- Email: [email protected]
Some studies on structural and optical properties of ZnxCd1−xSe thin films
Vacuum 60 (2001) 355}360
Some studies on structural and optical properties of Zn Cd Se thin "lms V \V A.H. Ammar* Faculty of Education, Physics Department, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt Received 18 February 2000; received in revised form 21 August 2000; accepted 13 September 2000
Abstract Thin Zn Cd Se "lms with a thickness ranging from 100 to 300 nm are prepared by thermal evaporation under V \V a vacuum of 4.0;10\ Pa. Films deposited at substrate temperatures ranging from 570 to 625 K were found to be of polycrystalline nature, with sphalerite structure for x*0.6 and wurtzite structure for x(0.6. The optical constants n and k of Zn Cd Se thin "lms of di!erent composition were determined in the spectral range 400}2000 nm. The V \V analysis of the accuracy of the adopted technique gave $1.0 and $0.5% for the real part of the refractive index n and the extinction coe$cient k, respectively. Th band gap showed a non-linear variation with the value of x. The e!ective masses of the carriers and the band gap bowing parameters of Zn Cd Se thin "lms were estimated. 2001 V \V Published by Elsevier Science Ltd. Keywords: Zn Cd Se; Thin "lms; Optical constants; Electron e!ective mass V \V
1. Introduction
2. Experimental procedure and calculations
Results on the structural and optical properties of zinc and cadmium selenide thin "lms have indicated [1}5] promising applications for these materials in light-emitting diodes [6], photovoltaic and photoelectrochemical devices [7,8]. The energy gap of Zn Cd Se alloys has been determined at V \V 300 K by re#ection spectroscopy [9], spectroscopic ellipsometry [10], and using transmission and re#ection measurements in the temperature range from 5 to 300 K [5]. The present work was performed in order to investigate the structural and optical properties of Zn Cd Se thin "lms. V \V
The source materials Zn Cd Se used in the V \V deposition of thin "lms was prepared by direct reaction of high-purity elemental Zn(6N), Cd(5N) and Se (4N). Stoichiometric quantities of the elements were placed in a vacuum-sealed (1.33;10\ Pa) silica tube which was gradually heated at a rate of 103C/h to a temperature in the range 1220}1250 K depending on the speci"ed composition. The tube was then maintained at the optimum temperature for 72 h and thereafter cooled to room temperature. Following this procedure four Zn Cd Se solid V \V solution ingots with x"0.2, 0.4, 0.6 and 0.8 were prepared. Thin "lms were deposited onto wellcleaned glass and quartz substrates using an E306A Edward vacuum system. A vacuum of the order of
* Fax: #20-24552138. E-mail address: [email protected] (A.H. Ammar).
0042-207X/01/$ - see front matter 2001 Published by Elsevier Science Ltd. PII: S 0 0 4 2 - 2 0 7 X ( 0 0 ) 0 0 4 2 4 - 3
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A.H. Ammar / Vacuum 60 (2001) 355}360
4.0;10\ Pa was maintained during evaporation. The evaporation rate, as monitored by a quartz crystal oscillator (Edwards type FTM4) was about 1.2 nm/s. The "lm thickness (100}300 nm) was measured using the multiple-beam Fizeau fringes method [11]. The chemical composition of the "lms was determined by means of energy dispersive X-ray spectrometry. An EDX unit attached to a scanning electron microscope (type Joel, JSM-T 200) operating at 25 kV, was employed. An X-ray di!ractometer (type Shimadzu XD-3) provided with Ni-"ltered Cu K radiation was used to inves? tigate the Zn Cd Se thin "lms deposited onto V \V the glass substrates. The analytical method described by Cullity [12] was utilized for indexing the planes of the obtained X-ray di!raction patterns. The substrate temperature was maintained in the range 570}625 K for each deposited "lm. The transmittance ¹(j) and re#ectance R(j) at normal incidence were measured using a doublebeam UV-3101 PC scanning Shimadzu spectrophotometer, provided with a V}N absolute specular re#ection attachment. The optical constants n and k were determined using a recently developed technique [13], which involves a bivariant search based on minimizing (*R) and (*¹) simultaneously, where *R"R
!R , CVN A?J *¹"¹ !¹ CVN A?JA
The subscripts exp. and calc. refer to the experimental and calculated results, respectively, and both the transmittance ¹ and re#ectance R are given by Murmann's exact equations [14,15]: A exp@#B exp\@#2C cos a#4D sin a R" , E exp@#F exp\@#2G cos a#4H sin a 16n n (n#k) Q ¹" , E exp@#F exp\@#2G cos a#4H sin a where A"[(n!n )#k] [(n#n )#k], Q B"[(n!n )#k] [(n#n )#k], Q
C"(n#k) (n #n)!(n#k)!n n Q Q !4n n k, Q D"k(n !n ) (n#k#n n ), Q Q E"[(n#n )#k] [(n#n )#k], Q F"[(n!n )#k] [(n!n )#k], Q G"(n#k) (n #n)!(n#k)!n n Q Q #4n n k, Q H"k(n !n ) (n#k!n n ), Q Q 4pnt , a" j 4pkt b" , j in which n is the refractive index of air, n is the refractive index of substrate, t is the "lm thickness, and j is the wavelength of incident beam. The real and imaginary parts of the complex refractive index, n "n!ik, were determined for di!erent "lm compositions.
3. Results and discussion Structural analysis of X-ray di!raction patterns for the prepared Zn Cd Se thin "lms revealed V \V the existence of two composition ranges. The "rst range extends from x"0 to x(0.6, where the "lm was found to crystallize in the wurtzite-type crystal lattice. The second composition range extends from x)0.6 to x"1, where the "lms were found to crystallize in the sphalerite-type crystal lattice corresponding to the (1 1 1) plane for the sphalerite structure and (0 0 2) plane for the wurtzite structure. The calculated lattice parameters of the prepared "lms were found to vary with composition in a linear relation for each type of structure. Thus, the "lms showed a behaviour in accordance with Vegard's law for each crystal type, being continuous and homogeneous. Fig. 1 illustrates the relation between the d-spacing of the (1 1 1) re#ecting plane of sphalerite and
A.H. Ammar / Vacuum 60 (2001) 355}360
357
Fig. 1. Lattice-spacing (d) of (1 1 1) and (0 0 2) re#ecting planes vs. "lm compositions.
Fig. 2. Energy dispersive X-ray spectrum of Zn Cd Se "lm.
the (0 0 2) plane of the wurtzite with composition, revealing two straight lines extending into each other. A typical energy dispersive X-ray spectrum of As-deposited Zn Cd Se "lms is shown in Fig. 2. This "gure is used to "nd the percentage
elemental composition of the "lm given in column 2 in Table 1. The spectral behaviour of the refractive index n given in Fig. 3, shows abnormal dispersion at di!erent wavelengths depending on "lm composition.
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Table 1 Elemental analysis of a typical vacuum-deposited "lm compared to the bulk material of Zn Cd Se Element
At% (thin "lm)
At% (bulk material)
Zn Cd Se Total
6.256 48.962 43.782 100.000
7.1853 49.4192 43.3955 100.0000
Fig. 4. The extinction coe$cient k vs. j for Zn Cd Se thin V \V "lms of di!erent compositions.
Fig. 3. The refractive index (n) as a function of wavelength (j) with di!erent "lm compositions (x).
For x"0.6, or 0.8 the peak lies at j+650 nm and is equal, but for x"0.2 and 0.4 the peak shifts towards shorter wavelength (j+600 nm). For wavelengths above 650 nm, the refractive index n shows normal dispersion for all compositions. The dispersion curves of Fig. 3 indicate that the refractive index n increases with increasing Zn content. The spectral behaviour of the extinction coe$cient k is represented in Fig. 4. It shows that for any "lm composition, k decreases with increasing wavelength. Also Fig. 4 shows that k values are greater for lower x values. The absorption edge shifts to the short-wavelength side as the "lm composition parameter x increases. The results in the absorption region were analysed using the relation ahl"A(hl!E ) , for direct E band gap semiconductors. Typical plots of (ahl) vs. hl shown in Fig. 5 clearly reveal a linear increase in (ahl) with hl beyond a certain photon energy (varying from 1.79 to 2.38 eV depending on the value of the "lm composition parameter x). The values of the optical band gap E estimated E
Fig. 5. Plot of (ahl) vs. hl for Zn Cd Se thin "lms with V \V di!erent compositions x: x"0.2, 0.4, 0.6, 0.8.
from the intercepts of the straight lines for Zn Cd Se polycrystalline thin "lms are shown V \V in Fig. 5. The transition was found to be direct for all the "lm compositions studied here. The band gap showed a nonlinear variation with "lm
A.H. Ammar / Vacuum 60 (2001) 355}360
359
Fig. 6. Variation of band gap (Eg) with composition for polycrystalline Zn Cd Se thin "lms. V \V
composition parameter x and obeyed the relation [16,17] Eg(x)"E #(E !E !b)x#bx, (1) where E and E are the band gaps of CdSe ("1.67 eV) and ZnSe ("2.63 eV), respectively, and b is the bowing parameter. The variation in E (x) "tted the above expression, (1), well for E b"0.45. This value of b di!ers substantially from the experimental values of b"1.6 obtained by Gupta et al. [18] for Zn S}Zn Te alloy "lms. For such systems, a plot of [*E(x)a]/(1!x) vs. x should give two linear portions corresponding to the two phases which exist according to the "lm composition (the change in phase from wurtzite to sphalerite at x"0.6). *E(x) is assumed to be equal to E !E(x), where [16] E "E #(E !E )x. H H The plots of [*E(x)a]/(1!x) vs. x for Zn Cd Se "lms are shown in Fig. 7. The band V \V edge e!ective mass (mH) of the carrier can be exA pressed as [19] 1 p m " "1# , mH mH 2mE A E so that the band gap E can be expressed as E P mH E " , E 2m 1!mH P " f (mH), 2m
(2)
(3) (4)
where mH"mH/m, m being the free electron mass A and P is the momentum matrix element which may
Fig. 7. Plot of [*E(x)a]/(1!x)] vs. x for Zn Cd Se "lms. V \V
be approximated as P"(h/2p) G, where G is the smallest reciprocal lattice vector. Therefore, P becomes equal to h/a where a is the lattice constant: mH f (mH)" . 1!mH Using Eq. (4) in Eq. (1) we obtain P P f (mH, x)" f (mH) 2m 2m
#
P P f (mH)! f (mH)!b #bx 2m 2m
or f (mH, x)"f (mH)#[f (mH)!f (mH)!b ]x#b x, (5) where b "b/(P/2m) and P/2m is constant and equal to 10.6 eV, mH ("0.1361) and mH ("0.1987) correspond to materials with x"0 and 1, respectively. Thus, the function f (m*) of a ternary compound semiconductor should show a bowing behaviour with the bowing parameter b which is related to b by the relation b "b/(P/2m). If the e!ective
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A.H. Ammar / Vacuum 60 (2001) 355}360
temperature +600 K. The "lms showed a mixed structure and exhibited a wurtzite phase for x)0.6, beyond which they showed a sphalerite phase. The energy gap of the "lms was determined and plotted as a function of "lm composition. An empirical formula E (x)"1.66#0.65x#0.25x E which describes the energy gap as a function of the "lm composition has been derived. A small deviation from a previously published empirical formula can probably be ascribed to a di!erent method of determining the "lm composition x.
References Fig. 8. Variation in m* and f (m*) with x.
masses (mH and mH) of the carriers of the constitu ent semiconductors and band gap bowing parameter, b are known, one can compute the e!ective mass of the semiconductor alloy for any required composition by using Eq. (5) [18]. The variations in f (mH) and mH with "lm composition parameter x for Zn Cd Se as computed above are shown in V \V Fig. 8. It can be seen that the variation in f (mH) shows a bowing behaviour with b "0.439. The b value calculated from b was found to be equal to 0.466 which agrees very well with the value 0.45 obtained from Fig. 6 relating E vs. x. It is interesting to note E that in this case, the values of m* can be "tted well to be empirical formula mH"mH#(mH!mH!c)x#cx. The value of c (0.0258) obtained from the "t of m* vs. x plot (Fig. 8) agrees well with the numerical value (0.0439) of b . 4. Conclusion Polycrystalline Zn Cd Se thin "lms can be V \V obtained by thermal evaporation at a substrate
[1] Dawar AL, Shishodia PK, Chauhan G, Jagadish C, Kappoor SK, Mathur PC. J Crystal Growth 1990; 100:281. [2] Shaalan MS, MuK ller R. Sol Cells 1990;28:185. [3] Rao DR, Islam R. Thin Solid Films 1993;224:191}5. [4] Soliman HS, Ali NA, El-Shazly AA. Appl Phys A 1995;60. [5] Lunz U, Kuhn J, Goschenhofer F, SchuK ssler V, Einfeldt S, Becker CR, Landwehr G. J Appl Phys 1996;80(12). [6] Ren J, Bowers KA, Sneed B, Dreifus DL, Cook Jr. JW, Schetzina J-F, Kolbus RM. Appl Phys Lett 1990; 57:1901. [7] Yoo JB, Fahrenbruch AL, Bube RH. Sol Cells 1991;34:171. [8] Pandey RK, Kumar SR, Rooz AJN, Chandra S. Thin Solid Films 1991;200:1. [9] Samarth N, Luo H, Furdyna JK, Alnoso RG, Lee YR, Ramdas AK, Qadri SB, Otsuka N. J Appl Phys Lett 1990;56:1163. [10] Kim YD, Klein MV, Ren SF, Chang YC, Luo H, Samarth N, Furdyna JK. Phys Rev B 1994;49:7262. [11] Tolansky S. In multiple-beam interference microscopy of metals. London: Academic, 1970. p. 55. [12] Cullity BD, Elements of X-ray di!raction, 2nd ed. New York: Addison Wesley, 1978. p. 327. [13] Abo Ghazala MS, Ammar AH, El-Gohary Z, El-Badawy Z. Egyptain J Sol 1995;18(1):49}59. [14] Heavens OS. Optical properties of thin solid "lms. New York: Dover, 1965. [15] Heavens OS. Thin "lm physics. London: Methuen, 1970. [16] Hill R, Richardson D. Thin Solid Films 1973;18:25. [17] Hill R, Richardson D. J Phys 1973;C6:L115. [18] Gupta P, Maiti B, Chaudhuri S, Pal AK. Thin Solid Films 1993;277:66}73. [19] Ferry DK. Semiconductors. New York: Macmillan, 1991 [Chapter 5].
Some studies on structural and optical properties of Zn Cd Se thin "lms V \V A.H. Ammar* Faculty of Education, Physics Department, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt Received 18 February 2000; received in revised form 21 August 2000; accepted 13 September 2000
Abstract Thin Zn Cd Se "lms with a thickness ranging from 100 to 300 nm are prepared by thermal evaporation under V \V a vacuum of 4.0;10\ Pa. Films deposited at substrate temperatures ranging from 570 to 625 K were found to be of polycrystalline nature, with sphalerite structure for x*0.6 and wurtzite structure for x(0.6. The optical constants n and k of Zn Cd Se thin "lms of di!erent composition were determined in the spectral range 400}2000 nm. The V \V analysis of the accuracy of the adopted technique gave $1.0 and $0.5% for the real part of the refractive index n and the extinction coe$cient k, respectively. Th band gap showed a non-linear variation with the value of x. The e!ective masses of the carriers and the band gap bowing parameters of Zn Cd Se thin "lms were estimated. 2001 V \V Published by Elsevier Science Ltd. Keywords: Zn Cd Se; Thin "lms; Optical constants; Electron e!ective mass V \V
1. Introduction
2. Experimental procedure and calculations
Results on the structural and optical properties of zinc and cadmium selenide thin "lms have indicated [1}5] promising applications for these materials in light-emitting diodes [6], photovoltaic and photoelectrochemical devices [7,8]. The energy gap of Zn Cd Se alloys has been determined at V \V 300 K by re#ection spectroscopy [9], spectroscopic ellipsometry [10], and using transmission and re#ection measurements in the temperature range from 5 to 300 K [5]. The present work was performed in order to investigate the structural and optical properties of Zn Cd Se thin "lms. V \V
The source materials Zn Cd Se used in the V \V deposition of thin "lms was prepared by direct reaction of high-purity elemental Zn(6N), Cd(5N) and Se (4N). Stoichiometric quantities of the elements were placed in a vacuum-sealed (1.33;10\ Pa) silica tube which was gradually heated at a rate of 103C/h to a temperature in the range 1220}1250 K depending on the speci"ed composition. The tube was then maintained at the optimum temperature for 72 h and thereafter cooled to room temperature. Following this procedure four Zn Cd Se solid V \V solution ingots with x"0.2, 0.4, 0.6 and 0.8 were prepared. Thin "lms were deposited onto wellcleaned glass and quartz substrates using an E306A Edward vacuum system. A vacuum of the order of
* Fax: #20-24552138. E-mail address: [email protected] (A.H. Ammar).
0042-207X/01/$ - see front matter 2001 Published by Elsevier Science Ltd. PII: S 0 0 4 2 - 2 0 7 X ( 0 0 ) 0 0 4 2 4 - 3
356
A.H. Ammar / Vacuum 60 (2001) 355}360
4.0;10\ Pa was maintained during evaporation. The evaporation rate, as monitored by a quartz crystal oscillator (Edwards type FTM4) was about 1.2 nm/s. The "lm thickness (100}300 nm) was measured using the multiple-beam Fizeau fringes method [11]. The chemical composition of the "lms was determined by means of energy dispersive X-ray spectrometry. An EDX unit attached to a scanning electron microscope (type Joel, JSM-T 200) operating at 25 kV, was employed. An X-ray di!ractometer (type Shimadzu XD-3) provided with Ni-"ltered Cu K radiation was used to inves? tigate the Zn Cd Se thin "lms deposited onto V \V the glass substrates. The analytical method described by Cullity [12] was utilized for indexing the planes of the obtained X-ray di!raction patterns. The substrate temperature was maintained in the range 570}625 K for each deposited "lm. The transmittance ¹(j) and re#ectance R(j) at normal incidence were measured using a doublebeam UV-3101 PC scanning Shimadzu spectrophotometer, provided with a V}N absolute specular re#ection attachment. The optical constants n and k were determined using a recently developed technique [13], which involves a bivariant search based on minimizing (*R) and (*¹) simultaneously, where *R"R
!R , CVN A?J *¹"¹ !¹ CVN A?JA
The subscripts exp. and calc. refer to the experimental and calculated results, respectively, and both the transmittance ¹ and re#ectance R are given by Murmann's exact equations [14,15]: A exp@#B exp\@#2C cos a#4D sin a R" , E exp@#F exp\@#2G cos a#4H sin a 16n n (n#k) Q ¹" , E exp@#F exp\@#2G cos a#4H sin a where A"[(n!n )#k] [(n#n )#k], Q B"[(n!n )#k] [(n#n )#k], Q
C"(n#k) (n #n)!(n#k)!n n Q Q !4n n k, Q D"k(n !n ) (n#k#n n ), Q Q E"[(n#n )#k] [(n#n )#k], Q F"[(n!n )#k] [(n!n )#k], Q G"(n#k) (n #n)!(n#k)!n n Q Q #4n n k, Q H"k(n !n ) (n#k!n n ), Q Q 4pnt , a" j 4pkt b" , j in which n is the refractive index of air, n is the refractive index of substrate, t is the "lm thickness, and j is the wavelength of incident beam. The real and imaginary parts of the complex refractive index, n "n!ik, were determined for di!erent "lm compositions.
3. Results and discussion Structural analysis of X-ray di!raction patterns for the prepared Zn Cd Se thin "lms revealed V \V the existence of two composition ranges. The "rst range extends from x"0 to x(0.6, where the "lm was found to crystallize in the wurtzite-type crystal lattice. The second composition range extends from x)0.6 to x"1, where the "lms were found to crystallize in the sphalerite-type crystal lattice corresponding to the (1 1 1) plane for the sphalerite structure and (0 0 2) plane for the wurtzite structure. The calculated lattice parameters of the prepared "lms were found to vary with composition in a linear relation for each type of structure. Thus, the "lms showed a behaviour in accordance with Vegard's law for each crystal type, being continuous and homogeneous. Fig. 1 illustrates the relation between the d-spacing of the (1 1 1) re#ecting plane of sphalerite and
A.H. Ammar / Vacuum 60 (2001) 355}360
357
Fig. 1. Lattice-spacing (d) of (1 1 1) and (0 0 2) re#ecting planes vs. "lm compositions.
Fig. 2. Energy dispersive X-ray spectrum of Zn Cd Se "lm.
the (0 0 2) plane of the wurtzite with composition, revealing two straight lines extending into each other. A typical energy dispersive X-ray spectrum of As-deposited Zn Cd Se "lms is shown in Fig. 2. This "gure is used to "nd the percentage
elemental composition of the "lm given in column 2 in Table 1. The spectral behaviour of the refractive index n given in Fig. 3, shows abnormal dispersion at di!erent wavelengths depending on "lm composition.
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Table 1 Elemental analysis of a typical vacuum-deposited "lm compared to the bulk material of Zn Cd Se Element
At% (thin "lm)
At% (bulk material)
Zn Cd Se Total
6.256 48.962 43.782 100.000
7.1853 49.4192 43.3955 100.0000
Fig. 4. The extinction coe$cient k vs. j for Zn Cd Se thin V \V "lms of di!erent compositions.
Fig. 3. The refractive index (n) as a function of wavelength (j) with di!erent "lm compositions (x).
For x"0.6, or 0.8 the peak lies at j+650 nm and is equal, but for x"0.2 and 0.4 the peak shifts towards shorter wavelength (j+600 nm). For wavelengths above 650 nm, the refractive index n shows normal dispersion for all compositions. The dispersion curves of Fig. 3 indicate that the refractive index n increases with increasing Zn content. The spectral behaviour of the extinction coe$cient k is represented in Fig. 4. It shows that for any "lm composition, k decreases with increasing wavelength. Also Fig. 4 shows that k values are greater for lower x values. The absorption edge shifts to the short-wavelength side as the "lm composition parameter x increases. The results in the absorption region were analysed using the relation ahl"A(hl!E ) , for direct E band gap semiconductors. Typical plots of (ahl) vs. hl shown in Fig. 5 clearly reveal a linear increase in (ahl) with hl beyond a certain photon energy (varying from 1.79 to 2.38 eV depending on the value of the "lm composition parameter x). The values of the optical band gap E estimated E
Fig. 5. Plot of (ahl) vs. hl for Zn Cd Se thin "lms with V \V di!erent compositions x: x"0.2, 0.4, 0.6, 0.8.
from the intercepts of the straight lines for Zn Cd Se polycrystalline thin "lms are shown V \V in Fig. 5. The transition was found to be direct for all the "lm compositions studied here. The band gap showed a nonlinear variation with "lm
A.H. Ammar / Vacuum 60 (2001) 355}360
359
Fig. 6. Variation of band gap (Eg) with composition for polycrystalline Zn Cd Se thin "lms. V \V
composition parameter x and obeyed the relation [16,17] Eg(x)"E #(E !E !b)x#bx, (1) where E and E are the band gaps of CdSe ("1.67 eV) and ZnSe ("2.63 eV), respectively, and b is the bowing parameter. The variation in E (x) "tted the above expression, (1), well for E b"0.45. This value of b di!ers substantially from the experimental values of b"1.6 obtained by Gupta et al. [18] for Zn S}Zn Te alloy "lms. For such systems, a plot of [*E(x)a]/(1!x) vs. x should give two linear portions corresponding to the two phases which exist according to the "lm composition (the change in phase from wurtzite to sphalerite at x"0.6). *E(x) is assumed to be equal to E !E(x), where [16] E "E #(E !E )x. H H The plots of [*E(x)a]/(1!x) vs. x for Zn Cd Se "lms are shown in Fig. 7. The band V \V edge e!ective mass (mH) of the carrier can be exA pressed as [19] 1 p m " "1# , mH mH 2mE A E so that the band gap E can be expressed as E P mH E " , E 2m 1!mH P " f (mH), 2m
(2)
(3) (4)
where mH"mH/m, m being the free electron mass A and P is the momentum matrix element which may
Fig. 7. Plot of [*E(x)a]/(1!x)] vs. x for Zn Cd Se "lms. V \V
be approximated as P"(h/2p) G, where G is the smallest reciprocal lattice vector. Therefore, P becomes equal to h/a where a is the lattice constant: mH f (mH)" . 1!mH Using Eq. (4) in Eq. (1) we obtain P P f (mH, x)" f (mH) 2m 2m
#
P P f (mH)! f (mH)!b #bx 2m 2m
or f (mH, x)"f (mH)#[f (mH)!f (mH)!b ]x#b x, (5) where b "b/(P/2m) and P/2m is constant and equal to 10.6 eV, mH ("0.1361) and mH ("0.1987) correspond to materials with x"0 and 1, respectively. Thus, the function f (m*) of a ternary compound semiconductor should show a bowing behaviour with the bowing parameter b which is related to b by the relation b "b/(P/2m). If the e!ective
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temperature +600 K. The "lms showed a mixed structure and exhibited a wurtzite phase for x)0.6, beyond which they showed a sphalerite phase. The energy gap of the "lms was determined and plotted as a function of "lm composition. An empirical formula E (x)"1.66#0.65x#0.25x E which describes the energy gap as a function of the "lm composition has been derived. A small deviation from a previously published empirical formula can probably be ascribed to a di!erent method of determining the "lm composition x.
References Fig. 8. Variation in m* and f (m*) with x.
masses (mH and mH) of the carriers of the constitu ent semiconductors and band gap bowing parameter, b are known, one can compute the e!ective mass of the semiconductor alloy for any required composition by using Eq. (5) [18]. The variations in f (mH) and mH with "lm composition parameter x for Zn Cd Se as computed above are shown in V \V Fig. 8. It can be seen that the variation in f (mH) shows a bowing behaviour with b "0.439. The b value calculated from b was found to be equal to 0.466 which agrees very well with the value 0.45 obtained from Fig. 6 relating E vs. x. It is interesting to note E that in this case, the values of m* can be "tted well to be empirical formula mH"mH#(mH!mH!c)x#cx. The value of c (0.0258) obtained from the "t of m* vs. x plot (Fig. 8) agrees well with the numerical value (0.0439) of b . 4. Conclusion Polycrystalline Zn Cd Se thin "lms can be V \V obtained by thermal evaporation at a substrate
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