This document proposes an approach called "invisible dopants" to improve the figure of merit (ZT) in semiconductors by enhancing electrical conductivity (σ) and Seebeck coefficient (S) while decreasing thermal conductivity (κ). The idea is inspired by anti-resonant scattering in the Ramsauer-Townsend effect and involves embedding core-shell nanoparticles in semiconductors with specific parameters to minimize electron scattering. Modeling suggests this could increase carrier mobility through dopant invisibility and introduce sharp features enhancing S. The core-shell structure may also decrease κ through phonon scattering at the interface. This concept aims to advance beyond traditional doping by optimizing all three factors influencing ZT.

1. ‘Invisible’ Dopants for Enhancing
Semiconductor Figure of Merit
MAE 409 -- Direct Energy Conversion
Joseph R. Groele
June 26, 2013

2. An optically inspired approach to improving ZT.

3. Agenda
• Figure of Merit
• ‘Invisible’ Dopants
– Idea
– Inspiration
– Theory
•
•
•
•
Suggested Design
Application
Conclusions
Q’s

4. S T
Figure of Merit: ZT 

2
• Dimensionless parameter of a material
• Major goal of energy research is to increase ZT
• Recent strategies make use of benefits from:
• Electron quantum confinement [2]
• Phonon scattering in nanostructures [3]
• Sharp features in differential conductivity [4]
• Optimizing ZT is still a major challenge mainly
because σ, S, and κ are interdependent

5. ‘Invisible’ Dopants - Idea
Use freedom of design to construct nanoparticles with a specific radial potential
function profile that minimizes the electron
scattering cross section (Σ) within the Fermi
window (εf + kT) to ensure increased mobility
• Minimization appears as a sharp dip in Σ vs.
carrier energy – called anti-resonant scattering

6. ‘Invisible’ Dopants - Idea
Anti-resonance can
enhance TE materials
in two ways:
1. Dopant invisibility to
conduction carriers
(σ increases)
2. Sharp features in
relaxation times
(S increases)
Figure 1: The total electron – nanoparticle
scattering cross section vs. electron
energy (bottom scale) or ka (top scale)
depicted with a solid line. Contributions
from the 0th and 1st order partial waves
plotted as dashed lines.

7. ‘Invisible’ Dopants - Inspiration
• Use of anti-resonances was inspired by the
Ramsauer-Townsend (RT) effect. [5]
• A corresponding anti-resonance effect could
be observed in solids
Example:
To embed spherically symmetric core-shell
particles of specific size, effective mass, and
band offset inside a semiconductor

8. Expect reduction in
thermal conductivity
when core-shell and
host matrix materials
have a large acoustic
mismatch
(κ decreases)
Figure 2: Cartoon of core – shell
nanoparticle, and below,
Potential profile of the nanoparticle
plotted as a function of radius
• Dashed line: band offset profile
across core – shell nanoparticle
• Solid line: screened bent
potential

9. ‘Invisible’ Dopants - Theory
• Mathematically, partial wave method is used
to write the total scattering cross section
• Make phase shifts (δl) become multiples of π
• Potential is “screened” and the incoming and
outgoing waves appear identical
… as if there was no scattering center.

10. ‘Invisible’ Dopants - Theory
• These phase shifts are achieved through a
core-shell structure with six parameters:
– Inner and outer radii of the scattering core-shell
structure, the corresponding band offset, and the
effective mass
• By controlling the amplitude of the barrier and
well in the core-shell structure, the effect of
the two can be cancelled out

11. Suggested Nanoparticle Design
• There is a great flexibility of design as a result
of many adjustable parameters
Table 1: Parameters of the suggested core-shell structure [*]

12. Application to Modulation Doping
• 3D Modulation Doping – improves
performance by reducing impurity scattering
- 40% improvement in carrier mobility
• Nanoparticle scattering limits the improvement
• By making the nanoparticles ‘invisible’ to the
conduction carriers, mobility can be improved

13. Conclusions
• Concept or RT anti-resonance can enhance all
three parameters relevant to determining ZT
1. Dopant invisibility to conduction carriers
(σ increases)
2. Sharp features in relaxation times
(S increases)
3. Core-shell and host matrix materials have a
large acoustic mismatch (κ decreases)

14. Conclusions
• Represents an advance over traditional
nanoparticle- and impurity-doped materials
• Improvement over modulation-doping
The concept could be applied to semiconductor
design whenever high carrier mobility is
desired.

15. Questions?

16. References
[1] M. Zebarjadi, B. Liao, K. Esfarjani, M. Dresselhaus, G.
Chen, Adv. Mater. 2013, 25, 1577-1582.
[2] L. D. Hicks, M. S. Dresselhaus, Phys. Rev. B 1993,
47,12727.
[3] G. Chen, Phys. Rev. B 1998, 57, 14958-14973.
[4] G. D. Mahan, J. O. Sofo, Proc. Natl. Acad. Sci. U.S.A.
1996, 93, 7436.
[5] a) V. A. Bailey, J. S. Townsend, Phil. Mag.
1921, S.6, 42, 873;
b) C. Ramsauer, Annal. Phys. 1921, 4, 64, 513.