Narrow-Gap Semiconductors

280 Pages·1983·11.496 MB·English

by  Dr. Ralf Dornhaus, Professor Dr. Günter Nimtz, Dipl.-Phys. Burghard Schlicht (auth.)

paG-worraN Lead Salts
By G. Nimtz and .B Schlicht
.1 Introduction
ehT narrow-gap semiconductors gnoma the family of IV-VI sdnuopmoc dna their pseudo-
binary alloys show emos extraordinary aspects of solid-state physics. ehT polymor-
phism of IV-Vl sdnuopmoc indicate the inherent structural instability which is based
no the average five valence electrons. ehT most interesting point, however, is that
the bonds are based no the itinerant electrons in the valence band which is sepa-
rated from the conduction band by a narrow energy gap. In such a situation eno ex-
pects the electronic properties to eb strongly correlated with the lattice insta-
bility. Another interesting feature follows from the many-valley band structure in
combination with a strongly non-isotropic effective mass in lead telluride: the
Auger mechanism is expected to play a dominant role in free-carrier recombination.
During the last twenty years many experimental dna theoretical studies were per-
formed to elucidate the basic properties of the IV-VI .sdnuopmoc In addition ynam
activities in the field of infrared devices have been successful in producing laser
diodes dna photodetectors for the wavelength range between 4 dna 03 .m~
It is our intention to present in this article the basic data of the lead salt
narrow pag semiconductors currently available. eW should like to encourage further
efforts towards a better understanding of this fascinating semiconductor family,
dna supply data for the development of efficient devices. eW are aware of the fact
that this article is not a complete presentation of all investigations published
os far.
.2 The Crystal
This chapter is devoted to the basic physical properties of the four lead salt
narrow-gap alloys Pbl_xSnxTe, Pbl_xSnSe, PbSl_xSe x, dna Sx_1eTbP x dna their binary
.sdnuopmoc In the first section the lattice, elastic dna related data are presented.
ehT lattice instability representing eno of the outstanding physical properties of
these IV-VI binary dna ternary sdnuopmoc is also discussed in this section. In the
second section phase diagrams are introduced, dna the third section deals with lat-
tice imperfections dna their properties. I
2.1 Basic Properties
ehT pag-worran lead salt alloys era erom or less ionic crystals. ehT ionicity -ed
creases in going from SbP to eSbP to .eTbP ehT ionic nature of the gnidnob of the
~
lead chalcogenides is impressively nwohs yb the spatial valence charge distributions.
~P b b
eS
Fig. 2.1. ehT total valence electron F!g. 2.2. ehT total valence electron
egrahc density for eSbP derived from egrahc density for eTbP derived from
pseudopotential band-structure calcu- pseudopotential band-structure calcu-
lations. ehT values are given in units lations. ehT values era given in units
of electrons per unit-cell .emulov of electrons rep unit-cell .emulov
ehT charge around the cation sites is ehT charge dnuora the cation sites is
mainly of s character saerehw dnuora mainly of s character saerehw dnuora
the anion sites it clearly exhibits eht anion sites it clearly exhibits
contributions from htob s dna p states contributions from both s dna p states
/75SI/ /75SI/
RETOLHCS et al. /75SI/ have calculated the contours of constant charge density in a
)001( plane for various .sdnab ehT results for the mus of the five valence sdnab
are nwohs in Fig. 1.2 for eSbP dna in Fig. 2.2 for .eTbP In Table 1.2 the calcu-
lated approximate fractional charges inside touching spheres dnuora anions dna
cations desopmoced into I = O, 1, 2 angular ,stnenopmoc era given for the valence
sdnab /75SI/. morF these na approximate charge transfer of 9.1 )eSbP( dna 5.1 )eTbP(
electrons from cation to anion nac eb estimated (in the "totally ionic" ledom owt
electrons of the cation era transferred to the anion).
tsoM of eht binary ,sdnuopmoc e.g. ,eTbP ,SbP ,eSbP eTnS era found to eb iso-
suohprom with rocksalt, its lattice is nwohs in Fig. 2.3. ehT wol molecular weight
material ,eSnS no the other hand, is found in na orthorhombic structure (Fig. 2.4).
ehT nature of chemical binding in these crystals is mixed ionic-covalent. ehT phy-
Table 2.1. Calculated fractional charges (in percent) inside touching spheres
around anions dna cations. The sphere radii were chosen as rcation = 1.29 ~,
ranio n = 1.94 X for PbTe dna rcation = 1.22 X, ranio n = 1.83 X for PbSe (from
/75SI/)
eSbP eTbP
bP eS bP eT
dnaB s d s p d s p d s p
1 1 0 79 1 0 3 1 0 59 i
2 55 0 81 42 3 07 0 0 31 31
3 - 5 9 1 1 87 4 5 9 2 0 08
1 - 5 61 4 1 32 25 4 81 6 1 22 05
12 97 52 57
Simple 02
0 0 02 06 0 02 0 0 02 06 0
ionic
sical background of the crystal structure of IV-VI compounds saw recently discussed
extensively in papers by DOOWELTTIL /80LI/. The covalent binding is assumed to eb
predominant which is concluded for instance from analysis of carrier scattering
/7OR/. Investigations of the carrier scattering in various lead chalcogenides have
shown that both optical dna acoustical phonons are important, the latter being na
indication of predominant covalent binding.
All the compounds with NaCI structure have a structural phase transition eud to
their mixed ionic-covalent chemical binding. With decreasing ionicity the NaCl struc-
ture becomes more dna more unstable, accompanied by both an increasing electronic
1
Fig. 2.3. ehT rocksalt structure
tm
r,o l"D o o 3 f3 ~ 0 ~ ~ rD
om ~- <" E3 v ~, ~ o ~- ~ ~ ~cr OO v CD 0 fD 0 ~--CJ fD ~l:lJ fD %g g~ I~ g~
)
\ p~ .--t g I o g- 3
g
i
"2)
e~
(
Oo I
\
I
--O
I o\+
U')
POLARISABILITY I 2. ~
"~1" ~ ~ ~ ~<
LATTICE -/ g ::0 N r-- A ~ C~ ' ~0 -~ g'-og -.g fD
and lattice polarisability /77L5/. This behaviour is shown in Fig. 2.6 and will eb
discussed in more detail in Sect. 5.4.
The cubic to rhombohedral phase transition can eb explained sa a result of a
large electron-TO phonon coupling eud to the resonant nature of the half-filled
p states. Below the transition temperature T C (for most of the sdnuopmoc T C < 0
holds sa will eb shown below) the two neighbouring ions along the <111> axis ekam
displacements in opposite directions forming a rhombohedral, As-type crystal struc-
ture as shown in Fig. 2.5. The cubic rocksalt structure of the lead chalcogenides
is stabilised by perpendicular p bonds, with the s states fully occupied dna making
only a small contribution to the bonding. ehT lack of hybridisation between the s
and p bands in the lead salts arises from the large energy splitting between s and
p states. The rhombohedral structure is na intrinsic instability of the unsaturated
p bonds in the rocksalt structure. Because there are only six p electrons per atom
pair, dna yet there are six neighbours for each atom, the p bonds are unsaturated.
The rocksalt structure is thus a resonantly bonded system /68KI , 73L2/ in which the
bonding electrons are relatively free to move from the bond no eno side of the atom
to the bond no the opposite side in response to na external field. In the rhombo-
hedral phase the six cubic nearest neighbours are displaced along the <III> direc-
tion with respect to the central atom os that each atom won has three nearest neigh-
bours and three second-nearest neighbours in the distorted phase. The nearest neigh-
bours bond strongly together in a layer perpendicular to the <111> direction. The
bonds in the rhombohedral structure are won more nearly saturated than in the cubic
system, because the bonding electrons are localised in the nearest-neighbour bonds.
The cubic-rhombohedral phase transition can eb understood as the result of the
electron-TO phonon coupling for modes propagating in the <III> direction. Coupled
to this is a shear which distorts the cube into a rhombohedron, and lengthens the
<111> axis.
The orthorhombic structure found in SnSe arises because of the strong sp hybridi-
sation in IV-VI compounds with low molecular weights/8OLIA The orthorhombic struc-
ture also seems to present the high pressure phase of IV-VI compounds and their
alloys, which were found in the rocksalt structure at atmospheric pressure /e.g.:
40B,48B, 54B,67M,68K3,68W,80S,81S1/. Data of the lattice constants of the
pressure induced orthorhombic structure of several IV-VI compounds are given in
Table 2.2. From a study of this high pressure phase transition in Pbl_xSnxTe IKSUS
et ai./81S1/ conclude that a metallic-covalent transition takes place. They emussa
a promotion of an s electron to p states due to the decrease in interatomic dis-
tance.
Consequences for the transport properties as well sa the accompanied softening
of the transverse optical phonon due to the structural phase transition are dis-
cussed in Sects. 4.2 and 5.4 respectively. Experimental data of the transition
temperature are shown for Pbl_xSnxTe in Fig. 2.7. These data published by ESARUM
Table 2.2. Lattice constants of the pressure-induced orthorhombic (Pnma) crystal
structure /67M/
Material T (K) a (~) b (~) c (~) P (kbar)
SbP 300 11.28 3.98 4.21 52
eSbP 300 11.61 4.00 4.39 43
eTbP 300 11.71 4.36 4.42 42
SnTe 300 11.59 4.37 4.48 20
' I ' III' I ' I,' I r I
002
cT 150 '""'"l I' ' ' I I
)K(
051 oTe }K{cT ;
001
001
05
1
0
05
(cid:12)9 "~'~" 050-
5~.0
-50 Pbl. x SrkTe
l'
-I00 ' ,,,,,,,,l I .... 1 I
21( L.O 6,0 8.0 0.1 1 2 3 5
eTbP x eTnS P )3~nc020I'(
Fig. 2.7 Fig. 2.8
Fig. 2.7. Composition dependence of the transition temperature for sample series
grown by different methods /82MI/. Band inversion occurs at the T b line /68D/. The
data () represent the Curie temperature deduced from dielectric ~onstant. Transi-
tion temperature data of bulk material are from (4) /82MI/, (o) /79K2/. The values
(e) are obtained from epitaxial layers on FaB 2 substrates /82M1/
Fig. 2.8. Pbl_xSnxTe. Transition temperature as a function of carrier concentra-
tion for various tin compositions x /76K2,82MI/: x = 1 (~), x = 0.8 (o),
x : 0.7 (-), x = 0.6 (+), x = 0.5 (A), x = 0.45 (e)
dna NISHI /82M1/ present values of the Curie temperature (see Sect. 5.4) dna the
transition temperature obtained from bulk material. ehT Curie temperature saw de-
termined by a tangent line to i/c o = f(T) at T ~ 09 ,K whereas the transition tem-
perature saw obtained from the resistivity anomaly eud to na increment of electron-
nonohp scattering near the transition temperature. ehT anomaly is demussa to orig-
inate from na increasing relaxation rate eud to soft OT phonons dna screened OL
snonohp /76K2,76K3,80K2,82M1/ (see also Sect. 4.2). Data of the temperature of
band inversion as a function of composition are also presented in Fig. 2.7.
ehT transition temperature also appears to eb a function of the free-carrier
concentration /69C2,7511,76K2,78K2/. This property is shown in Fig. 2.8 for var-
ious mixtures of Pbl_xSnxTe. sA will eb discussed in Sect. 5.4 this nonemonehp is
caused by electron-TO phonon coupling eud to the optical deformation potential.
NOTHGUAD dna ED OICAF /78D2/ published calculated values for T c assuming a ledom
for the structural phase transition, which saw developed by LEFFOTSIRK dna NISNOK
/68K3,73K3/ dna by IROTAN /76N2,76N3/, (see also Sect. 5.4). For the time being
a quantitative agreement is not obtained either between experimental results or
between various theoretical data. enO reason for this situation yam eb that the
lattice instability does depend not only no carrier density dna no band pag but
also no the crystal quality, e.g., the number of lattice defects, or no strain
which yam eb induced in thin films (see also Sect. 5.4).
ehT lattice constants as well as density, melting temperature, dna thermal ex-
pansion coefficient of the binary sdnuopmoc are given in Table 2.3. It saw found
that both lattice constant dna energy pag vary approximately linearly with composi-
tion in the ternary alloys as shown in Fig. 2.9. ehT large difference in the lat-
tice constants between PbTe dna SbP causes the ternary dnuopmoc PbTel_xS x to eb
brittle. nO the other hand, the crystalline properties of Pbl_xSnxTe, eSx_1SbP x
dna Pbl_xSnxSe are comparable to those of the binary compounds. ehT mixed crystal
Pbl_xSnxSe crystallizes in the cubic rocksalt structure no the lead-rich side pu
to x < 0.43. A two-phase region is observed for 0.43 ~ x ~ 0.75 dna eventually for
x ~ 0.75 na orthorhombic structure is established /61K/. ehT lattice constant as
a function of the composition is plotted in Fig. 2.10. ehT lattice constants wohs
a linear dependence no composition only in the cubic crystal phase of the PbxSnl_xSe
alloy.
Elastic data of the binary sdnuopmoc are given in Table 2.4. There is not hcum
data published no the IV-VI alloys. For Pbl_xSnxTe (x = 0.13) NOTHGUAD et al. /76D/
have calculated elastic constants from phonon dispersion data.
ehT pressure dependence of the elastic constants of PbTe dna SnTe were studied
by RELLIM et al. /81M/. emoS third-order elastic constants sa obtained in this
study are presented in Table 2.5.
Ref. /64N/ /64N/ /64N/ /64N/ /64N/ /64N/ /64N/ /64N/ /64N/ /68H2/ /68H2/
(K)
30 30 30
T 300 100 300 100 300 100 300
77-300
940
(10-5/K) 2.027 1.755 0.754 1. 1.737 0.765 1.980 1.770 0.902 2.04 1.97
, ,
coefficient Ref. /74HI/ /70S 74H1/ /70S 74H1/ /73H1, 74L2/ /74HI/ /70S/
(~
expansion T M Iiii 1082 924 874 857 805 807
thermal Ref. /67W/ /67W/ /67W/ /80M/ /81M/ /80M/ /74H1/ /81M/ /76S1/
linear (K)
T 299 288 293 300 300 300 300 300 300
and
3)
point, (kg/m
7500 8100 8160 8242 8219 6179 6445 6383 6410
melting density
density, Ref. /69D1/I /67M/ /69D1/ /67M/ /69D1/ /67M/ /80M/ /80M/ /80M/ /74H1/ /67M/
(K)
T 299 300 299 300 299 300 300 300 300 300 300
constants,
4.46 4.14 11.47
Lattice a (10-10m) 5.936 5.929 6.124 6.117 6.462 6.443 a = b = c = 6.327 6.303
2.3.
Table Compound PbS (cubic) PbSe (cubic) PbTe (cubic) SnSe (ortho- rhombic) SnTe (cubic)
Pbl_xSnxTe PbTel_xS x bP SI.xSe x Pbl_xSnxSe
56-
('V~l six ~~,-J- f ~ f i
I~ A \ t "-'-t I
1 . o o , 1ol t \ / t \ T "" t
n
1&-
o T ~ T \
21 . .V, " i
eTnS eTbP SbP eSbP eSnS
}C( )C( )C( )C( ).bmohr(
Fig. 2.9. citamehcS representation of energy pag ,~E gnidnopserroc citengamortcele
htgnelevaw ,~ dna lattice constant a versus noitisopmoc for various ternary alloys
/P97/
ehT crystal binding energies of binary sdnuopmoc were estimated from eht heat
of crystal formation yb AKANAT dna ATIROM /79TI/. ehT values are: :SbP 32.6 eV,
:eSbP 32.5 eV, :eTbP 31.4 eV, :eTnS 31.9 .Ve ataD of the eybeD erutarepmet of
eht binary sdnuopmoc sa well sa emos of their ternary alloys era listed in
/83L/.
I
At .... 11.60
0,~.11
02.4
81..4 b
4..16
/*./~7
4.~,5
~.r/*3
eSbP 02 0~ 06 08 SnSe Fig. 2.10. Lattice constants sv elom
fraction for eht eSxnSx_lbP alloy
ELOM NOITCARF /K16/
Table 2.4a. Elastic moduli (1010 m/N 2)
Substance T (K) Cli 21C 44C Ref.
SbP 13.9 3.47 1.69 /63Cl/
(cubic) 003 12.7 2.98 2.48 /51B/
003 12.61 1.624 1.709 /76P/
eSbP 892 12.37 1.93 1.59 /71L2/
(cubic) 195.8 13.37 1.98 1.642 /71L2/
77.4 13.98 1.97 1.695 /71L2/
4.2 14.18 1.94 1.749 /71L2/
eTbP 003 10.53 0.70 1.322 /81M/
(cubic) 003 10.80 0.77 1.343 /68H2/
003 10.40 0.437 1.30 /62C/
eTnS 003 10.43 0.178 1.133 /81M/
(cubic) 392 10.93 0.21 0.97 /76S1/
Table 2.4b. Sound velocity (m/s), T = 300 K (wave vector, polarisation)
SbP klo0 , transv. klo0 , long. k011 , transv.
0051 0804 0281 /63CI/
eSbP klo0 , transv. klo0 , long. k011 , transv.
5141 3860 0961 /63C2/
eTbP klo0 , transv. klo0 , long. k011 , transv.
0621 3590 0161 /62C/
klo0 , transv. klo0 , long. k111 , long.
7721 0263 6762 /68H2/
eTnS transv. k110 , long. transv.
k110 ' 001 kllO ' 110
1388 2103 0092 /76SI/
01