Optical functions and bands of II-IV-V2 group phosphides

OPTICAL FUNCTIONS AND BANDS OF II--IV--V2 GROUP PHOSPHIDES

V~ V. Sobolev and V. E. Grachev UDC 621.315.592

INTRODUCTION

The semiconducting II--IV--V2 phosphides, crystallizing in the chalcopyrite structure, are the closest isoelectronic and structural analogs of diamondlike phosphides from III--V group compounds [i]. Because of the reduction of the symmetry owing to the presence of two types of cations, the displacement of anions from the equilibrium (in the cubic lattice) positions, and the tetragonal compression of the lattice, the band structure of II--IV--V2 semiconductors is more complicated than that of III--V semiconductors. The selection rules for dipole-allowed transitions predict complex polarized optical spectra in the region of the fundamental absorption [2-8].

II--IV--V2 phosphides are divided into direct gap~ which have a direct gap at the center of the Brillouin zone (BZ) F, corresponding to the direct gap of the binary III--V analog, and pseudodirect gap, whose direct gap (in F) corresponds to the indirect (F § X) gap of the III-- V binary analog [2, 3].

At the early stages of the study of the optical properties of II--IV--V2 semiconductors, spectral features close to those of the III--V analogs were observed, correctly assuming that the similarity of the structural properties and the weakness of the tetragonal distortions should lead to close optical properties. Some of the spectral features, however, cannot be explained starting from the optical properties of the binary analogs. The first measurements of the polarized reflection spectra already revealed the purely chalcopyrite structures Ec~ , Ec2, Ec3 and EC~ [9]. The procedure proposed in [i0] for calculating the electronic band structure over the entire BZ made it possible to establish that the E c structures indeed occur because of the transitions into a new Van Hoff singular point, which appears in the structure of chaicopyrite because of the reduction of symmetry. It became obvious that precision measurements of the reflection spectra for II--IV--V2 compounds were necessary. It was also necessary to increase the accuracy of band calculations over the entire BZ and of optical spectra obtained from them.

Among the II--IV--V2 compounds the phosphides have been studied in greatest detail. The main reason for this is that the single crystals of these compounds are grown by different methods with natural faces of high quality sufficient for studying dimensions, and the region of the fundamental absorption in them begins in an energy interval which is easily accessible for measurements. In recent years we have studied the reflection spectra of some of the phosphides in the group of compounds under study on a precision spectral setup, assembled based on a double DFS-12 monochromator. These spectra served as a basis for the calculations of complexes of optical functions from the Kramers-Kronig relations. In this review, we dis- cussed the optical reflection spectra and the optical functions as well as the reflection be - tween the features in the reflection spectra and the available band calculations.

I. ZnSiP=

The semiconducting compound ZnSiP= is a pseudodirect-gap analog of the binary compounds AIP and GaP. Its energy bands were calculated by the empirical pseudopotential method at the high-symmetry points of the BZ F, N, T 9 and P [2] (here and in what follows the notation for points and directions in the BZ introduced in [2] is used); at the points F, N, P, T, and L; along the symmetric directions A and R [5, 6], and, over the entire BZ [ii]. The energy bands were also calculated over the entire BZ by the self-consistent method of the total electron density functional [12]. The most accurate and detailed calculation of the band structure [ii] showed that, like for other II--IV--V2 compounds, in ZnSiP2 the top of the valence band lies at the center of the BZ and has P~ symmetry. Below this lies the Fs top, split off by the noncubic crystal field. The bottom of the conduction band consists of two types of aniso-

Institute of Applied Physics t Academy of Sciences of the Moldavian SSR. Translated from Izvestiya Vysshikh Uchehnykh Zavedenii t Fizika, No. 8, pp. 54-67, August, 1986.

0038-5697/86/2908-0627512.50 �9 1987 Plenum Publishing Corporation 627

' j:'.A

1 ; , . < " -

i 2

R

0.$

oh

0.2

~ ~ ~,~v

~5

~0

//,\

8:'21

Z 4 6 ~ " [, eV

Fig. I Fig. 2 Fig. 3

Fig. i. Reflection spectra of ZnSiP2. i) 2) Theory of [ii]; 3, 4) experiment, our data at 103 K. The solid curves correspond to EJc , and the broken curves correspond to Elle (theory) and E}[[011].

F i g . 2. S p e c t r a c I ( c u r v e s 1 and 2) and e2 ( c u r v e s 3 and 4) o f CdSiP2 a t room t e m p e r a - t u r e . The s o l i d c u r v e s c o r r e s p o n d to E• and the b r o k e n c u r v e s c o r r e s p o n d to Eil[0 1 1].

F i g . 3. S p e c t r a r ( c u r v e s 1 and 2) and e2 ( c u r v e s 3 and 4) o f CdSiP2 a t 98 K. The s o - l i d c u r v e s c o r r e s p o n d to E i c , and t he b r o k e n c u r v e s c o r r e s p o n d to EJlI0 I 1].

tropic competing minima r3 and Ts) corresponding to the states x, and x3 in the III--V analog. According to [Ii], the absolute minimum of the bottom of the conduction band in ZnSiP2 is displaced somewhat from the point T and lies on the line B at the point with coordinates (0, 0.15, I). The width of the indirect gap equals 1.96 eV.

Optical studies of the band structure of ZnSiP2 began in the second half of the 1960s. The spectra of the fundamental absorption edge [13-18] and the luminescence spectra [19] confirm the calculations of [ii]. The polarized reflection spectra, however, in a wide range of fundamental absorption, which make it possible to refine the band calculations performed by the empirical pseudopotential method, have still not been obtained. The reflection spectra from the natural face ([, [, 2) of ZnSiP2 in the region 1-1.5 eV in polarized light and in the region 5-12 eV in unpolarized light were measured at roomtemperature in [21]. Our measurements of the reflection spectra from the natural faces ([) [, 2) and (0, [, i), obtained at room temperature and at the temperature of liquid nitrogen [20], differ somewhat from the spectra of [21]. Thus the main maximum E~ at 4.54 eV, which is unpolarized in [21], turned out to be strongly polarized in our experiments, and the principal maximum of the polarization E If[0 ! l] was displaced into the region of high energies (E G = 5.03 eV at 103 K) (Fig. I). On the long wavelength drop off of the reflection spectrum we observed many more weak structures than in [21]. In addition, an additional weak structure Es was observed in E H[0 1 I] polarization at 103 K| this structure vanishes as the temperature is raised up to room temperature (Fig. i, Table i). Table 1 gives the interpretation of the observed structures according to [ii]. As is evident from the table I the maxima E, and E2 are determined primarily by transitions in the R direction contribution to El and transitions in Fs-F3 to E2.

The quality of the samples in both our measurements and in [21] was apparently inadequate which is indicated by the drop off of the reflection in the region above 4.5 eV in the spectra [20, 21].

2. CdSiP2

The compound CdSiP2 is an isoelectric analog of (GaP + InP)/2 [6, 21]. The band structure was calculated by the empirical potential method in [3, 6]. As pointed out in [22], however, aside from the noncubic corrections to the choice of pseudopotential given in [6], the band structure depends on the choice of the form factors at those reciprocal lattice vectors for which there are no experimental values. Based on the edge absorption spectra, some authors [23-26] consider CdSiP2 to be a direct-gap compound in which direct forbidden transitions r~v-F~ c ("pseudodirect") are realized, while other authors assume that indirect transitions are realized at the absorption edge [27-31].

628

TABLE I.

Energies (in eV), Polarizations, and Temperature Coefficients

AE

/AT

(in i0 -a eV/K) of Structures in

the Reflection Spectra of ZnSiP2 and the Corresponding Transitions

Stru

ctur

o

......

.. E

xper

imen

t ]

......

...

The

ory

[11"

]"

our

data

[2

r]

I tr

ansi

tion

in

BZ,

ban

d nu

mbe

rs,

poil

riza

t[on

29

5 K

10

3 K

[

--A

E/A

T

ener

gy,

eV

W!

W2

W3

Ved

A)

W~

(B+

C)

y&

v&

W7

W8

v4

E,

&

E3

b,'4

&

E8

Eg

Eio

2,83

11

2,97

11

7,3

--

Nt-

-N,

(15,

16

--17

, 18

) II

2,94

11

3~05

11

5,7

--

"1"5

+4-

-T,+

~

(15,

16

--d9

, 20

) I[

3,00

1 3,

06]_

3,

1 --

B

t--B

t (1

5---

17)

LI_'

3,08

11

3361

1 4,

2 --

FG

(F4)

- FT

(l',)

[I

(A_)

3,

17'].

_ 3,

26 [

_ 4.

7 --

1"

7(I"

5) --

l'r

(lh)

22

I'

s(F

s)--

Fr(

I'0

/,

II 3,

3311

3,

4511

6,

3 ~

Ft-

-F,

(16-

-17)

ne

ar

(0,2

5; 0

,25;

0,5

) I],

2_

3,34

22

3,46

22

6,3

--

B,-

-B~

(15

--17

) (0

; 0,

25;

1)

22

R2-

-R2

(16-

-17)

(0,

38;

0,38

; 0)

I[,

_1_

3

,42

1

3,5r

6,

3 3,

461[

3,48

11

3,58

11

5,2

F,-

-F,

(16-

-17)

(0

,32;

0,

32;

0,64

) II,

2_

3,57

1 --

--

3,

58]_

F

2--F

, (1

5--1

7)

(0,3

2;

0,32

; 0,

64)

22

(][)

N

,--N

I (1

3,

14--

17,

28)

~_l_

--I

[",-

-F,

(16-

-19)

(0

,23;

0,2

3;

0,60

) II

(-L

) --

3,

7811

3,

75_L

, [I

3,81

'1

--

t R

2--R

I (1

6--1

9)

(0,3

; 0,

3;

0)

_[_

I:,-

-F,

(16-

-19)

(0

,25;

0,2

5;

0,5)

II

(_L)

3,

8511

3,

941t

4,

7 3,

91 2

2.,

11

3,92

,]..

3,98

_1_

3,1

I'5--

I'3

(12,

13

--17

) %

1_

--

~ --

4,

08..1

_, l

[ F

~--

F2

(14-

-17)

(0

,25;

0,2

5; 0

,5)

2-,

1[ F

t--F

t (1

4---

M8)

(0

,25;

0,2

5; 0

,5)

[[ (_

.L)

--

4,30

11

--

--

l'5--

Fs

(14,

15

--20

, 21

) 11

At-

-At

(14-

-19)

(0

; O

; 0,

4)

I[ 4,

4822

4,

5322

3.

6 i

Nr-

N~

(1

6--2

0)

2_

4,54

s

II 4,

4811

4,

66il

4,2

(15-

-18)

re

g. n

ear

(0;

0.44

; 0,

25)

II A

,--A

2 (1

5--1

9) (

0; 0

,5; 0

) II

(i)

4,9,

31_

5,00

'1

3,6

4,8(

>.3_

N

I---

,VI

(16-

-21)

[1

._ N

I~,V

t (1

5,

16--

21,

22)

[I 5,0

011

5,031

1 1.

6 --

- N

,--N

~ (1

3, 1

4--1

9, 2

0)

I[, _

L.

--

5,17

22

--

--

I'~.--

1".

(12.

13

--19

) 2-

(1

1)

2,88

3.

03

3,3

2,98

3,

03

3,10

3,

15

~3,

2 N

3,2

5

3,26

3,

37

3,39

3,

59

3,5

3,79

4,00

4,

00

4,06

4.

30

4,30

4,

53

4,50

4,

60

5.00

5,

00

5,16

5,

00

O~

bO

n,)~ I

I,K \G ?_

o N ~ J Z , , 2 3 4 t_, ev

Fig. 4

i ,

~ffl

;'.o!

fro! J

0.5

0 i

/ t I ) 1

4 6 8 [, eV

0,6

0.5

3.4

3.5

3.2

R

0,4 I

(15 } ~~-"---)kJ _,.. 02

! t

Fig. 5 Fig. 6

R

05

Fig. 4. Spectra of the refraction and extinction coefficients of CdSiP2. Curves 1 and 2 show n and curves 3 and 4 show K at 300 K. The solid curves correspond to s177 and the broken curves correspond to s I i ] ,

Fig. 5. Spectra of the effective number of electrons neff, the electronic losses Ime -I and surface plasmons Im(l + e) -I at 300 K for the CdSiP= crystal in Eic polarization.

Fig. 6. Reflection spectra of ZnGeP2. i, 2) Theory [i0]; 3, 4) experiment, our data 98 K. The solid curves are for Eic and the broken curves are for EIIC

The optical reflection spectra, measured at 80 and 300 K, from the natural face (0, T, i) in the range (1-5.5 eV) with a spectral resolution of 5 meV and a reproducibility of AR < 0.03% revealed on the long-wavelength edge of fine structure with a distinct polarization de- pendence, taking which into account, under the assumption that the observed features are associated with the rs-F1 and F~-F, transitions) it was found that Acf = -0.162 eV and Aso = 0.067 eV at 80 K. A series of new weak features was also observed.

Based on these spectra) the spectra of complexes of 12 optical functions were calculated using the Kramers--Kronig relations at temperatures of 80 and 293 K and for two polarizations E ~ _ c and E IL[Ol l ] . The position of the features in the reflection spectra is given in Table 2. The computed optical functions are shownin Figs. 2-5. Figure 2 shows the curves of

and 82 for two polarizations at room temperature. The behavior of the curves is strongly affected by the values of the absorption coefficients, which are used in the extrapolation of the reflection curves in the region of transparency. In addition) it is necessary to intro- duce data on absorption deep in the fundamental absorption band, where there are no experimental values (the program "feels" absorption >i0~ cm-1). An increase in the absorption nar- rows and increases the amplitude of the first peak in the curves e, and reduces the second peak. In addition, the quantities nef f remain within reasonable limits. Therefore, in order to carry out an accurate calculation of the optical functions, it is necessary to perform measurements on thin (less than 5 ~m thick) films) which presents definite difficulties because of the lack of samples.

The results of the calculations (Figs. 2-5) are preliminary.

3. ZnGeP2

The semiconducting compound ZnGeP= -- the closest isoelectronic analog of the indirect-gap compound GaP -- is a pseudodirect semiconductor. The band structure and theoptical properties of ZnGeP2 have been studied in greater detail and more fully than other If--IV--V2 compounds. Calculations over the entire BZ were carried out first for this crystal among the II--IV--V= group, and the polarization reflection spectra were calculated based on them [I0]. Recently an attempt was also made to take into account the effect of the d levels of transition ele- ments on the energy spectrum [12].

Spectral studies of the edge absorption [13) 30, 31] and luminescence [33] showed that ZnGeP2 has F~ Valence hand top, below which the Fs level lies. The order of the levels at the bottom of the conduction band is F3 < F2 < rl. Weak minima) associated with the transitions r4,s + F2)I [35], were observed in the thermoreflection spectra [34]. The reflection spectra

630

TABLE 2.

Energies (in

eV), Polarizations, and Temperature Coefficients AE/AT (in

i0 -~

eV/K)

of Structures in the

Optical Spectra of

CdSiP2, th

e Values (in

eV)

of the

Crystal Field and th

e Spin-Orbital Splittings an

d Correspond-

ing Transitions

"'

__

..

....

-E

xpem

-nen

t ..

....

....

....

...

.__-

[ ..

....

....

....

....

. T

he o

ry ..

....

....

....

....

..

I I

] en

ergy

, eV

S

truc

ture

re

flec

tion

[2

91__

_1

^e.,

Aw

lref

lect

io n

th

erm

ore-

I

tran

siti

on

in B

Z,

band

"

I fl

ecti

on

num

bers

, po

lari

zati

on

~ ...

....

....

....

80

K

'1

293

K

I ...

..

/'~

'][2

1,30

0"K

] [2

6,90

.,i<:

3 ]

] [6

1 [

[31

C

2,73

11,

_L

2,64

il, 3

_ 4,

2 --

2,

7111

, .2

_ B

2,

78

2_

2.69

~

4,2

-.-

2,75

11,

_L

A

2,92

511

2,84

11

4,0

--

2,94

5 A

ct

--0,

162

---0

,167

.

..

.

0,20

A

so

0,06

7 0,

067

..

..

0,

07

Et

3,06

11

--

3,16

!1

E2

3,30

11

3,24

II

2,8

3,30

11

3,41

11

3,32

2.

3,26

2.

2,8

3,24

2-

:1,3

42.

E3

3,66

il 3,

55ii

5,2

3,55

A.,

l[ 3,

71L

, II

E~

3,71

! 3,

672-

1,

9

E5

3,95

11

--

--

EG

4,27

2-

4,17

2-

4,7

E7

4,30

11

--

--

E8

4,53

11

4,50

11

1,4

E9

4,72

11

4,63

[!

4,2

El0

4,

952-

--

--

Etl

5,

28_/

. --

--

5,

3111

--

--

EI.~

--

5,

122-

--

El3

--

- 5,

20!1

--

1'~-

-1',

.,'__

,,ii)

2,31

2,

50

1"4-

-1'i

1[ 2,

47

1,92

--

0,14

--

NI-

-NI

(15,

16

--17

, 18

) I1

2,81

:3

,01

NI-

-N1

(13,

14

---1

7,18

) 2-

3,

17

4,11

l'5

--1'

a (1

2,

13--

17)

_L

(II)

3,

38

4,65

.R

z--R

~

(16-

-18)

ne

ar

(0,5

; 0,

5;

0)

2-,

II 3,

48

--

LI-

-L2

(1

6---

17)

11, .

2-

3,53

--

P

t--P

,~

(13,

14

.---

17,

18)

II, _

1_

3,69

4,

43

3,67

-k

3,

82.1

P

z--P

2

(15,

16

--17

, lb

) _k

3,

51

4,69

L

2.--

L,~

(1

5--1

7)

2-

3,75

--

L

I--L

I (1

6--1

8)

2.

4,05

--

--

--

N

~--

NI

(15,

16

--19

, 20

) [I,

3_

4,18

4,

45

N~

--N

~

(11,

12

---1

7,

18)

0, .

2-.

4,19

4,

23

4,15

~_

4,37

'[.

Tt+

2--

Ts

(13,

14

--17

, 18

) .1_

4,

22

5,22

Fs

--I'

~ (1

2,

13--

19)

3_

(I!)

4,

35

5,18

A

~+

4--

A 2

(1

2, 1

3--1

9)

near

(0

; 0;

0,2

) 2-

4,

42

--

Tra

nsit

ions

ne

ar

P, L

, an

d on

R

A_,

II

4,3

5,06

--

--

7

"s--

l~

(11-

-17)

1[

4,39

5,

62

NL

--N

~

(13,

14

--19

, 20

) ii,

•

4,54

5,

54

4.42

1[

,I,,5

31i

F:,-

-l's

(1

5,

I6--

20,

21)

II 4,

62

5,4.

t A

2--

A2

(1

1--1

7)

near

(0;

0;

0,3)

li

.t,80

--

--

4

R3~,

f, T

3-~

4-.'

T s

(1

5,

16-.

-21,

22

) 11

4,

88

5,64

.

..

.

I'S-

-I'4

(1

5,

16--

--22

) I

(11)

:1

,87

5,52

I'

~--F

5 (1

4-.2

0,

21)

Z (i

!)

4,72

5,

88

--

--

P~--

P~

(13,

14

--21

, 22

) 2-

5,

62

5.36

--

--

P

~--

P~

(1

5,

16--

21,

22)

II, 2

- 5,

44

5,63

A

2--

A2

(1

1--1

9)

near

(0;

0; 0

,6)

II 5,

5 --

--

~

T~

---T

I+2

(9,

10.-

I9,

20)

.L

5,82

,t.

27

5,3O

.

..

.

T~

..-T

5 (9

, 10

--17

, 18

) 11

5,

66

5,62

Lm

TABLE 3.

Energies (in eV) and Polarizations of the Structures in the Optical Spectra of ZnGeP2 and the Corres-

ponding Transitions

t E

xper

imen

t

�9

re f

lect

ion

I the

rmo-

--

-

-

re fl

ec-

our

data

:-

- 11

0]

[36]

[d

on

[34,

98 K

I

300 K

I ,,

5 K

I

80K

./12

0*K

]

[lO]

Theory

[7]

tran

siti

on i

n B

Z a

nd

tran

siti

on

in B

Z a

nd

ener

- po

lari

zati

on

......

po

lari

zati

on,

gy

1,17

11

..

..

..

.

1,63

11

--

--

2.0"--

811

r4--

r3

--

e n

e r

"-'-

~

IgY

2,14

52-,

II

rs-r

3 2,

21_L

2

,30

r~

-rz

2,46

1[, .

L I

'6 (r

~)--

r~(r

,)

2,53

222

r,(r

,)-r

,(r,

) 2,

59[I

l'6(r

s)-r

r(r;

) --

N

I--N

, (1

5,

16--

17,

18)

B'

2,03

11,-L

1,

9611

, 2-

--

C"

--

2,11

1 2,

14]1

, 2-

--

B

" --

--

2,

29_L

--

C

"

--

2,31

1J

--

Es

2"~5

[I 2,

25ll

2,51

11,

2-

--

--

--

2,63

2-

--

--

--

2,

6711

--

E4

. 2,

9511

2,

8911

3,

0211

, 2.

3,

041[

2,

981

--

--

3,02

_.1_

--

--

3,

08L.

2-

Es"

3,

23_L

. 3,

042-

3,

2222

(11)

3,

201[

E

r 3,

432.

3,

282.

. 3,

412-

3,

441[

--

--

--

3,

4222

2 E

s 3,

7611

3,

701[

3,

7411

3,

6811

3,

7422

2 --

3,

722-

3,

7222

2 E

9 4,

202-

4,

21_1

_ 4,

17_L

4,

18[i

4,20

2-

E~o

4,3i

l 4,

211[

4,

311

4,44

1[

4,38

2-

Eu

4,

5122

2 --

4,

462-

4,

4622

2 t'

4,75

2-

E12

4,72

1!

4, 66

!1

4,73

11

/ 4,

861!

]4

,792

- E1

s 4,

932-

4,

80_I

_ 14

,932

22

4,86

2-

/z'1

4 5,

0911

4,

90][

4,

9211

--

5,

1011

--

5,2

11

Eis

5,

1722

2 --

--

5,

22-

E~

--

5301

1, .L

--

5,

6.L

, II

3,02

1r,_

LF,

--Ft

(1

6--1

7)

(0,2

; 0,

2;

0,4)

3,15

2-

F2-

-FI

(15-

-17)

(0

,2;

0,2;

0,

4)

3,22

[l

F2-

-F,

(16-

-17)

(0

,3;

0,3;

0,

38)

3,48

_1_

R2-

-R~

(16-

-18)

(0

,25;

0,

25;

0)

3,75

1~,:.

.LN

,--N

, (1

1,

12--

17,

18)

A

(13-

-17)

(0

; 0;

0,

6)

4,14

u R

(1

4--1

7)

(0,2

5;

0,25

; 0)

4,

38u

A(1

5--1

7)

(0,3

4;

0;

0)

4,38

u l's

--F3

(1

3--1

8)

4,75

u (t

4.--

17)

(0,1

6;

0,5;

0)

N,-

-N,

(15,

16

--19

, 20

) A

(15-

-18)

(0

; 0,

50;

0)

Ts-

-Ts

(ll,

12-

-17,

18)

and

on A

nea

rT

fFs-

-I'4

(1

5,

16--

22)

(F

4--1

"s

(14-

-20,

21

) N

~--

N,

(9,

10--

17.

18)

--

F4--

rs

II 1,

96

--

Fs--

l'3

_L

(ll)

1,96

II 2,

31

--

--

2-

2,27

. N

x--N

~ (1

5,

16--

17,

18)

II, 2

- 2,

56

]1,

2-

2,43

--

II

3,0

4

--

--

[l (J

_)

3,4

2

N,-

.-N

, (1

3,

14

--1

7,

18)

[[,

2-

3,0

6

2-

3,50

2-

3,

6 R

2--R

, (16

--18

) (~

5;

0,25

; 0)

2-

3~

5 2-

3,

95

R,-

-R2

(16-

-18)

(0

,25;

0,

25;

0)

2-

4,05

I], _

L 3,

9 Fs

--l'3

(1

2,

13--

17)

-1-

3,73

N

t--N

I (1

1,

12--

17,

18)

2-(1

1)

4,13

_L

4,

6 A

3,4

--A

: (0

; 0,

05;

l)

2-

4,15

--

4,76

N

,--N

t (1

5,

16--

19,

20)

]l, 2

- 4,

32

2-

4,77

Fs

--l'~

(1

2,

13--

18)

J_

4,50

--

5,0

5

Fs-

-Fs

(14,

1

5--

20

, 21

) "

4,7

3

2.

4.9

6

N,-

-N,

(ll,

]2

--1

9,

20

) 2

- 4

,84

[I,

2-

5,21

N

t--N

, (1

5,

16--

21,

22)

[I, 2

- 5,

12

I1 5

,05

--

_

.i_

5,2

--

__

.L

]], -

L

5,6

Nj-

-N~

(1

3,

14--

21,

22)

5.6

0.5' t

O.& / . k f ' X " ~

0.5 ~ ,

(13

0.2 o i ;, ; ; E', v

R

53

~5

OA GS'

112

! ',, 1~

Z 4 6 8 [, eV

ne f~ i

Fig. 7 Fig. 8 Fig. 9

Fig. 7. Reflection spectra of CdGeP2, CdSnPz and ZnSnP2 crystals in unpolarized light. i) CdGeP2 8 K, [42]; 2) CdGeP2 290 K, [43]; 3) ZnSnP2 300 K, [25, 45]; 4) CdSnP2 300 K, [25, 45].

Fig. 8. Spectra e, (curves i, 2) and e2 (curves 3, 4) of CdSnP2 at 98 K. The solid curves correspond to E!c and the broken curves correspond to gH[l ; lJ.

Fig. 9. Spectra of the effective number of electrons neff, the electronic losses Ime-* and surface plasmons Im(l + c) -* of the crystal CdSnP2 at 98 K. Curve I shows nef f on the left-hand scale! curves 2 and 3 show --Ime -* and Im(l + e) -* on the right-hand scale.

of ZnGeP2 were obtained at 300 and 5 K in the region 1-5 eV [i0] and at 77 K in the region 2- 26 eV [36]. In the region above 4 eV higher reflection than in [10] was recorded in the spectra of [36], and the reflection increases further, while in [i0] the reflection begins to drop off here. In [36] the drop-off is observed above 8 eV.

We obtained reflection spectra of ZnGeP2 which confirm the results of [36] (Fig. 6, Table 3). As can be seen from the figure, the spectrum of ZnGeP= in the region 1-5 eV contains two wide bands with a fine structure and principal maxima near 3 and 5 eV. The first band in the E• polarization has a complicated structure E~, Eb, Es, E7 while in the E i! c polarization it has a structureless maximum E~. The second band consists of a large number of polarized structures in the polarization EJr -- E,, E**, E,s, E,s, E,6 and in the polarization E !i c -- E1o, E,=, E,~, E16. The Es peak with the predominate polarization E [; c lies be- tween the first and second bands. Table 3 gives, in addition to the interpretation proposed in [i0], an alternative interpretation of the transitions [7]. The increase in the reflection [36], predicted theoretically in [10], continues in the region above 5.5 eV.

The measurements of [36] in the region E > 5 eV are apparently the most complete and cor- rect. A drawback of all investigations of reflection is that they were carried out on polished (our data and [36]) and even etched [10] samples, which must have led to broadening of the structures in the spectra and vanishing of the weak structures. With the exception of [36], whose results are not presented the optical functions have not yet been calculated.

4. CdGeP2

CdGeP2 is a direct-gap compound, which is the ternary analog of InP and GaP.

The band structure has been calculated only in [4]. The optical polarization spectra were obtained at 300 K in [37]and [38] and at i00 K in [37]. The unpolarized spectra were studied in [37-39] and [42]. In a recent work [42] the reflection spectra were measured in unpolarized light at 8 K and all structures (Fig. 7) observed in [39] at 120 K in the thermoreflection spectra were recorded. The energy positions of the features in the reflection spectra of CdGeP2 from [37-41] are compared in Table 4) and their interpretation is given in terms of the dipole-allowed transitions based on the calculations of [4]. A detailed analysis of the transitions and calculations of the optical functions requires precision measurements of the reflection spectra, performed in polarized light at several temperatures, as well as band calculations over the entire BZ.

633

L~

TABLE 4.

Energies (i

n eV

) and Polarizations of Structures in the Optical Spectra of CdGePa and the Correspond-

ing Transitions

Str

uc-

tu

re

Ex

per

imen

t

re f

lect

ion

[371

[3

8]

295

K

100

K

300

K

u 'l

,t I•

I ,,

I•

ur'l

,I_L

E

o .

..

..

.

1,72

1,

66

1,72

--

El

2,62

2,

62

2,62

2,

70

2,70

2,

70

2,66

2,

63

2,70

2,

64

E2

..

..

..

..

.

2,97

--

2,

98

E 3

..

..

..

..

..

.

/2." 4

.

..

..

..

..

..

E5

..

..

..

..

..

.

E6

3,50

--

3,

50

3,55

3,

55

3,44

3,

46

3,43

3,

48

Er

..

..

3,

95

3,95

--

--

4,

00

--

4,00

/2" 8

Eo

Elo

E

tt

T,~

._.r

mor

e fl

ecti

o n

[391

I [4

2]

[39]

290

[ ,<

po

ar -

320 K

, 120

za

tton

--

1,70

1,

75

II,

-L

--

1,89

1,

97

_I_

1,97

2,

04

;_L

(1[)

2,

75

2,70

2,

77

I1, 1

2,

95

2,75

2,

85

I1 3,

08

3,04

3,

14

I_

3,27

3,

22

3,28

_L

--

~

3,38

..1

_ 3,

48

3,51

3,

53

II, _

L --

3,

64

3,76

II

3,96

--

3,

95

II --

--

4,

05

[1, _

.L

4,25

4,

25

4,25

4,

29

4,29

4,

29

4,38

4,

37

4,40

4,

34

4,25

4,

25

4,25

4,

29

4,29

4,

29

4,38

4,

37

4,4

4,34

--

--

4,

9 4,

9 --

4,

9 4,

82

4,94

4,

86

4,9

4,17

4,

13

--

_L

4,41

4,

38

--

A_

4,41

4,

50

---

I], 1

4,

94

4,73

--

..L

?

El2

.

..

..

*U

P

--

un

po

lari

zed

.

--

--

5,16

--

5,

16

5,2

5,16

--

The

ory

[4]

.._

tran

siti

on

in B

Z

and

po

lari

zati

on

en

ergy

, eV

lh--

F,

I] 1,

81

Fs-

-I'l

_L

1,

95

1"5-

-I'~

_k

2,

15

l's-

-I'2

.A

.. 2,

33

Nl-

-h'l

..L

, d

2,37

T:

~ i-+

--T

l+2

It 3,

2

Ni-

-Nt

i_L,

II

3,4

Nt-

-N

l _L

, II

3,4

:Vr-

-NI

LI, .

3-

3,6

Pt-

-P2

1[ 3,

7 Ta

+4-

-TI

t.2

II 4,

0 Ts

--TI

-~2

.A-

4,2

Ta+

4__T

5 _1

_ 4,

2 P

s--F

t .t_

3,

9 P

L--

Pt

l 3,

8 p2

__p2

_L

4,

1 l'

s--l

'a

J_

(1[)

4,

2 I'5

--1'

2 ',2

_ (1

1)

4,3

NI-

-N l

_L,

[J 4,

3 Ps--F4

-I-

4,8

1'~-

-1"5

_L

5,

0 N

I--N

L

II, _

L.

4,9

T3-,-

4--T

5 ._

L 5,

0 F

4--F

I [1

4,9

l'~--

Pa

11

5,0

F4-

-F5

~ 5,

4 P

I--P

t l_

5,

1

TABLE 5. Energies (in eV) and Polarizations of Structures in the Reflection Spectra of CdSnP~ and the Corresponding Transitions

Exper iment [52]

93 K ] 295 K

I Theor l [4]

[ transition tn ~Z, band num- ~ K - - K [' berg polarization

8~uc- tore energy,

eV

E, 2,74E1, ; ! 2,631t, _L 2,77ll, _L NI--Nt (15, 16--17, t8) H, _L 2,67 E~ 2,92• ( [ I ) 2,88]_ (II) 2,995- (ll) N~--NI (13, 14--17, 18) _[_ 3,01

NI---Na (11, 12--17, 18) J_, it 3,15 P~--P2 (15, 16--17, 18) [], _L 3,32

E3 3,02_3._ -- 3,07-1- F~--F~ (12, 13--17) _[2 3,32 P~--P2 (13, 14--17, 18) _1_ 3,39

E4 3,38ii 3,30]1 3,40[I,_L T3+4--T[+~ (11, 12--17, 18) [] 3,66 Es 3,47-[- -- - - Ts--Tl+2 (9, 10--17, 18) 5- 3,78

Fs--Y~ (1t--17) 5- 3,81 Fs--F3 (11--18) _L 3,96

E6 3,5511, 5- 3,5511, 5- 3,6211, _L N,--N~ (15, 16--19, 20) II, 5- 4,14 El 4,00II ~J_) 3,9211 ( ! ) 4 ,06] [ r , - - r , (8--17) i1 4,12

4,00J_ (ll) PL--P~ (15, 16--19, 20) A_ 4,15 Ta+~--T~ (t5, 16--19, 20) 5- 4,t5 Tz+2--T5 (13, 14--19, 20) .J_ 4,17

E~ 4,14-I_ - - 4 2 8 i F4--Y5 (16--20, 21) 5- 4,3 E9 4,345- ([1) 4,25j_ (11) 4,40_[_ (11) T3+4--Zs (15, 16--21, 22) 5- 4,36

TI+z--T~ (13, 14--21, 22) 5- 4,38 P2--P~ 13, 14--17, 18) 5- 4,38 Fs--P2 (12, 13--19) 5- 4,37

E~o 4,55II ('[_) 4,451[ (_[_) 4,6211 (_L) P~--Pz (15, 16--21, 22) It, 5- 4,35 F~--Fs (14, 15--20, 21) i! 4,44 N1--NI (13, 14--19, 20) 5-, t} 4,48 NI--N~ (9, 10--17, 18) I], _.L 4,53 NI--NI (11, 12--19, 20) II, .% 4,62

En 4,893_ 4,78./. 4,88/ P2--P2 (13, 14--21, 22) _L_ 4,50 P ~ - - P I (15, 16--2,3, 24 ) A_ 4,56 I'5--F~ (14, t5--22) • 4,56 T3+4--T5 (11, 12--19, 20) .1_ 4,70 T3+4--T~ (11, 12--21, 22) _L 4,91

EI~ 5,001[ 4,9[[ - - P,2--P~ (13, 14--23, 24) II, 5- 4,71 TI--T5 (9, 10--19, 20) II 4,82 F~--F2 (9, 10--19) II 4,84 T~--TG (9,10--2t, 22) II 5,03 Fs--F5 (14, 15--23, 24) [] 5,05

El3 5,09• - - - - P2--P2 (1t, 12--21, 22) J_ 4,99 F4--F5 (t6--23, 24) • 4,91

5,225_ Et4 5,28-[.- - - P2--Pl (1l, 12--23, 24) l[, 5_ 5,20

P,--P, (15. 16--27, 28) 3_ 5,38 E,s -- 5,331I - - Nt--Nt (15, 16--21, 22) [I, .J_ 5,27

Pt--P2 (15, I6--25, 26) tl, 5- 0~'~

5. ZnSnP2

The direct-gap compound ZnSnP= I the ternary analog of GaP and InP, because of the absence of tetragonal compression crystallizes into polycrystalline blocks with a domain structure= The optical axes of the different domains in these blocks are mutually perpendicular. Because of thisp the optical measurements in polarized light for ZnSnP= have not yet been performed. The electroreflection spectra [43] and reflection spectra [44, 45] have been measured. The most complete reflection spectra in the region of the fundamental absorption apparently are published in [45] (Fig. 7). A strict analysis of the band structure based on the reflection and thermoreflection spectra requires that polarization measurements be performed for separate domains.

6. CdSnP2

The compound CdSnP2 is the closest isoelectronic analog of the direct-gap binary compound InP. Its band structure has been calculated by the empirical pseudopotential method [4] and the model potential method in the direct space [8]. The computed reflection spectra for unpolarized light and for polarization Eic are presented in [8].

The optical properties of CdSnP= have been studied by modulation methods [46-50], based on the luminescence spectra [51], and based on the reflection spectra in unpolarized light in the region 1-12 eV at room temperature (Fig. 7) [44] and in polarized light in the region 1-5 eV (by us) at 295 and 93 K [52] and at 2 K [9]. On the whole our spectra [52] agreej according to the number of structures observed, with the spectra of [9]. As noted in [52], howeverp

635

polishing and subsequent etching strongly reduced the reflection in [9] and caused an intense drop in R in spectra above 3.5 eV.

Using the reflection spectra [52], we calculated complexes of 12 optical functions for the polarizations E_hc and E tl[0] I] �9 Figure 8 shows the functions e, and e2 for two polarizations at 93 K.

It is evident from a comparison with the spectra e, and e2 for CdSiP2 (Fig. 2) that the replacement of the light silicon atom by the heavier tin atom caused an appreciable shift in the first maximum in the curves e, and e= into the region of longer wavelengths, while the position of the second maximum changed insignificantly. The electronic loss function Ime-*, the volume plasmon function Im(l + e)-*, and the function nef f remain monotonic in the region under study in both compounds (Fig. 9).

CONCLUSIONS

The optical spectra of the ternary pseudodlrect-gap phosphides CdSiP2 and SnSiP2 are similar to one another. In both crystals in the region 1-5.5 eV three basic structures, which are apparently associated with transitions at the same points of the BZ, are observed in each of the two polarizations. In Tables 1 and 2 the structures of like nature are denoted by the same indices. In the region of the edge absorption of ZnSiP2 there is a larger number of weak structures than in CdSiP2. Some of them could be associated with indirect transitions from r into T and N, as well as with pseudodirect transitions F4-F= and Fs-F= [7]. In the spectra of ZnGeP2 the reflection spectrum is not polarized in the same way as in the compounds closest to it CdSiP2 and ZnSiP2, namely, the form of the reflection curve of ZnGeP2 for EJ_c is similar to that of ZnSiP2 for E llc and vice versa, i,e., in these compounds the polarizations of the transitions seem to be mixed up, which, however, agrees with the computed reflection curves [I0, ii] (see Figs. 1 and 6).

The unpolarized reflection curves of the dlrect-gap compounds CdGeP2, ZnSnP2 and CdSnP2 are similar to one another (Fig. 7). For this reason, we assume that peaks with the same form are of the same nature. Tables 4 and 5 give the interpretation of the peaks in the reflection curves, obtained by different authors.

It follows from general theoretical considerations that the features in the reflection spectra could be related not only with dipole-allowed band-band transitions but also with the metastable excitons. However, a detailed theory of metastable excitons still does not exist.

Thus it follows from a comparison of the reflection spectra and calculations of the bands of II--IV--V2 group phosphides that definite results have been achieved both in the band theory and in the experimental studies. Many unsolved questions remain however. Detailed calculations of the bands of CdGeP=, CdSnP2 and ZnSnP= have not yet been performed. The reflection spectra of almost all II--IV--V2 group phosphides, with the exception of ZnGeP2 [36], in the region of the vacuum ultraviolet radiation have not been adequately studied. There are no re- liable experimental data on absorption deep in the band for all II--IV'V= group crystals. The field of workremains quite extensive for both experimenters and theoreticians alike.

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636

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KI43-KI47 (1985).

PHOTOPLEOCHROMISM AND THE PHYSICAL PRINCIPLES OF THE PREPARATION

OF SEMICONDUCTOR POLARIMETRIC PHOTODETECTORS

Yu. V. Rud' UDC 621.315.592

INTRODUCTION

The intensity and polarization are basic characteristics of a light wave [1-3]o A complete analysis of polarized radiation with the help of polarization insensitive photodetectors is possible only after the recorded radiation is converted with the help of an external polarization device, as a result of which the polarization characteristics of the radiation are calculated from the measured intensity [4-7]. The use of polarization insensitive photodetectors for determining polarization parameters requires that the polarization element be spectrally matched with the photodetector, which gives rise to additional losses of radiation. A photodetector which does not require external polarization devices -- a polar,metric photodetector -- is obviously most suitable for such purposes.

The rapid expansion of the areas of application of linearly polarized radiation (LPR) in science and technology [2-13] has made necessary the development of polarization photoelec- ,tonics. For this reason, the study of the anisotropy of photoelectric phenomena has become an important part of the physics and technology of semiconductors and, primarily, semiconductors with an anisotropic crystalline structure. In spite of the fact that the first investigations of the anisotropy of photoconductivity (PC) were carried out on crystals with a hexa- gonal lattice~ the anisotropy of PC has been studied in greatest detail in the ternary group II--IV--V2 semiconductors with the chalcopyritelattice, whose study was initiated comparatively recently [14].

The importance of such studies has increased in recent years because of the fact that the method developed for performing polarization studies of PC has proven to be very useful for studying the electronic spectrum of anisotropic semiconductors and the perfection of their structure and has opened up the possibility of creating semiconductor devices with new func- tioal possibilities. It rurns out that in order to create polarization sensitive photodetectors it is no longer sufficient to establish the general characteristics of the polarization photosensitivity (PS); the effect of the nature of the positional ordering of the atoms~ the behavior of specific impurities, and the characteristic parameters of semiconductors and in- strumental structures must also he studied in detail.

The study of the anisotropy of PS in group II--IV--V2 semiconductors was initiated I0 years ago [14-17] and a significant amount of experimental data has now been accumulated. ~ In this review the main results of polarization studies of PS of anisotropic uniform semiconductors with the chalcopyrite lattice and other crystalline classes, as well as diode structures based on them, are generalized. The characteristic features of the method of polarization measurements of PC are described and the parameters introduced for the characteristics of polarization PS of semiconductors are elucidated.

I. Basic Characteristics of Polarization PS

A series of characteristics has been introduced for quantitative description of the anisotropy of PS [18]. The method developed is based on the measurement of the aximuthal depend- ence of the photocurrent i. An oriented plate of the semiconductor is illuminated by a beam

A. F. loffe Physicotechnical Institute, Academy of Sciences of the USSR~ Translated from Izvetiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 68-83~ August, 1986.

638 0038-5697/86/2908-0638512.50 �9 1987 Plenum Publishing Corporation

Documents

Optical functions and bands of II-IV-V2 group phosphides