c-cds 77475_v3_10

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Chanter 10

Cubic Cadmium Sulphide

(c-CdS)

10.1 STRUCTURA L PROPERTIES

10.1.1 Ionicity

Table 10.1.1 Phillips's ionicityAfor c-CdS [ I ,11.

f;

0.685[1.11 J. C. Phillips, Bonds and Bands in Semiconductors (Academic, New York, 1973).

10.1.2 Elemental Isotopic Abundance and Molecular Weight

Isotopic abundance

Table 10.1.2 Isotopic abundance in percentfor cadmium and sulfirr [1,2].

Isotope YO at. abundance Isotope % nat. abundance Isotope % nat. abundance

Io6Cd I .25 I2Cd 24.13 32s 95.02

"'Cd 0.89 'I3Cd 12.22 33s 0.75"'Cd 12.49 'I4Cd 28.73 34s 4.2 1

'"Cd 12.80 Ii6Cd 7.49 36s 0.02

[1.2] D. R. Lide, CRC Handbook of Chemistry and Physics, 78th Edition (CRC Press, Boca Raton,1997).

255

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256 Cubic Cadmium Sulphide (cCdS)

0 M olecular weight

Table 10.1.3 Molecular (average atomic) weight Mfor e-CdS.

M (amu)

144.477

10.1.3 Crystal Structure and Space Group

Table 10.1.4 Crystal structure and its space and pint groupsfor e-CdS.

Crystal structure Space g o u p Point group

Zincblende (Cubic) F 4 3 m T d

10.1.4 Lattice Constant and Its Related Parameters0 Lattice constant, near-neighbor distance, etc.

Table 10.1.5 Lattice constant (a), near-neighbor distance (4, unit cube volume (a3), andmolecular density (dn)for e-CdS at 300 K.

Parameter Value

Lattice constant a (A)

d (Cation-Anion) (A)

d (Cation-Cation) (A)

Unit cube volume a3 (10-22m3)

5.825 [1.3]

2.522"

4.119"

1.976"

Molecular density dM (1022 m - ~ ) 2.024"

[1.31W. R. Cook, Jr., J . Am. Cerum.Soc. 51,5 18 (1 968).

*Calculated.

0 Crystal density

Table 10.1.6 Crystal density gfor e-CdS at 300K. *

g (gicm3)

4.855

*Calculatedusing ~ 5 . 8 2 5 .

10.1.5 Structural Phase Transition

Table 10.1.7 Structural phase transition in e-CdS at high temperatures.~~

Structure Transition temperature ("C)

Zincblende (F 4 3 m ) Room temperatureWurtzite (P63mc) 300 [1.41

[1.410.Zelaya-Angel and R. Lozada-Morales, Phys. Rev. B 62,13064 (2000).

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10.2 Thermal Propert ies

p 1475'C -/

/

1400-

257

- -

10.1.6 Cleavage Plane

Table 10.1.8 Cystallogra phic plane most readily cleaved o r e-CdS.*

Cleavage plane

(110)

*Expected.

I600

/

-

-

800

ooo-

400 -Cd 0

200 -

-

-

-

-cdS

Surface energy

Table 10.1.9 Surface enevgyfor e-CdS (in J/m2).

-tI

-

- -

- -I7'

213' ,,Se

d

-(6 CdSe

Plane

1.06 1.07 0.69 Calc. r1.51

11.51 B N:Oshcherin, Phys. Status Solidi A 34, K18 1 (1976).

I0.2 THERM AL PROPERTIESI10.2.1 Melting Point and Its Related Parameters

Table 10.2.1 Melting poin t T,,, and its related parameter f o r CdS.

Parameter Value

Melting point T,,, (K) 1748 [2.1]

Entropy of fusion AS, (cal/mol K) 16.21 [2.2]

[2. ] H. H. Woodbury, J. Phys. Chem. Solids 2 4 , 8 81 (1963).[2.2] See, B. R. Nag, J. Electron. Matel: 26, 70 (1997).

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258 Cubic Cadmium Sulphide (c C d S )

10.2.2 Specific Heat

No detailed data are available for c-CdS .

10.2.3 Debye Temperature

No detailed data are available for c-CdS.

10.2.4 Thermal Expansion Coefficient


10.2.5 Therm al Conductivity and Diffusivity


10.3 ELA STIC PROPERTIES

10.3.1 Elastic Constant0 Room-temperature value

Table 10.3.1 Elastic stifiess a n d compliance constantsfo r c-CdSa t 300K.

Parameter Value

Stiffness (10" dyn/cm2) [3.1]

CI 1 7.70CI 2 5.39c44 2.36

SI 1 3.07

S44 4.24

[3. ] Average values [see,Data andFunctiona1 Relationships in Science and Technology,edited by K.-H.Hellwege and A. M. Hellwege, Landolt-Bornstein, New Series, Group 111 Vol. 11 (Springer, Ber-lin, 1979)l.

[3.2] Calculated from C, values.

Compliance (lo-'*cm2/dyn) [3.2]

SI2 -1.26

10.3.2 Third-Order Elastic Constant

Table 10.3.2 Third-order elastic constant of c-CdS [3.3].

Modulus Value (10' dyn/cm2)

Clll -2.5

CI 12 -2.8c123 -1.9

c144 +0.3

c456 +0.4

c166 -0.6

[ 3 . 3 ]Numerical Data and Functional Relationships in Science and Technology, edited by K.-H. Hell-wege and A . M. Hellwege, Landolt-Bornstein, New Series, Group 111 Vol. 11 (Springer, Berlin,1979).

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10.3 Elast ic Properties 259

10.3.3 Young’s M odulus, Poisson’s Ratio, and Similar0 Young’s modulus

Table 10.3.3 YoungS modulus Y fo r c-CdS at 300K. *

Crystallographic plane Y (10” dyn/cm2)( 100)plane

[ O O l ] direction 3.26[Ol l ]direction 5.09

[ O O l ] direction 3.261111 direction 6.26

(110) plane

( 1 1 1 ) plane 5.09

*Calculated using Sll= 3.07,S 12 =-l 26, and S ~ 4 . 2 4all in cm’idyn).

0 Poisson’s ratio

Table 10.3.4 Poisson . ratio P fo r c-CdS at 300 K. *

Crystallographic plane P

( 100)planem=[010], =[001] 0.4 10

m=[011], =[ 0i1] 0.079

m=[001], =[li01 0.410(1 10)plane

( 1 11 ) plane 0.454

*Calculated using Sll=3 .07,SI2=1.26, and S4=4.24 (all in cm2/dyn).

0 Bulk modulus, shear modulus, etc.

Table 10.3.5 Bulk modulus, B , ,pressure derivative of B, , dB, /dp, shear modulus, C,, isotropy

factor;A, linear com pressibility,C,,, Caucy ratio, C,, and Born ratio, B o ,for c-CdS at 300K ,Parameter Value

~~ ~

B, (10’ dyn/cm2) 6.16 [3.4]

dB, ldp 4.8 [3.5]

C, (10’ d y d c m 2 ) 1.16 [3.4]

A 0.489 [3.4]

C , (1O-I3 cm21dyn) 5.41 [3.4]

ca 2.28 [3.4]

Bo 1.04 [3.4 ]

[3.4] Calculated using Cll= 7.70,C12=5.39, and C ~ = 2 . 3 6all in 10” dyn/cm2).[3.5] Theor. [S.-H. Wei and A . Zunger, Phys. Rev. B 60,5404 (1999)l.

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10.3.4 Microhardness


10.3.5 Sound VelocityTable 10.3.6 Sound velocitypropagating in c-CdS at 300 K. * LA=longitudinal acoustic; TAl,TAZ=transverse acoustic.

Propagation direction Mode Sound velocity (1Os c d s )

3.98

2.20

4.28

1.54

2.204.38

[ 1 1 1 1 TAl,TA2 1.79

*Calculated using Cl =7.70x10" dyn/cm2, CI2=5.39x 0" dyn/cm2, C 4=2.36x 10" dyn/crn2, andg4.855 g/cm3.

I0.4 PHONO NS AND LATTICE VIBRON ICI PROPERTIES

10.4.1 Phonon D ispersion Relation

Lattice dynamics and phonon dispersion curves for c-CdS has been discussed theoretically byM . A.Nusimovici and J. L.Birman [Phys.Rev. 156,925 1 967)].

10.4.2 Phonon Frequency0 Room-temperature value

Table 10.4.1 Long-wavelength (q4)n d zone-boundary phonon fiequencies for c-CdS. *

Critical point Phonon Phonon frequency (cm -')

r TO 237

L O 303

X TALA

TO

LO

L TA 41

LA

TO 255

LO

*Estimated from w-CdS data.

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10.6 Energy-Band Structure: Energy-Band Gaps 261

10.4.3 Mode Gruneisen Parameter

No detailed data are av ailable for e-CdS.

10.4.4 Phonon Deformation PotentialNo detailed data are available for c-CdS.

10.5 COLLECTIVE EFFEC TS AND RELATEDPROPERTIES

10.5.1 Piezoelectric Constant

No detailed data are available for e-CdS.

10.5.2 Frohlich Coup ling Constant

No detailed data are available for e-CdS.

10.6 ENERGY-BAND STRUCTURE: ENERGY-BAND

GAPS

10.6.1 Basic Properties0 Electronic energy-band structure

Fig. 10.6.1 Electronic energy-band structure of c-CdSas calculated within the local-density-functional for-malism. [From A. Zunger and A. J. Freeman, Phys.Rev. B 17 , 4850 (1978).] The locations of several in-terband transitions are included by the vertical arrows.

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262 Cubic Cadmium Sulphide ( c C d S )

0 Electronic density of states

-I5 -10 - 5 0 5

ENERGY ( e V )

Fig.10.6.2

Electronic density of states for c-CdS as calculated within the local-density-functional for-malism. [From A. Zunger and A. J. Freeman, Phys. Rev. B 17,4 850 (1978).]

Energy eigenvalue

Table 10.6.1 Energy eigenvalues at thetion bands of c-CdS [6, ] .

X and L points fo r the valence andfir st m onduc-

Value (eV)

Calc. ExDer.*ritical point Level

r r6"(r > -1 1.46

I-7" (TI57 0.00 -0.07

TSV 0.00

r7c (r15c) 7.61 7.4

rsc

r6c (rlc) 2.62 2.40-2.55

X x6" (XI") -11.42 -13.85

x6" (x3") -2.64 -3.7, -4.8

x6" (x5") -1.06 -1.54, -1.9x7"

x7c (X37 5.45

x6c (XI') 5.24

L Lgv (Ll") -1 1.43

L6" (L ") -2.75 -4 .18 , -4 .8

Lgv (L3") -0.4 1 -0.62, -0.8

L4,5"

L4,5'

Lgc 04') 4.04

L6c (L37 8.36

[6.1]A. Zunger and A. J. Feeman, Phys. Rm. B 17,4 850 (1978).*The data are gathered from various sources.

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10.6 Energy-Band Structure: Energy-Band Gaps 263

10.6.2 &-Gap RegionTemperature dependence

Table 10.6.2 Eo- and EOiAo-gap energiesfor c-CdS determined at various temperatures.

Temperature (K) EO W EO+& ( e v ) C o m m e n t4.2 2.48 Epilayer on (1 1O)InP [6.2]

300 2.50 * '2.55 *2

Epilayer on (1 11)GaAs [6.3]

2.4 1

2.40f0.01 Polycrystalline film [6.5]

2.45 Polycrystalline film [6.6]

2.42 Polycrystalline film [6.7]

2.46 (2.53) Mean value (T=300 K)

Epilayer on (1 10)InP [6.4]

[6.2] D. R. T. Zahn, G Kudlek, U. Rossow, A. H o fh a n n , I. Broser, and W. Richter, A h , Matex Opt.

[6.3] M. Cardona, M. Weinstein, and G A. Wolff, Phys. Rev. 140, A633 (1 965).[6.4] U. Rossow, T. Weminghaus, D. R. T. Zahn, W. Richter, and K. Hom, Thin Solid Films 233, 176

[6.5]0.Zelaya-Angel, J. J. Alvarado-Gil, R. Lozada-M orales, H. Vargas, and A. F. da Silva, Appl. Phys.

[6.6]0.Zelaya-Angel and R. Lozada-Morales, Phys. Rev. B 62, 13064 (2000).[6.7]0.Vigil, 0.Zelaya-Angel, and Y. Rodriguez, Semicond. Sci.Technol. 15,2 59 (2000).* ' Peak in R.* 2 Peak in E ~ .

Table 10.6.3 Empirical equationfor the heavy-hole (HH) and light-hole (LH) band-gap energyvariation with temperature Tfor c-CdS.

Electron. 3, 11 (1 994 ).

(1993).

Lett. 64,2 91 (1994).

ParameterC o m m e n t

EO 0) (eV) a ( o4 e V K ) P (K )

2.445 (HH) 3.451 208 n=1 exci ton, epi layer on (1OO)GaAs,

[6.8] T. Nagai, Y. Kanemitsu, M. Ando, T. Kushida, S . Nakamura, Y. Yamada, and T. Taguchi, Phys.Status Solidi B 229,611 (2002).

Table 10.6.4 Empirical equationfor the heavy-hole (HH) and light-hole (LH) band-gap e n e wvariation with temperature Tfor c-CdS.

2.455 (LH) 3.966 222 T=13-200 K [6.8]

2.464 (HH) 20.5 165 n=l exci ton, epi layer on (1 OO)GaAs,

[6.9] T. Nagai, Y. Kanemitsu, M . Ando, T. Kushida, S. Nakamura, Y Yamada, and T. Taguchi, Phys.

2.479 (LH) 25.4 177 T=13-200 K [6.9]

Status Solidi B 229,611 (2002).

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Table 10.6.5Spin-orbit-splitofenergy A0f o r e-CdS.*

dn (eV) C o m m e n t

0.079 Calc. [6.10]

-0.07 T=1.7 K 16.111[6.10] M. Willatzen, M. Cardona, and N . E. Chnstensen, Phys. Rev. B 51, 17992 (1 995).[6.11] See, D. W. Niles and H. Hochst, Phys. Rev. B 44, 10965 (1991).*Note that &, may not vary with temperature if one supposes the valence-band rigidity of the 111-V

compounds.

0 Temperature and/or pressure coefficient

Table 10.6.6 Linear temperature and pressure coe8cient.s of the Eo- and Eo+Argap energiesfor e-CdS.

B a n d gap Coefficient Value CommentEO dE, ldT (1O4 e V K )

dE, ldp ( I 0-2 Vl GP a ) 5.5 Calc. [6.12]

4.7 Calc. [6.13]

-0.7 p>6 GPa [6.14]

EO+& dE, IdT (1O4 e V K )

dE, ldp (10-2 V/GPa)

[6.12] K. J. Chang, S. Froyen, and M. L. Cohen, Solidstate Commun. 50, 105 (1984).

[6.13] S.-H. Wei and A . Zunger, Phys. Rev. B 60,540 4 (1999).[6.14] See, B. Ray, ZI-VI Compounds (Pergamon, Oxford, 1969).

10.6.3 Higher-Lying Direct Gap

0 Temperature dependence

Table 10.6.7 Higher-lying d irect-gap energies o r c-CdS at several temperatures.

Value (eV )B a n d g a p

T=90 K [6.15]

El 5 O 5.1E2 6.4,6.9

EO’ 7.4

El’ 8.3

T=300 K [6,16]

[6.15] Ph. H ofinann, K. Horn, A. M . Bradshaw, R. L. Johnson, D.Fuchs, and M . Cardona, Phys. Rev. 47,

[6.16] U. Rossow, T. Werninghaus, D. R. T. Zahn, W. Richter, and K. Horn, Thin Solid Films 233, 1761639 (1 993).

( 1 993).

10.6.4 Lowest Indirect Gap0 Theoretical value

Table 10.6.8 Theoretically obtained lowest indirect-gap enevgy or c-CdS (in ev ).~~ ~ ~

E; * l E$ * 2 Ref.

4.04 5.24 [6.17]

4.30 4.72 [6.18]

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10.7 Energy-Band Structure: E lectron and Hole Effect ive M asses 265

Table 10.6.8 Continued.

E: * ' E$ * 2 Ref.

4.13 4.05 [6.19]

4.82 5.08 16.20116.171A . Zunger and A . J. Feeman, Phys . Rev. B 17,4 850 (1978).16.181M.-Z. Huang and W. Y.Ching, J . Phys. C hem. Solids 46,977 (1985).[6.19]Y.Li and P. J. Lin-Chung, Phys. S tatus Solidi B 153,215 (1 989).16.2010.Zakharov, A . Rubio, X. Blase, M. L. Cohen, and S. L. Louie, Phys. Rev. B 50, 10780 (1994).* I rgv (rl;)+~:(~Ic).* 2 r; (rl:)+&c(xlc).

0 Temperature and/or pressure coefficient

Table 10.6.9 Linear pressure co eflcient of the lowest indirect-gap energy o r c-CdS.

Coefficient Value Com men t

dE:ldp (10-2 VIGPa) 4.2 Calc. [6.21]

3.6 Calc. r6.221

d Ez l d p (10-2eVIGPa) -1 .o Calc. [6.21]

-1.4 Calc. [6.22]

16.211K. J. Chang, S. Froyen, and M. L. Cohen, Solid State Com mun. 50, 105 (1 984).16.221 S.-H. Wei and A . Zunger, Phys . Rev. B 60,5404 (1 999).

10.6.5 Conduction-Valley Energy Separation


10.6.6 Direct-Indirect-Gap Transition Pressure

No detailed data are available for c-Cd S.

I0.7 ENERGY-BAND STRUCTURE: ELECTRON ANDI HOLE EFFECTIVE M ASSES

10.7.1 Electron Effective Mass: I'Valley

Theoretical value

Table 10.7.1 Theoretically obtained electron efective mass m erat the r va ll eyfor c-CdS.

m:/mo Technique~~~~ ~ ~

0.14 $sum rule [7.1]

0.209 Linear combination of atom ic orbital method r7.21

17.13 R. Dalven, Phys. Status SolidiB 48, K23 (1971).17.21 M.-Z. H uang and W. Y .Ching,J. Phys. Chem . Solids 46,9 77 (1985).

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10.7.2 Electron Effective Mass: Satellite Valley


10.7.3 Hole Effective Mass0 Luttinger's valence-band parameter

Table 10.7.2 Luttinger j . valence-bandparameter fo r c-CdS (in h2/2m0).

n M Y3

4.11 0.77 1.53

*Estimated fiom a plot of Eo versus 3.;; for som e cubic group-IV, 111-V, and 11-VI sem iconductors (seefigure, below).

20

10

012

9

3

I I Fig. 10.7.1 Luttinger's valence-band parameter y, versus

Eo for a num ber of the group-IV, 111-V, and 11-VI

~=0.77,nd yj=1.53 (in A2/2rno).

-

semiconductors in the cubic structure. From this plot,we can estimate y, values for c-CdS to be 84 .11 ,

-a -I I ,

a

0 2 4 6 8Eo (W

0 Band mass, cyclotron mass, etc.

Table 10.7.3 Band (m", mLH), density-of-states heavy-hole (m"*), averaged light-hole (mLH*),and spherically-averaged heavy-hole (m"", and light-hole masses ( m d ) n c-CdS.*

Mass Value (mo)

WZ" ([OOl] direction) 0.39

mLH ([0011 direction) 0.18

m" ([1111direction) 0.95

mLH ([11 1] direction) 0.14

~ H H * 0.68

~ L H * 0.15

~ H H ~ 0.60

mLHS 0.15

*Calculated using a set of the Luttinger's parameters , ~ 4 . 1 1 ,r=0.77, and yj=l.53.

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10.8 Electronic Deformation Potential 267

Spin-orbit-splitoff hole effective mass

Table 10.7.4 Spin -orbit-splitofh ole efective mass msofor c-CdS.

msdmo

*Obtained from the Luttinger’s parameter (ms o= llp ).

10.8 ELECTRONIC DEFORMATION POTENTIAL

10.8.1 Intravalley Deformation Potential:r Point

0 Conduction bandTable 10.8.1 Peonduction-band intravalley deformationpotential acr (=El 3for c-CdS,

a: (eV> Comment

-27.1 Calc. [8.1]

[8.1] A . Blacha, H. Presting, and M. Cardona, Phys. Status Solidi B 126, 1 1 (1984).

0 Valence band

Table 10.8.2 r-valence-band deformationpotentials a, b, and dfor c-CdS.

Commenteformation potential (ev )

~ ~~

-17.5 1.6 Calc. [8.2]

0.92 -1.18 Calc. [8.3]

-1.07 Calc. [8.4]

-1.05 Calc. [8.5]

- 4 .7 Exper. [8.6]

[8.2] A . Blacha, H. Presting, and M. Cardona, Phys. Status Solidi B 126, 11 (1984).

[8.3]A. Qteish and R. J. Needs, Phys. Rev. B 45 , 13 17 (1992).[8.4] T. Nakayama, Solid-state Electron. 37 , 1077 (1994).[8.5] R. Said,A. Qteish, and N. Meskini,J . Phys.: Condens. Matter 10 ,87 03 (1998).[8.6] D. W. Niles and H. Hochst, Phys. Rev. B 44, 10965 (1991).

Eo gap

Table 10.8.3 Hydrostatic deformation potential aorfor the EO ap of c-CdS.

-9.6 Calc. [8.7]

-3.77 Calc. [8.8]

-2.27 Calc. [8.9]

-2.94 Calc. [8.10]

+0.43 ExDer. *[8.7] A . Blacha, H. Presting, and M. Cardona, Phys. Status Solidi B 126, 1 1 (1984).[8.8] T. Nakayama, Solid-state Electron. 37, 1077 (1 994).[8.9] R. Said,A . Qteish, and N. Meskini,J. Phys.: Condens. Matter 10,8 703 (1998).

[8.10] S.-H. Wei and A. Zunger, Phys. Rev. B 60,5 404 (1999).*Estimated from dEddp value.

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[ , $ h ' ) = ~ ~ ( E ) + i ~ ~ ( h ' ) ]nd (b ) complex refractive-index s^

tical Constants of Crystalline and Amophous Semicon-

1 -pectra [n*(E>=n(E>+ik(E>]or c-CdS at 300 K. The nu-

merical data are taken from tabulation by S. Adachi [Op-

0 Optical-phonon deformation potential

Table 10.8.4 Optical-phonon deformation potential do at the I--valence band of c-CdS,

B -7-----,n

:: -

t- ' x 10---*..

6.9 Calc. [8.11]

[8.11] A. Blacha, H. Presting, and M. Cardona, Phys. Status Solidi B 126, 11 (1984) .

10.8.2 Intravalley Deform ation Potential: High-Symmetry Points


10.8.3 Intervalley Deformation Potential


10.9 ELEC TRO N AFFINITY AND SCHOTTKYBARRIER HEIGHT

10.9.1 Electron Affinity


10.9.2 Schottky Barrier Height

N o detailed data are available for c-CdS.

10.10 OPTICAL PROPERTIES

10.10.1 Summary of Optical Dispersion Relations

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10.10 Opt ica l Propert ies

c-CdS (b ) j

-

-

I I

269

0 H E ) and R(E) spectra

I I

0.35 L I I 1

Fig. 10.10.2 (a) Absorption [or(E)] an d (b) nor-mal-incidence reflectivity spectra [R(E)] or c-CdSat 300 K. The numerical data are taken from tabu-lation by s. Adachi [Optical Constants of Crystal-line and Amorphous Semiconductors: NumericalData and Graphical Information (KluwerAcademic, Boston, 1999)l.

10.10.2 The Reststrahlen Region

0 Static and high-frequency dielectric constants

Table 10.10.1 Static a nd high-frequency dielectric constants E~and E, for c-CdS.

E, E, Comment9.8 5.4 T=300 K

* Estimated fiom w-CdS data [ E ~ = ( E ~ ~ E ~ ~ ~ ) ” ~ ,~ S = ( E ~ S ~ ~ ~ ) ’ ” ] .

10.10.3 At or Near the Fundamental Absorption Edge0 Refractive index

Table 10.10.2 Refractive index n near the fund am ental absorption edge of c-CdS at 300 K[lo. ] .

0.51

1.5

2

2.02

2.04

2.06

2.08

2.12.12

2.14

2.479

1.240

0.826

0.620

0.614

0.608

0.602

0.596

0.5900.585

0.579

2.30

2.33

2.37

2.486

2.494

2.503

2.5 13

2.523

2.5322.542

2.551

2.16

2.18

2.2

2.22

2.24

2.26

2.28

2.3

2.322.34

0.574

0.569

0.563

0.558

0.553

0.548

0.544

0.539

0.5340.530

2.563

2.575

2.586

2.599

2.6 14

2.630

2.650

2.673

2.7032.739

[10.11 See, S . Adachi, Optical Constants of Crystalline and Amorphous Semiconductors: NumericalData and Graphical Information (Kluwer Academic, Boston, 1999).

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Cubic Cadmium Sulphide (cCdS)70

Fig. 10.10.3 Refractive index n for c-CdS at T=300 K.The experimental data are taken from S. Adachi [Op-tical Constants of Crystalline and Amorphous Semi-conductors: Numerical Data and Graphical Informa-tion (Kluw er Academic, Boston, 1999)l. The solid linerepresents the calculated result usingn2=4.46+[0.806A2/(A2-0.203)]ith A n pm.

0 0.5 1.0 1.5 2.0Photon energy (eV)

0 Fundamental absorption edge

0 As-grown

2.3 2.4 2.5 2.6 2.7

2.5

Fig.10.10.4

(ahv ) ~

ersus photon energy h v plots for as-grownand two annealed samples. Polycrystalline thin films in theceCdS phase were grown on glass substrates at 80fl"C bychem ical bath deposition. Solid-solid phase transform ation fromthe cubic, zinc-blende or sphalerite metastable modification ofCdS (c-CdS) to the hexagonal, wurtzite stable phase (w-CdS)gradually occurred by annealing in A r + S 2 in the temperaturerange 100-550°C. The extrapolation of the straight line to the h v

axis gives EO.[From 0.Zelaya-Angel and R. Lozada-Morales,Phys. Rev. B 62, 3064 (2000).]

10.10.4 The Interband Transition Region0 Fundam ental optical spectra

Fig. 10.10.5 Complex dielectric function,~ ( E ) = E ~ ( E ) + ~ E ~ ( E ) ,undamental reflectivity,R(E) , and energy-loss function, -ImE'(E),for c-CdS at 300 K. The experimental dataare taken from tabu lation by S. Adachi [Op-tical Constants of Crystalline and Amor-phous Semiconductors: Numerical Data andGraphical Information (Kluwer Academic,Boston, 1999)l.

10

8

6

2

0

Q 4

0.4 I I I I I 10.20

0 ' I I / I I I ' 0

0 1 2 3 4 5 6Photon energy (eV)

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10.11 Elastoopt ic , E lect roopt ic , and Nonl inear Opt ical Proper t ies 27 1

10.10.5 Free-Carrier Absorption and Related Phenomena


10.11 ELASTOOPTIC, ELECTROOPTIC, ANDNONLINEAR OPTICAL PROPERTIES

10.11.1 Elastooptic EffectNo detailed data are available for c-CdS.

10.11.2 Linear Electrooptic ConstantNo detailed data are available for c-CdS.

10.11.3 Quadratic Electrooptic ConstantNo detailed data are available for c-CdS.

10.11.4 Franz-Keldysh EffectNo detailed data are available for c-CdS.

10.1 1.5 Nonlinear Optical ConstantSecond-order nonlinear optical susceptibility

Table 10.11.1 Theoretical second-order nonlinear optical susceptibilityx;;:-20; w ;w ) n thestatic limit ( tZw-4 ev)for c-CdS,

7.4 r11.11

[11, I ] M.-Z. Huang and W. Y. Ching, Phys. Rev. B 47,9464 (1993).* 1 m N = 3x 104/4nesu.

0 Third-order nonlinear optical susceptibility

Table 10.11.2 Theoretical third-order nonlinear optical susceptibilityX$ (-313; w ,w ,w ) n thestatic limit @w+O ev)for c-CdS.

1 oo 0.57 F11.21

[11.21W. Y. Ching and M.-Z. Huang, Phys. Rev.B 47,9479 (1993).

* 1 m N 2= 9x OS/4nesu.

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272 Cubic Cadmium Sulphide ( c C d S )

10.12 CAR RIER TRANSPORT PROPERTIES

10.12.1 Low-Field Mobility: Electrons

Table 10.12.1 300-K (&*OK) and pea k H all mobilities (ppeuk)o r electrons in c-CdS.

Mobility Value (c m 2 N ) Comment

p300K 70-85 MO CVD-grown layer on GaAs(100)

n=5.Ox 1Ol8-6.5x 1019 ~ m ' ~12.13

Pp e a k

[12.11K. Yasuda, H. B. Samion, M. Miyata, N. Araki, Y. M asuda, and Y. Tom ita,J. Cryst.Growth 222,

477 (2001).

10.12.2 Low-Field Mobility: Holes


10.12.3 High-Field Transport: Electrons

0 LO-phonon-scattering-limited electron saturation drift velocity

Table 10.12.2 Calculated LO-phonon-scattering-limited electron saturation driftvelocity v,,,,,in the lowest-conduction -band valley afor c-CdS at 300 K. *

I-

e,sat 3 4I

*Calculated w ith r =0.14mo an d a 0 = 3 0 3 cm-'.

10.12.4 High-Field Transport: Holes


10.12.5 Minority-Carrier Transport: Electrons in p-Type Materials

N o detailed data are available for c-CdS .

10.12.6 Minority-Carrier Transport: Holes in n-Type Materials


10.12.7 Impact Ionization Coefficient


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