The Modern Student laboratory: Spectroscopy Dependence of Semiconductor Bandgap on Cluster Size
Theoretically, this size dependence of the semiconductor bandgap can be understood most simply in terms of an expression proposed by Brns (4).
where E, is the bulk bandgap value; me and mh are the effective masses for the electron and hole, respectively; R is the radius of the semiconductor particle; and E is the bulk optical dielectric coefficient. Thus, the observed shift from the bulk bandgap value is a balance between the positive kinetic energy of the system and a negative Coulombic interaction. Dependence of the Bandgap on the Nature of the Metal
This experiment illustrates another important aspect of semiconductor properties: the dependence of the bandgap on the nature of the metal and the chalcogen of a compound semiconductor. In this experiment, the effect of substituting Zn and Pb for Cd in a binary sulfide semiconductor MS is analyzed for a given, fured, meta1:sulfide ratio. M. = [SZl = 4 x Typical results are shown for [Mt21 (See Fig. 4.) The relatively large bandgap of the ZnS is reflected in an adsorption edge near 310 nm. CdS has an intermediate value near 480 nm, and PbS has the smallest bandgap of the three, near 650 nm. These observed differences in absorption threshold values can also he loosely interpreted in terms of eq 1.In this case, each semiconductor begins with a radically different bulk value (3.7 eV for ZnS: 2.4 eV. CdS: 0.4 eV. PbS) (8). Assuming comparable diameter;, the observed absorption edce is influenced most strondv bv the differences in effGctive electron masses (m*io? eiectrous and holes between the different semiconductors. This, in turn, explains why PbS is shifted the most to higher energy from its bulk value; PbS has the smallest effective mass values of the three (me* = 0.1; mh* = 0.1). This is contrasted to effective mass values of 0.310.6 for m.*lmh* of ZnS and 0.2010.50 of CdS (8). Modifications of the Experiment
There are also many ways in which to modify or expand this experiment. In the first part, students can test addi-
tional solutions with different ratios of watertosurfactant, that is, with water poolsofdiflerent sizes. In either part of the experiment, it is quite feasible for the students to use different concentrations of metal cation and sultide to test the possible range of absorption shifts Summary Through this experiment, students are exposed in a laboratory setting to the concepts of band structure in semiconductor clus&r materials.-Twofundamentally important notions are clearly illustrated:
How the energy of these bands change with particle size Why the magnitude of the bandgap is dependent upon chemical compmition Also, the undergraduate student is given the opportunity to work with a polynucleic acid, the DNA, and a microemulsion, the AOT inverse micelles. This experiment has very straightforward procedures, and it is economical in the amounts of reagents used. Increased emphasis has been placed on topics concerning solids and materials in the undergraduate curriculum. e ssemiconductor clusThis ex~erimenton the ~ r o ~ e r t i of ters can'serve a s an inte;esGng and straightforward introduction to such topics for the chemistry student. Acknowledgment We thank the NSF for the funds to purchase a diodearray spectrophotometer under the auspices of the ILI program, Grant no. USE-9151597. We also thankTexas Christian University for a contribution of matching funds. Literature Cited 1, "Clvetwand Clusb~AsswbledMatetiala"; Awrha&,R. S.;Bemhalc, J.;Ndaan,D. L., Ed% Mator Ros. Soc. Symp h. 1991,206. 2. Mptol c1uatera;Moslrwits, M., Ed.;W h y : New York,1988. 3. Mptal CluaterainPrmpiis; W e ,L., Ed.:(ACS Symp. Ser. No. 312). Amdesn ChemidSc&ty, Washishipton,DC. 1988. 4. Steiwmald.M. L.: B m . L. E.AEets. Chem. R e . 1880.23.183. 6 FM a n s r r e l l ~ n cr w e w o r d d l v r s n r d p p r r s c h r s t c rlu,lcr atabdraatmn. ace S u ~ c m a l dY . L. BNI. L E.4nn. f i t . Mare?.Srr lss9.19.471 6 hlcym,M . W a l l k g . C. K u h a r a . K.:Fcndlcr,J. J. Chem. S a Chrm C,mm 1984
.
90 7. CaITer, J. L;Chand1er.R. R. Macm Res. Sa. Symp.Pme.1881,206,521. 8. P h v e , J. I. OptimlRaeeama in &mimndmtom:Rentia-HaU: Englewmd Cliff., 1911;p 413.
Second Edition of Modern Experiments for Introductory College Chemistry The second edition of Modern Experiments for Introductory Chemistry, containing experiments from the Journal of Chemical Education that were selected because they reflect exciting innovations in lahoratory work,is available. Compiled by H. Anthony Neidig and Wilmer Stratton, the experiments are written for professors to use, not a prestyled, specific laboratory directions, but as inspiration and guide for adoption and adaptation in their individual courses. The 144-pagepaperback is $18.50 ($19.50 foreign)and can be purchased by sending a prepaid order to Subscription and B w k Order Department, Journal of Chemical Education, 1991Northampton Street, Easton, PA 18042. AU orders must he prepaid, aid the price includes the shipping.
I A10
Journal of Chemical Education
