-30 times.This phenomenon can be explained as follows:because Cd interstitials are much more mobile than Te vacancies (self-diffusion data of Chern27), during quenching (whenCdsolubility decreases) they canquickly migrateintoprecipitates:
nCdf + + 2ne~ <-► (Cd°) n
It leadstoadecrease in [e ], whichisobservedinour experiments(TableI). Thus Cdf+ is themainnative donorspecies at T>970K(orevenatlower T) but notatT > 1,070 K,aswas proposed by Chern.3 dominatesatsufficiently lowertemperatures.
The [e ]temperature dependencies (Fig.3)inthe 600-1,200 Ktemperaturerangeatconstant PCd reveal two definite slope behaviors (AE): at lower temperatures, the slopesare equalto ДЕ ~ 0.5 eV; at highertemperatures, their valueswere foundto be AE ~ 0.8 eV. It means that the [e~]iscontrolled by two types of PDs:atlowertemperaturebyVTe mainly,and at highertemperature by Cdf+.This fact agrees with results of annealing (see Table I and corresponding explanation).
Table I. Electron Concentration in CdTe at High-Temperature PD Equilibrium and after Quenching (cm3)
to 300 К
8 x 1016
~ 4 X 1015
3 x 1017
~ 8 x 1015
5 x 1017
~ 1.6 x 1016
0.8 1.0 1.2 1.4 1.6
Fig. 3. Temperaturedependenceofelectron concentrationinundoped CdTe at constant PCd:(1) 0.001atm,(2) 0.01 atm, (3)0.1 atm, (4) 1atm.
Usingthe formalisms of mass action lawand KrOger's theory,26 one canobtain the following formula5:
where A HD2 + is the formation enthalpy of the doubly chargednative donors (Cdf+ or V|e). Because Cdf+ dominates at high temperature only, where its content is 10-15 times higher than that of [VTe ], and therefore the latter PD canbeneglected,itwas possible to calculate the Cdf+ formation enthalpy from experimental T dependencies. Theobtained result was AHCdf+ = 2.5 eV.The enthalpy valuefor could thenbeobtained: ДНуТЄ = 1-3 eV (for comparison, Chern's3 data are2.28 and 1.47 eV forCdf+ and VTe,respectively).
Usually, Chern's set of defect formation con-stants3 for PD structure modeling is used (Table II). But some of his constants (for example, VCd) are not accurate. Otherauthors also propose some constants (Table II), but in practice they cannot satisfactorily describe the CdTe PD structure. Using our experimental resultsinmany undoped and doped crystals, furtheroptimization of ourbasic set of these constants28 was performed(Table III).
Using this set of constants, it is possible for us to obtain goodagreement withexperimental data over awiderange of temperaturesand Cd vapor pressures (Figs. 4-7).At 870 Kfor the entire rangeof Cd pressure [VTe]ishigherthan [Cdf+](Fig. 4), at 1,070 Kthe situation is differentand now Cdf+ acts as the dominant donor (Fig.5). At high temperature and PCd = 1atm, only Cdf+ is responsible for the behavior and concentration of [e~](Fig. 6). At lower temperaturesand PCd = 0.1 atm, however,itisalso necessary to take into consideration (Fig. 7). It is clearly seen that up to ~ 930 K, the[VTe]is greater than [Cdf+]; at highertemperatures, they exchanged their roles.
In the Te saturation region, p-typeconductivity was observed up to ~750 K(Fig. 8). At highertem-peratures, it changed to bipolar conductivity, and > 900 Konly theelectron influence became significant. Compared to Smith's4 results, ourhole mobility valuesare smaller. The reason could be as follows:for Hall measurements,weused undoped CdTe while Smith defined thehole mobilityinphos-phorus doped CdTe, where the acceptor PD content was very high.
Theholeconcentration ([h+]) varied in the (3-9) X 1016 cm~3 range in different samples up to 800 K. Experimental resultsshow that it does not depend on PTe2.Athigher temperature,above the region of
Table II. Main QCDR Equations of Native PDs in CdTe and Their Formation Thermodynamic
Parameters According to the References
0 <-> e~ + h+
Ki = [e"][h+]
(b) 6.7 x
(c) 8.24 X
Cd (v ) + vCd- CdCd
CdCd + e" <-> Cd( v )+VCd
K16 = [VCd]_1PCd
Ku = [VCd][^_iPCd
CdCd + 2e~ - Cd( v )+VCd Cd (v) <-> Cd?
K10 = [VCd KC^Cd
K17 = [Cd^][^]PCd K9 = [Cdf+][^]2PCd