Subscriber access provided by UNIV OF REGINA
Article
Functionally graded Ge1-xSix thermoelectrics by simultaneous band gap and carrier density engineering Ellen M. J. Hedegaard, Simon Johnsen, Lasse Bjerg, Kasper A. Borup, and Bo B. Iversen Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/cm502042e • Publication Date (Web): 20 Aug 2014 Downloaded from http://pubs.acs.org on August 25, 2014
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Chemistry of Materials is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Chemistry of Materials
Functionally graded Ge1-xSix thermoelectrics by simultaneous band gap and carrier density engineering Ellen M. J. Hedegaard, Simon Johnsen, Lasse Bjerg, Kasper A. Borup, and Bo B. Iversen* Center for Materials Crystallography, Dept. of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark. KEYWORDS Thermoelectricity, Czochralski method, functionally graded materials
ABSTRACT: Exploiting the material gradients inherent to crystal growth techniques, boron doped Ge1-xSix (x= 0 to ~0.25) samples graded in both band gap and carrier concentration have been prepared by the Czochralski method. Along the length of the Ge1-xSix samples x changes continuously giving rise to changes in the band gap from 0.87 eV to 0.65 eV. Similarly, gradients in the boron content results in continuous carrier density changes along the sample. This results in samples graded in all material parameters relevant to thermoelectric performance. The present study thereby demonstrates a one-step method for preparing thermoelectrics graded in both carrier concentration and band gap. By careful matching of dopant and material system, it is demonstrated how the gradient in dopant and band gap can work in synergy and mutually enhance the thermoelectric performance over the individual contributions.
INTRODUCTION Thermoelectricity, directly interconverting thermal and electrical energy by solid state materials, has long been suggested as one of the answers to the worlds rising energy demand.1 Conversion of waste heat into electricity would result in a better utilization of currently available energy sources and new sources may be exploited. However, development of new materials as well as optimization of known materials is needed before costefficiency allows for the widespread consumer use which has long been strived for. The efficiency of a thermoelectric material increases monotonically with its figure of merit, .1-2 =
(1)
α is the Seebeck coefficient, σ the electrical conductivity, T is the absolute temperature, and the thermal conductivity given by = + where e and l specify the electrical and lattice contributions respectively, and = , being the Lorentz number.
a necessity to enhance the exploitation of the temperature gradient. This is an important result as achieving a predetermined property profile through a material is a complex experimental task.3 The decrease in is caused by the onset of bipolar conduction.5 Therefore, the larger the band gap the higher the optimal working temperature, i.e. the peak in . This is illustrated by the “10 rule”, which states that a material should have a band gap of roughly 10 , with being the optimal operating temperature.6 Similarly, the carrier concentration shifts the peak in , such that the higher the dopant concentration, the higher the peak temperature in .3 Grading of the band gap along the sample can be done by grading the sample composition by ensuring overall directional solidification through bulk crystal growth techniques such as Bridgman-Stockbarger or Czochralski. . Suitable materials systems are therefore (pseudo-) binary with full or partial miscibility, see figure 1. For this to result in a grading of the band gap this must be a function of composition.
For a homogeneous material peaks in a narrow temperature range.1 However, in a module application the material is often subjected to a large temperature gradient.3 By grading the properties determining through the sample, the peak position along the length of the sample can be shifted to match the local operating temperature and consequently improve the efficiency of the thermoelectric device. This idea was first introduced by Ioffe in 1949.3-4 It has later been proven that an exact match between parameters and temperature profile is not
ACS Paragon Plus Environment
Chemistry of Materials
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
increase being steeper at compositions below 15 mol% Si than above. By inspection of the phase diagram,7 it is seen that a Czochralski pulled Ge1-xSix sample will have decreasing Si content as solidification proceeds, leading to decreasing band gap. By chosing a low concentration of Si the highest effect from band gap grading is expected. A decreasing dopant concentration, i.e. a segregation coefficient above one, is therefore needed to enhance the effect on the properties from band gap grading. The most commonly used p-type dopant in germanium-silicon alloys is boron. Bridgers et al.12 report the equilibrium segregation coefficient of B in Ge to be 17.4 although other values have also been reported.13 However, all of these are significantly above one, making boron a suitable proof of principle dopant in germanium and germaniumrich GeSi alloys.
Figure 1: Schematic phase diagram of a solid solution with full miscibility showing how, for a given composition of the melt, the composition of the resulting solidified sample can be found by drawing a line at constant temperature. The development in composition as crystallization proceeds is indicated by the arrows. Phase diagram reproduced from 7 reference
Whereas many studies in recent years have focused on improving the thermal contributions to , the present study focuses on manipulating the electronic contributions to the thermoelectric figure of merit and therefore these have been isolated from the equation:
Furthermore, assuming complete equilibrium in the system, grading of the dopant concentration along a Czochralski or Bridgman-Stockbarger grown crystal is given as:8 = 1
Page 2 of 9
=
= =
(3)
where is the Lorenz factor, which is dependent of carrier density, scattering mechanism and band structure. Focusing on acoustic phonon scattering in a single parabolic band assumes values from 1.49·10-8 WΩK-2 to 2.44·10-8 WΩK-2.14
(2)
is the dopant concentration at the crystal-liquid interface at a given time during solidification, is the equilibrium segregation coefficient, is the original dopant concentration in the melt, and is the fraction of the melt solidified at the given time. The value of thereby determines the development in dopant concentration, i.e. whether it decreases (>1) or increases (
