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Defects in PbTe single crystals
Journal of Crystal Growth 58 (1982) 399—408 North-Holland Publishing Company
399
DEFECTS IN PbTe SINGLE CRYSTALS R. BRESCHI CAMEN, S. Piero a Grado, Pisa, Italy
A. CAMANZI Assoreni, Monterotondo, Roma, Italy
and V. FANO Maspec Institute of CNR, Parma, Italy Received 9 July 1981; manuscript received in final form 20 February 1982
Micro-size defects in PbTe single crystals grown by the vertical Bridgman technique have been studied using samples selected from different regions of ingots. The influence of both the Pb : Te ratio in the melt and the role of doping elements using different growth conditions has also been tested. The data thus obtained show that two types of defect are formed: (a) void regions localized in the first-to-freeze cone-shaped region; (b) Te-rich and Pb-rich phases depending on melt compsition.
1. Introduction Although PbTe is a well-known IV—VI group semiconductor used in thermoelectric energy conversion devices and in the synthesis of thermoelectric and optoelectronic PbTe—SnTe alloy systems, its defect structural properties have not been systematically studied. Low grain substructures have been investigated by Muhlberg [1] and by Crocker [2]. Moreover, there is another defect, involving second phase formation, which is highly undesirable both for technological applications and for scientific research; it influences, for example, both the physical characteristics and the performance of the materials. Brebrick and Strauss [3,4] assumed the presence of Te-rich precipitates. However, attempts to observe them directly have been inconclusive in ref. [5], while Sealy [6] has observed microdefects in areas near the last-to-freeze end of an ingot grown from a melt containing 0.5 at% excess of tellurium. Unfortunately there are not enough data available to advance any hypothesis 0022-0248/82/0000—0000/$02.75
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about the origin of the observed defect. In this work particular attention has been paid to analysing monocrystalline ingots grown by the vertical Bndgman technique in order to obtain both evidence for, and an understanding of, the origin of defects. Thus, we have examined: (a) ingots grown from melts having different Pb—Te ratios; (b) ingots doped with either the commonly used silver or bromine. These ingots were grown using different growth conditions (thermal gradient, G, and growth velocity, V).
2. Experimental The starting elements, 99.999% pure or better, were further purified from oxygen by keeping them at their melting points for a few hours in a flow of H2. The crystals were grown from the melt by the vertical Bndgman technique. Unless otherwise specified the typical dimensions of the ingots were 1.3 cm in diameter and 7 cm in length of which the
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Defects in PbTe single crystals
first-to-freeze 1.5 cm had a conical shape. The crystal growth rate and the thermal gradient ranged between 0.02—1 cm/h and 10—50°C/cm respectively. Single crystals were grown: (a) from the melts of composition Pb1 ±5Te, where 1.01 ~ 1 + ~ ~ 0.999; (b) from the stoichiometric melts doped with 0.05 mol% PbBr2. Specimens cleaved from different areas of monocrystalline ingots have been examined. A Jeol JXA 50A scanning electron microscope was used to observe the surface of freshly cleaved specimens A Jeol Ortec dispersive X mi croanalyzer was employed to study the defect composition of the cleaved surfaces and of the polished and electrochemically etched samples. The samples, etched according to Tilly [7], have also been examined using a metallographic microscope. The electrical conductivity type of the ingot in different regions was tested using a thermoelectric microprobe. The carrier concentration was measured by Hall effect using cross modulation of both the sample current at a frequency of 84 Hz and the magnetic field at the frequency of 36 Hz, 1500 G. The Hall voltage is detected at the sum frequency (120 Hz).
3. Results and discussion 3.]. General remarks In fig. 1 some characteristics of the ingots synthesized by vertical Bridgman technique are reported. In fig. Ia the position and dimensions of the first-to-freeze end (region B) wich is characterized by void regions is sketched. Fig. lb shows the maximum dimensions and the position of the n-type region of the single crystals grown from the melt using normal growth conditions (V = 0.5 cm/h, G = 20°C/cm).The formation of the n-type region is due to the fact that the maximum melting point for PbTe occurs at a Te-rich composition. In single crystals grown from a stoichiometric melt the first-to-freeze end must have a composition very close to the composition corresponding to that of the maximum melting point. This should produce the concentration gradient along the growth direction, due to normal lead segregation, causing n-type electrical conductivity (PbTe is an
re~
___________________
~
t
Fig. I. (a) Regions used for sample selection. (b), (c) Electrical conductivity type for indicated ingot regions using different Pb: Te ratios. The length of the n-type part of the ingot, grown from a stoichiometnc melt, is not rigidly fixed.
amphoteric semiconductor; a Pb excess causes ntype electrical conductivity). Gomez et al. [8] reported the formation of an n-type last-to-freeze end in ingots for starting melt composition having a slight Pb excess. Other authors have found [9,10] that single crystals are always p-type. Miller et a!. [11] have reported that n-type PbTe crystals cannot readily be grown from the melt. However, Lawson [12] reported that n-type and p-type crystals can be grown using lead-rich or telluriumrich melts respectively. We have found that PbTe grown from stoichiometric melts by the Bridgman technique under typical growth conditions (G = 20°C/cm, V= 0.5 cm/h) produces single crystals which randomly exhibit the electrical conductivity sign variation in the last-to-freeze end (half of the twenty charges do not show any sign variation). The uncertainty of the length of the n-type zone cannot be ascribed only to the presence of uncontrolled impurity content because all the charges are synthesized by using the same stock of previously homogenized starting Pb and Te materials. One can attempt to remove this uncertainty by synthesizing the charges of longer length in order to increase the terminal transient length. However, charges which are 1.5 times the usual length (lO—ll cm in length) do not show any different behaviour. Thus, it can be hypothesized that this variation in
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Defects in PhTe single crystals
the length of the n-type zone or its complete disappearance is due to the lead trapping caused by the supercooling effect. Nevertheless a growth velocity as low as 0.02 cm/h and thermal gradient as high as 50°C/cmdo not modify the behaviour
U
401
of this system, in which the melt mixing is by diffusion only. An estimate of the growth conditions necessary for avoiding constititional supercooling can be made from the phase diagram [8]. This estimate shows that G/V 2.5>< 103°C h
~
Fig. 2. T~pical cleavage fractures, river patterns: (a) Te-excess-doped l’hfe: (h) Ag_Ic-doped Ph Ic; (c) stoichiometric PbTe; (d) PbBr 2-doped PbTe.
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cm2 is not enough to avoid the constitutional supercooling (more than two orders of magnitude lower than necessary). We shall return to this later. 3.2. Mechanical The brittleness of the central part of the ingots has been qualitatively tested. Test specimens show typical cleavage fracture with sub-grain boundaries from which further cleavage fronts arise and river patterns appear at (100) orientation pole determined by etch pits (fig. 2). Freshly cleaved specimens were polished and etched using the electrolytic technique described in ref. [7]. This etching does not reveal the inclusions but it makes it possible to count the dislocations. We have measured an average concentration of dislocations 2. Moreover, we have measured of about I0~cm the link angles between the river patterns in order to evaluate the brittleness of the materials. In fact, link angle measurements may be inserted in the relationship sin( co/2) F/2T, where ca is the angle value, F is the retarding force on the disloca-
in PbTe single c,ystals
tion motion, and T is the line-strain caused by the dislocations on the cleavage step. Greater plasticity roughly corresponds to smaller F/T ratios, when other parameters are constant. According to the above the single crystals grown from Te-rich melts (Pb 0 999Te melt) were the most brittle while the PbBr2-doped specimens were the least brittle (maximum plasticity) (see table 1). 3.3. Void regions The samples of the first-to-freeze end of the ingot grown from the stoichiometric melt and cleaved from the conical end of the ingot, as shown in fig. 1 a (set B), present a complex picture. No matter what thermal gradient and growth velocity are used inclusions, and L-shaped voidspheroidal regions (figs. 3a and I-shaped 3b) are present. The cross-section of the void regions is frequently a geometrical figure with sharp angles (fig. 4a). Sometimes the angles are broadened to the point of forming a circular cross-section (fig. 4b). For determining the origin of these defects,
Table I Summary of the results pertaining to the cylindrical part of the single crystals Melt composition
Link angle values a) (river patterns) (deg)
Description of the Te-rich defects in the last-to-freeze end b)
Remarks
Stoichiometric PbTe °~
20—25
—3 ~sm spheroidal Te-rich defects: io~—io~ cm2
PbTe+0.l mol% Te ~
35
PbTe + 0.2 mol% Pb ~
25—30
—3 ~im spheroidal Te-rich defects: l0~— lO~cm2 <1 ~srn spheroidal Te-rich defects: l0~cm~2
PbTe+0.3 mol% Pb ~
28
The average diameter of defects decreases (
PbTe+ I mol% Pb c) PbTe+0.05 mol% PbBr 2 ~> PbTe+0.05 mol% Ag2Te°
2000 A spheroidal Te-rich defects: l0~cm2 No defects
—
18 30
No defects No defects
—
Lowest brittleness
The average values are measured on the last-to-freeze solid. The first-to-freeze solid values are 4—6° smaller. The first-to-freeze end is always highly 3 at defective room temperature (see text). (RT). c) Hole concentration: (2—6)X 1018 cm ~1) Electron concentration: (3—l0))< 1019 cm3 at RT. a)
b)
°
Hole concentration: (0.9_3.5))<
3 at RT. 10i9
cm
—
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/ Defects in
PbTe single crystals
403
U’~ Fig. 3. I-shaped (a) and L-shaped (b) void regions in the first-to-freeze end.
we first consider the void regions, because the inclusions are not located only in this zone. Frequently, a higher Te concentration is detected on the surface of the void regions and a correspondingly smaller Pb concentration is found; fig. 5b shows the Lct1 Te X-ray emission profile across the
defect of fig. 5a (note the opposite intensity variation of the La1 Pb X-emission profile). One can
hypothesize that the void regions are due to a tellurium excess, which makes the crystal more brittle. If this is true, the cracks must be absent in n-type electrical conductivity single crystals, in other words in Te-deficient single crystals in which
no Te-rich defects are present. However, the analysis carried out on all the charges shows that the cracks are present in all specimens cut from the
I
Fig. 4. Typical cross-sections of void regions : (a) cross-sections with sharp angles: (h) circular cross-sections.
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Defects in PbTe single crystals
L~
-
1Pb
—
L ~Te
—
a
—
20,LA
~
r
Fig. 5. X-ray microanalysis of the void region surface: (a) the examined defect; (b) the dotted lines refer to La1 Te and Lai Pb X-ray emission intensity profile across the defect (arbitrary units for I).
first-to-freeze ends, that is in samples grown from stoichiometric, Te-, Pb- or Ag~Te-dopedmelts and in n-type samples also, grown from PbBr2-doped melt. Thus the formation of the cracks does not depend upon the melt composition. After this was done, the etched samples were examined by a metallographic microscope. The observed orientation of the etch pits shows that the sides of the Ior L-shaped void regions lie in the (100) directions, the void regions are thus oriented along the easy cleavage faces (lead telluride has NaCl type cubic crystal structure). This fact suggests the presence of stresses upon the crystalshape). because the geometry of acting the ampoule (conical It of is well known that the macroscopic interface shape strongly influences the generation and propagation of defects during directional solidification. Thermal stresses are generally minimal for a planar interface. However, the shape and the position of the interface for a cylindrical shape in the Bridgman technique are determined primarily by heat transport. In this case the heat transfer does not affect the interface shape if the ampoules are sufficiently long [13], especially since in this systern the solute flow, which can also cause deviation from the isotherm, can be neglected. On the other hand, the case of the initial growth stage, carried
out in a quartz-tube with a variable inner diameter, is quite different. Under these complex heat transfer conditions it has been shown that an increase of the cross-sectional area of a growing system leads to an increase in the solid—liquid interface curvature [14]. Therefore, it seems reasonable to ascribe the principle cause of the cracks to the stresses occurring in the conical zone of the ingots; these stresses are induced by interface variation during the growth. These highly defective zones are obviously dislocation nests (fig. 6); the dislocation concentration is much higher than l0~ 2. cm 3.4. Precipitates p-Type PbTe samples, cleaved from the ingot represented in fig. 1 a, region A, and grown from the stoichiometric melt under normal growth conditions (G 20°C/cm, V 0.5 cm/h), show spheroidal inclusions which are usually darker than the matrix (fig. 7). Their density is about l0~—l0~ cm~2.The presence of such inclusions did not seem to be related to the preparation procedure. A decrease of the growth rate to as low as 0.2 mm/h and/or an increase of the thermal gradient to as high as 50°C/cmdid not affect them. The X-ray microanalysis measurements are similar to those ~
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405
Defects in PbTe single crystals
~
,
~
~
~
4
~ Fig. 6. Etch pits on polished and electrochemically etched surfaces by electron microscope (highl~defective region): (a) dislocation 2. density _~l06cm~2. (b) dislocation density ~ l0~cm~
shown in fig. Sb. In other words, these defects, which exhibit an average diameter of about ~ 3 ~tm, are Te-rich. This analysis does not take into account the possibility of an impurity effect. Therefore we assumed that these inclusions were produced by the decrease of the homogeneity range on cooling (retrograde solubility). In fact the composition at the maximum melting point has 0.0 13 ‘~-
U
Fig. 7. Spheroidal defects in PbTe with p-type electrical conductivity.
at% excess Te [8]. At temperatures lower than 600°C the solubility decreases significantly (see fig. 8). At temperatures of about 400°C the Te solubility seems to be about one order of magnitude lower. The question arises whether Te-rich precipitates form so quickly that they develop during growth from the melt. Scanlon [15] showed from thermoelectric power measurements that they
R. Breschi et a!.
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t t -Ir
d
406 start~ng edt
cpdsit~crn corr~d t~n cO f
ece
~
Defects in PbTe single crystals
I
—‘y----’-
900
(
800 —
7OC~
p-type
PbTe
I J / /
n-t~e 500
PbTe
/ (
300
I
50.000
cOOl
ATOMIC PERCENT
Fig. 8. PbTe phase diagram near the stoichiometric composition (extrapolated from Gomez et al. [8]).
could monitor the Te precipitation process in PbTe samples submitted to a postgrowth annealing process in an inert atmosphere at temperatures lower than 400°C. These results are compared to the theory of stress-assisted precipitation on dislocations. At 370°C, 4 h were required to reach the equilibrium; at 385°C the equilibrium time was estimated to be 2 h. Therefore no data are available for higher temperatures ranging between 400°C 405°Cis the temperature at which PbTe + Te eutectic solidifies) and 600°C(at this temperature the PbTe composition is close to the composition of the maximum melting point). However, it has (—.-
been calculated [16] that the cooling of PbTe samples from temperatures higher than 600°C,even if rapid, is not effective, i.e., it cannot prevent the diffusion, which would then result in the change of the temperature Thus at it can high be assumed that Te-rich Te-rich composition. precipitates form least at temperatures which are just below 600°C. 3.5. Te precipitate free PbTe Now we shall examine some cases in which PbTe free of Te-rich precipitates, in addition to n-type single crystals (for example n-type single crystals grown from PbTe + 0.05 mole% PbBr 2)
which are precipitate-free, will occur: (a) The ingots containing a p—n junction as shown in fig. 1, have a composition between the charge extremes changing from close to the maximum melting composition and Pb-rich side composition related to the micro-phase diagram (fig. 8). Even if the homogeneity range decreases below 600°C, it still has a certain magnitude at both sides of the stoichiometric composition approaching room temperature. Thus a certain p-type zone free of Te-rich precipitates must occur. This zone was found by examining the p-type zone by starting the analysis from the p—n junction. This showed that just 1—2 mm of the length of the p-type zone are Te-rich, precipitate free. The rest of the p-type ingots grown from stoichiometric or lead-rich melt (Pb1 ~8Te, 0 ~ 6 ~ 0.1 at%) shows a precipitate concentration 2 along the randomly whole cylindrical ranging part between of the 10~—l0~ ingot. Increasing the Pb concentration in the melt (0.2— cm 0.3 at%), the diameter of precipitates decreases 2000 A) (see table I). This behaviour has also been observed in the cylindrical part of the p-type ingot grown from stoichiometric melt, when a very low growth rate (0.2 mm/h) is used; this is in accordance with the increase of lead concentration in the melt, due to the normal lead segregation increase. According to the above, the possibility of producing ingots with a linear composition variation between the extremes as assumed by Gomez et al. [8] is questionable for the above indicated compositions. (b) Further increase of lead concentration in the melt (Pb 1 +aTe melt, 6 ~ 1 at%) produces ingots free of Te-rich precipitates. In this case the 1 cm last-to-freeze length (see fig. lc) shows n-type electrical conductivity, while the rest of the ingot shows p-type electrical conductivity (p (2—6)>< 3). The structure of this n-type zone is 1018 cm polycrystalline and is formed by idiomorphic PbTe grains with a Pb-rich phase segregated at the grain boundaries (fig. 9). The change of the monocrystalline structure into a polycrystal structure is abrupt: the n-type region and the p-type region separate easily, when the charge is taken out of the quartz tube. The question arises about the disadvantage of using the growth from the lead-rich melt, which (—.-
compensates for the advantages of having samples
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Defects in PbTe single crystals
407
Fig. 9. Ph segregation in single crystals grown from a Pb
1 01Te melt (last-to-freeze 1 cm): (a) image by back-scattered electrons in SEM; (b) Lai Te X-ray emission image. Enlargement of lower right hand corner of (a).
free of Te-rich precipitates. If the supercooling effect takes place, the lead concentration increases in the melt, and in turn increases the electrically non-active Pb-rich defect concentration in the solid matrix. We have not observed any Pb-rich defect in the p-type matrix by electron microscopy. However, a control of the carrier concentration after annealing, which induces the lead excess diffusion, confirms the presence of Pb-rich defects. In fact the Hall effect measurements show that the asgrown p-type PbTe, which is Te-rich, precipitation-free and grown from Pb1~6Temelt, 8 = I at%, changes the sign of electrical conductivity after 100—200 h of annealing in a non-reactive atmosphere (N2 or H2) at 400°C(at this temperature no evaporation process takes place) (see table 1). This behaviour is also observed in samples grown from the melt with lower Pb excess: all p-type samples grown from Pb1 + ~Temelt with 6 0.1—0.3 at%, having Te-rich microprecipitates, change their electrical conductivity sign after annealing. Also in these cases a growth velocity as low as 0.2 mm/h and a thermal gradient as high as 50°C/cmdo not modify the results. (c) The formation of Te-rich precipitates may be avoided by growing single crystals from a melt doped with materials which form solid solutions with PbTe. In fact, microprecipitates have not been found in p-type as-grown PbTe doped with AgATe.
4. Conclusions Evidence for Te-rich microprecipitates in single crystals grown from a stoichiometric or near stoichiometric melt has been obtained. This defect disappears when single crystals are grown from a lead-rich melt (lead excess ~ 1 at%). However, when using this excess of Pb it seems to be impossible to synthesize single crystals which are cornpletely homogeneous and free from micron-size defects. In fact, even single crystals grown from melts which are less rich in Pb (—~0.1 at%) contain significant amounts of lead electrically inactive as a dispersed second phase. Compared with ingots grown with a Te-excess, that produces precipitates, this amount of lead produces precipitates at least of the same order of magnitude or larger because the as-grown p-type samples irreversibly change carrier sign after annealing in a non-reactive atmosphere at 400°C.Thus, in the single crystals grown from a melt having a Pb-excess < 1 at%, two dispersed second phases, produced by different causes, coexist: a lead-rich and a Te-rich microphase. Void regions, another type of defect, are expected to appear when there is a significant variation of the crystal diameter which induces isotherm variations during the growth. This is what happens in the growth of the first-to-freeze end, having conical shape, by the Bridgman technique.
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Defects in PbTe single crystals
References [I] M. Muhlberg, Kristall Tech. 15 (1980) 565. [21A.J. Crocker, Brit. J. Appi. Phys. 17 (1966) 433. [3] FR. Brebrick, J. Electron. Mater. 6 (1977) 659. [4] A.J. Strauss and R.F. Brebrick, J. Physique 29 (1968) C4-21. [5] E. Levine and RN. Tauber, J. Electrochem. Soc. 115 (1968) 107. [6] B.J. Sealy, J. Mater. Sci. 9 (1974) 1201. [7] G.P. Tilly, Brit. J. AppI. Phys. 12 (1961) 524. [8] M.P. Gomez, D.A. Stevenson and R.A. Huggins, J. Phys. Chem. Solids 32 (1971) 335.
[9] Y. Sato, M. Fujimoto and A. Kobayashi, Japan. J. Appl. Phys. 2 (1963) 688. [10] Y. Kanai and K. Shohno, Japan. J. AppI. Phys. 2 (1963) 3. [11] J.F. Miller, J.W. Moody and R.C. Himes, Trans. Met. Soc. AIME 239 (1967) 342. [12] W.D. Lawson, J. AppI. Phys. 23 (1952) 495. [13] C.E. Chang and W.R. Wilcox, J. Crystal Growth 21(1974) 135. [14] NA. El-Mahallawy and MM. Farag. J. Crystal Growth 44(1978) 251. [15] W.W. Scanlon, Phys. Rev. 126 (1962) 509. [16] W. Albers, C. Haas and H.J. Vink, Philips Res. Rept. 18 (1963) 372.
399
DEFECTS IN PbTe SINGLE CRYSTALS R. BRESCHI CAMEN, S. Piero a Grado, Pisa, Italy
A. CAMANZI Assoreni, Monterotondo, Roma, Italy
and V. FANO Maspec Institute of CNR, Parma, Italy Received 9 July 1981; manuscript received in final form 20 February 1982
Micro-size defects in PbTe single crystals grown by the vertical Bridgman technique have been studied using samples selected from different regions of ingots. The influence of both the Pb : Te ratio in the melt and the role of doping elements using different growth conditions has also been tested. The data thus obtained show that two types of defect are formed: (a) void regions localized in the first-to-freeze cone-shaped region; (b) Te-rich and Pb-rich phases depending on melt compsition.
1. Introduction Although PbTe is a well-known IV—VI group semiconductor used in thermoelectric energy conversion devices and in the synthesis of thermoelectric and optoelectronic PbTe—SnTe alloy systems, its defect structural properties have not been systematically studied. Low grain substructures have been investigated by Muhlberg [1] and by Crocker [2]. Moreover, there is another defect, involving second phase formation, which is highly undesirable both for technological applications and for scientific research; it influences, for example, both the physical characteristics and the performance of the materials. Brebrick and Strauss [3,4] assumed the presence of Te-rich precipitates. However, attempts to observe them directly have been inconclusive in ref. [5], while Sealy [6] has observed microdefects in areas near the last-to-freeze end of an ingot grown from a melt containing 0.5 at% excess of tellurium. Unfortunately there are not enough data available to advance any hypothesis 0022-0248/82/0000—0000/$02.75
©
about the origin of the observed defect. In this work particular attention has been paid to analysing monocrystalline ingots grown by the vertical Bndgman technique in order to obtain both evidence for, and an understanding of, the origin of defects. Thus, we have examined: (a) ingots grown from melts having different Pb—Te ratios; (b) ingots doped with either the commonly used silver or bromine. These ingots were grown using different growth conditions (thermal gradient, G, and growth velocity, V).
2. Experimental The starting elements, 99.999% pure or better, were further purified from oxygen by keeping them at their melting points for a few hours in a flow of H2. The crystals were grown from the melt by the vertical Bndgman technique. Unless otherwise specified the typical dimensions of the ingots were 1.3 cm in diameter and 7 cm in length of which the
1982 North-Holland
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Defects in PbTe single crystals
first-to-freeze 1.5 cm had a conical shape. The crystal growth rate and the thermal gradient ranged between 0.02—1 cm/h and 10—50°C/cm respectively. Single crystals were grown: (a) from the melts of composition Pb1 ±5Te, where 1.01 ~ 1 + ~ ~ 0.999; (b) from the stoichiometric melts doped with 0.05 mol% PbBr2. Specimens cleaved from different areas of monocrystalline ingots have been examined. A Jeol JXA 50A scanning electron microscope was used to observe the surface of freshly cleaved specimens A Jeol Ortec dispersive X mi croanalyzer was employed to study the defect composition of the cleaved surfaces and of the polished and electrochemically etched samples. The samples, etched according to Tilly [7], have also been examined using a metallographic microscope. The electrical conductivity type of the ingot in different regions was tested using a thermoelectric microprobe. The carrier concentration was measured by Hall effect using cross modulation of both the sample current at a frequency of 84 Hz and the magnetic field at the frequency of 36 Hz, 1500 G. The Hall voltage is detected at the sum frequency (120 Hz).
3. Results and discussion 3.]. General remarks In fig. 1 some characteristics of the ingots synthesized by vertical Bridgman technique are reported. In fig. Ia the position and dimensions of the first-to-freeze end (region B) wich is characterized by void regions is sketched. Fig. lb shows the maximum dimensions and the position of the n-type region of the single crystals grown from the melt using normal growth conditions (V = 0.5 cm/h, G = 20°C/cm).The formation of the n-type region is due to the fact that the maximum melting point for PbTe occurs at a Te-rich composition. In single crystals grown from a stoichiometric melt the first-to-freeze end must have a composition very close to the composition corresponding to that of the maximum melting point. This should produce the concentration gradient along the growth direction, due to normal lead segregation, causing n-type electrical conductivity (PbTe is an
re~
___________________
~
t
Fig. I. (a) Regions used for sample selection. (b), (c) Electrical conductivity type for indicated ingot regions using different Pb: Te ratios. The length of the n-type part of the ingot, grown from a stoichiometnc melt, is not rigidly fixed.
amphoteric semiconductor; a Pb excess causes ntype electrical conductivity). Gomez et al. [8] reported the formation of an n-type last-to-freeze end in ingots for starting melt composition having a slight Pb excess. Other authors have found [9,10] that single crystals are always p-type. Miller et a!. [11] have reported that n-type PbTe crystals cannot readily be grown from the melt. However, Lawson [12] reported that n-type and p-type crystals can be grown using lead-rich or telluriumrich melts respectively. We have found that PbTe grown from stoichiometric melts by the Bridgman technique under typical growth conditions (G = 20°C/cm, V= 0.5 cm/h) produces single crystals which randomly exhibit the electrical conductivity sign variation in the last-to-freeze end (half of the twenty charges do not show any sign variation). The uncertainty of the length of the n-type zone cannot be ascribed only to the presence of uncontrolled impurity content because all the charges are synthesized by using the same stock of previously homogenized starting Pb and Te materials. One can attempt to remove this uncertainty by synthesizing the charges of longer length in order to increase the terminal transient length. However, charges which are 1.5 times the usual length (lO—ll cm in length) do not show any different behaviour. Thus, it can be hypothesized that this variation in
R. Breschi et al.
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Defects in PhTe single crystals
the length of the n-type zone or its complete disappearance is due to the lead trapping caused by the supercooling effect. Nevertheless a growth velocity as low as 0.02 cm/h and thermal gradient as high as 50°C/cmdo not modify the behaviour
U
401
of this system, in which the melt mixing is by diffusion only. An estimate of the growth conditions necessary for avoiding constititional supercooling can be made from the phase diagram [8]. This estimate shows that G/V 2.5>< 103°C h
~
Fig. 2. T~pical cleavage fractures, river patterns: (a) Te-excess-doped l’hfe: (h) Ag_Ic-doped Ph Ic; (c) stoichiometric PbTe; (d) PbBr 2-doped PbTe.
402
R. Breschi et al.
/ Defects
cm2 is not enough to avoid the constitutional supercooling (more than two orders of magnitude lower than necessary). We shall return to this later. 3.2. Mechanical The brittleness of the central part of the ingots has been qualitatively tested. Test specimens show typical cleavage fracture with sub-grain boundaries from which further cleavage fronts arise and river patterns appear at (100) orientation pole determined by etch pits (fig. 2). Freshly cleaved specimens were polished and etched using the electrolytic technique described in ref. [7]. This etching does not reveal the inclusions but it makes it possible to count the dislocations. We have measured an average concentration of dislocations 2. Moreover, we have measured of about I0~cm the link angles between the river patterns in order to evaluate the brittleness of the materials. In fact, link angle measurements may be inserted in the relationship sin( co/2) F/2T, where ca is the angle value, F is the retarding force on the disloca-
in PbTe single c,ystals
tion motion, and T is the line-strain caused by the dislocations on the cleavage step. Greater plasticity roughly corresponds to smaller F/T ratios, when other parameters are constant. According to the above the single crystals grown from Te-rich melts (Pb 0 999Te melt) were the most brittle while the PbBr2-doped specimens were the least brittle (maximum plasticity) (see table 1). 3.3. Void regions The samples of the first-to-freeze end of the ingot grown from the stoichiometric melt and cleaved from the conical end of the ingot, as shown in fig. 1 a (set B), present a complex picture. No matter what thermal gradient and growth velocity are used inclusions, and L-shaped voidspheroidal regions (figs. 3a and I-shaped 3b) are present. The cross-section of the void regions is frequently a geometrical figure with sharp angles (fig. 4a). Sometimes the angles are broadened to the point of forming a circular cross-section (fig. 4b). For determining the origin of these defects,
Table I Summary of the results pertaining to the cylindrical part of the single crystals Melt composition
Link angle values a) (river patterns) (deg)
Description of the Te-rich defects in the last-to-freeze end b)
Remarks
Stoichiometric PbTe °~
20—25
—3 ~sm spheroidal Te-rich defects: io~—io~ cm2
PbTe+0.l mol% Te ~
35
PbTe + 0.2 mol% Pb ~
25—30
—3 ~im spheroidal Te-rich defects: l0~— lO~cm2 <1 ~srn spheroidal Te-rich defects: l0~cm~2
PbTe+0.3 mol% Pb ~
28
The average diameter of defects decreases (
PbTe+ I mol% Pb c) PbTe+0.05 mol% PbBr 2 ~> PbTe+0.05 mol% Ag2Te°
2000 A spheroidal Te-rich defects: l0~cm2 No defects
—
18 30
No defects No defects
—
Lowest brittleness
The average values are measured on the last-to-freeze solid. The first-to-freeze solid values are 4—6° smaller. The first-to-freeze end is always highly 3 at defective room temperature (see text). (RT). c) Hole concentration: (2—6)X 1018 cm ~1) Electron concentration: (3—l0))< 1019 cm3 at RT. a)
b)
°
Hole concentration: (0.9_3.5))<
3 at RT. 10i9
cm
—
R. Breschi et al.
/ Defects in
PbTe single crystals
403
U’~ Fig. 3. I-shaped (a) and L-shaped (b) void regions in the first-to-freeze end.
we first consider the void regions, because the inclusions are not located only in this zone. Frequently, a higher Te concentration is detected on the surface of the void regions and a correspondingly smaller Pb concentration is found; fig. 5b shows the Lct1 Te X-ray emission profile across the
defect of fig. 5a (note the opposite intensity variation of the La1 Pb X-emission profile). One can
hypothesize that the void regions are due to a tellurium excess, which makes the crystal more brittle. If this is true, the cracks must be absent in n-type electrical conductivity single crystals, in other words in Te-deficient single crystals in which
no Te-rich defects are present. However, the analysis carried out on all the charges shows that the cracks are present in all specimens cut from the
I
Fig. 4. Typical cross-sections of void regions : (a) cross-sections with sharp angles: (h) circular cross-sections.
404
R. Breschi et a!.
/
Defects in PbTe single crystals
L~
-
1Pb
—
L ~Te
—
a
—
20,LA
~
r
Fig. 5. X-ray microanalysis of the void region surface: (a) the examined defect; (b) the dotted lines refer to La1 Te and Lai Pb X-ray emission intensity profile across the defect (arbitrary units for I).
first-to-freeze ends, that is in samples grown from stoichiometric, Te-, Pb- or Ag~Te-dopedmelts and in n-type samples also, grown from PbBr2-doped melt. Thus the formation of the cracks does not depend upon the melt composition. After this was done, the etched samples were examined by a metallographic microscope. The observed orientation of the etch pits shows that the sides of the Ior L-shaped void regions lie in the (100) directions, the void regions are thus oriented along the easy cleavage faces (lead telluride has NaCl type cubic crystal structure). This fact suggests the presence of stresses upon the crystalshape). because the geometry of acting the ampoule (conical It of is well known that the macroscopic interface shape strongly influences the generation and propagation of defects during directional solidification. Thermal stresses are generally minimal for a planar interface. However, the shape and the position of the interface for a cylindrical shape in the Bridgman technique are determined primarily by heat transport. In this case the heat transfer does not affect the interface shape if the ampoules are sufficiently long [13], especially since in this systern the solute flow, which can also cause deviation from the isotherm, can be neglected. On the other hand, the case of the initial growth stage, carried
out in a quartz-tube with a variable inner diameter, is quite different. Under these complex heat transfer conditions it has been shown that an increase of the cross-sectional area of a growing system leads to an increase in the solid—liquid interface curvature [14]. Therefore, it seems reasonable to ascribe the principle cause of the cracks to the stresses occurring in the conical zone of the ingots; these stresses are induced by interface variation during the growth. These highly defective zones are obviously dislocation nests (fig. 6); the dislocation concentration is much higher than l0~ 2. cm 3.4. Precipitates p-Type PbTe samples, cleaved from the ingot represented in fig. 1 a, region A, and grown from the stoichiometric melt under normal growth conditions (G 20°C/cm, V 0.5 cm/h), show spheroidal inclusions which are usually darker than the matrix (fig. 7). Their density is about l0~—l0~ cm~2.The presence of such inclusions did not seem to be related to the preparation procedure. A decrease of the growth rate to as low as 0.2 mm/h and/or an increase of the thermal gradient to as high as 50°C/cmdid not affect them. The X-ray microanalysis measurements are similar to those ~
R. Breschi et a!.
/
405
Defects in PbTe single crystals
~
,
~
~
~
4
~ Fig. 6. Etch pits on polished and electrochemically etched surfaces by electron microscope (highl~defective region): (a) dislocation 2. density _~l06cm~2. (b) dislocation density ~ l0~cm~
shown in fig. Sb. In other words, these defects, which exhibit an average diameter of about ~ 3 ~tm, are Te-rich. This analysis does not take into account the possibility of an impurity effect. Therefore we assumed that these inclusions were produced by the decrease of the homogeneity range on cooling (retrograde solubility). In fact the composition at the maximum melting point has 0.0 13 ‘~-
U
Fig. 7. Spheroidal defects in PbTe with p-type electrical conductivity.
at% excess Te [8]. At temperatures lower than 600°C the solubility decreases significantly (see fig. 8). At temperatures of about 400°C the Te solubility seems to be about one order of magnitude lower. The question arises whether Te-rich precipitates form so quickly that they develop during growth from the melt. Scanlon [15] showed from thermoelectric power measurements that they
R. Breschi et a!.
/
t t -Ir
d
406 start~ng edt
cpdsit~crn corr~d t~n cO f
ece
~
Defects in PbTe single crystals
I
—‘y----’-
900
(
800 —
7OC~
p-type
PbTe
I J / /
n-t~e 500
PbTe
/ (
300
I
50.000
cOOl
ATOMIC PERCENT
Fig. 8. PbTe phase diagram near the stoichiometric composition (extrapolated from Gomez et al. [8]).
could monitor the Te precipitation process in PbTe samples submitted to a postgrowth annealing process in an inert atmosphere at temperatures lower than 400°C. These results are compared to the theory of stress-assisted precipitation on dislocations. At 370°C, 4 h were required to reach the equilibrium; at 385°C the equilibrium time was estimated to be 2 h. Therefore no data are available for higher temperatures ranging between 400°C 405°Cis the temperature at which PbTe + Te eutectic solidifies) and 600°C(at this temperature the PbTe composition is close to the composition of the maximum melting point). However, it has (—.-
been calculated [16] that the cooling of PbTe samples from temperatures higher than 600°C,even if rapid, is not effective, i.e., it cannot prevent the diffusion, which would then result in the change of the temperature Thus at it can high be assumed that Te-rich Te-rich composition. precipitates form least at temperatures which are just below 600°C. 3.5. Te precipitate free PbTe Now we shall examine some cases in which PbTe free of Te-rich precipitates, in addition to n-type single crystals (for example n-type single crystals grown from PbTe + 0.05 mole% PbBr 2)
which are precipitate-free, will occur: (a) The ingots containing a p—n junction as shown in fig. 1, have a composition between the charge extremes changing from close to the maximum melting composition and Pb-rich side composition related to the micro-phase diagram (fig. 8). Even if the homogeneity range decreases below 600°C, it still has a certain magnitude at both sides of the stoichiometric composition approaching room temperature. Thus a certain p-type zone free of Te-rich precipitates must occur. This zone was found by examining the p-type zone by starting the analysis from the p—n junction. This showed that just 1—2 mm of the length of the p-type zone are Te-rich, precipitate free. The rest of the p-type ingots grown from stoichiometric or lead-rich melt (Pb1 ~8Te, 0 ~ 6 ~ 0.1 at%) shows a precipitate concentration 2 along the randomly whole cylindrical ranging part between of the 10~—l0~ ingot. Increasing the Pb concentration in the melt (0.2— cm 0.3 at%), the diameter of precipitates decreases 2000 A) (see table I). This behaviour has also been observed in the cylindrical part of the p-type ingot grown from stoichiometric melt, when a very low growth rate (0.2 mm/h) is used; this is in accordance with the increase of lead concentration in the melt, due to the normal lead segregation increase. According to the above, the possibility of producing ingots with a linear composition variation between the extremes as assumed by Gomez et al. [8] is questionable for the above indicated compositions. (b) Further increase of lead concentration in the melt (Pb 1 +aTe melt, 6 ~ 1 at%) produces ingots free of Te-rich precipitates. In this case the 1 cm last-to-freeze length (see fig. lc) shows n-type electrical conductivity, while the rest of the ingot shows p-type electrical conductivity (p (2—6)>< 3). The structure of this n-type zone is 1018 cm polycrystalline and is formed by idiomorphic PbTe grains with a Pb-rich phase segregated at the grain boundaries (fig. 9). The change of the monocrystalline structure into a polycrystal structure is abrupt: the n-type region and the p-type region separate easily, when the charge is taken out of the quartz tube. The question arises about the disadvantage of using the growth from the lead-rich melt, which (—.-
compensates for the advantages of having samples
R. Breschi et a!.
/
Defects in PbTe single crystals
407
Fig. 9. Ph segregation in single crystals grown from a Pb
1 01Te melt (last-to-freeze 1 cm): (a) image by back-scattered electrons in SEM; (b) Lai Te X-ray emission image. Enlargement of lower right hand corner of (a).
free of Te-rich precipitates. If the supercooling effect takes place, the lead concentration increases in the melt, and in turn increases the electrically non-active Pb-rich defect concentration in the solid matrix. We have not observed any Pb-rich defect in the p-type matrix by electron microscopy. However, a control of the carrier concentration after annealing, which induces the lead excess diffusion, confirms the presence of Pb-rich defects. In fact the Hall effect measurements show that the asgrown p-type PbTe, which is Te-rich, precipitation-free and grown from Pb1~6Temelt, 8 = I at%, changes the sign of electrical conductivity after 100—200 h of annealing in a non-reactive atmosphere (N2 or H2) at 400°C(at this temperature no evaporation process takes place) (see table 1). This behaviour is also observed in samples grown from the melt with lower Pb excess: all p-type samples grown from Pb1 + ~Temelt with 6 0.1—0.3 at%, having Te-rich microprecipitates, change their electrical conductivity sign after annealing. Also in these cases a growth velocity as low as 0.2 mm/h and a thermal gradient as high as 50°C/cmdo not modify the results. (c) The formation of Te-rich precipitates may be avoided by growing single crystals from a melt doped with materials which form solid solutions with PbTe. In fact, microprecipitates have not been found in p-type as-grown PbTe doped with AgATe.
4. Conclusions Evidence for Te-rich microprecipitates in single crystals grown from a stoichiometric or near stoichiometric melt has been obtained. This defect disappears when single crystals are grown from a lead-rich melt (lead excess ~ 1 at%). However, when using this excess of Pb it seems to be impossible to synthesize single crystals which are cornpletely homogeneous and free from micron-size defects. In fact, even single crystals grown from melts which are less rich in Pb (—~0.1 at%) contain significant amounts of lead electrically inactive as a dispersed second phase. Compared with ingots grown with a Te-excess, that produces precipitates, this amount of lead produces precipitates at least of the same order of magnitude or larger because the as-grown p-type samples irreversibly change carrier sign after annealing in a non-reactive atmosphere at 400°C.Thus, in the single crystals grown from a melt having a Pb-excess < 1 at%, two dispersed second phases, produced by different causes, coexist: a lead-rich and a Te-rich microphase. Void regions, another type of defect, are expected to appear when there is a significant variation of the crystal diameter which induces isotherm variations during the growth. This is what happens in the growth of the first-to-freeze end, having conical shape, by the Bridgman technique.
408
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/
Defects in PbTe single crystals
References [I] M. Muhlberg, Kristall Tech. 15 (1980) 565. [21A.J. Crocker, Brit. J. Appi. Phys. 17 (1966) 433. [3] FR. Brebrick, J. Electron. Mater. 6 (1977) 659. [4] A.J. Strauss and R.F. Brebrick, J. Physique 29 (1968) C4-21. [5] E. Levine and RN. Tauber, J. Electrochem. Soc. 115 (1968) 107. [6] B.J. Sealy, J. Mater. Sci. 9 (1974) 1201. [7] G.P. Tilly, Brit. J. AppI. Phys. 12 (1961) 524. [8] M.P. Gomez, D.A. Stevenson and R.A. Huggins, J. Phys. Chem. Solids 32 (1971) 335.
[9] Y. Sato, M. Fujimoto and A. Kobayashi, Japan. J. Appl. Phys. 2 (1963) 688. [10] Y. Kanai and K. Shohno, Japan. J. AppI. Phys. 2 (1963) 3. [11] J.F. Miller, J.W. Moody and R.C. Himes, Trans. Met. Soc. AIME 239 (1967) 342. [12] W.D. Lawson, J. AppI. Phys. 23 (1952) 495. [13] C.E. Chang and W.R. Wilcox, J. Crystal Growth 21(1974) 135. [14] NA. El-Mahallawy and MM. Farag. J. Crystal Growth 44(1978) 251. [15] W.W. Scanlon, Phys. Rev. 126 (1962) 509. [16] W. Albers, C. Haas and H.J. Vink, Philips Res. Rept. 18 (1963) 372.