heat source, TPV, radiant energy, emitter, solar cells, AM0, temperature, thermophotovoltaic, energy band, TPV technology, TPV cell, black body spectrum, the spectrum, radiation spectrum, electron-hole pair, recombination rate, incident radiation, photogeneration, Planck's Law, pair generation, Jadavpur University, power source, Thermo-Photovoltaic, TCAD, space satellites, solar cell array, space missions, Radioisotope Thermoelectric Generator, Manipur Institute of Technology Imphal-795004, space application, Geostationary Satellites, Khomdram Jolson Singh Dept., deep space, solar cell, space mission, Technology Computer Aided Design, dilution factor
Modeling of an efficient Thermo-Photovoltaic (TPV) cell as a power source for space application
Khomdram Jolson Singh Dept. of ECE. Manipur Institute of Technology Imphal-795004 (India) [email protected]
Subir Kumar Sarkar Dept. of ETCE. Jadavpur University
Kolkata-70032 (India) [email protected]
ABSTRACT A reliable high efficiency GaSb and InGaAs based thermophotovoltaic cells were modeled by using numerical simulation
TCAD tool ATLAS. Both these two potential materials were compared and analyzed their performance parameters. GaSb based TPV cells are found to be a better choice. The cell is optimized for operation with outer space solar spectrum AM0 and allowed further increasing the efficiency up to 27.31% at black body
spectrum (TBB =1300K) i.e. temperature equivalent with artificial heat source
from radioisotope Plutonium Pu-238 currently used in NASA's RTG for powering up deep space mission
Satellites. Optimization of doping concentration and layer thickness of GaSb cell is performed by simple successive iteration algorithm written in MATLAB script
s. Further, efficiencies at varied temperature range
(1100K to 2000K) is also investigated. Up to 35% efficiency is attained at 1800K radiation in this proposed cell. General Terms Thermo-Photovoltaic(TPV) device modeling, an implementation of latest TCAD, Energy Convers
ion methods. Keywords ATLAS, RTG (Radioisotope Thermoelectric Generator), TPV (Thermo-photovoltaic), TCAD (Technology Computer Aided Design). 1. INTRODUCTION The ultimate source of power in space satellites is solar cell array. Geostationary Satellites and satellites that stationed around Earth can get adequate Power supply
using these solar arrays. However, massive arrays may require for powering deep space missions
Satellites which are farther away from Sun. The intensity of light from the sun decreases with the square of the distance from it making solar cells
an inadequate source of power on distant space missions because of the requirement of the cell area would be tremendous. Again, the amount of batteries for power storage to provide primary power for a long mission would also be too massive to even launch into space because they are only capable of providing a few hundred watt hour per kg. Thus, the need for a better light weight source of power capable of providing adequate power to these deep space exploration Satellites for the entire life of the mission becomes vital. Currently NASA deep space Satellites use an alternative source of power known as a radioisotope thermoelectric generator or (RTG). NASA Glenn has been developing Stirling engine technology since the 1970's and has been
developing radioisotope power system
s RTG for deep space missions since 1990. An RTG consists of a heat source radioisotope Plutonium Pu-238 and SiGe thermocouple as a means to convert that heat into electricity . The electrical power produced in this thermocouple is proportional to the difference in temperature between the hot and cold junctions. These devices do a relatively poor job of power conversion, however, only achieving efficiencies of a few percent in optimum working conditions
. The most attractive replacement for the thermocouple is currently the thermophotovoltaic (TPV) cell. Research has been ongoing in this field since the 1950's, but the exotic materials necessary for high efficiency cells has only been recently available. Recent research has shown that gallium antimonide (GaSb) and indium gallium arsenide (InGaAs) are two of the most promising materials for new TPV cells . 2. THERMOPHOTOVOLTAIC SYSTEM TPV cell operates in a manner very similar to how a solar cell works. The difference is the band of the electromagnetic spectrum the cell is designed to respond to. Where a solar Cell Res
ponds to the visible band of the spectrum, TPV cells respond to the infrared region. In the case of PV, the source is the sun, while in TPV there are many sources. The distance between the source and the converter is fixed in the case of PV (SunEarth), while in TPV it can be any distance. There are standard spectra for PV (AM1.5D, AM1.5G, etc.), but there are no standard spectra for TPV. Fig 1: Thermophotovoltaic system under IR radiation. There are more parts to a thermophotovoltaic system than just the TPV cell. Fig.1 shows the four main components of a typical TPV system. The first component is a heat source. The second
is a selective emitter. The purpose of this emitter is to help shape the radiation spectrum of the heat source. As with solar cells radiation absorbed by the cell that does not have enough energy to create an electron-hole pair just adds heat to the cell, thereby lowering the efficiency. Rare earth oxides such as ytterbium oxide (Yb2O3) and yttrium aluminum garnet (YAG) have proven to be very effective material for selective emitter layer . The filter performs a similar function to the selective emitter. It is designed to reflect incident radiation that does not have enough energy to create an electron-hole pair in the TPV cell. The radiation is reflected back to the emitter. This helps to keep the temperature of emitter as high as possible which improves the efficiency of the system . Photo-Electric Converter uses a thermophotovoltaic (TPV) cell to convert heat into electricity. 3. TPV CELL MODELING A 0.72 eV Gallium antimonide (GaSb) is the most commonly published material used for TPV cells. Although it does not have a low enough energy band gap to respond to most of the radiant energy from a current RTG heat source (~1300K), the cells are relatively easy to fabricate and are capable of producing a significant amount of power per square centimeter. Indium gallium arsenide (InGaAs) is another popular material for TPV cells. As a ternary compound, many of its electrical and optical properties including energy band gap changes with varying molar concentrations of indium and gallium. As a 0.55 eV cell, its low open-circuit voltage is not very suitable for single junction cells, but it is attractive for use in multijunction cells . Here, GaSb TPV cell model is developed and optimized for both the sun's spectrum, AM0, and the spectrum from a 1300K blackbody which represents well the spectrum from an RTG heat source. Using the various data from recent literatures and by verifying the very similar characteristics from the reported device structures in Ref. B. Davenport , we obtained the theoretical simulation of GaSb TPV cell used in this design. Fig.2 shows the Schematic diagram
of this optimized design. Fig 2: Schematic diagram of optimized GaSb TPV Cell. 3.1 Incident Spectrum design An ideal emitter, a blackbody, radiates energy over the whole electromagnetic spectrum as a function only of temperature and wavelength. A blackbody emitter radiates energy per wavelength into a unit solid angle in a distribution described by Planck's Law for spectral radiance as .
where h is Planck's constant, c is the speed of light in a vacuum, and k is Boltzmann's constant. T and are the only two variables and refer to the blackbody temperature in Kelvin and the wavelength of energy emitted in meters. The unit spectral radiance L(T) is W/m2/sr/µm. As can be seen from Planck's Law for spectral radiance, at a given temperature, the amount of radiation varies as function of wavelength. An important feature is that at any wavelength, the magnitude of radiant energy increases as temperature increases . This means that a hotter blackbody will emit more energy than a colder one. Another important feature of Planck's Law is the distribution of radiant energy. More radiant energy is emitted at shorter wavelengths for hotter blackbodies . This phenomenon is described by Wien's Displacement Law . 2897.8 = This equation gives the wavelength at which the maximum radiation is emitted from a blackbody at a given temperature as shown in Table 1.
Table 1. Peak wavelength for varied temperature ranges. T(0K) 300 500 1000 1300 1500 1800 2000 max 9.65 5.79 2.89 2.23 1.93 1.61 1.44
It can easily be seen that the location of this peak is inversely proportional to the temperature of the blackbody. In order to find the total power emitted by a blackbody, it is necessary to integrate Planck's Law over all wavelengths. This calculation yields the Stefan-Boltzmann Law ,
where =5.670x10-8[W/m2/K4]. Here it can be seen that the total
radiated power is dependent only on temperature. When
working with solar cells, the spectrum of interest is AM0. This
spectrum corresponds to the radiation from blackbody at a
temperature of 5800K. Because energy is radiated outward from
a body at an average angle perpendicular to its surface, the
magnitude of radiation in a given direction is equal to only one-
fourth the total radiation . This corresponds to steradians.
With this information, the equation for the hemispherical
spectral radiant flux in any direction from a flat surface emitter
can be derived as 
() = () =
The unit of M (T) is W/m2/µm. In order to find the AM0 spectrum, there is one more factor that must be considered. The magnitude of radiation emitted from a source is inversely proportional to the square of the distance from the source. The factor used to calculate the AM0 spectrum is found by taking the square of the ratio of the sun's radius to the mean distance between the earth and the sun. This factor, referred to as the dilution factor, comes out to 2.165x10-5 . The final equation for the AM0 spectrum can now be expressed as
0 = () =
where f is the dilution factor. The unit of AM0 is also W/m2/µm The actual AM0 spectrum as measured by NREL  is plotted in Fig.3. Using the above equation, Fig. 4 below shows the spectrum from a 1300K blackbody adjusted by the dilution factor. These two spectra are used for illuminating our model.
way, a number of minimum triangles are created; this determines the resolution of the simulation.
Fig 3: AM0 Space Solar Spectrum. . Fig 4: 1300K Blackbody Spectrum. 3.2 TPV Model Simulation The first step in modeling the device is specifying the mesh on which the device will be constructed shown in Fig. 5. This can be 2D or 3D and can be comprised of many different sections. Orthogonal and cylindrical coordinate system
s are available. Several constant or variable densities can be specified while scaling and automatic mesh relaxation can also be used. This
Fig 5: Our TPV design with finer mesh model.
A detailed set of major material parameters shown in Table.1 used in our designs has been produced by literature research and calculations as well as calibration from wellknown cells. Table 2. Standard major parameters used in our model
Band gap Eg[eV] @300oK
Permittivity es/eo Affinity [eV] Epsilon e mobility MUN [cm2/VЧs] h+ mobility MUP [cm2/VЧs] e density of states NC [cm3]
14.4 4.06 15.7 4000 1400 5.68E+18
14.3 4.66 14.2 1945 141 1.15E+17
h+ density of states NV [cm3] Lifetime (el)[ns] Lifetime (ho)[ns] ni (per cc)
2.95E+18 1 1 3.66E+12
8.12E+18 1 1 1.56E+13
Vsatn (cm/s) Vsatp (cm/s)
ATLAS is used to model this TPV cell with the physical parameters
such as the kind of materials and their compositions, thicknesses, doping concentrations from the above tables and (SILVACO Data Systems Inc 2010). ATLAS permits the user to identify a variety of physics models for calculating carrier mobility and recombination. In our design, we used the following models for our analysis. The ConcentrationDependent Low Field Mobility model (CONMOB) was used to model the doping-dependent low-field mobilities of electrons and holes in GaSb at 300K.The recombination models utilized were the Optical Recombination (OPTR) and the ShockleyRead-Hall (SRH) recombination models. SRH recombination
model takes into account the electrons being emitted or captured by donor and acceptor- like traps. The OPTR determines the possibility that a photon is generated when an electron and hole recombine. Green has also shown that the OTPR model increase the accuracy of the photovoltaic cell simulation. The ATLAS developed GaSb TPV cell model is shown in Fig. 6.
Fig.7 is the detail photogeneration rate obtained under AM0 related 1300K Black Body illumination. The legend within the figure defines the TPV cell's photogeneration rates. These are expressed using the log of the electron-hole pair generation rates that correspond to the color-coded display. For example the highest numerical value (e.g., 22.6) corresponds to the colorcoded horizontal layer that is generating1022.6 electron-hole pairs per cm3. Here, most of the higher photo generation rates are observed in the upper solar cell layers (Red region) because a significant majority of the IR photon energy
is absorbed here prior to reaching the remaining body (e.g., the yellow & green region) of the simulated device. Fig.8 show recombination rate which is higher at the front surface and junction area. This is a normal expected TPV condition.
Fig 6: ATLAS model of GaSb TPV Cell. 4. RESULT AND DISCUSSION The primary importance to the simulation of a PV or TPV cell is the accurate modelling of electron-hole pair generation. LUMINOUS, the optoelectronic simulation module in ATLAS determines the photogeneration at each mesh point in an ATLAS structure by performing two simultaneous calculations. The refractive index n is used by LUMINOUS to perform an optical ray trace in the device. The extinction coefficient
k is used to determine the rate of absorption and photogeneration (electron-hole pair generation) for the calculated optical intensity at each mesh point. Together, these simulations provide for wavelength-dependent photogeneration throughout a cell. These n and k values of our designs are based on SOPRA N&K database 2010.
Fig 8: Recombination rate generated under illumination. Fig. 9 shows the electron current density in A/cm2 for different layers inside the GaSb cell. The generation of current is low under the Gold electrode layer anode contact since it blocks the incident spectrum to reach the underneath layer.
Fig 7: Detail Photogeneration rate inside the cell
Fig 9: Distribution of e-current density in different layer.
Fig.10 shows the potential voltage (V) developed under 1300K spectrum. Highest V is observed in bulk GaSb based layers.
from 1100K 2000K for 26um Thickness GaSb TPV cell. Efficiencies as high as 27-35% are predicted in this cell assuming 90% cell-emitter reflectance for sub-bandgap photons and TBB > 1300 K.
Fig 10: Potential voltage developed at 1300K BB radiation.
The efficiency of the cell is calculated as
where Pin is the power in the incident spectrum; for AM0 this is
1367 W/ m2. The squareness of the I-V curve fill factor (FF) is
calculated using Voc and Isc as
Fig. 11 shows the complete I-V curve of GaSb and InGaAs TPV
and their calculated corresponding performance parameters.
Under same structure, GaSb performed much better with
efficiency of 27.31% than InGaAs based cell with only 22% at
1300K black body spectrum.
Fig 11: I-V curve of optimized GaSb and InGaAs TPV cell. Corresponding conversion efficiency data are plotted in Fig. 12 as the function of a black body IR-emitter temperature ranges
Fig 12: Efficiencies Vs Black Body Radiation Temperatures. 5. FUTURE SCOPES This TPV cell may serve more useful in the design of hybrid solar-fuel system
s for energy source generation in various terrestrial applications. Hybrid solar-fuel system may allow operating a TPV generator 24 hours a day: at night a thermal TPV and in the daytime a solar powered TPV (STPV) system with a sunlight concentrator. 6. CONCLUSION An accurate modeling of both concentrator TPV cells for AM0 spectrum and TPV converters for RTG application is absolutely necessary in order to guide TPV technology to increase the performance of these devices. To give a real understanding and realization of all the phenomena occurring inside the TPV cell devices, the development of a reliable simulated model first is also essential prior to actual fabrication. Intensive work in determining the suitable material
parameters of the TPV semiconductors of interest is still going on. After this, TPV devices will take advantage of the modeling previously developed for solar cells. In this paper, a novel method for developing a realistic model of an efficient TPV cell is presented. This modeling technique may prove to be of great importance in aiding in the design and development of advanced TPV cells. 7. REFERENCES  Atomic Insights: RTG Heat Sources Webpage (http://www.atomicinsights.com/sep96/materials.html), last accessed Dec 2010.  NASA Glenn Research Center, Thermo-mechanical systems
Branch: Stirling Radioisotope Power for Deep Space Webpage(http://www.grc.nasa.gov/WWW/tmsb/stirling/doc/stirl_r adisotope.html), last accessed June 2010
 Office of Space & Defense Power Systems: History Webpage :(http://www.ne.doe.gov/space/spacehistory.html , last accessed Oct 2010.
last accessed Oct 2010.
 R. Nelson, A Brief History of Thermophotovoltaic DevelopmentWebpage,(http://www.iop.org/EJ/article/02681242/18/5/301/s30501.html), last accessed Dec 2010.
 H. Sai, H. Yugami, Y. Akiyama, Y. Kanamori, and K. Hane, "Surface micro structured selective emitters for TPV systems", Proc. 28th IEEE Photovoltaic Specialists Conference, pp. 1016-1019, Kissimmee FL,2000.
 W. Horne, M. Morgan, and V. Sundaram, "Integrated Band pass Filter Contacts For Radioisotope Thermophotovoltaic Cells," Proc. of the 31st Intersociety IEEE Energy Conversion Engineering Conference, Volume: 2 , 11-16 Aug.1996
 S. Wojtczuk, P. Colter, G. Charache, and B. Campbell, "production data
On 0.55 eV InGaAs Thermophotovoltaic Cells", Proc. 25th IEEE Photovoltaic Specialists Conference, pp. 77-80, Washington, D.C.
, 1996.  B. Davenport, "Advanced thermophotovoltaic cells modeling, optimized for use in radioisotope thermoelectric generators (RTGs) for Mars and deep space missions," Master's thesis, Naval PostGraduate School
, 2004  F. Incropera and D. DeWitt, Fundamentals of Heat and mass transfer
, Fifth Edition
, John Wiley & Sons
, Inc., New York, 2002.  National renewable energy
Laboratory, Renewable ResourceDataCenter,(http://rredc.nrel.gov/solar/spectra/am 0/NewAM0.xls), last accessed July2010.  SILVACO Data Systems Inc.: Silvaco ATLAS User's Manual (2010).  SOPRA."N & K Database" http://www.sopra-sa.com Accessed (15 june 2010).