‘Invisible’ Dopants for Enhancing Semiconductor Figure of Merit

MAE 409 -- Direct Energy ConversionJoseph R. Groele

June 26, 2013

An optically inspired approach to improving ZT.

Agenda• Figure of Merit• ‘Invisible’ Dopants– Idea– Inspiration– Theory

• Suggested Design• Application • Conclusions• Q’s

Figure of Merit:

TSZT

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

‘Invisible’ Dopants - Idea

Use freedom of design to construct nano-particles 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

‘Invisible’ Dopants - IdeaAnti-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.

‘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

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

Expect reduction in thermal conductivity when core-shell and host matrix materials have a large acoustic mismatch(κ decreases)

• Mathematically, partial wave method is used to write the total scattering cross section

‘Invisible’ Dopants - Theory

• 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.

• 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

‘Invisible’ Dopants - Theory

• By controlling the amplitude of the barrier and well in the core-shell structure, the effect of the two can be cancelled out

Table 1: Parameters of the suggested core-shell structure [*]

Suggested Nanoparticle Design• There is a great flexibility of design as a result

of many adjustable parameters

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

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)

• 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.

Conclusions

Questions?

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.