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A general optical characterization method for determining the composition of Hg1−xCdxTe samples
ooz0-0891/93 s6.00 + 0.00
hyked Phys. Vol. 34, No. I, pp. 83-87,1993 Printed in GreatBritain.All right.9 -cd
c0pyright Q 1993 Fw@mofl Prcsa Ltd
A GENERAL OPTICAL CHARACTERIZATION METHOD FOR DETERMINING THE COMPOSITION OF Hg, _ xCd,Te SAMPLES VISHNUGOPAL, R. ASHOKAN
and A. K. GUPTA
Solid State Physics Laboratory, Lucknow Road, Delhi 110 054, India (Received 16
September
1992)
hatract-The rata of variation of transmission as a function of fhquency or energy exhibits a maximum in the fundamental absorption region of the alloy semiconductor Hg, _,cd,Te. The maximum steepness occurs in the tail region of the absorption edge and its frequency can be correlated analytically with the composition. From the experimental measurements of room temperature IR transmission on both bulk grown and epilayers of Hg, _,cd,Te, it is shown that an analysis of the transmission curve at (dT,/dE), leads to the determination of composition and compositional uniformity in the given sample.
I.
INTRODUCTION
An exponential tail in the fundamental absorption region of Hg,_,Cd,Te has been extensively used for routine determination of composition (x) of this alloy semiconductor system, from a simple room temperature IR transmission measurement. The suggested methods involve the determination of composition either from zero transmission cut-or&‘” (ZITCO) frequency or from the frequency corresponding to 50% of the maximum transmission(S (Z&, or from the position of the frequency of the transmission derivative minimum. 0 It is, however, interesting to note that ZITCO has largely been used for determining the composition of bulk grown thicker wafers, and Zuz has been exclusively used in the case of epilayers only. Recently Gopal et al.(‘) also applied ZITCO for determining the composition of epilayers, but their calibration relation differs from the relation applicable to the thicker samples. The transmission derivative minimum method”) though, seems to be applicable over a wider range of thicknesses, and is based on the assumption that the frequency of the transmission derivative minimum is related to the band gap energy, and thus uses another band gap (E,) versus composition (x) relation@ to determine the composition of the given sample. In this paper, we show that the first derivative of transmission (i.e. dT,/dE) w.r.t. the energy of the incident radiation actually exhibits a maximum rather than a minimum, and that the transmission derivative maximum method may be developed into a general method for the compositional characterization of both epilayers and bulk grown samples of Hg, _,Cd,Te directly, without the help of another Es vs x relation. II.
THEORY
Optical absorption in the tail region of the fundamental be described by the following relation,“) a = croexpW
absorption
- &MT + T,))
edge of Hg, _,Cd,Te
can (1)
where T,=81.9
(la)
- 0.3424 + 1.838x
(lb)
c = 3.267 x lO’(1 + x)
(lc)
cr, = exp(- 18.88 +53.61x).
(ld)
&=
83
VIsmu GoPAL et al.
84
In the above relations, E is in eV, T is in K and a in cm-‘. Neglecting interference effects, but including multiple reflections, the general expression for the transmission through a mercury cadmium telhuide sample of thickness t may be written as,(‘) T,
=
(1
-
R,)T2,3a,
1 - R, R,R,a:
T2.3
(1 - R2)(l - Rda2 1 - R2Raa:
=
(W
a, = exp( - at)
(2b)
a, = ew(-wA
(24
where subscript 1 corresponds to the MCI-air interface, subscripts 2 and 3 respectivley correspond to the MCT-transparent substrate and transparent substrate&r interfaces in the case of an epilayer sample. The subscript “s” refers to the substrate. The reflection coefficients R, , R2 and R3 at the various (i,j) interfaces are given by: R
=
04- n,12 04+ nil2’
(2d)
Since the refractive index of MCT is a more slowly varying function of energy as compared to the absorption coefficient in the region of the absorption edge, the reflection coefficients R,, R2 and R3 in equation (2) may be treated as constant. It can then be shown from the algebraic manipulation and differentiation of equations (1) and (2) that,
dT’dE--T,
0
T+81.9a’
1 + RI R2Ra exp( - 2at) l-R,R2Rsexp(-2at)’
(3)
The minus sign on the r.h.s. of equation (3) signifies that the transmission decreases with increasing frequency (or energy) of incident radiation. Thus the maximum in the dT,/dE vs E curve should not be interpreted as a minimum because of the negative sign of dT,/dE. An important relationship between the various variables appearing in equations (1) and (2) can now be obtained at the frequency of the transmission derivative maximum by equating d2T,/dE2 = 0, which gives 1 - [R, R,R, exp(-2at)12 at =4R,R2R3exp(-2at)+[l + R,R,R,exp(-2at)12’
(4)
Since for a given sample R,, R2 and R, can now be obtained from equation (2d), given the refractive indices of various materials in question, a numerical value of at corresponding to the frequency of transmission derivative maximum (hereafter referred to as EM) can now be calculated from equation (4). Let us say, at = K.
(5)
A relation between EM and x can now be obtained in a straightforward manner, by substituting the set of equations (1-ld) in equation (5). The resulting relation is as follows: EM= (T + 81.9){ln(K/O - 53.61~ + 18.88) + 1 838x _ o 3424 . . 3.267 x lO'(1 + x)
(6)
Compositionof Hg, _ .cd,Te samples
85
Equation (6) is a quadratic equation in x and can be solved to obtain composition ‘x’ from the observed room temperature (7’ = 300 IQ frequency, EM. X=
-3+p=m
WO
2A
where A = 1.838 3 = 0.86892 - EM
C= 116.9 x lo-‘In(K/t)-0.1217--EM. Each sample of the alloy semiconductor Hg, _Xcd,Te in general has some positions inhomogeneity, The above analysis is therefore likely to give a kind of average estimate of x. However, an estimate of compositional uniformity in the given sample can also be obtained by this method as discussed in the following paragraph. Let us assume that the tangent drawn to the transmission curve at the frequency EMintersects the xero transmission line at a frequency, say, Br+hsas shown in Fig. 1. Then, after some mathematical. manipulations of equations (l-ld), (2), (4) and (S), one can obtain the following relations: T+81.9 1 1 -R,R,R,exp(-2R) 3.267x 104(1+x)~1+R,R,RSexp(-2K)
E,,=E,-
(7)
and AEW
-2= Ax
1.838x - 0.969 - EMa 1+x
+ 1.838.
(f-9
40
-0.1
35
-0.2
30
-0.3
-0.6
:II_ ~~ , 1800
1600
1400
/ ~~~ 1200
10000
Wave number (cmql)
Fig. 1. Room temperatureIR trwimhion and derivativespectra of rrsmpleE 26264. The podions of the derivativemaximum and the zero cut-point of the tangent at the derivativemaximum am Micated ~s,=d&dTiW=ti~Y.
Table 1. The measured and udcuiated values of compoeition and absorption coeffi&ent.sfor some enilayersof Hn, _ ,Cd.Te
44
&wi
Sample
(cm-‘) Meas.
(cm_‘) Meas.
E 26264 E 26264 E 26264
1572.8 1538.8 1557.3
1686.5 1610.2 1658.7
21
Xf
0.22497 0.22153 0.22340
0.0184 0.0142 0.0172
475.717 475.710 475.714
475.817 475.808 475.813
E 26293 E 26293 E 26293
1577.3 1582.3 1585.4
1678.3 1694.5 1685
;;
0.22613 0.22664 0.22695
0.0171 0.0182 0.0169
434.352 434.353 434.354
434.441 434.444 434.443
E 26370 E 26370 E 26370
1572.7 1538.1 1557.9
1677.7 i618.3 1657.6
;: 20
0.22458 0.22107 0.22308
0.0175 0.0151 O.OI70
499.502 499.495 499.499
499.607 499.600 499.604
E 10035 E 10035 E 10035
2782.29 2755.71 2797.10
2861.5 2844.7 2891.03
16.2 16.2 16.2
0.34053 0.33804 0.34191
0.0127 0.0136 0.01401
616.939 616.933 616.942
617.080 617.069 617.080
Thick Eqs&id) ~~,
23
Equation (7) gives the calculated value of ~5~ for an exigency measured frequency EM, if the sample was of uniform composition. On the r.h.s. of equations (7) and (8), both x and & are calculated values obtained from equations (6) and (7) respectively. The extent of compositional uniformity (AX)can then be obtained by equation (8) from measured AE=, which is the difference of calculated and ex~~ment~y measured frequencies EM=. III. RESULTS AND DISCUSSION In this section we present some typical experimental results obtained on Hg, _,Cd,Te epilayers grown on CdTe substrates and the bulk grown Hg,_,cd,Te wtiers. The epilayers (E 26264, E 26293, E 26370 in Table 1) were procured from Fedora Corp., U.S.A. The bulk grown B4101-39sample (Table 2) was procured from Con&co, U.S.A. and the BOll-2 sample was grown in our laboratory by solid state recrystallixation. The room temperature IR transmission measurements were carried out on a FTIR spectrometer model ETS-40, from Bio-Rad. This spectrometer has a computerized data acquisition system, and the required software necessary for taking the fkst derivative of the measured transmission spectrum. Figure 1 shows a typical measured room temperature IR transmission spectrum along with the derivative (dT,/dE) spectrum of the sample E26264. Similar curves (not shown here) were obtained for all other samples. The required measurement data have, however, been listed in Tables 1 and 2 for all these samples. Three readings on each sample correspond to three different spatial locations. The values of x and Ax calculated from equations @a) and (8) respectively are &en in the 5th and 6th columns of Tables 1 and 2. In order to verify the value of x thus obtained, we first determine a by making use of equations (I-ld) from the calculated value of x. The values of a for each sample Table 2. The measuredand cakxlated values of composition and absxption coetEcientsfor some bulk samples of Hg, _,CdxTe Thick Ocm) Meas.
Sample
EM (~-9 Meas.
fE2
B4101.39 B4101-39 B4101-39
1110 1124 1179.4
1161.7 1188.4 1243.8
485
Boll-2 Boil-2 Boll-2
1163.8 1157.8 1184.2
1208.6 120!+*4 1234.5
z:
ET
::
663
Eqs.i&id) 0.2036 0.2050 0.2105
0.0130 0.0142 0.0141
18.802 18.805 18.813
18.804 18.807 18.815
0.2114 0.2108 0.2135
0.0121 0.0124 0.0126
13.762 13.762 13.762
13.764 13.764 13.764
Composition of Hg, _ J!dxTe samples
87
Table 3. Summary of K values mquimd for the calculation in the case of @layers on different substrates and bulk Hgl_,CdxTe sampks substrate Silicon GaAS CdTe sapphire Bulk Hg, _,Gd,Te Bulk Hg, _,cd,Te
Ref. index
K x IO-’ (x = 0.2)
R x to-3 (x Q 0.3)
3.43 3.32 2.72
999.977 999.918 999.044 998.049 912.431 -
999.998
::: 3.35
z?z 998:420 925.348
are given in the last column of Tables 1 and 2. Next, we determined a for each sample (shown in the 7th column of Tables 1 and 2) from equation (5) from the known thickness (determined from interference fringes) of the Hg, _ XCd,Te sample, and tabulated the K values as summarized in Table 3. Note that determination of a from equation (5) is simply based on the fundamental equations (1) and (2) only, which do not make use of x at any stage. The agreement between both values of a thus obtained provides an adequate verification of x value shown in Tables 1 and 2. In addition, the present paper also provides an indirect confirmation of the form and the values of the numerical constants appearing in equations (la)-(ld). One may observe from Tables I and 2 that AX obtained for epilayers is in general higher than that obtained for the bulk samples, even though the spatial ~o~ty in ~rn~~tion is very good. The higher AXfor epilayers is the manifestation of the presence of a graded transition layer at the substrate-Hg, _,Cd,Te interface, whereas in the case of bulk samples, the observed Ax is real indicating the inbomogeneity along the thickness of the wafer or along the area. In the present case, since the spatial compositional uniformity in the bulk samples is very good, the observed AXmay be interpreted as indicating the com~sition~ i~omogeneity along the thickness of the given wafer. Table 3 summarizes the numerical value of K to be used in the above calculations for the epilayers grown on some of the commonly used substrates. It may be observed that the value of K differs markedly for bulk Hg, _XCd,Te samples as compared to epilayers grown on different substrates. This also explains the need for using different calibration relations in the case of bulk samples and epilayers as stated by the previous investigators. (2-r)However, the present work has shown that basically the same calibration relation may be used for both epilayer and bulk samples by simply using the appropriate value of K. The exact value of the latter can also be determined in each case. IV.
CONCLUSION
In conclusion we have presented a general method to determine the composition and compositional uniformity of Hg,_,Cd,Te samples, be it a bulk wafer or an epilayer, from room temperature IR transmission measurements. This method gives the composition x directly without involving another Eg vs x relation. Acknowierlgementp-Tiie authors thank
the Director, Solid State Physics Laboratory, Delhi for his pumisuion to publish this work. They are also gratefid to Dr 8. B. Sharma for providing the bulk Hg,_,Cd,Te sample grown by SSR.
REFERENCES 1. 2. 3. 4. 5. 6. 7.
E. Finkman and S. E. !Schacham, J. appk Phys. 56, 2896 (1984). W. F. H. Mi~le~~~ J. appt. Phys. 63,2382 (1988). M. Anandan, A. K. Kapoor, A. Bhaduri and A. V. R. War&, Z&v& P!~ya.31,485 (1991). Vishnu Gopal, R. Aahokan and V.. Dhar, Infrared Phys. ;U 39 (1992). E. Sand and Y. Nemirovsky, In&red Phy~. 25, 591 (1985). G. L. Hansen, J. L. Sehmit and T. N. Cassehnan, J. appl. Phys. 53, 7099 (1982). C. A. Hougen, 1. appl. Phys. 66, 3763 (1989).
hyked Phys. Vol. 34, No. I, pp. 83-87,1993 Printed in GreatBritain.All right.9 -cd
c0pyright Q 1993 Fw@mofl Prcsa Ltd
A GENERAL OPTICAL CHARACTERIZATION METHOD FOR DETERMINING THE COMPOSITION OF Hg, _ xCd,Te SAMPLES VISHNUGOPAL, R. ASHOKAN
and A. K. GUPTA
Solid State Physics Laboratory, Lucknow Road, Delhi 110 054, India (Received 16
September
1992)
hatract-The rata of variation of transmission as a function of fhquency or energy exhibits a maximum in the fundamental absorption region of the alloy semiconductor Hg, _,cd,Te. The maximum steepness occurs in the tail region of the absorption edge and its frequency can be correlated analytically with the composition. From the experimental measurements of room temperature IR transmission on both bulk grown and epilayers of Hg, _,cd,Te, it is shown that an analysis of the transmission curve at (dT,/dE), leads to the determination of composition and compositional uniformity in the given sample.
I.
INTRODUCTION
An exponential tail in the fundamental absorption region of Hg,_,Cd,Te has been extensively used for routine determination of composition (x) of this alloy semiconductor system, from a simple room temperature IR transmission measurement. The suggested methods involve the determination of composition either from zero transmission cut-or&‘” (ZITCO) frequency or from the frequency corresponding to 50% of the maximum transmission(S (Z&, or from the position of the frequency of the transmission derivative minimum. 0 It is, however, interesting to note that ZITCO has largely been used for determining the composition of bulk grown thicker wafers, and Zuz has been exclusively used in the case of epilayers only. Recently Gopal et al.(‘) also applied ZITCO for determining the composition of epilayers, but their calibration relation differs from the relation applicable to the thicker samples. The transmission derivative minimum method”) though, seems to be applicable over a wider range of thicknesses, and is based on the assumption that the frequency of the transmission derivative minimum is related to the band gap energy, and thus uses another band gap (E,) versus composition (x) relation@ to determine the composition of the given sample. In this paper, we show that the first derivative of transmission (i.e. dT,/dE) w.r.t. the energy of the incident radiation actually exhibits a maximum rather than a minimum, and that the transmission derivative maximum method may be developed into a general method for the compositional characterization of both epilayers and bulk grown samples of Hg, _,Cd,Te directly, without the help of another Es vs x relation. II.
THEORY
Optical absorption in the tail region of the fundamental be described by the following relation,“) a = croexpW
absorption
- &MT + T,))
edge of Hg, _,Cd,Te
can (1)
where T,=81.9
(la)
- 0.3424 + 1.838x
(lb)
c = 3.267 x lO’(1 + x)
(lc)
cr, = exp(- 18.88 +53.61x).
(ld)
&=
83
VIsmu GoPAL et al.
84
In the above relations, E is in eV, T is in K and a in cm-‘. Neglecting interference effects, but including multiple reflections, the general expression for the transmission through a mercury cadmium telhuide sample of thickness t may be written as,(‘) T,
=
(1
-
R,)T2,3a,
1 - R, R,R,a:
T2.3
(1 - R2)(l - Rda2 1 - R2Raa:
=
(W
a, = exp( - at)
(2b)
a, = ew(-wA
(24
where subscript 1 corresponds to the MCI-air interface, subscripts 2 and 3 respectivley correspond to the MCT-transparent substrate and transparent substrate&r interfaces in the case of an epilayer sample. The subscript “s” refers to the substrate. The reflection coefficients R, , R2 and R3 at the various (i,j) interfaces are given by: R
=
04- n,12 04+ nil2’
(2d)
Since the refractive index of MCT is a more slowly varying function of energy as compared to the absorption coefficient in the region of the absorption edge, the reflection coefficients R,, R2 and R3 in equation (2) may be treated as constant. It can then be shown from the algebraic manipulation and differentiation of equations (1) and (2) that,
dT’dE--T,
0
T+81.9a’
1 + RI R2Ra exp( - 2at) l-R,R2Rsexp(-2at)’
(3)
The minus sign on the r.h.s. of equation (3) signifies that the transmission decreases with increasing frequency (or energy) of incident radiation. Thus the maximum in the dT,/dE vs E curve should not be interpreted as a minimum because of the negative sign of dT,/dE. An important relationship between the various variables appearing in equations (1) and (2) can now be obtained at the frequency of the transmission derivative maximum by equating d2T,/dE2 = 0, which gives 1 - [R, R,R, exp(-2at)12 at =4R,R2R3exp(-2at)+[l + R,R,R,exp(-2at)12’
(4)
Since for a given sample R,, R2 and R, can now be obtained from equation (2d), given the refractive indices of various materials in question, a numerical value of at corresponding to the frequency of transmission derivative maximum (hereafter referred to as EM) can now be calculated from equation (4). Let us say, at = K.
(5)
A relation between EM and x can now be obtained in a straightforward manner, by substituting the set of equations (1-ld) in equation (5). The resulting relation is as follows: EM= (T + 81.9){ln(K/O - 53.61~ + 18.88) + 1 838x _ o 3424 . . 3.267 x lO'(1 + x)
(6)
Compositionof Hg, _ .cd,Te samples
85
Equation (6) is a quadratic equation in x and can be solved to obtain composition ‘x’ from the observed room temperature (7’ = 300 IQ frequency, EM. X=
-3+p=m
WO
2A
where A = 1.838 3 = 0.86892 - EM
C= 116.9 x lo-‘In(K/t)-0.1217--EM. Each sample of the alloy semiconductor Hg, _Xcd,Te in general has some positions inhomogeneity, The above analysis is therefore likely to give a kind of average estimate of x. However, an estimate of compositional uniformity in the given sample can also be obtained by this method as discussed in the following paragraph. Let us assume that the tangent drawn to the transmission curve at the frequency EMintersects the xero transmission line at a frequency, say, Br+hsas shown in Fig. 1. Then, after some mathematical. manipulations of equations (l-ld), (2), (4) and (S), one can obtain the following relations: T+81.9 1 1 -R,R,R,exp(-2R) 3.267x 104(1+x)~1+R,R,RSexp(-2K)
E,,=E,-
(7)
and AEW
-2= Ax
1.838x - 0.969 - EMa 1+x
+ 1.838.
(f-9
40
-0.1
35
-0.2
30
-0.3
-0.6
:II_ ~~ , 1800
1600
1400
/ ~~~ 1200
10000
Wave number (cmql)
Fig. 1. Room temperatureIR trwimhion and derivativespectra of rrsmpleE 26264. The podions of the derivativemaximum and the zero cut-point of the tangent at the derivativemaximum am Micated ~s,=d&dTiW=ti~Y.
Table 1. The measured and udcuiated values of compoeition and absorption coeffi&ent.sfor some enilayersof Hn, _ ,Cd.Te
44
&wi
Sample
(cm-‘) Meas.
(cm_‘) Meas.
E 26264 E 26264 E 26264
1572.8 1538.8 1557.3
1686.5 1610.2 1658.7
21
Xf
0.22497 0.22153 0.22340
0.0184 0.0142 0.0172
475.717 475.710 475.714
475.817 475.808 475.813
E 26293 E 26293 E 26293
1577.3 1582.3 1585.4
1678.3 1694.5 1685
;;
0.22613 0.22664 0.22695
0.0171 0.0182 0.0169
434.352 434.353 434.354
434.441 434.444 434.443
E 26370 E 26370 E 26370
1572.7 1538.1 1557.9
1677.7 i618.3 1657.6
;: 20
0.22458 0.22107 0.22308
0.0175 0.0151 O.OI70
499.502 499.495 499.499
499.607 499.600 499.604
E 10035 E 10035 E 10035
2782.29 2755.71 2797.10
2861.5 2844.7 2891.03
16.2 16.2 16.2
0.34053 0.33804 0.34191
0.0127 0.0136 0.01401
616.939 616.933 616.942
617.080 617.069 617.080
Thick Eqs&id) ~~,
23
Equation (7) gives the calculated value of ~5~ for an exigency measured frequency EM, if the sample was of uniform composition. On the r.h.s. of equations (7) and (8), both x and & are calculated values obtained from equations (6) and (7) respectively. The extent of compositional uniformity (AX)can then be obtained by equation (8) from measured AE=, which is the difference of calculated and ex~~ment~y measured frequencies EM=. III. RESULTS AND DISCUSSION In this section we present some typical experimental results obtained on Hg, _,Cd,Te epilayers grown on CdTe substrates and the bulk grown Hg,_,cd,Te wtiers. The epilayers (E 26264, E 26293, E 26370 in Table 1) were procured from Fedora Corp., U.S.A. The bulk grown B4101-39sample (Table 2) was procured from Con&co, U.S.A. and the BOll-2 sample was grown in our laboratory by solid state recrystallixation. The room temperature IR transmission measurements were carried out on a FTIR spectrometer model ETS-40, from Bio-Rad. This spectrometer has a computerized data acquisition system, and the required software necessary for taking the fkst derivative of the measured transmission spectrum. Figure 1 shows a typical measured room temperature IR transmission spectrum along with the derivative (dT,/dE) spectrum of the sample E26264. Similar curves (not shown here) were obtained for all other samples. The required measurement data have, however, been listed in Tables 1 and 2 for all these samples. Three readings on each sample correspond to three different spatial locations. The values of x and Ax calculated from equations @a) and (8) respectively are &en in the 5th and 6th columns of Tables 1 and 2. In order to verify the value of x thus obtained, we first determine a by making use of equations (I-ld) from the calculated value of x. The values of a for each sample Table 2. The measuredand cakxlated values of composition and absxption coetEcientsfor some bulk samples of Hg, _,CdxTe Thick Ocm) Meas.
Sample
EM (~-9 Meas.
fE2
B4101.39 B4101-39 B4101-39
1110 1124 1179.4
1161.7 1188.4 1243.8
485
Boll-2 Boil-2 Boll-2
1163.8 1157.8 1184.2
1208.6 120!+*4 1234.5
z:
ET
::
663
Eqs.i&id) 0.2036 0.2050 0.2105
0.0130 0.0142 0.0141
18.802 18.805 18.813
18.804 18.807 18.815
0.2114 0.2108 0.2135
0.0121 0.0124 0.0126
13.762 13.762 13.762
13.764 13.764 13.764
Composition of Hg, _ J!dxTe samples
87
Table 3. Summary of K values mquimd for the calculation in the case of @layers on different substrates and bulk Hgl_,CdxTe sampks substrate Silicon GaAS CdTe sapphire Bulk Hg, _,Gd,Te Bulk Hg, _,cd,Te
Ref. index
K x IO-’ (x = 0.2)
R x to-3 (x Q 0.3)
3.43 3.32 2.72
999.977 999.918 999.044 998.049 912.431 -
999.998
::: 3.35
z?z 998:420 925.348
are given in the last column of Tables 1 and 2. Next, we determined a for each sample (shown in the 7th column of Tables 1 and 2) from equation (5) from the known thickness (determined from interference fringes) of the Hg, _ XCd,Te sample, and tabulated the K values as summarized in Table 3. Note that determination of a from equation (5) is simply based on the fundamental equations (1) and (2) only, which do not make use of x at any stage. The agreement between both values of a thus obtained provides an adequate verification of x value shown in Tables 1 and 2. In addition, the present paper also provides an indirect confirmation of the form and the values of the numerical constants appearing in equations (la)-(ld). One may observe from Tables I and 2 that AX obtained for epilayers is in general higher than that obtained for the bulk samples, even though the spatial ~o~ty in ~rn~~tion is very good. The higher AXfor epilayers is the manifestation of the presence of a graded transition layer at the substrate-Hg, _,Cd,Te interface, whereas in the case of bulk samples, the observed Ax is real indicating the inbomogeneity along the thickness of the wafer or along the area. In the present case, since the spatial compositional uniformity in the bulk samples is very good, the observed AXmay be interpreted as indicating the com~sition~ i~omogeneity along the thickness of the given wafer. Table 3 summarizes the numerical value of K to be used in the above calculations for the epilayers grown on some of the commonly used substrates. It may be observed that the value of K differs markedly for bulk Hg, _XCd,Te samples as compared to epilayers grown on different substrates. This also explains the need for using different calibration relations in the case of bulk samples and epilayers as stated by the previous investigators. (2-r)However, the present work has shown that basically the same calibration relation may be used for both epilayer and bulk samples by simply using the appropriate value of K. The exact value of the latter can also be determined in each case. IV.
CONCLUSION
In conclusion we have presented a general method to determine the composition and compositional uniformity of Hg,_,Cd,Te samples, be it a bulk wafer or an epilayer, from room temperature IR transmission measurements. This method gives the composition x directly without involving another Eg vs x relation. Acknowierlgementp-Tiie authors thank
the Director, Solid State Physics Laboratory, Delhi for his pumisuion to publish this work. They are also gratefid to Dr 8. B. Sharma for providing the bulk Hg,_,Cd,Te sample grown by SSR.
REFERENCES 1. 2. 3. 4. 5. 6. 7.
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