3716
J. Phys. Chem. 1991, 95, 3716-3723
Slze Quantlzatlon in Semlconductor Partlculate Films Xiao Kang Zbao and Janos H. Fendler* Department of Chemistry, Syracuse University, Syracuse, New York 13244-41 00 (Received: September 19, 1990)
Slow infusion of H2Sonto cadmium arachidate, zinc arachidate, or metal-ion-coated monolayers resulted in the formation of metal sulfide particles which, when transferred to solid substrates in different stages of their growth, produced semiconductor particulate films. CdS and ZnS semiconductor particulate films were established to be predominantly hexagonal and cubic crystallites by X-ray diffraction. Transmission electron and scanning tunneling microscopies, as well as absorption spectroscopy, provided evidence for the initial formation of 30 f 5 A, three-dimensional, size-quantized particles. Longer exposure to H2S resulted in the formation of 30-40-A-thick, 30-80-A-diameter CdS polyparticles which ultimately evolved into porous semiconductor films of different thicknesses. The optical-thickness-dependent, direct bandgap shifts and the recovery of bulk bandgaps upon heating the 150-300-A-thick CdS and ZnS semiconductor particulate films were rationalized in terms of size quantization.
Introduction Altered chemical, mechanical, electrical, and electrooptical properties accompanying size and/or dimensionally reduction have prompted the increasing current interest in size-controlledsemiconductor particles.'+ Size control has been accomplished by colloidal chemical techniques using controlled mixing of the precursors under well-adjusted conditions. Alternatively, advantage has been taken of organized media to control the growth of in situ generated particles.' We reported previously that the controlled infusion of H2S onto metal-ion-containing monolayers resulted in the formation of semiconductor particles that could be transferred, essentially intact, to solid substrates at different stages of their growth.*I3 Reflectivity, absorption spectrophotometry, transmission electron microscopy, scanning tunneling microscopy, and electrical measurements established the presence of porous semiconductor particulate films.l0 Preliminary investigations indicated that, while the individual particles in these films were connected physically, however, electrically they remained relatively isolated.I0 They are quite distinct, therefore, from the usual chemically deposited semiconductor films." To the best of our knowledge, there is only one previous report on the morphological characterization of a nonannealed particulate film; optical microscopic, electrical, and photoelectrical examination revealed the presence of separated 30-80-A crystallites in chemically deposited, cadmium selenide films.I5 Evidence is presented in the present publication for size quantization. Semiconductor particles transferred to solid supports at their earliest stages of growth will be shown by X-ray diffraction, transmission electron microscopy, scanning tunneling (1) Henglein, A. Top. Curr. Chem. 1988, 143, 113. (2) Brus, L. A. J . Phys. Chem. 1986,90, 2555. (3) Andrea, R. P.; Averback, R. S.; Brown, W. L.; BNS, L. E.; Gcddard,
W. A.; Kaldor, A,; Louie, S. G.; Moskovits, M.; Percy, P. S.;Riley, S. J.; Sicgel, R. W.; Spaepen, F.; Wang, Y. J . Mater. Res. 1989, 4, 704. (4) Fendler, J. H. Chem. Rev. 1987,87, 877. (5) Henglein, A. Chem. Rev. 1989, 89, 1861. (6) Steigerwald, M. L.; Brus, L. E. Am. Chem. Res. 1990, 23, 183. (7) Smotkin, E. S.;Lee, C.; Bard, A. J.; Campion, A.; Fox, M. A.; Mallouk, T. E.: Webber, S. E.; White, J. M. Chem. Phys. Lcrt. 1988, 152,265. (8) Smotkin, E. S.; Brown, Jr., R. M.; Rabenberg, L. K.; Salomon, K.; Bard, A. J.; Campion, A.; Fox, M. A.; Mallouk, T. E.; Webber, S. E.; White, J. M. J . PhyJ. Chrm. 1990.94, 7543. (9) Zhao, X. K.; Xu, S.;Fendler, J. H. hngmuir, in press. (10) Zhao, X. K.; Fendler, J. H. Chem. Mater. 1991, 3, 168. (11) Yuan, Y.; Cabasso, 1.; Fendler, J. H. Chem. Mater. 1990, 2, 226. (12) Yi, K. C.; Fendler. J. H. Longmuir 1990.6, 1519. (13) Zhao, X. K.; Yuan, Y.; Fendler, J. H. J . Chem. Soc., Chem. Com.mum. ..-... 1990. - - - -, 1248. - - . -. (14) Hodes, 0.;Fonash, S.J.; Hellcr, A.; Miller, B. Adu. Electrochem. Electrochem. Eng. 1985, 13, 113. (1 5) Hodes. G.; Albu-Yaron, A.; Decker, F.; Motisuke, P. Phys. Reu. B. 1987, 36, 4215.
0022-3654/91/2095-3716$02.50/0
microscopy, and absorption spectrophotometry to have 30-50-A diameters and bandgap energies substantially higher than the corresponding bulk materials. Size quantization will also be demonstrated in thicker, porous, particulate semiconductor films formed at metal ion-monolayer interfaces by increasingly longer exposures to H2S.
Experimental Section Bovine brain phosphatidylserine, PS (Avanti Polar Lipids, Inc.), arachidic acid, AA (Sigma), dioctadecyldimethylammonium bromide, DODAB (Eastman), cadmium chloride, zinc chloride (Fisher), high-purity dry N2(Union Carbide), H2S (Matheson), and spectroscopic grade chloroform (Aldrich) were used as received. Preparation and purification of polymerizable surfactants n-hexadecyl-1 1-(viny1benzamido)undecyl hydrogen phosphate, 1,16 bis(2-(n-hexadecanoyloxy)ethyl)methyl@-vinylbenzyl)ammonium chloride, 2,16and poly(styrenephosph0nate diethyl ester), PSP,I7 have been described. Water was purified by a Millipore Milli-Q filter system provided with a 0.22um Millistack filter at the outlet. The in situ generation of monolayer-sup rted semiconductor particles followed the described procedure.gOBriefly,monolayers were compressed to their solid states by using a film balance enclosed in a Plexiglas hood. Injection of 200-250 pL of H2S into the nitrogen-filled Plexiglas hood led to the slow development of semiconductor particles at the monolayer-metal ion interface. The monolayer-supported semiconductor particulate film was transferred to solid substrates by horizontal lifting through the surface layers. Well-cleaned (chromic acid, dust-free water), 1.O cm X 4.5 cm X 0.1 cm,spectroscopic-grade quartz plates, cellulose nitrate coated copper grids, highly oriented, pyrolytic graphite (HOFG,Union Carbide, freshly cleaved), and 2 0 0 4 " copper grids were used as substrates for absorption spectrophotometry, transmission electron microscopy, scanning tunneling microscopy, and X-ray diffraction measurements, respectively. Absorption spectra were taken either on a Hewlett-Packard 8450 A diode-array spectrophotometer or on a PV 8800 Phillips spectrophotometer. Transmission electron micrographs were taken on a JEOL JEM-2000 EX 120-keV instrument. Samples were obtained on specially prepared substrates. Several pieces of 200-mesh copper grids were placed on a glass slide (1 .O cm X 4.5 cm X 0.1 cm) and immersed horizontally under the surface of purified water. A drop of cellulose nitrate (1.0% in amyl acetate, Ernest F. Fullam, Inc.) was allowed to spread evenly on the water surface. Subsequent to the formation of a thin, cellulose nitrate film, the glass slide carrying the copper grids was horizontally lifted through the (16) Rolandi, R.; Paradiso, R.; Xu, S.;Palmer, C.; Fendler, J. H. J . Am. Chem. Soc. 1989, 111, 5233. (17) Sun,J.; Cabasso, 1. J. Polym. Sci., Parr A 1989, 27, 3985.
0 1991 American Chemical Society
Size Quantization in Semiconductor Particulate Films cellulose nitrate coated water surface. Drying in a vacuum desiccator for a day produced the copper grid substrates used in transmission electron microscopic measurements. Scanning tunneling microscopic images were acquired by means of an Angstrom Technology (Mesa, AZ) TAK 2.0 instrument operated in the constant-current mode. A Pt-Ir wire was used for the tunneling tip. Images were scanned with 5 lines/s and +O.S to +1.O V tip bias. Images were plotted on a CP 200U Mitsubishi color videocopy processor. Subsequent to transferring to graphite, the films were dried for 24 h and surfactant monolayers were removed by gentle rinsing with CHC13,ethanol, and dust-free water. Eight separately prepared samples of CdS and ZnS were investigated. Images were taken in each sample in 50-100 different areas. X-ray diffraction were obtained by using Cu Ka (A = 1.541 78 A) irradiation through the Ni filter of a Phillips X-ray spectrometer. Semiconductor particulate films were removed from the monolayer surface by horizontal lifting using a 0.1-mm-thick Teflon film having a 2.0-mm pinhole. The X-ray beam (40 kV, 20 mA) was focused onto the center of the pinhole (Le., the center of the unsupported semiconductor particulate film). Transmission X-ray diffraction patterns were taken with Kodak DEF-5 film and 10-20-h exposure times. Semiconductor particulate films were found to be quite rigid. Films of 200-1 500-A thickness were transferred onto 2Wmesh copper grids without any additional support and remained stable in air for several weeks. Conversely, films thicker than 2000 A broke up upon drying in air. All experiments were carried out, therefore, on films thinner than 2000 A. The color of the semiconductor particulate films varied with thickness. Optical microscopy of 200-300-A-thick semiconductor particulate films showed the presence of some micron-long, chained structures. X-ray Diffraction. X-ray diffraction data were obtained for 300-A-thick CdS semiconductor particulate films, using 15 h of exposure time. X-ray diffraction patterns of a CdS particulate film show the typical polycrystalline powder pattern (Figure 1). The 28 angles between the incident and scattering directions were calculated to be 24.9O, 26.4O, 28.2O, 30.3O, 36.6O, 43.9O, 47.7O, and 52.0" from the diffraction patterns. The diffraction rings were indexed as (loo), (002), (IOl), (102), (1 lo), (103), and (1 12) for a hexagonal lattice constant of a = 4.135 A and 6 = 6.749 A. Indexing the strongest peak is, however, not entirely unambiguous. In the preferred orientation of the crystallites, the strongest reflection can be indexed as either hexagonal (002) or cubic (1 1 1). Distinction can be made, however, by considering the known diffractions of pure hexagonal and pure cubic CdS crystallites. Since, in the diffraction of pure hexagonal crystallite, the peak with interplane spacing corresponding to (200) is missing and since, in cubic crystallite, the (101) and (100) peaks are missing, ratios of peak intensities l(m)/f(a) and I(lol)/l(m) relate to the extent that these two phases are present in the sample. Analysis of the data led to f(2w)/l(w2)= 0.04 and 1(101)/1(002~ = 0.64, indicating the predominance of the hexagonal phase in CdS particulate films. Orientation of CdS crystallites was reported to depend on the presence of cation (Cd2+)or anion (S2-, SH-) impurities. Excess cadmium ions in CdS were shown to result in the predominance of the hexagonal (002) peak. In the presence of excess anions, the hexagonal (101) peak became the ~trongest.~%'~ The strongest (002) hexagonal diffraction, seen in Figure 1,is indicative of the presence of excess cadmium ion in the CdS particulate film. The angular broadening of the diffraction line of powder patterns is related to the diameter of the crystallite, D, by the Scherrer equa tionn'
( I 8) Chambcrlin, R. R.; Skarmon, J. S. J. Electruchem. Soc. 1966, J 13, 86. (19) Gupta, B. K.; Agnihotri, 0. P. fhilos. Mug.B 1978-37, 631.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3717
A
e
25
50
213
Figure 1. (A) X-ray diffraction pattern of a 300-A-thick, unsupported CdS particulate film. Exposure time was 15 h. (B) X-ray diffraction intensity vs diffraction angle (28) plot for the same. The symbols H and C indicate hexagonal and cubic phases, respectively.
where A(28) is the width of the peak at its half-maximum intensity and X is the wavelength of the incident light. Substituting the observed A(28) values into eq 1 led to Sodo A for the size of CdS particles in situ prepared at the interfaces of cadmium arachidate monolayers. The X-ray diffraction pattern and the diffraction intensity vs 28 plot for 1500-A-thickZnS particulate films are shown in Figure 2. The 28 angles between the incident and scattering directions were calculated to be 28.6O, 47.6O, and 56S0, corresponding to (1 1 l), (220), and (3 1 1) planes of face-centered cubic crystalline ZnS (sphalerite). The lattice constant is identical with that (20) Jeffrey, J. W. Methods in Crystullogruphy;Academic Press: New York, I971.
3718 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
Zhao and Fendler semiconductor particle that is formed. Thase formal at cadmium arachidate interfaces after 3 min of HS exposure are not visible, in fact, by the naked eye and correspond to CdS particles of 30 f 5 A diameters (Figure 3A). Nascent individual semiconductor particles are well separated at their earliest stages of growth. Longer exposures to Hfi result in the aggregation ("clumping") of the smaller particles, in the appearance of larger ones, and, ultimately, in chain and disk formation. Individual small crystallites in the larger particles are resolved in some of the electromicrograms (Figure 3B,C). A similar situation has been encountered in the formation of ZnS semiconductor particulate films. Scanning Tunneling Microscopy (STM). Evolution of ZnS particulate films from their earliest stages of growth can be convincingly Seen in STM images (Figure 4). The initially formed (typically 2-6 min of H2S exposure), well-separated, 2&30-Adiameter and 5-6-A-high nanoclusters (Figure 4A) grew quickly in height to longer and more densely packed, conical particles (Figure 4B). Longer exposure (>20 min) to HIS resulted in increased lateral growth of the nanocrystallitesand their clumping into interconnected arrays. Quite often, individual nanocrystallites of chained or disk-shaped semiconductor particulate assemblies are visible in the STM images (Figure 4C). Large CdS clusters were also demonstrated to be composed of much smaller (1 540-&diameter) nanoparticles by STM.22 Prolonged exposure (>30 min) ultimately lead to the formation of a "first layer" of particulate semiconductor film. Inspection of STM images at this stage revealed the presence of 30-40-A-thick, 3&80-A-diameter, disk-shaped semiconductor particles (Figure 4D). Absorption Spectropbotometry. Absorption spectra of semiconductor particulate films on quartz substrates were found to be highly sensitive to the method used in their preparation. Specifically, w e l l - c o m p d cadmium arachidate, zinc arachidate, or metal-ion-coated PSP monolayers, an appropriate subphase, and, most importantly, slow infusion of H2S for a limited time were required for shifting the absorption threshold to higher ener ies. Typical absorption spectra of 8-, 35-,218-, 298-, and 328- -thick CdS particulate films, in situ generated at cadmium arachidate monolayer-aqueous 1.O X 1W3 M CdS0, interfaces, are shown in Figure 5A. The relationship between absorption spectra of CdS particles and their sizes has been studied extensi~ely.~*~' In particular, Henglein and co-workers prepared CdS particles with different mean diameters and obtained a curvilinear relationship between their absorption thresholds (4)and their independently determined The thinnest particulate CdS films (8 A thick), prepared from cadmium arachidate monolayers, had an absorption threshold (A,) of 450 nm (Figure 5A). This value led to an assessment of 30 f 5 A for the mean diameter of CdS particles on using Henglein's X, vs particle size curve,ZSin good agreement with those obtained in transmission electron microscopic (Figure 3A) measurements. The absorption spectra of semiconductor particulate films thicker than 30-40 A showed long tails near their absorption edges (Figure 5A). This long tail could be due to defect states, indirect transitions, and particle size distribution. Theoretical calculations for semiconductor crystallites established that the square of absorption coefficients times energy, increases gradually above the bandgap (Eo transition) with increasing energy.26 This increase can be approximated by
54
50
30
28
Fig" 2. (A) X-ray diffraction pattern of a 1 SOO-A-thick, unsupported ZnS particulate film. Exposure time was 19 h. (B) X-ray diffraction intensity vs diffraction angle (28) plot for the same. The symbol C indicate cubic crystalline structures.
reported for colloidal ZnS particles generated from Zn(N03)2 in methanol2' and agrees within a few percent to that given (5.406 A) for bulk ZnS.I9 Lack of resolution did not allow the assessment of the dimension of the ZnS crystallites from eq 1. Transmission Electron Microscopy (TEM). Transmission electron micrographs of CdS semiconductor particulate films, in situ generated at cadmium ion-PSP monolayer interfaces by 3, 15, and 30 min of exposure to H2S,are shown in Figure 3. The shorter the H2S exposure time is, the smaller the size is of the (21) Rosetti, R.; Hull, R.; Gibson, J. M.; Bnrs, L. E. J. Chem. Phys. 1985, 82, 552.
= ( h o - EJC
(2)
where ha is the photon energy, E8 is the direct bandgap, and c is a constant. Reflectivity measurements*provided values for the thickness (d;) of the semiconductor particulate films, which (22) Zen, J.-M.; Fan, F.-R. F.; Chen, G.; Bard, A. J. Lungmuir 198!9,5, 1355. Bard, A. J. Acc. Chem. Res. 1990.23.357. (23) Weller, H.;Schmidt, H. M.; Koch, V.; Fojtik, A,; Baral, S.;Hmglein, A.; Kunuth, W.; Weiss, K.; Dieman, E. Chem. Phys. L r r r . 1986,124, 557. . 129,615. (24) Schmidt, H. M.; Welter, H. Chem. Phys. ~ I I 1986. (25) Spankel, L.; Haase, M.; Weller, H.; Hengtein, A. J . Am. Chem. Soc. 1987,109, 5649. (26) Zunger, A.; Freeman, A. J. Phys. Rev. 1978,817,4850.
Size Quantization in Semiconductor Particulate Films
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3719
1 - -
I
A
B
C
Figure 3. Transmission electron micrographs of CdS particles, in situ formed at PSP monolayers by exposure to H# for 3 (A), 15 (B), and 30 min (C). The bars underneath each image represent 50 nm.
Figure 4. Three-dimensional STM images of ZnS particles on HOPG, in situ generated on zinc arachidate monolayers by 5 (A), 15 (B), 30 (C), and 40 min (D)of exposure to Hfi. Bird's-eye views of the same areas in two dimensions (x and y axes are shown on the same scale as in the three-dimensional plots) are shown in the inserts.
permitted the calculation of u (u = A/& where A is the measured absorbance) and, upon substitution into eq 2, led to the plot of against ho. Ignoring the weak absorption tail, as is c~stomary,~'resulted in the precise determination of direct bandgaps by using extrapolated values. Changes of the direct bandgap as a function of the optical thickness of the CdS particulate film are shown in Figure 5B. The optical thickness of (27) Wan& Y.;SUM, A.; Mahlcr, W.; Kasowski, R.J. Ckm. fhys. 3987, 87,7315.
the 'first layer" CdS particulate film (30-40 A) corresponds to the thickness of disk-shaped particles. At this stage of growth, coalescence of the small particles resulted in a sharp decrease of bandgap energy. The direct bandgap energy, E* = 2.83 eV, for 10-A-thick CdS particulate films dropped to El = 2.6 eV for 35-A-thick particulate films (Figure 5B). Transmission electron and scanning tunneling microscopies established that the "first layer" CdS particulate film was made up of connected, 30-40A-thick, 30-80-Adiameter, disk-shaped polyparticles? The average particle size of ca. 47 A was in good agreement with the
3720 The Journal of Physical Chemistty, Vol. 95, No. 9, 1991 I
ls2O
Zhao and Fendler
'I
t
*l
1.0
0.80
0.60
0.40
0.20
0.0
I
I
200
I
I
I
I
300
400
I
I
500
600
UAVBLENOTH, nm I
I
I
I
B -
2.9
2.8
R g m 6. (A) Two-dimensional STM image of an annealed (20 min, 400 "C),300 i 50 A thick, CdS particulate film on H O E . (B) The vertical dimension ( 2 ) is shown under the STM image. The particulate film was prepared by the infusion of H$3 into a cadmium arachidate monolayer.
2.1
2.6
% r'
8z
2.5
2.4
2.3 0
100
200
300
400
OPTICAL THICKNESS.
5. (A) Absorption spectra of 8-, 35-,218-, 298-, and 328-A-thick (indicated on the curves) CdS particulate films on quartz supports. The arrow indicates the absorption spectrum of a 328-A-thick, quartz-sup ported CdS particulate film after it was heated at 400 OC for 20 min. Particulate films were prepared by the infusion of H# onto a cadmium arachidate monolayer. (B) The optical-thickness-dependent, direct bandgap energy. Determined direct bandgaps are plotted against the optical thicknesses of the CdS particulate film.
observed 0.2-eV higher energy shift of bandgap energy.= After their earliest stages of aggregation, the direct bandgap energy (E,) decreased more slowly, with increasing optical thickness of the semiconductor particulate film, and tended to reach a steady value (0.1 eV higher than bulk bandgap energy for CdS). Heating the 328-A-thick (limiting thi~kness)~*'~ CdS particulate films to high temperatures irreversibly shifted the absorption edge (28) RoMti, R.; Nakahara, S.; Bnu, L. E.J. Ckm. Phys. 1983, 79,1086.
to longer wavelengths (indicated by an arrow in Figure 5A) and resulted in the recovery of the bulk bandgap energy of 2.4 eV (Figure 5B). A two-dimensional STM image of an annealed CdS particulate film is shown in Figure 6. Although heating increased the particulates in the film plane (i.e.* in the x and y directions) to 50-300 A, it did not appreciably alter their depths. The vertical distances of CdS particles are seen in Figure 6 to be in the 20-40-A range. Typical absorption spectra of 32-, 90-, and 326-A-thick ZnS particulate films and the dependence of the determined bandgap on the optical thickness are shown in Figure 7, A and B, respectively. A direct bandgap of 3.93 eV was determined for the 32-&thick "first layer" ZnS particulate film. An absorption edge blue shift of 0.28 eV led to the assessment of ca. 40 A for mean diameters of ZnS particles on using the model given by Brus,2' in good agreement with those obtained by STM measurements (Figure 4D). Along with ZnS particulate films growing normal to the monolayer plane, the direct bandgap energy (E ) decreased to a plateau value of 3.76 eV. Heating the 326-A-thick ZnS particulate films to high temperatures (300-400 "C) resulted in marked shifts of their absorption edges to longer wavelengths (spectra indicated by the arrow in Figure 7A) until the bulk bandgap was reached (Figure 7B).
Discussion Demonstration of size quantization in semiconductor particulate films is the most significant result of the present work. Confinement of the electron and the hole in a particle that is smaller than the exciton diameter (i.e.* the DeBroglie wavelength) of the bulk semiconductor results in the quantization of the energy levels. This is in contrast to a bulk semiconductor in which the conduction bands constitute virtual continua. The length of the exciton diameter depends on the extent of electron delocalization and on
Size Quantization in Semiconductor Particulate Films
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3721
TABLE I: M o r p M ~ g i dEvolution of ZnS Semicooductor Particulate Films
particle size, A height diameter 5-6 10-20 20-30
20-30 25-45 30-60
the particulate film, A
optical thickness of
classification regime“
bandgap shift, eV
d,
0.60
C
0.50
+ + 4- t +
+-r 4 1
t
i
-t-
+++
0.40 Bl
5
0.30
d
m
Pm
0.20
0.10
0.0
t
l
200
250
i
300
350
400
WAVELENGTH, nm 4.0
I
I
I
B
+++++i
i
4
. +
For spherical semiconductor clusters of radius R near k = 0, the mass tensor is nearly isotropic with the average diagonal element, me; thus eq 3 is simplified to
3.9
Ei 3.8
%
*g
+++++
Figure 8. Proposed schematics for the initial (a) and subsequent (b, c, d) growth of a monolayer-supported, porous, semiconductor particulate film. The d, and dy dimensions are in the plane and the d, dimension is normal to the plane; they refer to the earliest observable particles. d k d k and d: are dimensions in the plane and are normal to the plane; they refer to particles observed at later stages of their growth.
heating
3.7
W
w
E,
7r2h2 +2m$2
(5)
In principle, particles are unlikely to have complete spherical symmetry and the calculation should be repeated in all three dimensions. For rectangular parallelepipedons with the unique axis in the z direction, the kinetic energy operator (second term in eq 3) can be written as
I
band-gap 3.6
0
100
200
OPTICAL THICKNESS,
300
400
where mll and ml are the effective masses in the direction of and transverse to the z axis, respectively. The shift by localizing the electron in the side wall is
61
Figure 7. (A) Absorption spectra of 32-, 90-, and 326-A-thick (indicated on the curves) ZnS particulate films on quartz substrates. The arrow indicates the absorption spectrum of a 326-A-thick, quartz-supported ZnS particulate film after heating at 300 "C for 15 min. Particulate films were formed by infusion of H2S onto a zinc arachidate monolayer. (B) The optical-thickness-dependent,direct bandgap energy. Determined direct bandgaps are plotted against the optical thicknesses of the ZnS particulate film.
Le., the short axis of the disk-shaped particles), already observed in the thinnest film, remained essentially unaltered as the film grew. In small semiconductor clusters, the size-dependent electron energy is given by2
where E, is the conduction band energy. The second term on the right-hand side of eq 3 is essentially the particle-in-the-box quantum energy. The related expression of the second of the effective mass tensor, mu, is (4)
If dz
