J . Phys. Chem. 1991, 95, 1420-1424
1420
Temperature Dependence of the NMR Line Shifts and T , Relaxation Times of '*?e in the Semiconductor Alloys Hg,-,Cd,Te H.M. Vieth,+ S. Vega,*.* N. Yellin? and D. Zamirs lnstitut f u r Atom und Festkorperphysik, Freie Universitat Berlin, WE1 Arnimalle 14, 0-1000 Berlin 33, West Germany, Isotope Department, The Weizmann Institute of Science, 76 100 Rehovot, Israel. and Soreq Nuclear Research Center, Yavne, Israel (Received: May 9, 1990: In Final Form: August 6. 1990)
The 12sTeN M R spectra of the semiconductor alloys Hg,-,Cd,Te are studied. The temperature dependence between 15 and 300 K of the frequency shifts and the TI relaxation times of the five tellurium lines in the spectra of a set of Hg,-,Cd,Te polycrystalline samples with a large variety of x values are measured. In addition to those for samples prepared stoichiometrically, N M R results are recorded for samples containing an excess and a deficiency of metal atoms. The results are reported, and qualitative conclusions are made concerning the electronic interaction, chemical shift, and Knight shift contributions governing the N MR experimental parameters. This study demonstrates the ability of NMR spectroscopy to monitor and characterize the clusters Hg,,,Cd,,Te with n = 0-4 in the alloys separately.
Introduction The steady interest in the semiconducting compounds Hg,,Cd,Te and other alloys of groups 11-VI has resulted in many publications concerning experimentall" and theoreticall-" aspects of these materials. These alloys are particularly important because their electronic properties can be modified by changing their x values. The use of the Hg,-,Cd,Te alloys as infrared SensorslO has provided a stimulant to study these properties and their crystallographic parameters." They belong to a class of pseudobinary alloys of the form AI-,B,C, which can be formed from stoichiometric mixtures of the pure tetrahedral compounds AC and BC. This group of semiconductor alloys can be considred to comprise local clusters of the form A4-,,BnC, with n = 0-4, consisting of a central C anion coordinated to four cations A and B. For each composition x of AI,B,C, one expects a distribution of such clusters with relative probabilities P,(x), which is a function of the temperature at which the sample was prepared. These probabilities will influence the energy gaps, the average bond lengths, and other macroscopic properties of the alloys and should therefore be inspected separately when p o ~ s i b l e . ' ~ - ~ ~ Wei and ZungeP formulated an ab initio theory of these cluster probabilities. They noted that these probabilities reflect the chemical interaction energies &, within an A,_,,B,C cluster, where 4-n 4
6, = E(A,-,B,C) - -E(A,C)
n
- iE(B4C)
is the interaction energy with respect to equivalent amounts of the pure A4C and B4C clusters and E is the total (electron + ion) energy of the pure clusters. For 6, = 0 (analogous to a noninteracting, or ideal gas), all probabilities P,(x) would equal the random probabilities, whereas for 6, < 0 or &, > 0, the pure cluster probabilities are depressed or enhanced, respectively, relative to a random probability distribution. Both the ab initio self-consistent calculation of Wei and ZungerI6 and the tightbinding calculations of Sher et al.'7.18predicted for Hg,-,Cd,Te that G 3 > 0 and 6 , > 0 (the two calculations disagree on hence, both calculations predict an excess of the Hg,Te and Cd4Te clusters. When 6, 0, one expects also long-range ordering of the alloy. Wei and Zunger16 found 6, < 0 for all alloys of groups Ill-V and Il-VI except for the lattice-matched AI,,Ga,As and Hgl-,Cd,yTesystems for which 6, > 0. Experimental evidence of long-range order and local clustering of the cations in ternary alloys was observed, for example, in AI,G~,_,AS,'~ GaAsl-,Sb,,Zo and Gal-,ln,P.21 These reports support the theories predicting that certain ordered phases are
more stable than the corresponding random atomic arrangements. NMR studies of Hgl-,Cd,Te2~23and Cdl,Zn,Te24 have shown that the probabilities P,,(x) for each cluster n can be obtained experimentally. It was found that the IzsTe NMR spectra in both alloy systems consist of five distinguishable lines which can be assigned to the five possible cluster environments of the tellerium atoms: Hg,-,,Cd,Te and Cd,-,,Zn,,Te with n = 0-4. In both systems, deviations from a random distribution have been found, but while in Cdl-,Zn,Te the signs of the deviations for n = 0 and 4 were the same (both showing a positive deviation relative to their random distribution values), in H&,,,Cd0,,,Te a positive deviation is observed for the Cd4Te cluster, and in Hh,,sCdo,2sTea negative deviation is observed for the Hg4Te cluster. Furthermore, if the integrated amplitudes of the N M R lines are to be used as quantitative measures of the cluster populations, the observed negative/positive deviations are larger than those While the reasons for these discrepancies between experiment and ( I ) Wooley, J. C. Compound Semiconductors; Willardson, R. K., Goering, H . L., Eds.; Reinhoid Publishing: New York, 1962; p 3. (2) Abrikosov, N . K.; Banhina, V. F.; Poretskaya, L. V.; Shelimova, L. E.; Shudnova, E. V. Semi-conducfing II- VI, V- V and V-VI Compounds; Plenum Press: New York, 1969. (3) Mikkelsen, J. C., Jr.; Boyce, J . B. Phys. Reu. B 1983, 28, 7130. (4) Spicer, W. E.; Silberman, J . A.; Morgen, P.; Lindau, 1.; Chen, A . B.; Sher, A.; Wilson, J. A . Phys. Reo. Lett. 1982, 49, 948. ( 5 ) Kirschfield, K. E.; Nelkowski, K.; Wagner, T. S.Phys. Reu. Letr. 1972, 29, 66. (6) Reznitsky, A.; Permagorov, S.;Verbin, S.; Naumov, A.; Korostelin, Y.; Novozhilov, V.; Prohovev, S. Solid State Commun. 1984, 52, 13. (7) Chen, A. 9.; Sher, A . Phys. Reu. B 1980, 22, 3886. (8) Srivastava, G. P.; Martins, J. L.; Zunger, A . Phys. Reo. B 1985, 31, 256 I . (9) Bernard, J . E.; Zunger. A. Phys. Reu. 1987, 36, 3199. (IO) Wei, S. H.; Zunger, A . Phys. Reo. B 1979, 39, 3279. ( I I ) Ferreira, L. G.; Wei, S. H.; Zunger, A. Phys. Reu. B 1989, 40, 3197. (12) Lawson, W. D.;Nielsen, S.;Pulley, E. H.; Young, A. S.Phys. Chem. Solids 1959, 9, 325. (13) Higgins, W. M.; Pultz, G. N . ; Roy, R. G.; Lancaster, R. A.; Schmit, J . L. J . Vac. Sci. Technol., A 1989, 7, 271. (14) Martin, J . L.; Zunger, A . Phys. Reo. B 1964, 30, 6217. (IS) Zunger, A . Appl. Phys. Left. 1987, 50, 164. (16) Wei, S . H.; Zunger, A. J . Var. Sei. Terhnol., A 1988,6, 2597; Phys. Reo. B 1988, 37, 8958. (17) Chen, A. 9.; Sher, A.; Berding, M. A . Phys. Reu. B 1988,37,6285. (18) Patrick, R. S.; Chen, A. B.; Sher, A,; Berding, M. A . J . Vac. Sci. Technol.. A 1988. 6. 2643. (19) Kuan,T. S.;'Kuech,T.F.; Wang, W. 1.; Wilkie, E. L. Phys. Reu. Left. 1985, 54, 20 I . (20) Jen, H. R.; Chvng,:M. J.; Stringfellow, G. 9. Appl. Phys. Left. 1986,
48, 1603.
(21) Kondow, M.: Kakibayashi. H.; Tanaka, T.; Minagawa, S.Phys. Reu. Letr. 1989, 63* 884. (22) Zax. D. B.; Vega, S.;Yellin, N . ; Zamir, D. Chem. Phys. Left. 1987, 130. 105.
To whom correspondence should be addressed.
' Freic Universitat Berlin.
'The Weizmann institute of Science. Nuclear Research Center.
8 Soreq
0022-3654/9l/2095-l420%02.50/0 0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 1421
12STein the Semiconductor Alloys Hg,-,Cd,Te theory for Hg-rich alloys is yet unclear, Wei and ZungerI5 raised the possibility that the nominal macroscopic Hg concentration in the alloy (e.g., as measured by X-rays) may not reflect the microscopic concentration of Te-bonded Hg in the bulk of the sample (as measured by the Te NMR chemical shift), due to possible loss of bonded Hg (e.g., by surface segregation or occurrence of metallic Hg microclusters in the bulk etc.). In order to account for the observed deficiency of Hg, one expects to see a large amount of free Hg on the surface or in the bulk. No direct evidence for such a phenomenon has been found. However, in order to clarify this point, it is necessary to study the NMR spectra of a well-characterized single crystal, where the value of x is well-defined and the existence of free Hg can be tested directly. This is under investigation, and the results will soon be discussed in an additional publication. It is, however, first necessary to characterize the frequency bands in the tellurium spectra in terms of the possible electronic interactions present in the alloys. For this purpose, new Hg,-,Cd,Te powder samples were prepared with different x values from stoichiometric and nonstoichiometric mixtures of the metallic and nonmetallic elements. In the present work, we examine the basic interactions governing these frequency bands. The three main experimental parameters definingthe NMR lines are their positions in the frequency spectrum and their longitudinal ( T I )and transverse ( T2)relaxation times. These parameters are functions of the Knight shift and chemical shift interactions between the free and bond electrons and the observed nuclei, r e s p e c t i ~ e l y . ~To ~ -distinguish ~~ between these two types of interactions, a temperature study of the shifts and TI relaxation times is made. The influence of the local bond electrons in the Hg,-,Cd,Te clusters on the tellurium atoms is expected to be much less temperature dependent than that of the free conduction electrons. The electron populations of the conduction bands and the free carrier concentrations are more strongly dependent on temperature than the diamagnetic and paramagnetic contributions to the chemical shift. Previous chemical shift measurements of mercury, cadmium, and tellurium in Hg,-,Cd,Te did not result in resolved lines and can therefore not be considered as a comparative Direct homonuclear dipole-dipole interactions between lz5Tenuclei can be neglected in the interpretation of the experimental results due to the low natural abundance of 6.99%. Spin diffusion effects and heteronuclear interactions are also expected not to contribute significantly to the reported results. The rest of this paper is organized as follows: After describing the preparation procedure of the Hg,,Cd,Te powder samples and the NMR spectrometers involved in this study, we present the temperature dependences of the shifts of the tellurium spectral lines and make a comparison between the shifts of samples prepared with an excess and a deficiency of tellurium. After summarizing these results, we present a temperature study of the spin-lattice relaxation times of all individual lines in a set of Hg,-,Cd,Te spectra and follow that with a general discussion of our experimental findings. Sample Preparation and N M R Experiments
Hg,-,Cd,Te samples of different compositions were prepared with x = 0.05, 0.10, 0.25, 0.50, 0.75,0.90,and 0.95.28For the x = 0.25 and 0.75compositions, two nonstoichiometric samples were prepared also, one with I % excess and one with 1% deficiency of Te. The nominal compositions of the six samples were Hg0,75Cd0,25Te,(Hg0.25Cd0.7S)l.01Te~(Hg0.2SCd0,7S)Tel.01 Hg0,7SCdO,25Te3 (Hh.75C4125) I.OITe, and (H&,7SCdo.25)I.OITel.!I. Weighed amounts of high-purity elements were sealed under high vacuum (Torr) in a clean quartz ampule. The ampule was placed in a cold vertical furnace with a constant-temperature profile (fl 9
(25) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, U.K., 1961. (26) Slichter, C. P. Principles of Magnetic Resonance; Harper and Row: New York, 1963. (27) Willig. A.; Sapoval, 8.;Leibler, K.; Verie, C. J . Phys. C 1916.9, 1981. (28) Ben-Dor. L.; Ycllin, N.; Schacham, H. Mater. Res. Bull. 1983, 18, 1229.
OC). The furnace was heated to -350 OC and kept a t that temperature overnight. Then the temperature was raised to 650 "C, and the ampule was kept at that temperature in the furnace for 2 weeks. At the end of that period, the furnace was turned off and allowed to cool slowly. The sample compositions and homogeneities were checked by powder X-ray diffraction. The difference between the lattice constants of HgTe ( a = 6.462A) and CdTe ( a = 6.482 A) is only 0.3%, and therefore the accuracy in composition determination by X-ray methods cannot be high: Aao = 0.001 A yields an accuracy in x of Ax = f0.05. The Te NMR experiments were performed on two different spectrometers with magnetic fields of 4.70and 7.04T and 12sTe Larmor frequencies of 63.1 and 94.7 MHz, respectively. For the variable-temperature studies between I5 and 300 K,a helium gas flow cryostat from Oxford Instruments was used. In the range 170-365 K, a heated N, gas regulation system from Bruker was used. Most variable-temperature measurements were carried out at about 94.7 MHz. The NMR probes were home built and allowed us to use 90° pulses of about 4 p s and a receiver dead time of about 6 ps. The 8 mm diameter samples contained about 5 g of powdered alloys. All spectra were recorded after Fourier transformation of the free induction decay (fid) or Hahn echo signals and are presented in ppm units with respect to the line position of liquid dimethyl telluride ((CH3)2Te). Because of the large spectral width and the corresponding short fid signals, the experiments were very sensitive to the spectrometer dead time. To minimize the necessary waiting time between the end of the rf pulse and the first measurable point of the fid signal, an effort was made to compensate for rf-ringing artifacts. This was achieved by subtracting from each detected fid signal a signal obtained directly after an rf saturation sequence. For the line amplitude analysis, the spectra were recorded via a Hahn echo sequence with a proper cycling of 16 pulse phases. To avoid T , relaxation effects on the line shapes, a saturation recovery time of at least 4 times the longest TI measured in the sample was allowed. The echo refocusing time was chosen between 45 and 70 p s , so that for longer times the detected spectra did not show any changes. For the spin-lattice relaxation studies, a modified saturation-recovery pulse sequence was applied. Because of the electrical conductivity of the alloy materials and the resulting skin effect, the BI radio-frequency field was expected to be inhomogeneous over the sample volume and resulted in a varying ?r/2-pulse length. To achieve full saturation of the whole sample, a train of more than 20 rf pulses with different lengths and sufficient interpulse spacing was applied to the sample. After this saturation sequence and with no time permitted for saturation recovery, no residual spin polarization was detectable. Experimental Results
The lZSTeNMR spectra were recorded of the Hg,,Cd,Te alloy samples with all x values mentioned previously. Our spectra, featuring partially resolved lines attributed to different local Hg,-,Cd,Te clusters ( n = 0-4), reproduced the reported results of Zax et aL2* With the assumption that there exists a one-to-one correspondence between the spectral positions of the lines and the local environments of the Te atoms, the integrated line intensities determine the relative abundances of the different clusters. To provide additional evidence that, according to the N M R results, the distribution of these clusters is not random, the spectrum with x = 0.75obtained at 30b K was carefully recorded and analyzed. In this spectrum, the line at u = -1040 ppm, corresponding to the Cd,Te cluster, is sufficiently separated from the rest of the spectrum (see Figure I , top right) to obtain its relative integrated intensity. At least 48% of the entire spectral intensity must be attributed to this line, even when possible experimental distortions in the spectrum such as dead-time artifacts, base-line drifts, or phase errors are taken into consideration. As this line shows the slowest relaxation in the whole spectrum, insufficient spin polarization recovery would result in an underestimation of its intensity. The detected intensity is significantly higher than 32%, the probability of Occurrence of Cd,Te in a random distribution.
1422 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
I
n
1
-500
0
-1000
ppm -1500
0
-500
-1000 ppm -1500
Figure I . '2sTespectra of Hg,,Cd,Te for x = 0.75 (upper spectra) and x = 0.25 (lower spectra) at T = 50 and 300 K.
Similar deviations from a random distribution were also observed for most of the other alloys. However, in these spectra the separation of the frequency bands was less pronounced, and the experimental noise was too high to allow quantitative determination of the relative intensities. While it was not the original purpose of this study, a discussion of the cluster distribution from our N M R results will be presented later, together with our single-crystal measurements. Spectral Line Positions. To establish the interaction responsible for the differences in shifts of the various frequency bands, a temperature study of these shifts was made. The samples chosen for this study were the Hgo,25Cdo,75Te and Hgo,75Cdo,25Te alloys. Representative spectra of stoichiometrically prepared samples are shown in Figure 1. They were obtained with a sufficiently long recovery delay to allow full relaxation of all lines in the spectra. As can be seen from the figure, after full T , relaxation the spectral resolution between the various lines is partially lost. To enable accurate determination of the line positions of the five frequency
I
Vieth et al. bands, most experiments were conducted with recovery delays shorter than the longest T I . In this way, the relative intensities of the observable lines could be varied and their positions established. A comparison of the room-temperature spectra of all available alloys measured at magnetic field strengths of 4.7 and 7.04 T shows that all spectra scale with the external magnetic field. In addition, no changes in spectral resolution were detected, indicating that the frequency band positions and band widths are due to chemical shifts and Knight shifts only and not to field-independent interactions such as the homo- and heteronuclear dipolar couplings. The line shifts as a function of temperature are shown in Figure 2. For decreasing temperature, the spectral lines shift simultaneously to higher frequency without losing their separation. In the spectra of Hgo,25Cdo,75Te three separated lines were observed, while in the Hgo,,5Cdo,25Tespectra four lines could be distinguished. The same results were reported by Zax et The collectivevariation of the line positions as a function of temperature suggests that part of the line shifts are caused by the Knight shift. To obtain additional information on the nature of the differences in line shifts and its relation to the local environment of the tellurium, samples were prepared with slight modifications in their Hg and Cd to Te ratios. In Figure 3, typical IZ5Tespectra are also presented for samples with x = 0.75 and x = 0.25 in stoichiometric ratio (Figure 3a), with a 1% Te deficiency (Figure 3b), and with a 1% Te excess (Figure 3c). We observe very pronounced differences in the relative intensities of the tellurium lines in these spectra. These changes in the line intensities emphasize again the importance of the conditions under which these samples are synthesized. The actual composition of our samples as a function of the relative atomic concentrations of the starting materials in the initial stage of our preparation procedure must therefore be studied thoroughly. Such a study is underway and will be published shortly. The experiments in this study, however, were performed to establish line positions and T , relaxation times only, and no efforts were made to obtain accurate relative line intensities by letting the spin systems relax fully between individual experiments. In this NMR study, broad featureless components in the
d PP" X
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8
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+.
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-1200 100 200 300 T/K 400 100 200 300 T/K 400 Figure 2. '2STcline shifts as functions of temperature. Negative shift values correspond to lower frequency. The reference compound at 0 ppm was samples with (a) stoichiometric composition, (b) a 1% Te deficiency, and (c) dimethyl telluride. The shifts on the left correspond to Hgo,2sCdo,75Te a 1% Te excess. Assignment of the lines to the cluster compositions according to Zax et (+) Hg,,Cd,Te; ( 0 )Hg,Cd,Te; (A) Hg2Cd2Te. The shifts on the right correspond to Hg,,,,,Cd,,,,Te samples with (a) stoichiometric composition, (b) a I % Te deficiency, and (c) a 1% Te excess. Assignment of thc lincs: (A)Hg,CdoTe; (+) Hg2Cd3Te;( X ) Hg,Cd2Te; (0) Hg,Cd,Te.
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991 1423
IZSTein the Semiconductor Alloys Hg,,Cd,Te
TABLE I: Spin-Lattice Relaxation Times TI of Hgl-,Cd,Te at 300 K for Different Alloy Compositions H&,Cd,Te (0 In I 4)' T,lsb n=2
n = l
n=O
x'
n=3
n=4 474 f 58 215 f 8 418 f 21 (602 f 29) 262 f 22
I .oo 0.90 0.75 72 f 5 16.0 f 1.6 (20.6 f 3.2)
0.50 0.25 0.10 0.05 0.00
78.7 f 9.9 (271 f 31) 99 f 8 22.4 f 4.7 (44.1 f 8.6)
244 f 13 (386 f 75) 145 f 8 (60.2f 11.3)
7.0 f 0.3 4.1 f 0.4 4.4 f 0.5
aBo = 4.70 T; values in parentheses are for Bo = 7.04 T. The given error margins consider only the statistical uncertainty. bThe relaxation times of Hg,,75Cdo,,5Teand Hh,,,Cd0,,,Te in parentheses were measured at a frequency of 94.7 MHz; the rest of the TI times were measured at 63.1 MHz.
I\ 10000:
i
f
JLJ,L 0
-500
-1000
1500
ppm 0
-500
-1000
P
a
-1500
Figure 3. I2,Te spectra of Hg,_,Cd,Te at 300 K for x = 0.75 (left) and x = 0.25 (right) for samples with (a) stoichiometriccomposition, (b) a 1% Te deficiency, and (c) 1% Te excess. The spectra were recorded with
1000
f f€ !
saturation recovery times shorter than the longest TI in the samples for the first six significant points of the echo signal before Fourier transformation. spectra were suppressed by discarding the first accumulated points of the free induction decay signals and by using repetition times between the rf excitation schemes shorter than the TI values. These experimental procedures do not influence the reported line positions and shifts Figures 1 and 2. The temperature dependences of all line shifts are shown in Figure 2. Inspection of this figure reveals that the positions of the various lines in the three samples with equal x values do not vary substantially. The relative temperature dependences of all line positions are also rather invariant. Shifts on the order of 100 ppm are recorded for all lines on going from samples with an enhanced metal:non-metal ratio to a depleted one. This shift is smaller than the shirt differences between the lines of different clusters, supporting the chemical shift origin of the differences in line positions. The assignment of the spectral lines to the cluster Hg,-,Cd,Te, according to Zax et a1.,22is given in the figure caption. The variation with temperature of all lines shows a downfield shift for increasing temperature, which should be accounted for by the Knight shift. The observed temperature dependence is far from exponential, which would be expected and observed for intrinsic semiconductors, but exhibits rather a weak decrease in the magnitudc of the line shifts with increasing temperature. A discussion of the results in Figure 3 is given in the next section together with a dcscription of the TI relaxation results. TI Measurements. As was reported previously and mentioned above, each line in the spectra with a different x value has its own TIrealxation time. These TI values can be different by as much as a factor of 4 in a single sample. The room-temperature values of TI of eight samples with different x values are compiled in Table I. Relaxation times were detected at two external magnetic field opcrating levels. The observed times are correlated to the cluster parametcr n of the various lines. For all lines, the relaxation
,vu
100
200
T/K
300
Figure 4. '25Tespin-lattice relaxation time TI of Hgo,,,Cdo,,sTeas a function of temperature (A)HgoCd4Tecluster; ( 0 )HglCd3Tecluster; ( 0 ) Hg,Cd2Te cluster. The bars indicate only the statistical uncertainty. becomes shorter for an increasing mercury content of the sample. In each individual sample, the relaxation times also decrease for an increasing number of mercury atoms in the corresponding clusters. This dependence suggests that a substantial contribution to the relaxation originates from the fluctuating hyperfine interaction between the Te nuclei and the conducting electrons. An increase of the electron density at the tellurium positions close to the mercury atoms in the sample should then explain the differences in T I values. The ab initio calculations of Wei and ZungerI5 show indeed that the s-electron density at the tellurium is higher in pure HgTe than in CdTe. In Figure 4 the relaxation behavior of the various lines of Hg,,zsCdo.7sTe is shown as function of temperature. The dependence of 1/T2is not proportional to l / T as in the Korringa relation but is closer to l/p. In addition, the relaxation times of the nonstoichiometric alloys were recorded as functions of temperature. The results of these measurements are shown in Figure 5 as the average relaxation times for all the lines in a given sample spectrum. A change of I % in the metaknon-metal ratios of the samples does not change the relaxation times significantly. Discussion In the present work, we have studied the temperature dependence of the NMR frequency shifts and the spin-lattice relaxation
1424 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
- s " T
10000:
A
- 4
B 0
A
A
A
loo0l 1
t
t I
I
I
100
200
T/K
300
l2Ve spin-lattice relaxation time TI, averaged over all lines in a spectrum. The open symbols correspond to the relaxation times of Hh,75Cdo,z5Te and the full symbols to those of Hg,,z5Cdo,75Te.The triangles represent results for samples prepared from stoichiometric mixtures of the elements, the diamonds results for samples with a 1% Te deficiency, and the circles results for samples with a 1% Te excess. Figure 5.
times TI of the individual lines in the I2'Te spectra of the Hg,,Cd,Te alloy powder samples. The temperature-dependent parts of these parameters should be described by the Knight shift interaction, which originates from the hyperfine interaction between the magnetic moment of the tellurium nuclei and the free carriers that exist in the semiconductor (electrons and holes). The first step in discussing our results is to assume that the main contribution to the hyperfine interaction is due to the Fermi contact term. For such a case, it has been shown29that the Knight shift and the spin-lattice relaxation time are as follows:
where Hois the external magnetic field, n is the free carrier density (holes and electros), and ( I#K(o)12)& is the free electron density near the bottom of the conduction band for electrons or near the top of the valance band for holes. The Knight shift has an explicit 1 / T temperature dependence and an indirect dependence through the free carrier concentration n. It was not possible to determine the free carrier concentration in our powdered samples. However, considering the conditions under which they were prepared, we expect thcm to contain relatively high concentrations of Hg vacancies. As these vacancies act as acceptors, the material is of p type with il rclatively high density of free holes, on the order . ionization energies of these acceptors are of -IO1* ~ m - ~The smaller than kT,j0 and in the temperature range of our measurements most of the acceptors are ionized, so that the hole density becomes a constant. This is a well-known phenomenon in extrinsic scmicondu~tors.~~ The density of free electrons in ( 2 9 ) Wolf, D. Spin-Temperafure and Nuclear-Spin Relaxation in Matter; Oxford Science Publications: Oxford, U.K., 1979; p 400. (30) Kittel. C . Infroductionto Solid S f a f ePhysics; J. Wiley & Sons, Inc.: New York. 1967.
Vieth et al. this range is much smaller than the density of free holes. Thus, in eq I n, standing for the free-hole density, is assumed to be constant across the temperature range of our measurements. We expect therefore a 1 / T dependence of the Knight shift. It was shown that for narrow-gap semiconductors other interactions besides the Fermi contact interactions must be taken into account for the description of the temperature dependence of the frequency ~ h i f t s . ~ *Large % ~ ~spin-orbit couplings?deviation from parabolicity, and large effective g factors of the electrons and holes in these semiconductors cause the deviations from eq 1. In addition, it was found that for p type materials the Knight shift is negative and increases (becomes less negative) with temperature. This can explain the detected increase of the Knight shifts in Figure 2 with temperature. Inspection of our data shows that above 50 K the temperature dependence of all shifts is approximately proportional to - 1 / T. Below 50 K the temperature variation seems to become dependent on the above-mentioned interactions and deviates, in addition to changing sign, from the 1/T relation in eq 1. The differences between the temperature dependences of the Knight shifts of the Hgo,,5Cdo,25Teand Hgo,25Cdo,7STe alloys could be attributed to differences in the hole densities ( I#K(o)21)E: being part of the proportionality coefficient of 1/Tin eq 1. The samples with the higher mercury concentrations exhibit the largest increases in shift with temperature, suggesting a larger hole density for the mercury-rich than for the mercury-poor samples. The increase in the hole density for decreasing x should be due to the difference in the energy gap and the ionization energy of the samples with x = 0.75 and 0.25. Similar to the Knight shift, the temperature-dependent part of the relaxation time T I is also due to the hyperfine interaction of the nuclei with the free carriers. From eq 2, and assuming that n is constant, we obtian T , a This dependence corresponds to the experimental results of Figures 4 and 5, in which the TI values are proportional to p,5*0.1. The decrease in TI for increasing mercury content in the sample can again be due to the increase of the hole density coefficient in eq 2 for mercury-rich samples. It is important to mention that the results presented in this paper demonstrate clearly the ability of NMR spectroscopy to distinguish between the clusters Hg,,Cd,Te in the alloy samples. The NMR parameters of each cluster exhibit characteristic values and temperature dependences and make it possible to study local electronic structure as well as the global electronic properties of the semiconductor alloys. It is now necessary to quantate our results in terms of free carrier concentrations, local electron densities, and ionization and gap energies. The derivation of the Knight shift and TI should be based on the band structure parameters of HgCdTe, which then can be compared to the experimental results. For this to be accomplished, NMR studies of single crystalline samples are required. On these samples, quantitative measurements can be made, free carrier concentrations can be monitored, and annealing procedures can be executed to change these concentrations. In addition, it is now possible to study clustering via NMR intensity measurement in samples with varying x values and different preparation procedures. All these experiments are underway and will be published in the near future. Acknowledgment. This research was supported by the US-Israel Binational Science Foundation. We gratefully acknowledge helpful discussions with Dr. D. B. Zax and Dr.A. Zunger. Finally, we thank Mr. A. Shacna for his technical assistance in preparing the samples. Registry No. CdTe, 1306-25-8; Hgo,roCdo,90Te, 1 1 1 117-31-8; Hgo,,,Cd0,,,Te, 109225-10-7; Hgo.,oCdo,50Te, 106390-37-8; Hgo.,5Cdo,25Te, 1062 19-03-8; Hgo,90Cdo,,oTe, 1 I06 19-18-6; Hgo,9,Cdo,05Te, I I I 117-75-0; HgTe, 12068-90-5; I2,Te, 14390-73-9. ( 3 I ) Dornhaus, R.; Nimtz, G. Springer Tracfs Mod. Phys. 1983,98, 1 19. (32) Hewes, C. R.; Adler, M . S.; Senturia, S . D. Phys. Reo. B 1973, 7 , 5195. (33) Sapoval, B.; Leloup, J. Y . Phys. Reu. B 1973, 7, 5272.
