C.M. Expt. 5
Cadmium Selenide (CdSe) Quantum Dot/Quantum Mechanical Models
Developed by Karen S. Quaal and Jason Hofstein, Department of Chemistry and
Biochemistry, Siena College, Loudonville, NY. quaal@siena.edu
Several quantum mechanical models were used to predict the size of the Quantum Dots
based on the wavelengths observed for the first exciton. The results were compared to
the TEM values reported in the literature1.
Approximations2
1-Dimensional PIB:
E 
 2  2 (2n  1)
2mL2
where L = length of box in meters, me = 9.11 x 10-31 kg, and n = 1.
3 2 2 (2n  1)
E 
2mL2
3-Dimensional PIB:
where L = length of box in meters, me = 9.11 x 10-31 kg, and n = 1.
Particle in a spherical well:
E 
 2  2 (2n  1)
2ma 2
where a = radius of sphere in meters, me = 9.11 x 10-31 kg, and n = 1.
m *e m *h
Replace me with  for an exciton:   *
where me* = 0.13me and mh* = 0.45me.
m e  m *h
Show that  for an exciton = 0.1009/me or 9.18 x 10-32 kg.

Higher order Approximations
Weak Confinement Approximation: adot is small, but greater than ab
2
E1s1s
 a 
  b  Ry *
 adot 
Where ab is the Bohr radius (CdSe) = 4.9 nm and Ry* is the exciton Rydberg for CdSe = 0.016 eV.
Show that this is an INVALID approximation.
Strong Confinement Approximation: adot << ab
2
 a 
 a 
E1s1s  Eg   2  b  Ry * 1.786  b Ry *  0.248 Ry *
a dot 
a dot 
where ab is the Bohr radius (CdSe) = 4.9 nm and Ry* is the exciton Rydberg for CdSe = 0.016 eV.
Show that this is a VALID approximation, even though the conditions for the approximation are not
met. 
Application of Spectroscopic Data to Quantum Mechanical Models
Several quantum mechanical models were used to predict the size of the Q.D. The best
agreement with TEM values was found with the strong confinement model.
E1s1s = Eg + π2 (ab/adot)2 Ry* - 1.786 (ab/adot) Ry* - 0.248 Ry*
Where E1S1S = Energy calculated from UV/VIS spectrum
Eg= bang gap (CdSe= 1.84 eV)
ab= exciton Bohr radius (CdSe= 4.9 nm)
adot= radius of the Q.D
Ry* = Rydberg constant (CdSe= 0.016 eV)
Table 1: CdSe Spectral Data
Temp ºC
Lambda Max (nm)
128
453
138
473
148
501
158
510
168
521
178
522
188
530
198
538
208
546
218
555
Energy (J)
4.38E-19
4.20E-19
3.97E-19
3.90E-19
3.81E-19
3.81E-19
3.75E-19
3.69E-19
3.64E-19
3.58E-19
Radius (nm)
1.97
2.11
2.33
2.41
2.51
2.52
2.61
2.70
2.79
2.91
References:
1. Yu, W., Qu L., Guo W., and Peng X., Experimental Determination of Extinction
Coefficient of CdTe, CdSe, and CdS Nanocrystals. Chem. Mater. 2003, 15 (14) 28542860.
2. Gaponenko, S.V., Optical Properties of Semiconductor Nanocrystals, Cambridge,
U.K., Cambridge University Press, 1998.