Determination and analysis of optical constants for thermally evaporated PbSe thin films

Vacuum 86 (2011) 318e323

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Determination and analysis of optical constants for thermally evaporated PbSe thin films E.A.A. El-Shazly a, I.T. Zedan b, *, K.F. Abd El-Rahman c a

Physics Department, Faculty of Education, Ain Shams University, Cairo, Egypt High Institute of Engineering and Technology, El-Arish, North Sinai, Egypt c Physics Department, Faculty of Engineering, The British University in Cairo, Egypt b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 May 2011 Received in revised form 12 July 2011 Accepted 13 July 2011

PbSe films have been deposited on glass and quartz substrates at room temperature by thermal evaporation technique. X-ray diffraction patterns of the obtained films showed that they have polycrystalline texture and exhibit cubic FCC structure. The optical constants, the refractive index n and absorption index k were calculated in the spectral range of 400e4000 nm from transmittance and reflectance data using Murmann’s exact equations. Both n and k are practically independent on the film thickness in the range 28 nm to 210 nm. From the analysis of absorption index data, an indirect allowed energy gap of 0.16 eV and direct allowed energy gap of 0.277 eV were obtained. Other direct allowed optical transitions were obtained with energy gap of 0.49 eV and may be due to the splitting of valence band at the G point due to the effect of spin-orbit interaction. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: PbSe films Optical properties Energy gap

1. Introduction The band structure of semiconductor materials (amorphous or crystalline) has attracted increasing interest in recent years. Electrical and optical properties provided an extremely valuable insight in understanding the nature of their band structure, which related to the transport behaviour of the carriers. PbSe is a IV-VI compound with very interesting technological importance as detectors of infrared radiation [1] and more recently as infrared emitters, solar control coating [2e4] and solar cell devices [5]. Meanwhile, much attention has also been focused on the fundamental issues of those materials that possess interesting physical properties including high refractive index, and narrow band gap [6e8]. PbSe has the cubic NaCl-type structure [9]. Its structure has been studied by many authors [10e14]. The electrical and optical properties of PbSe in bulk form have been investigated and analyzed by many authors [5,15e18]. Several authors have investigated these properties for PbSe films prepared by chemical techniques [19e23], whilst few authors prepared PbSe films by thermal evaporation technique [24]. Hankare et al. [21] prepared PbSe films by modified chemical bath deposition method and found that the absorption edge is around 1200 nm and the thermal activation energy is

* Corresponding author. E-mail address: [email protected] (I.T. Zedan). 0042-207X/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2011.07.051

0.158 eV. Grozdanov et al. [22] prepared PbSe films by low temperature chemical bath deposition technique and found that an amorphous phase is present along with the polycrystalline. They reported some basic optical and electrical observations for PbSe films. Sashchiuk et al. work on and show that the bulk PbSe has cubic crystal structure (rock salt, a ¼ 0.61224 nm). It is a narrow direct band gap semiconductor (Eg ¼ 0.28 eV at 300 K at the L point of the Brillouin zone [25]). In the present work, an attempt has been made to determine and analyse optical constants for as-deposited PbSe films of different thicknesses deposited onto glass and quartz substrates using thermal evaporation technique under vacuum (2  104 Pa). The structure of the obtained films was identified. Our results are compared with those obtained previously.

2. Experimental technique Thin films of PbSe with different thicknesses were obtained onto cleaned glass and quartz substrates by thermal evaporation technique using high vacuum, 2  104 Pa, coating system (Edward model E306A, England). The evaporation rate is 20 nm/min using molybdenum boat and the distance between the boat and samples is about 30 cm. The substrate temperature was held at that of room during deposition process. The film thickness was measured by Tolansky’s interferometric method. The film thickness is ranged

E.A.A. El-Shazly et al. / Vacuum 86 (2011) 318e323

from 28 nm to 212 nm. The experimental errors were taken from reference [26] to be 3e5% for film thickness measurements. In order to get some information about the structure of PbSe in thin film form, X-ray diffraction was carried out using a filtered Cu-ka radiation (Philips PM 8203) operated at 40 kV and 25 mA. The optical transmittance and reflectance of the film samples of different thickness deposited onto quartz substrate was measured at room temperature using un-polarized light at normal incidence in the wavelength range (400e2500 nm) using a dual beam spectrophotometer ((JASCO model V-570 UVeVIS-NIR) and in the wavelength range (2500e4000 nm) using (ATI Mattson (Infinity Series FTIR)) in the same thickness range. The absolute values of transmittance T(l) and reflectance R(l) were calculated according to the following equation [27]:

T ¼


  Ift  1  Rq Iq

(1)

where Ift and Iq are the intensity of light transmitted through the film substrate system and the quartz reference, respectively. Rq is the reflectance of quartz substrate, and

R ¼



 h 2 i Ifr =Im Rm 1  Rq  T 2 Rq

(2)

where Im is the intensity of light reflected from the reference mirror, Ifr is the intensity of light reflected from the sample reaching the detector and Rm the mirror reflectance. The transmittance T(l) and reflectance R(l) can be expressed by Murmann’s exact equations [28] as:

T ¼

R ¼

  16no ns n2 þ k2 Eeb þ Feb þ 2G cos g þ 4H sin g Aeb þ Beb þ 2Ccos g þ 4Dcos g Eeb þ Feb þ 2G cos g þ 4H sin g

where,

d

d

g ¼ 4pn ; b ¼ 4pk l l

ih i h A ¼ ðn  no Þ2 ðn þ ns Þ2 þk2 ; ih i h B ¼ ðn  ns Þ2 þk2 ðn þ ns Þ2 þk2 ; C ¼



n2 þ k2



  2 n20  n2s  n2 þ k2 n20 n2s  4ns no k2 ;





D ¼ kðns  no Þ n þ k2 þ ns no ; ih i h E ¼ ðn þ no Þ2 þk2 ðn þ ns Þ2 þk2 ; ih i h F ¼ ðn  no Þ2 þk2 ðn þ ns Þ2 þk2 ; G ¼

    2 n2 þ k2 n20 þ n2s  n2 þ k2 n20 n2s þ 4ns no k2 ;

and

  H ¼ kðns þ no Þ2 n þ k2  ns no

(3)

(4)

319

As n0, ns and n are the refractive indices of air, substrate and film respectively, k is the absorption index of film and d is the film thickness. Some authors have applied different methods for determining n and k [29,30]. The most applicable methods consist of computerized algorithms intended to solve these complex equations. Several modifications have been made to speed up the computation and enhance accuracy. A computer based program was used in computation of R(n,k) and T(n,k) [31] which is basically an univariance search technique. First jRðn; kÞ  Rexp j was minimized with respect to n, then jTðn; kÞ  Texp j was minimized with respect to k; this strategy is not a good one for general optimization problems, where Rexp and Texp are the experimentally determined values of R and T respectively; R(n,k) and T(n,k) are the calculated values of R and T using Murmann’s equations [28]. A modified Bennett-Booty method was used by applying a computer program for this modified method, this modification is to overcome the problem produced due to an uni-variance search technique, where n and k are apparently not highly correlated quantities. The modified method is basically a bivariance search technique [31], by which the two values (DR)2 and (DT)2 are minimized simultaneously, where,

ðDRÞ2 ¼ jRðn; kÞ  Rexp j2 ¼ min

(5)

ðDTÞ2 ¼ jTðn; kÞ  Texp j2 ¼ min

(6)

The research in this method was carried out through two operations, which are the bivariant search operation and steplength optimization operation. In the first operation, ranges n1 to n2 and k1 to k2 are used to calculate R(n,k) and T(n,k) in each step. The variance (DR)2 and (DT)2 are calculated to obtain the minimum variance which converges to unique points and hence gives the optimum values of n and k simultaneously. The second operation was developed to speed up convergence (i.e. increase the runtime to improve the accuracy). The values of n and k obtained at the minimum variance are noted as nm and km. The values [nm  (n2  n1)/10] and [km  (k2  k1)/10] are then compared to specific tolerance values (tn ¼ 0.01) and (tn ¼ 0.001), if these values are smaller than the tolerance values, then n ¼ nm and k ¼ km and so the program will be terminated, otherwise the calculation will be repeated to obtain the equivalence.

3. Results and discussion 3.1. Structural identification X-ray diffraction patterns obtained for PbSe in powder form illustrated that, it has polycrystalline nature of as shown in Fig. 1. The result of indexing the pattern of the polycrystalline sample is found to be quite consistent with JCPDS card no. 6-354 for FCC PbSe. X-ray diffraction patterns of PbSe films of different thicknesses showed that films are polycrystalline, and crystallinity increases as the thickness of the film increases as shown also in Fig. 1. The calculated value of lattice constant (a) of PbSe in powder and thin film forms are 6.1212 Å and 6.1245  0.02 Å respectively. These values agree with that taken from the JCPDS card (6.1243 Å). They agree also with that determined by many authors, Hiroi et al. [9] (6.12 Å) for PbSe layers deposited on NaCl substrate, Bhardwaj et al. [32] (6.11 Å) for PbSe Nano-particle thin films, and Wang et al. [33] (6.124 Å) for PbSe films deposited onto GaAs.

320

E.A.A. El-Shazly et al. / Vacuum 86 (2011) 318e323

0.7

28 nm 92 nm 100 nm 119 nm 210 nm

0.6 0.5

R

0.4 0.3 0.2 0.1 0.0

500

1000

1500

2000

2500

λ (nm) Fig. 3. The spectral distribution of reflectance (R) for PbSe films of different thicknesses in the wavelength range 400 nme2500 nm.

1.0 0.8

T

0.6 0.4

28 nm 100 nm 119 nm 210 nm

0.2 0.0

Fig. 1. X-ray diffraction patterns of PbSe in powder and thin film forms.

The indexing of the pattern is therefore done by assuming the FCC structure. The number of molecules per unit cell has been computed using the relation [34]:

X

A ¼

rV 1:6604

(7)

P where A is a sum of molecular weight of all molecules in the unit cell, V the unit cell volume in Å3 and r the bulk density of PbSe (8.15 gm cm3) [19]. The number of molecules per unit cell is obtained by dividing Å3 with molecular weight of PbSe. The number of molecules per unit cell was found to be 3.997, which is nearly equal to 4 as expected for FCC system. Finally it was found that annealing films at 473 K does practically change the structure or crystallinity of the films. 3.2. Optical properties The spectral distribution of transmittance T(l) and reflectance R(l) at normal incidence in the wavelength range 400e4000 nm

2600

2800

3000

3200

3400

3600

3800

4000

λ , nm Fig. 4. The spectral distribution of transmittance (T) for PbSe films of different thicknesses in the wavelength range 2500 nme4000 nm.

were measured for as deposited films of PbSe in the thickness range (28e210 nm). Figs. 2 and 3 show T(l) and R(l) in the spectral range (400e2500 nm) for PbSe films deposited onto quartz substrates. It is shown that (T þ R < 1), in all range of wavelengths, indicating the existing of absorption in all wavelengths. Fig. 4 shows T(l) in the spectral range 2500 nme4000 nm for the same PbSe films in IR region of spectra. The optical constants (refractive index n and the absorption index k) were calculated in the spectral range (400e4000 nm) using Murmann’s exact equations [28] via the technique described above. By applying such a technique, unique values of n and k at any wavelength (l) are obtained within the desired accuracy. Fig. 5 shows the spectral distribution of the refractive index (n) and absorption index (k) for the investigated films. The maximum fluctuation between the data of the films of different thicknesses

1.0

28 nm 92 nm 100 nm 119 nm 210 nm

0.6

2.5 4.5

2.0

k n

0.4

1.5

n

T

4.0

1.0

3.5

0.2

0.5

3.0

0.0

500

1000

1500

2000

2500

(nm) Fig. 2. The spectral distribution of transmittance (T) for PbSe films of different thicknesses in the wavelength range 400 nme2500 nm.

k

0.8

0.5

1.0

1.5

2.0

2.5

3.0

0.0

hν [eV ] Fig. 5. Dispersion curve of refractive index (n) and absorption index (k) for PbSe films of different thicknesses.

E.A.A. El-Shazly et al. / Vacuum 86 (2011) 318e323 22

Table 1 Values of Eo, Ed,

20

15

16

ε1

14

ε2

10

12 10

ε2 = 2nk

ε1 = n2- k 2

18

5

8 6 0.5

1.0

1.5

2.0

2.5

3.0

0

hν [eV ] Fig. 6. The variation of real and imaginary parts of dielectric constants with photon energy (hn) for PbSe films.

lies within the range of experimental error; accordingly both n and k are independent of the film thickness in the investigated range. Cardona et al. [35] studied the optical properties of epitaxial PbSe films grown on KCl and NaCl substrates through reflection measurements in the photon energy range up to 15 eV. They calculated the optical constants using Kramers-Kronig relations. Their data agree well with our obtained data in the same range of photon energy. The dielectric constant was also calculated from the relation [40]: 3 ðh

nÞ ¼

3 1 ðh

nÞ  i3 2 ðhnÞ

n2

(8)

k2 Þ

here ð3 1 þ  is the real part and (3 2 ¼ 2nk) is the imaginary part of the dielectric constant and k is the absorption index. The photon energy dependence of both 3 1 and 3 2 is illustrated in Fig. 6, which is characterized by the existence of the same sharp structure associated with the valence to conduction band transitions. The refractive index dispersion in semiconductors has been analyzed using the concept of the single-oscillator model. In this concept the energy parameters, single-oscillator energy (Eo) and dispersion energy (Ed) are introduced and the refractive index n at any photon energy hn is expressed by the WempleeDiDomenico relationship [36]:

n2  1 ¼ 

Eo Ed Eo2  E2



(9)

The physical meaning of Eo is that it stimulates all the electronic excitation involved and takes values near the main peak of the imaginary part of the dielectric constant spectrum, while Ed is related to the average strength of the optical transitions. It is shown

321

3 N , 3 L,

N/m*, Eginda , and Egda for PbSe films.

Eo, eV

Ed, eV

3N

3L

1.7

25.17

15.83

22.61

N/m* m3 kg1

Eginda , eV

Egda , eV

Egda , eV

7.46  1055

0.16

0.277

0.49

by earlier workers [36,37] that: (i) Ed is independent of the absorption threshold (band gap), within experimental error (ii) Ed is independent of the lattice constant, within experimental error; and (iii) Eo is related to the lowest direct gap. In practice the dispersion parameters Eo and Ed are obtained using a simple plot of (n2  1)1 against (hn)2 as shown in Fig. 7. It is observed that the plots are linear over the energy range from 0.22 eV2 to approximately 0.85 eV2. The refractive index n(0) at zero photon energy, which is defined by the high frequency dielectric constant 3 N, can be deduced from the dispersion relationship by extrapolation of the linear part as in Fig. 7. The values of Eo, Ed and 3 N are calculated and tabulated in Table 1. The dielectric constant is partially due to free electrons and partially due to bound electrons as represented by the following relation [38]:


31

¼

3L



 e2 N l2 4p3 o C 2 m*

(10)

where 3 L is the lattice dielectric constant and N=m* is the ratio of carrier concentration to its effective mass. The dependence of 3 1 on l2 is linear as shown in Fig. 8. The lattice dielectric constant 3 L and the ratio N=m* can be calculated by extrapolating the linear part to intercept the 3 1 axis and the slope, respectively and given also in Table 1. The free carrier concentration, N, was calculated using the electron effective mass m* z 0.1me [39] and has the value of 6.76  1024 m3. It is also possible to calculate the volume and surface energy loss functions (VELF and SELF) as the relations in Ref. [41]

VELF ¼ 

3 3

SELF ¼ 

2 1

2 2

 3 22 3



2 2

ð3 1 þ 1Þ2 þ3 22



The VELF values are higher than the SELF values of the film as in Fig. 9. Also the real part of the optical conductivity s1 ¼ 3 2 =4p and the imaginary part s2 ¼ ðuð1  3 1 ÞÞ=4p for the as-deposited PbSe films are shown in Fig. 10. The above two Figs. 9 and 10 showed the existence of the possible optical transitions.

0.068

24

0.066

23

0.064

22

0.062

21

0.060

20

n2

(n2 - 1)-1

0.070

0.058

19

0.056

18

0.054

17

0.052

16

0.050 0.0

0.1

0.2

0.3

0.4 2

0.5

0.6

2

(hν) [eV ]

Fig. 7. The variation of (n2  1)1with (hn)2 for PbSe films.

0.7

15

0

1

2

3

4

λ2 [ μ m] 2 Fig. 8. The variation of n2 with l2 for PbSe films.

5

6

322

E.A.A. El-Shazly et al. / Vacuum 86 (2011) 318e323

0.07 0.06

0.06

SELF

0.04

0.03

0.03

0.02

0.02

0.01

0.01

0.00

0.5

1.0

1.5

hν [eV]

2.0

2.5

3.0

tan δ = ε 2 / ε1

VELF

0.04

2.0

0.05

SELF

0.05

VELF

2.5

0.07

1.5 1.0 0.5

0.00

0.0

Fig. 9. The variation of VELF and SELF with photon energy (hn) for PbSe films.

  ahy ¼ A hy  Eg r

(11)

where A is constant, Eg is the energy gap, and r determines the type of transitions, which is equal 2 and 1/2 in case of allowed direct and indirect transitions and is equal 1/3 and 2/3 in case of forbidden direct and indirect optical transitions. Fig. 12 shows the relation between (ahn)1/2 and (hn) for the investigated samples. The relation between (ahn)1/2 and (hn) for the deposited films of PbSe is linear in the region of strong absorption edge, and showing the existence of an allowed indirect gap. The values of the allowed indirect energy gaps, Eginda , for the films is found to be 0.16 eV. Fig. 13 shows the relation between (ahn)2 and hn for the investigated films. The linearity in the figure indicates the existence of direct optical energy gap of 0.49 eV. Another value of direct band gap (0.277 eV) is obtained at lower photon energy as shown in the inset of the figure. This value of energy gap (0.277 eV) agrees with the data obtained by many authors for PbSe films [5,11,42e44,46]. This may be due to the spin orbit interaction [45]. As an example of the effect of the spineorbit interaction, the valence band at the G point (k ¼ 0) which is labelled by G250 band is triply degenerate at k ¼ 0, each of the three orbital levels containing a spin up and a spin down electron. With spin orbit interaction, this band splits into the þ Gþ 8 (doubly degenerate) band and the G7 (non-degenerate) band. In þ the literature, the G7 band is called split-off band. In germanium þ the band gap is 0.8 eV and the splitting between the Gþ 8 and G7 bands is 0.3 eV. However, in InSb, the spin orbit interaction is large and the separation between the upper valence band and the split1.4x109 1.2x10

hν [eV]

2.0

2.5

3.0

300 250 200 150 100 50 0 0.0

0.1

0.2

0.3

hν [eV]

0.4

0.5

0.6

8.0x108

off band is 0.9 eV, which is much larger than the band gap of 0.2 eV between the valence and conduction band. The separation between the upper valence band and the splitoff band, in PbSe as a narrow band gap semiconductor, is 0.49 eV, which is also much larger than the band gap of 0.277 eV between the valence and conduction band. Allan et al. [46] consider that the interband transitions in which PbSe nanocrystals contain one extra electron, one extra hole, or an electronehole pair. Allan et al. [46] obtain a very broad spectrum, due to the fact that the S and P levels arising from the four equivalent valleys and from the two directions of spin are split by anisotropy effects, and intervalley couplings. Theoretical studies of the electronic properties of the IIeVI and IIIeVI semiconductors showed the need to consider six or eight

σ2

6.0x108

8

6.0x10

4.0x108

4.0x108 2.0x108

2.0x108 0.5

1.0

1.5

2.0

2.5

3.0

0.0

hν [eV]

Fig. 10. The real part and the imaginary part of optical conductivity for PbSe thin films.

0.7

Fig. 12. The dependence of (ahn)1/2 on photon energy (hn) for PbSe films.

8.0x108

1.0x109

σ1

1.5

1.0x109

σ1 σ2

9

0.0

1.0

Fig. 11. The variation of the loss factor with photon energy for PbSe thin films.

(αhν)1/2 [eV/cm]1/2

Also the loss factor, tan d, of the as-deposited films has been calculated using equation: tan d ¼ 3 2/3 1. The variation in the loss factor with photon energy for the as-deposited PbSe films is shown in Fig. 11. To obtain information about the optical band transitions, the fundamental absorption edge data was analyzed. The variation in absorption coefficient with photon energy for band-to-band transitions is obtained as:

0.5

Fig. 13. The dependence of (ahn)2 on photon energy (hn) for PbSe films.

E.A.A. El-Shazly et al. / Vacuum 86 (2011) 318e323

band mixing [39] (doubly degenerated heavy-, light-, and split-off hole states and doubly degenerated electron states). 4. Conclusion

[15] [16] [17] [18] [19]

PbSe films were prepared using thermal evaporation technique. X-ray diffraction analysis for the as-deposited films showed that FCC polycrystalline structure. The optical constants, n and k were calculated in the spectral range of 400e4500 nm. Both n and k are practically independent on the film thickness in the range 28 nme210 nm. From the analysis of absorption index data, an indirect allowed energy gap of 0.16 eV and direct allowed energy gap of 0.277 eV were obtained. Other direct allowed optical transitions were obtained with energy gap of 0.49 eV which is longer than the obtained band gap. This is may be due to the splitting of valence band at the G point due to the effect of spineorbit interaction.

[20]

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