## Publications

Here are presented recent RMT publications on thermoelectric subjects. Whole texts of the publications are available for download.

Energy Harvesting: RMT Components, Solutions, Developments

G. Gromov

Energy Harvesting and Storage Europe 2015, IDTechEx, Berlin, April 28, 2015.

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RMT, the manufacturer of thermoelectric modules, introduces a broad range of thermoelectric microgenerators for energy harvesting applications. The nomenclature covers many demands for harvesting devices, wearable and stationary ones. Unique Tabletop laboratory is presented as must-have solution for thermoelectric harvesting developments. New series of thermoelectric heat flux sensors is announced.

Объемные или тонкопленочные термоэлектрические модули

Громов Г.Г.

Компоненты и технологии №9, 2014, с.108

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В последние годы в технологии создания термоэлектрических микромодулей достигнут значительный прогресс. Причем одновременно с прогрессом в так называемой объемной технологии получила развитие и новая методика изготовления термоэлектрических модулей, вобравшая известные операции технологий тонких пленок. Данные термоэлектрические модули именуют тонкопленочными. При наличии обоих типов на рынке возникает важный вопрос о конкуренции двух технологий и изделий, созданных на их основе: является ли новая тонкопленочная технология более прогрессивной, способной вытеснить давно существующую «объемную»? Анализ показывает, что для большинства современных применений объемные термоэлектрические модули, как холодильные, так и генераторные, сохраняют свои преимущества. При внешне кажущихся бесспорных достоинствах тонкопленочных охладителей и генераторов рабочие параметры и эффективность «объемных» модулей заметно выше. За тонкопленочными модулями будущее. В широком диапазоне применений оба типа изделий имеют свои ниши и, если их правильно позиционировать, скорее не конкурируют, а дополняют друг друга.

Влияние различия в свойствах ветвей холодильного термоэлемента модуля на его эффективность

Драбкин И.А., Ершова Л.Б.

Вестник Международной Академии Холода, 1, 2011, с. 31

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Одна из современных тенденций в производстве термоэлектрических модулей – это создание термоэлектрических батарей большой мощности c большим количеством ветвей. При этом в некоторых пределах всегда имеет место различие в свойствах (геометрических и термоэлектрических) ветвей модуля. Казалось бы, свойства модуля должны неизбежно ухудшиться из-за различия в оптимальных токах для каждой из ветвей. Однако, если проводить усреднение по ветвям, то средняя величина термоэдс может отличаться от величины термоэдс при средней величине удельного сопротивления. В зависимости от этого соотношения, разброс свойств может приводить как к выигрышу, так и потерям в эффективности модуля. Рассмотрению влияния различия в геометрических и термоэлектрических свойствах ветвей модуля на эффективность его работы посвящена настоящая работа.

Оптимизация термоэлектрических генераторов с составными ветвями

Гочуа К.В., Драбкин И.А., Ершова Л.Б.

Сборник докладов "Термоэлектрики их применение", С.-Петербург, 2008, с. 403

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При конструировании термоэлектрических генераторов использование составных ветвей, т.е. ветвей состоящих из материалов, оптимизированных для работы в различных температурных интервалах, является обычной практикой. Такие модули имеют меньшие тепловые потери по сравнению с каскадными модулями, в которых неизбежно присутствуют потери на тепловых переходах между каскадами. Однако расчеты таких модулей с составными ветвями более сложны, чем расчеты каскадных модулей. Обычно модули рассчитываются из условий максимума кпд при фиксированных температурах холодного и горячего концов ветви. Такие задачи относятся к задачам оптимального управления, и их удобно решать используя принцип максимума Понтрягина . Этот метод успешно применялся для оптимизации различного вида холодильных модулей и каскадных генераторов. В данной работе рассматривается оптимизация генераторного модуля с составными ветвями.

Electrical Contact Resistance in Thermoelectric Pellet Based on Bi-Sb Chalcogenides

Drabkin I.A., Ershova L.B.

6th European Conference on Thermoelectrics, 2008, Paris, France

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It is well-known that electric contact resistance in thermoelectric pellets causes several per cent growth of the module electrical resistance and results in the drop of its efficiency in comparison with that of the thermoelectric material and the dependence of the efficiency on the pellet length. The contact resistance also causes a dependence of the module maximum temperature difference on the pellet length. In the paper the nature of the contact resistance is studied. The reasons of the above mentioned growth can be both the presence of the broken layer on the semiconductor border and the difference between the contact actual area and the geometrical one, the latter resulting in tightening lines of the electric current. The analysis of the relative contribution of these factors is done. The relation of the contact resistance with adhesion of the antidiffusion layer is considered.

Optimization of Thermoelectric Generator with Segmented Elements

Drabkin I.A., Ershova L.B., Gochua K.V.

Proceedings of the 6th European Conference on Thermoelectrics, 2008, Paris, France

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In designing thermoelectric generators it is common practice to apply segmented pellets, i.e. the elements of thermoelectric materials optimized for various temperature intervals. The advantage of segmented pellets in comparison with the multistage concept is the absence of thermal losses inherent in cascading. However for exact calculation of the segments length it is necessary to take into account temperature dependence of thermoelectric parameters. In this paper the procedure of calculating the dimensions of segments for a generating pellet is done by the Pontriagin maximum method, allowing for such dependences. Besides, this method allows obtaining both optimal values of segment cross-sections and taking into account restrictions imposed on these values.

Optimal Thermoelectric Cooling in Laser Diode Applications

Ershova L.B., Gromov G.G.

Proceedings of the 6th European Conference on Thermoelectrics, 2008, Paris, France

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Thermoelectric cooling is widely used in optoelectronics and telecommunication for cooling and temperature stabilization of laser diodes. In many applications there are no alternatives to thermoelectric cooling due to provided diminutiveness, control accuracy and high reliability.

The work outlines and solves the most typical optimizing problems of thermoelectric cooling for laser diode sub-assemblies in various telecommunication packages (Butterfly, HHL, TO3, and others).

Several levels of optimization are considered: that of the thermoelectric cooler itself (design and materials), optimization of a package (materials and gas filling), as well as the dependence of the efficiency on the operational conditions (ambient temperature) and heat sink thermal resistance.

The offered analysis gives quantitative estimations of efficiency of optimization, allows minimizing power consumption of the system and finding an optimum both for efficiency of cooling and for reliability of a design.

Curl Currents Occurrence in Homogeneous Isotropic Thermoelectric Elements

V.N. Abrutin, I.A.Drabkin, L.B.Ershova

Proceedings of the 5th European Conference on Thermoelectrics, 2007, Odessa, Ukraine

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Occurrence of curl currents in thermoelectric elements has been always regarded as an extremely undesirable phenomenon resulting in an inevitable efficiency reduction of the thermoelectric material. Curl currents usually appear due to local inhomogeneities in a thermoelectric material. In the given paper the occurrence of curl currents in a homogeneous material is investigated.

It is shown that in an element of the arbitrary shape the parallelism of the temperature and electric potential gradients is required to eliminate curl currents. As the electric and temperature fields in an element are described by different equations, in a general case there are no reasons for these gradients to be collinear. It means that an element of arbitrary shape always works worse than a quasi one-dimensional one, where electric and temperature fields depend on one coordinate.

We prove that for quasi one-dimensional elements in conditions of thermal exchange with environment there inevitably appear curl currents in a vicinity of the element side surface. As a result, even at the zero contact resistance there are additional reasons for the cooling efficiency of the thermoelectric module to become lower than that of the thermoelectric material it is made of.

Comparison of Approaches to Single-Stage Thermoelectric Modules Mathematical Optimization

I.A. Drabkin, L.B. Ershova

Proceedings of Seminar on Thermoelectrics and their Applications. November 2006, S.-Petersburg, Russia, p. 378

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For a long time all calculations for thermoelectric (TE) modules have been carried out applying an elementary model supposing TE parameters to be independent of temperature. Within this approach simple algebraic expressions for the optimal operation modes are found. Some complications of this approach involve effective TE parameters (the method of effective parameters) that allow precise description of thermal balances on the ends of a pellet, preserving unsophisticated consistency as the main advantage. On the other hand TE parameters temperature dependences were most stringently taken into account by the Pontriaguin maximum method. This method gives mathematically formalized recipes for optimal solutions. For this paper the derivation of the method equations has been redone and the result obtained and applied differs from the one offered earlier. The results of the two optimization methods are compared in this work and are shown to be in good agreement.

Comparison of Approaches to Multistage Thermoelectric Modules Mathematical Optimization

I.A. Drabkin, L.B. Ershova

Proceedings of Seminar on Thermoelectrics and their Applications. November 2006, S.-Petersburg, Russia, p. 386

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In the previous papers the comparison of the results on a thermoelectric (TE) module optimization obtained by the method of effective parameters and the Pontriaguin maximum method was carried out for a single-stage TE module. Both the methods allow for thermoelectric parameters temperature dependences. It was shown that both the approaches yield close results. Here the method of effective parameters is considered more stringently and the final comparison of the two methods is given for the case of a multistage TE module. The results compared are close enough for a designer to feel free about choosing one method or the other for an optimal TE modules search. The method of effective parameters provides a more evident relation between physical data and can be welcome for a comprehensible engineering.

Comparison of Approaches to Thermoelectric Modules Mathematical Optimization

I.A.Drabkin, L.B. Ershova

Proceedings of the 25th International Conference on Thermoelectrics:, ICT2006, IEEE, Vienna, Austria

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For mathematical simulation and optimization of thermoelectric (TE) modules different methods are applied. The paper numerically compares two most rigorous ones and shows that these approaches provide close results.

TE pellets behavior is described by the thermal conductance equation with temperature-dependent parameters. The usage of algebraic rate equations with effective parameters requires solving the thermal conductance equation as well. Usually a simulation of a pellet in operation is not sufficient as it is necessary to cope with the problem of optimization, commonly taking maximum coefficient of performance as a criterion. The Optimal Control Theory, based on the Pontriaguin maximum principle, provides an all-purpose approach to the problem. This paper proves that the method of effective parameters applied to TE module optimization yields a fairly good and reliable mathematical alternative.

Some Aspects on Thermoelectric Cooler Optimization for Applications in Photodetectors

Arakelov G.A., Yershova L.B., Gromov G.G.

Proceedings of 18th International Conference on Photonics and Night Vision Devices , 2004, Moscow, Russia

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There is a known practice to select a thermoelectric cooler (TEC) for application in photodetectors (PD) by the estimation of so-called maximal TEC parameters: maximal current Imax, voltage drop Umax, temperature difference DTmax and cooling capacity Qmax. DTmax at Q=0.

This practice is due to the fact that these maximal parameters are available as standard performance characteristics of TECs specifications, commonly applied in the international market.

But theoretical and experimental investigations demonstrate that an optimal TEC for a PD application and its most suitable operation parameters depend on a range of factors and application conditions.

At a given value of thermal resistance of heat sink onto which PD is mounted there are real parameters of TEC I0 < Imax and U0 < Umax that provide the optimal operation of the “PD+heat sink” system. Between two similar TECs with equal values of t heir Imax the type with higher Umax is preferable.

In the paper the example of optimal TEC estimation for the application in a 64-element PD array is advised.

Optimal Temperature Distribution on the Cascades of a Multistage Thermoelectric Module

I.A.Drabkin, L.B. Ershova

Proceedings of 3th European Conference on Thermoelectrics, 2005 Nancy, France

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The problem of finding the optimal sequence of temperature values on the cascades is expressed in terms of the system of linear equations. A multi-iteration search allows obtaining the solution with required accuracy. The method can be used for an arbitrary selection of thermoelectric (TE) materials on the cascades, taking into account temperature behavior of TE parameters. The method can allow for thermal losses on the TE module substrates.

The analysis of the solutions yielded by the offered method is given. It is shown that there exist a number of solutions close to the optimum. Each of them can be related to a new configuration of a TE module, which is very important for a designer‘s degrees of freedom.

Methods of Reducing Heat Losses on the Intermediate Substrates of Multistage TE Modules

I.A.Drabkin, Z.M.Dashevsky, L.B. Yershova, G.G. Gromov

Proceedings of Annual Seminar on Thermoelectricity, 2004, S.-Petersburg, Russia

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Temperature distribution on intermediate substrates of multistage thermoelectric (TE) modules is analyzed. It is shown that, depending on various thermal conditions of TE pellets operation, the temperature in the center of the substrate may significantly exceed the temperature on its edges, especially if the substrate material has a relatively low value of thermal conductivity (for example, ceramics based on Al2O3). To reduce heat losses it is suggested that TE modules with pellets cross-section widely varying from stage to stage should be applied. It results in decreasing intermediate substrates sizes and thus intensifying the heat flux density across them. This heat flux density growth makes the TE module more efficient as the pellets on the edge of the substrates are better involved in cooling. Some practical approaches of realizing this idea with the pellets connected in series and in parallel are studied.

The Effect of the Substrates Two-Dimensional Temperature Distribution on the TEC Performance

I.A.Drabkin, L.B. Yershova, D.A. Kondratiev, G.G. Gromov

Proceedings of 8th European Workshop on Thermoelectrics, 2004, Krakow, Poland

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Temperature distribution on a thermoelectric cooler (TEC) cold surface is of high practical value, as the sizes of the cooled object may not coincide with the dimensions of the TEC cold side and it is necessary to make the object temperature closer to the average cold substrate temperature. It is also very important to take into account the temperature distribution on the intermediate substrates of multistage TECs both in mathematical simulation and design modeling.

The approach to finding the approximate two-dimensional temperature distribution for the case of a heat source located on the surface has been developed in papers [1,2]. In this paper this method is analytically verified and applied to calculations of the temperature 2D-profiles of the TEC substrates. Application of the above-mentioned method for performance improvement of TEC systems is discussed.

- G.N.Dulnev, B.V.Polschikov. Temperature Field of a Plate with a Discrete Energy Source. Engineering Physics Journal, XXIX, 4, pp.722 – 727, 1975.
- G.N.Dulnev. Thermal and Mass Exchange in Radioelectronic Devices, Moscow, 1984, pp. 227-230

Complex Method to Control the Quality of Construction and Performance Reliability of Thermoelectric Modules in Optoelectronic Devices

L.B. Yershova, G.G. Gromov, I.A.Drabkin

Proceedings of 18th International Conference on Photonics and Night Vision Devices , 2004, Moscow, Russia

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International and national standards require high reliability from thermoelectric (TE) modules applied in optoelectronic devices. A standard criterion is the measurement and specification of the module electric resistance (R). At the manufacturing stage the module TE figure-of-merit (Z) is also controlled by the Harman method [[i], [ii], [iii]]. Paper [[iv]] suggested a complex quality control method by measuring TE module R, Z and time constant (t). As a follow-up of this approach the given paper shows the advantages of the complex (R, Z, t)-measurement for estimating the quality of assemblies based on TE modules as well as modules reliability control or failure while operating in optoelectronic devices. Theoretical backgrounds and experimental results are offered. The measurements were carried out with the help of Z, R, t-meters of the DX4065 and DX4165 series produced by RMT Ltd.

- V.P.Babin,S.M.Gorodetskiy. Thermoelectric modules quality testing by a manufacturer. Proc. XIV Int. Conf. on Thermoelectrics, June 27-30, St. Petersburg, Russia, 1995,pp. 338-340
- R.J. Buist. A new method for Testing Thermoelectric materials and Devices/Proc.XI Int. Conf. on Thermoelectrics. October 7-9,1992,Arlington, TX, USA.
- Gromov G., Yershova L et al, “Z-meter: Easy-to-use Application and Theory”. Proc. VI Eur. Workshop on Thermoelectrics, Freiburg, September, 2001.
- L.B. Yershova, G.G. Gromov, I.A.Drabkin. Complex Express TEC Testing. Proc. XXII Int. Conf. on Thermoelectrics, August

17-21, La

- Grande Motte, France, 2003 (printing)

Complex Express TEC Testing

L.B. Yershova, G.G. Gromov, I.A.Drabkin

Proceedings of The 22nd International Conference on Thermoelectrics, August 2003, La Grande-Motte (Herault - France)

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For express Thermoelectric Coolers (TEC) control in manufacturing and application, electrical resistance (R) and Figure-of-Merit (Z) measurement is widely spread. In the paper it is shown that there are TEC damage or defect instances not covered by one-parameter testing (R) and even two-parameter testing (R, Z). We offer a three-parameter approach to control TEC‘s quality: by measuring TEC electrical resistance (R), Figure-of-Merit (Z) and time constant (t). This method provides possibilities to diagnose TEC defect, which is of vital concern for technology and operational conditions correction. The paper yields theoretical and experimental results proving it. The experimental check is provided with the help of the original testing device R,Z,t-meter DX3065.

Measuring Methods of Thermoelectric Coolers Non-stationary Dynamics in Z-metering

L. Yershova, I. Drabkin, V. Volodin, D. Kondratiev

Proceedings of Annual Seminar on Thermoelectricity. November 2002, S.-Petersburg, Russia

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Temporal characteristics of a thermoelectric cooler (TEC) are important performance parameters for any device involving TEC. In paper [i] there are derived expressions for the time relaxation of single and two-stage multistage TEC. This paper studies transient processes concerned in figure-of-merit measurements with the Z-meter. It compares experimental and theoretical results and yields the evaluating approach for obtaining relaxation time values in real thermoelectric devices.

Measuring Methods of Thermoelectric Coolers Non-stationary Dynamics in Z-metering

L. Ershova, I. Drabkin, V. Volodin, D. Kondratiev

Proceedings of Seminar on Thermoelectrics and their Applications. November 2002, S.-Petersburg, Russia, p. 264

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Temporal characteristics of a thermoelectric cooler (TEC) are important performance parameters for any device involving TEC. In earlier papers there are derived expressions for the relaxation time of single and two-stage multistage TEC. This paper studies transient processes concerned in figure-of-merit measurements with the Z-meter. It compares experimental and theoretical results and yields the evaluating approach for obtaining relaxation time values in real thermoelectric devices.

Thermoelectric Cooling for Low Temperature Space Environment

L. Yershova, V. Volodin , T. Gromov, D. Kondratiev , G. Gromov, S. Lamartinie, J-P. Bibring, A. Soufflot

Proceedings of European Conference on Thermoelectrics, June 2002, Pamplona (Spain)

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The paper presents a multi-incremental work on the thermoelectric cooler (TEC) development for planetary space instrumentation. The technical specifications designated for cooling an infrared focal plane array detector involved strict dimensional, electrical and thermal constraints. The latter ones are the following: the operational temperature range is 160-180K and the cold side temperature to maintain is not higher than 140K at the heat nominally to be pumped 50mW. Within this guidance the optimum TEC was elaborated. That is a three-stage module with different pellets occupation density based on the low temperature optimized thermoelectric materials and improved thermal conductance substrates. The technology and assembling update was carried out. The reliability testing was performed. The compliance of the theory and experiment was verified and the results allow concluding that Mars-type mission r equirements are met.

Z-metering Development: Current and Non-stationary Processes Control

V.Volodin, G. Gromov, D. Kondratiev, A.Rogov, A. Ogryzko, A. Rogov, L. Ershova

Proceedings of Seminar on Thermoelectrics and their Applications. November 2002, S.-Petersburg, Russia, p. 264

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An easy-to-operate user-addressing device DX3065 for thermoelectric cooler (TEC) parameters measurement, as well as supporting mathematical and telemetry software are presented. It allows solving three problems posed by the Z-metering problem, its budding stem: electrical current little value for TEC-to-TEC control, thermal stationary transfer control and non-adiabatic dispersion verification via the current scanning and its partly compensation by the bipolar averaging. The device provides measuring TEC’s AC resistance, time constant and figure-of-merit. The device can be applied as an express means for TEC certification and mass production quality management.

Thermoelectric Cooling Modules

G. Gromov

Business briefing: Global photonics applications & technology, 2002

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Although thermoelectric phenomena were discovered more than 150 years ago, thermoelectric devices (TE modules) have only become commercially applied during recent decades. Actually for some period of time commercial thermoelectrics has been developing in parallel with two mainstream directions of technical progress – electronics and photonics, particularly optoelectronics and laser technique.Lately one can observe dramatical increase of application of thermoelectric solutions in optoelectronic devices: diode lasers, ptotodetectors, solid stage pumped lasers, charge coupled devices (CCDs) and others.

The progress in applications is provided by advantages of thermoelectric modules: they are solid state, have no moving parts, miniature, highly reliable, flexible in design to meet particular requirements.

Z-meter: Easy-to-use Application and Theory

G. Gromov, D. Kondratiev, A. Rogov, L. Yershova

Proceedings of European Conference on Thermoelectrics, June 2001, Freiberg (Germany)

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The paper is divided into two parts. The first part is an applying one. We present a handy, easy-to-operate user-addressing Z-meter. The device provides measurement of thermoelectric (TE) modules parameters: AC resistance (R), thermoelectric figure-of-merit (Z) and maximum temperature difference (DTmax).

The second part is of a theoretical value. As a rule, the device exposure does not happen to be ideally insulated and vacuum-like. Consequently need to take into consideration heat losses of various sorts. In this part we are to discuss specific formulae for estimating heat-exchanging uncertainties involved by Z-metering. All the expressions are explicit.

On the basis of theoretical estimations it is advised and realized in Z-meter new availabilities to measure performance parameters of single stage TE modules with corrections factors, as well as modules mounted into packages and two-stage modules.

TE Coolers Computer Simulation: Incremental Upgrading of Rate Equations Approach

D. Kondratiev, L. Yershova

Proceedings of European Conference on Thermoelectrics, June 2001, Freiberg (Germany)

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Thermoelectric (TE) technique and TE Cooler (TEC) exposure becoming more and more involved, both a manufacturer and a user are facing the problem of modeling and characterizing TEC mathematically. We suggest one of the approaches to do it based on (quasi-) tri-diagonal rate matrix of rate equations describing one-dimensional thermal dynamics through all intermediate stages and layers, including ceramics and solders, as well as a possible housing and temperature dependence of the parameters.