Status of semi-insulating cadmium telluride for nuclear radiation detectors

Status of semi-insulating cadmium telluride for nuclear radiation detectors

f>(!(1r ~~fy, r Nuclcar instruments and Methods in Physics Research A322 (1992) 313-323 North-Holland li,r fwC~ U ~çsrt~ll"r1, ~uLl ;.a G1J E=s~ ...

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f>(!(1r ~~fy, r

Nuclcar instruments and Methods in Physics Research A322 (1992) 313-323 North-Holland

li,r fwC~ U

~çsrt~ll"r1, ~uLl ;.a

G1J

E=s~ '

Section A

semi-insulating cadmium telluride for nuclear etect rs age--Ali and

. Siffert

Centre de Recherches Nucléaires (IN2P3), Laboratoire PHASE (UPR du CNRS n° 292), RP 20, 67037 Strasbourg Cedex 2, France

A brief review of our earlier self consistent model of pure and halogen compensated semi-insultating CdTe material is presented . We provide a new reading of this model, in view of recent results, concerning (Cl), (Cu), and (H) introduced in CdTe in order to understand the variation of founded levels and to improve our view of these problems. The defect levels behaviour must be seen in terms of general thermodynamic equilibrium between different charge states of structural defects, impurities and their complexes .

l . Introduction Before discussing high resistivity semi-insulating material and compensation of cadmium telluride (CdTe) a few remarks must be made . The major part of the actual applications of cadmium telluride, like in nuclear detectors [1,2], epitaxy substrates [3,4], and electro-optic devices [5], cannot allow more than 10 - ' A current leakage under electric fields of 1000-3000 V/cm, and they need an active volume, generally a depleted zone free of charge carrier, as large as possible in the mm-cm range. These requirements show the necessity of the use of high resistivity semi-insulating material in the range of p = 108_ 109 il cm . Theoretical calculations show that the limit of resistivity that can be obtained by chemical and physical purification of actual CdTe materials lies around 10 8 f1cm. [6], but experimental measurements show a maximum resistivity of 10 6 S2, cm. Commonly the resistivity is around 10 4 f1 cm [7] for the best purified CdTe grown by improved TLIM methods . Spectroscopic methods like thermostimulated current (TSC) [8], photoinduced current transient spectroscopy (PICTS) [9], photoluminescence (PL) and others, show more than 20-30 (fig. 1) different defect n the the ava forbidden CdTeav, viith differ .levels vav i. .a vawuvaa bond band bate gap of of wa v.s ma uraa a.a _

ent ionization states and signs . This led to a general decrease of the electrical characteristics : 1) a decrease of the resistivity by an increase in the whole density of carriers ; and 2) a decrease of the product la,r owing to the time constant of trapping and detrapping of the carriers, which decrease the mobility and the lifetime of these carriers .

Thus enhancement of the quality of the devices must arise from increasing the resistivity p and the product tLT . However, if extended purification can remove a great part of the chemical impurities, structural defects are more difficult to suppress, and the ultimate values that can be reached he around 10 6 fÈ cm for p and 10 -j for gT (as we have seen before) . Therefore, further improvement of semi-insulating CdTe cannot be done directly without chemical com-

CONDUCTION BAND

Ev VALENCE: BAND Fig . 1 . Energy levels diagram in CdTe band gap.

0168-9002/92/$015 .00 © 1992 - Elsevier Science Publishers B.V . All rights reserved

1. CdTe

AL Hugo-All, P.

314

Siffert

/ Stunts of send-insulating CdTc

pensation by the appropriate element, self-compensation being apparently largely insufficient. Common donors were considered for compensation : group III elements like In, substitutional to Cd sites, were used with some success [111 and (AI) was suggested but without evidence, on the other hand, group V11 (halogen) substitutionals to (TO sites were successfully used by many authors [6,12,14] . Compensations by ,L;icment like Cue [151, '10g, Se, Zn, are reported but without extensive study. Lately, the possibility of comlementary compensation by unexpected elements like Cu 116,171 appears to be evident and the extension of experiments performed for Si and GaAs shows a possibility of compensation by hydrogen . Modelization of compensation allows a better understanding of the material engineering process, a few models- were prepared with different degrees of difficulties: the simple compensation between isolated ionized species by De Nobel [181 generalized by Kr6ger [19]. Bell [201 and afterwards Hiischl, introduce the notion of chemical compensation with neutral and ionized complex formation . However, all these models include only a part of the problem and for this reason vve have developed earlier a rather complete self-consistent model which synthesizes the former models but which takes into account the mentioned shortcomings, the majority of known levels in the band gap, and the different ionization states of defects and complexes. Moreover, for calculation complexity reason, this model was directed only to halogen compensation but in view of recent works and results, a new reading of this model should be of great help, firstly to understand some unexpected results and general compensation mechanisms. and secondly to improve this model and modelling in general . However, in the model simulation, we must introduce supposed defect parameters like the type and the energy level with respect to bands, precise knowledge of these parameters results in a better fit of the model to reality . Thus, after reviewing and talking about defects and their corresponding level diagrams, we will begin with the case of the pure crystal model to introduce the compensated one. ekds Ddlects in Cd-1Tc are minainly structural. dicirccts, in, purities and complexes of these two, the excess, the lack or equilibrium between these different levels determine the absolute electrical behaviour of the material . They can be classified in few major families or bands : (TSC, PICTS, PL) < 0.14 cV, 0.14-0.20 cV, 030-41) eV, and 040030 eV. Ewers level or band

has its own specific action on the electrical characteristics of the material . Detailed discussion of the defect levels is well shown in different references [10,13,18.201, but prior to the study of their correlation, we give a brief overview of these defects and their simplified level diagrams as shown in mg . 1 . It should be noticed that assignment of levels is rather a thorough conviction than an absolute proof, but we expose here our and the general belief. - Level at E, + 114 eV or band 0.14-0 .20 eV: this important level was extensively studied and attributed to many defects but it is now generally admitted that this is a cadmium vacancy-donor ionized complex (Vj~ . X')-. - E, + 0.38 eV is attributed to a simply charged cadmium vacancy (Vcd). We think that 0.43 eV is more appropriate but for reasons of convenience, we still use 0.38 cV. - E, - 056 eV is generally attributed to interstitial cadmium (Cd 2+). - E, - 0.6 to 0.7 eV is due to a well established doubly charged cadmium vacancy . - E, - 0.06 is due to a neutral cadmium vacancydonors complex (Vc ;, 2X+)" . - E, - 0.02 is due to many donors doping like Cl, In, Br, and Al. - other levels have been found in some special cases and were not introduced in the model. We will discuss about that later on. 3. Model 1. Pure crystal Thc crystal is then supposed to be free of dopant, only structural defects are present like Frenkel disorders VCd %J + Cd'i'= CdCj , K F = [Vc"d ] jr Cd'il] ,

which can be neutral, simply and doubly ionized . Equilibrium between those states can be written as Cd'? = Cd i' + e -, Cd+= Cd 2+ +e -

(1) (2)

and the same equilibrium for the Vc"d . (3)(4) Let us apply the law of mass action to this equilibriurn if [e] and ',h] are the electron and the hole concentration : K, = [Cdi'][nl/[Cdi)],

(5)

K

(6)

I -,

=

K3 =

[Cd 2i ' J [n]/[Cd i' 9 [vd][PI/[V~Cd],

K4 = [VI

[P] /[Vd

(7) (8)

M Hage-Alt, P. Siffert / Status of semi-insulating CdTe m

315

We can see that all defects decreased drastically and uniformly from 1000"C to RT. that [Veal ] - [Cdr i ] - [p] are by 4 orders of magnitude greater than [Vcd ] - [Cd T ] - [n], that (Vjd ), (Cdz } ) are the major carriers with 10 13 /cm ; , that this (THM) material is of the (p) type at RT, and that its ultimate resistivity at RT under the assumptions we made is given by ([n] and [p] from fig. 2) : p = [e(nlL  + pl~t P )] -- ' = 4 X 10' 11 cm. This means that theoretically it is possible to make a semiinsulating material by purification . However. experimental measurements show a maximum :esistivity of highly purified crystals around 10' it cm, indicating the necessity of compensation .

z 0 d z w U z U 0

3.2 Compensated crystals We extend the former model to tree case of the presence of donor impurities (denoted X) mainly the more used ones (halogen atoms), because they are supposed to be shallow enough to be fully ionized . In addition to previous equations we introduce equilibria due to associations between Vcd and X [20] but here we take their ionization conditions into account :

Tn ("K) 3

1

X=Xr+e - ,

Fig . 2. Calculated defects concentrations in "pure" CdTe in terms of T .

The same treatment must be performed for the intrinsic thermal native electronic disorder : e ; + h ; = 0 : Ki =(9) [n ] [p] = n , where n i = K'/` is the intrinsic carrier concentration . Finally, the required electrical neutrality is expressed by : [n ]+ [Vcd ] + 2 [Vcd ] = [p ]+ [Cd' 1+2[Cd ;+1 .

(10)

We have a nonlinear system of six equations (5) to (10) which has been solved by De Nobel for particular cases. For - a more general approach, some additional developments are required, concerning the cadmium pressure-temperature relation in the THIVI case, Frenkel constant KF, intrinsic constant K i and the distribution of defects which are supposed to follow the Boltzmann statistics ; in this case equilibrium constants are given by : K x = aN, exp(-L x /KT), where a is the number of possible configurations of one electron in the defect (1/2 or 2), Nc is the state density in the conduction band (partition function) and E x is the energy level . Iterative solutions can then be done with the temperature as a parameter (see fig . 2) .

VCd + X+= (VcdX)'), X) 0 (Vcd +e - = (VcdX) (VcdX)

,

+ X += (VCdX) "-

(13)

Applying again the law of mass action on these equilibria : Ks= [(VCdX)()] /[Vcd][X+], K6 = [(VCdX)

] / [( vCd

I

(14)

)d] tnI,

K7 = [(VCd 2X) O /[(VcdX)

I [X + ] .

(16)

The electrical neutrality is now modified : [n] + [Vcd] + [(VcdX)

I + 2[Vcd J

= [p] + [Cd : ] + 2[Cd ; +] + [X+]

(17)

and the conservation of total impurity number [X]T requires [X]T = [X + ] + [(VCdX) o l + [(VC(J X) o + 2 [(Vcd 2X) ] .

] (18)

The new nonlinear system of ten equations to be solved is (5) to (9) and (14) to (18) when [X]T is the free parameter . fiere again., we need an additional development for K . It can be written as follows : K = C exp

(

AH ) KT , 1 . CdTe

hl. Hage-Ali, P Siffert / Status of semi-insulating CdTe

E z

IOI~e

10 13

CFILORVNE ®OPECD

CRYSTRL CX] = tp317 c~3

10 12

0.~

fl Q3

dig. ~ . Calculated

a 0.9

1

â

_t 1.2

1.1

fl l3

i l.t,

15

1000 1 oK T

)

defects concentrations in (Cl) compensated CdTe in terms of T.

~~here C and ~ H are the entropy and enthalpy variation of the reaction. ~° corresponds to the normalized nu~iâber ®t p~SSflble aSS®~flat8~n SflteS (~ in a cubic crystal), and ~ H can be found by comparing the heat formation of Cdr ~ and CdTe [20~. e can also sup_

pose that the ® H needed to form a simple or double association is the same, which means that KS = K~. Starting from these considerations, this system was solved by an iterative process again . The first set of results is given in figs . 3 anc~ 4.

~3017 BE u

C

~cdxIJ

~Cdi ++~ C~ ~J

[V~d2X)°~ û

1015

lv~ d~~

Z 0 U

10 14

1013 -

BROMINE DOPED MATcRIAL CX] = 101~cm 3

10 12 1 07

s 0 .8

i

0 .9

I

1

I 1 .2

1 1 .3

I 1.~

I 1 .5 1

O (°K1

T F'ig. 4. Calculated defects concentrations in (Br) compensated CdTe in terms of T.

M. Hage-Ali, P. Siffert / Status of semi-insulating CdTe

317

With the temperature as a parameter, with 1XIT 1017 at. /CM3 in the case of chlorine and bromine donor impurities, fig. 5 gives the concentration of the defects as a function of chlorine concentration at 400"C (below this, the system is "frozen" [21]). A few remarks can be deduced from these figures: - Cadmium vacancies and interstitial are independent of the nature of the halogen impurity. - (Vcd) of a compensated material is 10 times lower than in the pure one whereas Cdj is 10 times higher! 10-3 for chlorine but 10- ' for bromine . - IX + ]/[X]T ": - (VcdX) - , (Cd 2+ ) and (Vcd 2X)` are fairly predominant a! RT and IXIT = 10' 7 cm - ; . - Compensation is effective (fig. 5): both (VUX)(11 (Vcd 2X)() increase while (Vjd ) and (Vjd ) decrease, with the increasing MT, especially both [Cd j] rise also, but we must notice that the limit solubity of [X] is not introduced in the model On the other hand, we cars see that for really active of 1016 CM-3: IMT - the acceptor (VEd ) (E, + 0.4 eV) with 10' 5 cm - ; ; (E,, - the acceptor W,&-- 0.66 eV) with = 10 cm - ; ; - the donor (Cd2+) (E, - 0.56 eV) with = 101f) cm- 3 ; - the donor (Cd +) = (E, - 0.02 eV) with = 1014 CM -3; - the acceptor (VU X) _= (E, + 0 .14 eV) with = 10M Cm -3 .

10

,o" -3 CHLORINE CONCENTRATION (cm ) 17

Fig . 5. Calculated defects concentrations in (CI) compensated CdTe in terms of [Cl] concentration .

This means that even in the halogen compensated material with IXIT 1016 CM-3, we still have up to 1016 cm- 3, both signs ionized centers which can act as trapping and recombination centers with severe electrical effects like tailing, polarization and large time

200 100

I 60 Mm 40 20 Fig . 6. [Si], [CI], and [S] concentration profiles along a CdTe (THM) ingot and the (Te) zone . 0

1. CdTe

1t1. Flc :ge-Ali, P.

Siffert /

~onstaHlt decay. ere `ve see the necessity and the ossibility of material engineering in order to improve material characteristics. 4. ~ ~rlnHenta

s Its

-~. !. C'ltlor~rce r~scelts 1~Iany authors [22.23] think that the compensation f l0 a~ cm - ° donors (added halogen) is not possible, d e to the limitation of ionized acceptor vacancies. Indeed, many results show that the complete amount of added donors is not used only in compensation ; the maàor part is acting as a purifier (more than 9/ 10) and is beHng remov d to the end of the ingot `vith impurities by the Te zone. Eine analysis by heavy' ion induced -rays shows that [Cl] is nearly constant along the ingot even if the added [Cl] is ten times more (fig. 6). Consequently°. in procedures some kind of a (ClI solubility limit is reached by the [Vca] amount, the excess of (Cl) removes impurities by the (Te) zone and then p seems to be independent of the added amount of (Cl) in the range of 1-100 ppm, when starting frvm a high purity material. I-Iöschl [?4] found that p, d increases linearly up to 10=~ cm - ' i:? a material. ®n the other hand, we have found that added halogen of more than 10's cm -' decreases the resistivity and our material becomes ntype. is can be explained by the fact that poorly

Stutacs of senai-irasaelutirag CdTe

purifïed starting elernentc in the ~Iöschl case need more [Cl] for purification . Effectively, in our material with 10"-l0 ax cm - ; added (Cl), we have found 10'6 cm- ; (0.14 eV) (Vcd X)-, 10'S cm --~ (0.4 eV) (V~d) and 10 aß cm --~ (Vc~2X)a', all far lower than the [Cl] amount added; the excess is found in the (Te) zone as shown in fig. 6. 4.2. Copper results A large number of CdTe ingot and slices were studied by different techniques : resistivity, atomic absorption, nuclear detection, TSC, PICTS, [8,9]. Tentative correlations between chemicals and electrical characteristics are established . x.2.1. Copper lec~els Cot.~.;;r was considered fror:~ the beginning as a deep level acceptor at = E + 0.3 eV [25,26] but recently (Cu) has been assigned by PI. to an acceptor level at E~ + 0.147 [27,28] . In our investigation on a large number of crystals, we see that the situation is more complex : Cu is correlated directly or indirectly to two defect bands at 0.10-0.20 eV and 0.3-0.4 eV, which present a fine structure with many peaks in TSC and PICTS. lvlore precisely, Cu seems to be responsible of two levels at: E~ + 0.16 ± (0.02) eV and E + 0.35 ± (0 .03) eV. The behaviour of these two levels is strongly dependent of the type of studied ingots: high p (CI) compen-

10°a

chlorine

undoped

u C 0 u v chlorine

doped

ingots

l

10

101 Coppeâ~ concet~~ea~ion

1

,

I I III

10 j

c~

(pnb~

1

~

1

A

1

1 IIII

10

a

F'ig. 7. Correlation of 0.16 eV and 0.35 eV levels with Cooper concentration in (Cl) doped or undoped Cdîe.

M. Hage -Ali, P.

1

.16w 1®14 . 1 ed

Siffert / Status of semi-insulating CdTe

319

101° x-.

>

10 9 10®

W

10 7

1013 10 Fig.

10

106

E 1 TI I

107 Mc )

8. Correlation of 0 .16 eV and 0.19 eV levels with resistivity in (CI) compensated CdTe .

sated crystals or low p non-intentionally (Cl) cotàipensated ones. 4.2.2. Noncompetisated mo!eria!s (,g . 7) The 0.35 cV level increases up to 10'5 CM-3 with [Cu]. In fact, (Vcd) are abundant in pure crystals (fig. 2). We have more than 10'' CM-3 (Vcd-) at the solidification temperature of (THIS) CdTe. The small sized (Cu) atom can easily occupy (Cd) site as a dopant 250 o

a

10 6 101 i0

1. v 1

' 03

1

.

y îa7 1

ra,

10 2 1

10

1 60 :-*-&4 11,111j

60 1 ,

. -

10

COPPER

t 1

1 1S LI n

100

ppb

I.

ppb

e

1 1000

111111

CONCEHTRd.TI0P1 (ppb)

Fig. 10. Resistivity of CdTe(CI) wafers in terms ®f measured [Cu] concentrations . a Q z (Z

iv

T5

v

v

100

125

v 150

1 1T5

200

225

TEMPERATURE ° K Fig. 9. Detailed PICTS spectra of the 0.10-0.20 eV band in (Cl) compensated CdTe.

giving rise to this level with [Cu] (p decreases consequently). The 0.16 eV level has a more complex behaviour . It increases up to 1014 CM-3 at 200-300 ppb and then stabilizes or decreases . We can speculate that like in (Vcd, CI) - (0.16 eV), we can form a complex (Cd?+ , Cued ) [29] which can have an energy level of 0.18 eV which plays a role of compensation in the same manner as the (CI) 0.16 eV. Both levels show an increased concentration with increasing resistivity (fig. 8). In fact, this band of 0.10-0 .20 eV includes more than five levels (fig. 9). Few of them increase with the resistivity and give a good representation of the compensation . This means that the first part of the curve (fig. î) shows the compensation of (Cd 2+ ) by (Cu ed) up to its concentration 5 x 10" cm -3; if it decreases afterwards, it ;; due to a drastic increase of the [Cu ed] with [Cu] which decreases the complex formation (Cd;, Cued)-' I. CdTe

N!. Hage-Ali, P. Siffert / Status of semi-insulating CdTe

I320

Q--O H°IMPLANTED SAMPLE

Cal

r® E

C a

BEFORE H®

PLANTATION

AFTER

H`

IMPLANTATION

AFTER 24H ANNEALING AT 150°C

AFTER 15 Mn ANNEALING AT 230°C

AFTER 149Mr ANNEAAL ;NG AT 230°C

Fig . l l . (tfl -' P_ ctrl) CdTe resistivity behaviour after 2 McV (H + ) implantation and annealings .

-'.

«> ;.

Compensated miaterials by (CI) (f;. 7)

th the 0.16 and .35 eV levels increase with (Cu) but here we have more than 1016 Cm -3 = -,1 [CI] of (Cd ') (see figs. 3 and 5) that gives rise to the complex (Cd® ° , Cu~,1) at 0.18 eV up to this amount, (Vcd ) being here compensated in majority by (Cl); then the level 0.35 eV is 100 times lower than in uncompensated crystals (and (p) can be high). 4.2.-1. Resistirith An illustration of our speculation (fig. 10) shows the resistivity behavior versus [Cu] concentration . We see that for the Cl compensated material, the resistivity crosses a clear and sharp maximum for [Cu] in the 100-250 ppb range, the reached resistivity being a few times (5 X 109 Sl cm) higher than that of samples which were only compensated by (Cl). That clearly shows a compensation effect of CdTe by (Cu). Indeed, at really low and almost uncontrollable doping concentration, this is an unexpected result . As a conclusion of this part, we can say that (Cu) acts as a compensator, especially in complement with halogen . (Cu) is related to two levels : in the Cd site as dopant in complex with Cd; and it may be with the (Vcd C') - complex in the 0.15-0.18 eV band level ; the assumption is confirmed by recent ODMR results [30] which weaken the earlier assumption [27,28] . However, we must :moderate our purpose because of the fact that [Tel excess in THM is not introduced in the model which can modify [Cd ;]; the hlüoduction of

(Cu) can change this [Cdi]-[Vcd] equilibrium, because in some cases (Cu) shows an amphoteric behaviour [31] and complexes may be formed with (Cl +, Vcd, Cu ± ). 5. Hydrogen results Hydrogen can be introduced in several ways: ion implantation of atomic H + (proton) from the keV (1-60 keV) to the M-_V (0.5-4 MeV) range with currents ranging from the (mA) to (nA), or by annealing in a molecular hydrogen atmosphere. The introduced amount of (H) is well known in the high energy implantation case to be around 10 16-10 18 cmj-. The material is supposed to be sat ,-rated after low energy implantation with few mA dunag 20-30 min. During molecular (H .,) annealing the time is the parameter . 5.1 . Resistiuity

The Van Der Pawn resistivity (p) was measured before and after the implantation and time annealing . Fig . 11 shows the behaviour of (p) for the 10 4 f2, cm sample, (H + ) implanted at 2 MeV. The implanted sample shows a p increase by more than 2 decades after 24 h annealing at 150°C. Annealing at 2300C decreases p; the reference sample does not show any increase . Treatment of different CdTe samples with resistivities ranging from 10 ° up to 10`1 SZ cm shows an increas-

M. Hage-Ali, P. Siffert / Status of semi-insulating CdTe

321

0

a

RESISIU411rY

BEFORE HYDROGEN

IMPLANTATION

Fig. 12. The relative increase of CdTe resistivity after 2 MeV (H ' ) implantation and annealings. ing resistivity depending on the initial values (fig. 12) . For low resistivity materials (104 fl cm) it is increased by 2.5 decades whereas for high p (10 9 ft cm) it remains the same. BEFORE H'O'IMPL.

----

AFTER

W"

IMPL.

AFTER H+ IMPL .+ ANNEALING AT 150*C FOR 48 H SAMPLE CB3 t' =O .Sms

80

125

173

TEMPERATURECK)

221

Fig. 13. PICTS spectra showing the effect of 2 MeV (H + ) implantation in low resistiv4ty (104 11 cm) CdTe.

5.2. Defect legal

The spectrometric study of CdTe before and after H treatments shows a drastic change in level concentration behaviour (figs . 13 and 14). After annealing, levels higher than 0.15 eV generally decrease but we see a remarkable increase of levels which are lower than this band. The decrease of levels at 0.16 eV and 0.18 eV must decrease the resistivity. However, this band (0.10-0 .20 eV (VCd,X)-), as can be easily seen, represents the compensation level namely (VCd2X)o and (VCdX)0 (fig. 5). Atomic hydrogen can compensate the (VcdX) - and (VCd - ) to form the neutral complex species situated lower than 0.15 eV which cannot be seen by TSC, DLTS at liquid nitrogen . i n a nuclear detector polarization experiment, we see an increase of the rapid polarization after hydrogen treatment while slow polariztion decreases, demonstrating an increase of low levels owing to the hydrogen compensation around 0.020.1 eV. In the same time, photoconductivity of all the treated samples is increased up to 10 times, which is a clear demonstration of an increase of the ta product . Direct measurement of ta by nuclear detectors confirm these logical results owing to the compensation of the majority of ionized levels .

6. Summary We have seen hi this discussion that material engineering, theomficaNy and experimentally, can improve 1. CdTe

,11. Hage-Ali, P. Siffert / Status of semi- .,*nsitlating

322

CdTe

- BEFORE H4' IMPL .

SAMPLE CM3

AFTER H' IMPL . AFTER H"' IMPL .AND ANNEALING AT 1500 FOR 30 H

63

1

TEMPERATURE (K)

6

Al

I

1

270

1

A5

Fig. 14. PICTS spectra showing the effect of 2 keV (HT ) implantation in medium resistivity (107 0 cm) CdTe.

the

quality of the material in the case of Cd ic. emu . simple self-consistent model allows a reasonable understanding of the behaviour of levels . The introduction of recent results like those of WD (Cu) or (H) in this model aliows a better treatment of the theoretical from and experimental study. Starting this model and these results, we can see that compensation is a more general process than believed before and that it can be understood in terms of general equilibrium between structural defects, donor and acceptor impurity bounds and their different neutral and ionized complexes. This compensation is limited, in every element case, only by the solubility limit and the created structural defects for each specific system .

eferences

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