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Radiation damage to solar cells

This page is based on the Jet Propulsion Solar Cell Radiation Handbook, Third Edition [Tada et al., 1982].

Table of contents

Radiation effects

The behaviour of solar cells in a radiation environment can be described in terms of the changes in the engineering output parameters of the devices. This approach limits the understanding of the physical changes which occur in the device. Since other environmental factors may need consideration, an understanding of a physical model provides a basis for estimates of the behaviour in a complex environment. In addition, solar arrays of the future will become more complex and may utilise materials which are affected by different aspects of radiation damage. For these reasons, one should be aware of the process by which radiation interacts with matter, and understand the physical models which describe the processes.

The theory of radiation damage

The radiation usually of interest in the study of degradation of materials and devices consists of energetic or fast massive particles (i.e. electrons, protons, neutrons or ions). The origin of these particles may be particle accelerators, the natural space radiation environment, nuclear reactions, or secondary mechanisms such as Compton electrons produced by gamma rays. Because they have mass, energy and possibly charge, these particles or other particles generated by them can interact in several ways with materials. The dominant interactions are:
  1. Inelastic collisions with atomic electrons. Inelastic collisions with bound atomic electrons are usually the predominant mechanism by which an energetic charged particle loses kinetic energy in an absorber. In such collisions, electrons experience a transition to an excited state (excitation) or to an unbound state (ionisation).
  2. Elastic collisions with atomic nuclei. Energetic charged particles may have coulombic reactions with the positive charge of the atomic nucleus through Rutherford scattering. In some cases the amount of energy transferred to the atom will displace it from its position in a crystalline lattice. This energetic displaced atom may in turn undergo similar collisions with other atoms of the material. Energetic particles may also interact directly by a hard sphere collision with the nucleus. The probability of this type of event is usually less than that for Rutherford scattering, except at higher energies. If sufficient energy is transferred to displace an atom from its lattice site, that atom will probably be energetic enough to displace many other atoms.
  3. Inelastic collisions with atomic nuclei. This general category of interactions includes several processes which are important in radiation damage studies. Highly energetic protons undergo inelastic collisions with the atomic nucleus. In this process, the energetic proton interacts with the nucleus and leaves the nucleus in an excited or activated state. The excited nucleus emits energetic nucleons and the recoiling nucleus is displaced from its lattice site. This recoiling nucleus in turn causes more displacements. This process is also referred to as spallation. Collisions between neutrons of thermal energy and nuclei can also be included in this group. However, these interactions are of little importance in solar array degradation.

The major types of radiation damage phenomena in solids which are of interest to the solar array designer are ionisation and atomic displacement. It is important to classify an effect into one of these two categories, if possible, because the general behaviour of each phenomenon has been characterised to a large extent.


Ionisation occurs when orbital electrons are removed from an atom or molecule in gases, liquids, or solids. The measure of the intensity of ionising radiation is the roentgen. This unit is defined by a charge generation of 2.58x10-4 C/kg of air. The measure of the absorbed dose in any material of interest is usually defined in terms of absorbed energy per unit mass. The accepted unit of absorbed dose is the rad (100 erg/g or 0.01 J/kg). The SI unit of absorbed dose is the Gray (Gy), defined to be 1 J/kg.

Through the use of the concept of absorbed dose, various radiation exposures can be reduced to absorbed dose units which reflect the degree of ionisation damage in the material of interest. This concept can be applied to electron, gamma, and X-ray radiation of all energies. For electrons, the absorbed dose may be computed from the incident fluence Phi (in cm-2) as:

Dose (rad) = 1.6x10-8 dE/dx Phi ,

where dE/dx (in MeV cm2 g-1) is the electron stopping power in the material of interest. In this manner, the effects of an exposure to fluxes of trapped electrons of various energies in space can be reduced to an absorbed dose. In general, this practice is also applicable to proton irradiations, with some caution. In some types of materials, the effects of the ionisation caused by heavy particles are confined to the vicinity of the particle track. If homogeneous ionisation is produced by protons in the absorber material, one can convert proton fluences to absorbed doses and sum them with doses from other radiations.

The variations of stopping power and range for electrons and protons of vairous energies can be seen in Figs. 1 and 2. The data presented are for silicon and have been normalised for density. The stopping power and range of a fast particle are not strong functions of the atomic number of the absorber material. For this reason, the data in Figs. 1 and 2 can be used for materials with a similar atomic number with a negligible error.

Stopping power and range curves for electrons in Si
Figure 1. Stopping power and range curves for electrons in Si [Berger and Seltzer, 1966]

Stopping power and range curves for protons in Si
Figure 2. Stopping power and range curves for protons in Si [Janni, 1966]

Radiation may affect solar cell array materials by several ionisation related effects. The reduction of transmittance in solar cell cover glasses is an important effect of ionising radiation. The darkening is caused by the formation of colour centres in glass or oxide materials. The colour centres form when ionising radiation excites an orbital electron to the conduction band. These electrons become trapped by impurity atoms in the oxide to form charged defect complexes which can be relatively stable at room temperature.

Radiation produces many ionisation related effects in organic materials. These changes all result from the production of ions, free electrons, and free radicals. As a result of these actions, transparent polymers ae darkened and crosslinking between main-chain members may drastically alter the mechanical properties.

The use of silicon dioxide as a surface passivation coating and dielectric material in silicon devices results in a wide range of ionisation related radiation effects. The development of trapped charges in the silicon dioxides can cause increased leakage currents, decreased gain, and surface channel development in bipolar transistors and increased threshold voltages in MOS field effect transistors (MOSFETs). Ionising radiation in silicon excites the electrons of the valence band to the conduction band, creating electron-hole pairs in much the same way that carrier pairs are generated by visible light. Although an optical photon of energy equal to or greater than 1.1 eV will create an electron-hole pair, roughly three times this amount of energy must be absorbed from a high energy particle to produce the same carriers.

Atomic displacements

The loss of energy by fast electrons and protons caused by collision processes with the electrons of an absorber or target material accounts for a large fraction of the dissipated energy. For electrons and protons in the energy range 0.1-10 MeV, these electron collisions determine the particle range in an absorber. Despite this fact, a different type of collision process is the basis for the damage which permanently degrades silicon solar cells in the space environment. The basis for this damage is the displacement of silicon atoms from their lattice sites by fast particles in the crystalline absorber. These displaced atoms and their associated vacancies undergo other reactions and finally form stable defects which produce significant changes in the equilibrium carrier concentrations and the minority carrier lifetime.

The displacement of an atom from a lattice site requires a certain minimum energy similar to that of other atomic movements. The energy of sublimation for a silicon atom is 4.9 eV. The energy for the formation of a vacancy in the silicon lattice is 2.3 eV. The displacement of an atom involves the formation of a vacancy, the formation of an interstitial atom and other electronic and phonon losses. It is reasonable to expect that the energy of displacement is several times larger than the energy of formation for a vacancy. Seitz and Koehler [1956] have estimated that the displacement energy is roughly four times the sublimation energy. Electron threshold energies of 145 keV and 125 keV have been reported, with corresponding displacement energies of 12.9 eV and 11.0 eV, respectively. These displacement energies correspond to proton or neutron thresholds of 97.5 eV or 82.5 eV, respectively, in silicon. Since particles below the threshold energies cannot produce displacement damage, the space environment energy spectra are effectively cut off below these values.

For particles above the threshold energy, the probability of an atomic displacement can be described in terms of a displacement cross section. Using this concept, the number of displacements can be estimated as:

Nd = na sigma nu Phi ,

where Nd is the number of displacements per unit volume (cm-3), na the number of atoms per unit volume of absorber (5x1022 cm-3 for silicon), sigma the displacement cross section (cm2), nu the average displacements per primary displacement, and Phi the radiation fluence (cm-2).

Electron displacement damage

The displacement cross sections for fast electrons of various energies can be calculated from the relativistic generalisation of the Rutherford scattering cross section equation [Seitz and Koehler, 1956]. For silicon, the calculated displacement cross section for 1 MeV electrons is about 68x10-24 cm2 and increases only 10% for electron energies of 5 MeV and greater. The electron displaced silicon atom may receive enough energy to in turn displace other silicon atoms. The mechanism for these secondary displacements is Rutherford interactions for silicon atoms of energies greater than 1 MeV and hard sphere collisions for lower energy atoms. The average number of displacements in silicon is 1.53 for a 1 MeV electron [Kinchin and Pease, 1955]. The electron energy variation of the various parameters is shown in Table 1.

The direct result of the radiation is the production of vacant lattice sites (vacancies) and silicon atoms which come to rest in the interstices of the crystal lattice (interstitials). The distribution of vacancies will not be uniform, because the vacancies from secondary displacements will lie relatively close to the associated primary vacancy.

Table 1. Silicon displacement parameters as a function of electron energy
Electron Energy
(10-24 cm2)
sigma nu
(10-24 cm2)
na sigma nu

Proton displacement damage

The production of displacement damage in silicon by energetic protons is considerably different because the displacement cross sections are several orders of magnitude larger than those for fast electrons and vary rapidly with proton energy. The displacement cross section for protons in silicon is [Seitz and Koehler, 1956]:

sigma = 4pi a02 Mp Zp2 ZSi2 ER2 (M E Ed)-1 ,

where a0 is the Bohr radius (5.3x10-9 cm) and ER the Rydberg energy for hydrogen (13.6 eV). For protons of 1 MeV, the cross section in silicon is 3.5x10-20 cm2.

Kinchin and Pease [1955] give the following relationship for the average total number of displaced atoms produced for every primary knock-on including the primary knock-on:

nu = 0.5 [1 + ln(Lambda E/2Ed)] ,


Lambda = 4 M Mp (M + Mp)-2 .

The average number of atomic displacements resulting from such a primary displacement caused by a 1 MeV proton is 4.8, with a corresponding displacement rate of 8500 cm-1 in silicon. The range of a 1 MeV proton in silicon is only 17.5x10-6 m, therefore its energy and displacement rate will change rapidly after it enters the silicon crystal. The displacement rate is proportional to (lnE)/E for protons with energies between 1 and 10 MeV. The defect energy levels in proton irradiated silicon are in some respects similar to those previously discussed for electron irradiated silicon. The proton damage, however, is highly inhomogeneous because the numerous secondary displacements occur near the site of the primary displacement.

In addition to the displacement rates discussed above, Kinchin and Pease [1955] have computed the total number of displacements Ntd(E) a projectile will produce in a material as it enters with energy E and comes to rest in the material. For the specific case of protons in silicon their formula reduces to:

Ntd = [P(106 E - 567.3) + 283.6] / 12.9,


P = 6.81x10-5 [1 + ln(5162E)] / ln(12.82E)

and E is the proton energy in MeV. This expression is valid for E > 0.1 MeV.

Neutron displacement damage

Neutron displacement damage in silicon is characterised by two important differences. The silicon displacement cross section for a 1 MeV neutron is 2.4x10-24 cm2. This value is well below those for 1 MeV protons and 1 MeV electrons. For this reason, the number of primary displaced silicon atoms will be relatively small. The second difference involves the amount of energy transferred to the displaced silicon atom by the neutron. Since the 1 MeV neutron-silicon interaction is a hard sphere rather than coulombic collision, an average of about 70 keV is transferred to the recoiling silicon atoms. The subsequent secondary collisions between silicon atoms will displace about 1500 silicon atoms. This displacement damage will be clustered near the site of the primary displacement. Theoretical models of the neutron damage indicate that the high concentration of electrically active defects in the cluster causes the centre of the cluster to behave as intrinsic silicon. This intrinsic silicon core is separated from the bulk silicon by a layer of space charge. Extensions of this model have been used to explain the majority carrier removal and minority carrier recombination behaviour of neutron irradiated silicon.

Effects of displacement defects

The main importance of the displacement defects produced by the irradiation of silicon solar cells is in their effect on the minority carrier lifetime of the silicon. In particular, the lifetime in the bulk p-type of an n/p solar cell is the major radiation sensitive parameter. Since minority carrier lifetimes are inversely proportional to the recombination rates, the reciprocal lifetime contributions caused by various sets of recombination centres can be added to determine the inverse of the lifetime as follows:

tau-1 = tau0-1 + taue-1 + taup-1 + ...

where tau is the minority carrier lifetime, tau0 the minority carrier lifetime before irradiation, taue the minority carrier lifetime due to electron irradiation, and taup the minority carrier lifetime due to proton irradiation.

One of the most commonly used analytical tools for the determination of the particle type and energy dependence of degradation in silicon solar cells has been developed from the the basic relationship for lifetime degradation:

tau-1 = tau0-1 + Ktau Phi ,

where tau is the final minority carrier lifetime, tau0 the initial minority carrier lifetime, and Ktau the damage coefficient (lifetime). Minority carrier diffusion length is a more applicable and more easily determined parameter for solar cell analysis than minority carrier lifetime. Using L2 = D tau, the above expression becomes:

L-2 = L0-2 + KL Phi ,

where L is the final minority carrier diffusion length, L0 the initial minority carrier diffusion length, and KL the damage coefficient (diffusion length), with KL = Ktau/D. When the fluence is sufficiently high so that L<<L0, we have:

KL = L-2 Phi .

If a plot of lnL exhibits a -0.5 slope, the damage coefficient KL can be used to uniquely define the particle type and energy dependence of silicon solar cell degradation.

The minority carrier lifetime or diffusion length in an irradiated solar cell may be a function of the concentration of excess or non-equilibrium minority carriers present in the semiconductor. In solar cells, this behaviour is referred to as injection level dependence. This behaviour is usually associated with solar cells damaged by high energy protons or neutrons.

Theory of silicon solar cell damage

The basic solar cell equations can be used to describe the changes which occur during irradiation. This method would require data regarding the changes in the light generated current, series resistance, shunt resistance, and the basic diode parameters of saturation current and diode quality factor. Although such a method would be a logical analysis, most investigations have not reported enough data to determine the variations in the above parameters. The usual practice in the study of solar cell damage has been to reduce the experimental data in terms of changes in the cell short circuit current (Isc), open circuit voltage (Voc), and maximum power (Pmax).

It is also possible to characterise solar cell damage in terms of the changes in the minority carrier diffusion length. Since the diffusion length can be measured experimentally and is a measure of the amount of displacement damage in the base of the solar cell, this method has been widely used. There are several practical and fundamental limitations to this scheme. The most serious limitations involve the evaluation of low energy proton damage in terms of diffusion length. Very low energy protons do considerable displacement damage within the junction space charge region of a solar cell. This nonuniform damage increases the diode saturation current (I0) and quality factor (n) by mechanisms which are not related to minority carrier diffusion. This damage can cause serious reduction in solar cell Voc without changing the cell diffusion length. In addition, the relation between diffusion length and the solar cell output parameters is not well defined, diffusion length is more difficult to measure than cell output parameters (particularly in the case of proton irradiated cells), and accurate measurement of diffusion length of thin or drift field cells is extremely difficult. Because of these problems, methods have been evolved to evaluate solar cell radiation effects in terms of common engineering output parameters. Experience has shown that the variation of common solar cell output parameters during irradiation can be described as shown for Isc in the following case:

Isc = Isc0 - C log (1 + Phi / Phix) ,

where Phix represents the radiation fluence at which Isc starts to change to a linear function of the logarithm of the fluence. The constant C represents the decrease in Isc per decade in radiation fluence in the logarithmic region. Although the above relationship is empirical, there is some theoretical justification for the expression. The relation between the solar cell short circuit current and the diffusion length is:

Isc = A lnL + B .

The constants A and B are dependent upon the spectral content and intensity of the light source used to measure Isc. Tada [1966] has shown that the above expression is theoretically valid over a wide range of diffusion lengths for tungsten illumination and to a lesser range under solar illumination. The diffusion length equation of Sect. can be transformed as follows:

L = (KL Phi + L0-2)-0.5

and substituted in the second equation for Isc. The resulting expression has the same form as the first equation for Isc.

The variation of solar cell Voc during irradiation may also be empirically characterised by an expression similar to the first equation for Isc:

Voc = Voc0 - C' log (1 + Phi / Phix) .

In general, the open circuit voltage of a silicon solar cell can be represented as:

Voc = kT/q ln (1 + Isc / I0) .

In using this expression, it is assumed that the saturation current I0 is dominated by the diffusion component. In such cases, the saturation current density is given by:

J0 = q Dn np0 / Ln

and, using the above equation for L, the following expression for the saturation current as a function of radiation fluence is obtained:

I0 = q Dn np S (KL Phi + L0-2)0.5 ,

where S is the cell area. Substituting the equations for Isc and I0 into the equation for Voc, the following expression is obtained:

Voc = kT/q ln {[B - A/2 ln(KLPhi+L0-2)] / [q Dn np (KLPhi+L0-2)0.5]}

The radiation fluence Phi appears twice in the above expression. The fluence term in the numerator will have a much lesser effect on Voc than the term in the denominator because it varies as the logarithm of the fluence rather than as the square root of the fluence. It appears therefore that the Voc variation with radiation fluence is dominated by the denominator and can be approximated by the above equation for Voc.

The maximum power of a solar cell can be represented as the product of Isc, Voc, and a constant:

Pmax = F Isc Voc ,

where F is the form (or fill) factor. The fill factor is relatively insensitive to electron radiation which penetrates uniformly through a solar cell. In this case, the variation of Pmax with irradiation is the same as that for the product of Isc and Voc. The equations given above for Isc and Voc can be substituted into the equation for Pmax and the resulting expression approaches the form of:

Pmax = Pmax0 - C'' log(1 + Phi/Phix) .

Expressions of this form are found to closely describe the variation of Pmax during irradiation.

The concept of damage equivalence

The wide range of electron and proton energies present in the space environment necessitates some method of describing the effects of various types of radiation in terms of a radiation environment which can be produced under laboratory conditions. Since the changes in most solar cell parameters due to irradiation are in some way related to the minority carrier diffusion length, it is possible to determine an equivalent damage based upon this parameter. In Fig. 3, the diffusion length changes are shown for 10 ohm cm, n/p silicon solar cells which have been subjected to several different types of radiation. The results are described by the equation for L where the constant KL is dependent upon the radiation type.

Variation of solar cell diffusion length
Figure 3. Variation of solar cell diffusion length with fluence for various radiations

The concept of damage equivalence can alternatively be based on common solar cell parameters. The variation of short circuit current density for 10 ohm-cm n/P solar cells irradiated in various environments is shown in Fig. 4. The Isc variation in each environment is described by the equation for Isc. In this case, two constants, C and Phix, are required to describe the changes in Isc. Experience has shown that the constant C, under solar illumination, does not vary greatly for different radiation environments. For electron irradiations in the 1 MeV and greater range, C is approximately 4.5 to 5.5 mA cm-2-decade. For proton and neutron irradiations, C approaches 6 to 7 mA cm-2 decade-1. For solar cells with the same starting Isc, the constant Phix is a measure of the damage effectiveness of different radiation environments. The constant Phix for a particular radiation can be determined graphically on a semi-log plot at the intersection of the starting Isc and the extrapolation of the linear degradation region.

[Variation of solar cell short circuit current]
Figure 4. Variation of solar cell short circuit current density with fluence for various radiations

Since the value of Phix is dependent upon the starting Isc, it is not a good practical measure for relative damage effectiveness. It has been the practice to define an arbitrary constant referred to as the critical fluence Phic. One method of defining this value is that fluence which degrades a solar cell parameter 25% below its unirradiated state. Such a parameter is valid only when comparing cells with similar initial parameters. To eliminate this problem, critical fluence may be defined alternatively as that fluence which will degrade a cell parameter to a certain value.

By use of the critical fluence or the diffusion length damage coefficient, it is possible to construct a model in which the various components of a combined radiation environment can be described in terms of a damage equivalent fluence of a selected mono-energetic particle. 1 MeV Electrons are a common and significant component of space radiation and can be produced conveniently in a test environment. For this reason, 1 MeV electron fluence has been used as a basis of the damage equivalent fluences which describe silicon solar cell degradation.

The use of the damage equivalent fluence scheme involves two separate problems. The first problem is to adequately describe the degradation of an unshielded silicon solar cell under 1 MeV electron irradiation under laboratory conditions, i.e. normal incidence. The second problem is to reduce the effect of the space radiation environment (i.e. continuous energy spectra of electrons and protons, isotropic incidence) on a shielded silicon solar cell to a damage equivalent fluence of 1 MeV electrons under laboratory conditions.

Effect of electron energy on solar cell degradation

The concept of damage equivalent 1 MeV electron fluence requires some method of evaluating the damage effectiveness of electrons of various energies. This effectiveness can be measured by the diffusion length damage constant or solar cell critical fluence for various electron energies. The short circuit current is directly related to the minority carrier diffusion length in the base region. Experimental data show that the relative variations of KL and Phic-1 with electron energy are identical. The relative variations of both parameters with cell base resistivity are also identical. On the basis of experimental data, one can therefore define a relative damage effectiveness for each electron energy which will be a measure of the ratio of that electron fluence at a given energy to the 1 MeV electron fluence necessary to degrade an n/p solar cell to the same output parameter value. For instance, if a given 10 MeV electron fluence degrades a solar cell to a certain state of damage, then a 1 MeV electron fluence 16.5 times that of the 10 MeV electron fluence would be required to degrade the same cell to the same state.

Effect of proton energy on solar cell degradation

The concept of damage equivalent 1 MeV electron fluence can be extended to the effects of proton irradiation. The problem is more complex in the proton case, because the range of protons below 5 MeV is less than the usual solar cell thickness. For this reason, low energy protons produce non-uniform damage. This situation is further complicated by the fact that the damage produced per unit path length increases as the proton energy decreases. As a result, when a low energy proton is stopped in a solar cell, a large amount of damage is concentrated at the end of the proton track.

When radiation damage is uniform throughout a solar cell, the relative effectiveness of various energy particles is the same when measured by the diffusion length damage coefficients, or critical fluences determined by cell parameters such as Isc, Voc, or Pmax. In the case of protons with energies greater than 5 MeV, the damage to solar cells is relatively uniform. In this high energy range, the general concept of equivalency is directly applicable. At lower proton energies, the general concept of equivalency is not applicable; however, it can be used in a restricted manner as discussed below.

The degradation of n/p solar cells irradiated with protons of energies below 3 MeV is complex because of the nonuniform nature of the damage. Protons in the energy range from 1.5 to 3 MeV produce a maximum in relative radiation damage in silicon solar cells. The relative damage to silicon solar cell Voc and Pmax due to low energy protons is more severe than that exhibited by Isc.

Proton damage in silicon solar cells can be normalised to the damage produced by protons of one energy. The proton energy employed for normalisation of relative damage should be close to that producing maximum damage in space environments, produce relatively uniform damage, and be available for laboratory evaluations. The use of 10 MeV proton damage is based on a compromise of the above requirements. The results of several studies of proton damage have been summarised in terms of relative silicon solar cell damage as a function of proton energy. These relative damage results, normalised to 10 MeV proton damage, are shown in Fig. 5. The results in Fig. 5 have been shown to hold for both 10 ohm cm and 2 ohm cm solar cells at proton energies greater than 10 MeV.

[Relative damage coefficients]
Figure 5. Relative damage coefficients for proton-irradiated n/p solar cells

It is emphasized that the results in Fig. 5 are obtained by normal incidence laboratory irradiation of solar cells from the front side. If similar data were prepared for normal incidence rear irradiations, the result would be similar for proton energies above 10 MeV. For cells of 200 to 300 microns thickness, the effects due to rear incidence protons with energies below 10 MeV would be much lower than shown in Fig. 5. The lower effectiveness occurs because rear incident low energy protons have insufficient range in silicon to cause atomic displacements in the active region of the solar cell. However, 2 MeV protons have sufficient energy to reach the junction through 50 micron thick cells. Since the much higher values of the Voc and Pmax damage coefficients for low proton energies are due to the effects they produce near the junction, it should be pointed out that these higher values should only be used when the protons are incident on the front surface of the cells. When considering low energy protons incident on the rear cell surface, such as for the case of solar panels using lightweight substrates, only the Isc damage coefficients should be used.

The variation of solar cell output parameters with 10 MeV proton fluence is described by the equations for Isc, Voc, and Pmax in much the same way as is done for 1 MeV electrons. The values of the constants C, C', and C'' tend to be somewhat greater than those found for 1 MeV electron irradiation. These values determine the decrease in solar cell output parameter per decade of radiation fluence. The fact that these constants are somewhat different for electron and proton irradiation indicates that the concept of equivalency between the different types of radiation has limitations and is basically an approximation. This equivalence is further discussed below.

Junction effects of low energy protons

In addition to the low energy proton effects on unshielded cells discussed above, there are two aspects of low energy proton damage to be considered. These involve the effects of low energy protons on small unshielded gap areas on the front of solar cells and on unshielded backs of solar cells.

When the ATS-1 and Intelsat II-F4 satellites suddenly exhibited degradations in power output of the order of 20% in weeks to a month after launch, the importance of low energy proton damage was dramatically demonstrated. Subsequent efforts related this anomalous degradation to the bombardment of narrow exposed surface areas of the solar cells by the intense low energy proton fluence existing at geosynchronous altitude. The exposed areas resulted from slightly undersized or improperly applied coverglasses which exposed up to a 0.038 cm (15 mils) strip of solar cell surface. The high-intensity low energy proton fluence, though incapable of penetrating the solar cell to a depth of more than a few microns, was able to produce junction damage which would shunt the power-producing capability of the whole device. Exposed strips as narrow as 0.005 cm (2 mils) were sufficient to drastically alter the device's power-producing capability. The absence of this effect in earlier solar array systems was attributed to the use of a cell-shingling type panel construction and the presence of overlapping adhesive.

Low energy proton irradiation clearly has an inordinately greater effect upon solar cell Voc and Pmax as compared to similar irradiations with electrons or higher energy protons. Consequently, array manufacturers have taken measures to cover all areas of the silicon cell front surface with a coverglas and fill any gaps between the cell and coverglass with adhesive.

The changes caused by the irradiation of small unshielded areas of solar cells with low energy protons can be explained in terms of solar cell theory. It was previously mentioned that the range of low energy protons in silicon is limited to less than the cell thickness. Particles that do not penetrate the cell produce defects only to their depth of penetration. This limited penetration results in unusual effects in the case of protons because lower-energy protons produce more displacements per unit path length. The results of this behaviour are shown in Fig. 6. In this figure, the calculated number of displaced silicon atoms per unit proton path is plotted as a function of depth in silicon for a 3 MeV proton (range 92.7 microns). It can be seen that the damage rises rapidly to a maximum near the end of the proton track. Every proton which is stopped in the silicon produces such a damage peak at the end of its track. Protons which enter the silicon with energies of 0.5 MeV or less produce damage which is concentrated within a few microns of the cell surface. The space charge region of a modern cell extends from 0.4 to 1 micron below the cell surface. For this reason, low energy proton displacement damage is concentrated in the junction region.

[Atomic displacements]
Figure 6. Atomic displacements as a function of depth for a 3 MeV proton in silicon

The entire solar cell junction can be considered to be an array of small parallel diodes. Damage to only a small portion of this parallel diode array results in an increased effective leakage or saturation current for the entire array. The saturation current due to generation-recombination in the space charge region increases linearly as the carrier lifetime decreases (i.e. displacement damage increases) in the space charge region. The increased leakage current of a solar cell reduces the cell Voc because of the relationship of Voc and the junction leakage current. Since cell diode forward current is increased at all voltages, the current available to an external load decreases, and so Pmax will also decrease. Since solar cells are usually operated near the maximum power point, such changes have grave implications on in-flight performance.

The usage of body-mounted solar cells on spinning satellites provides a large measure of back shielding to a solar array. Oriented silicon solar panels with minimal back shielding can be degraded by low energy proton back side irradiation through carrier removal effects. The use of thin soldered back contacts or other minimal back shielding should greatly reduce these effects.

Annealing of irradiated solar cells

Annealing and reverse annealing of irradiated solar cells as a function of temperature has received considerable study. Though the situation is quite complex, it can be generally stated that irradiated conventional silicon solar cells cannot be significantly annealed at temperatures below 200° C, which is considered a practical limit for space applications. Significant annealing of conventional silicon solar cells irradiated with electrons or protons typically occurs in the 200° to 400° C range.

Of more practical importance is the fact that some ambient annealing of charged particle radiation damage exists. In the laboratory, the radiation exposure rate is usually many orders of magnitude greater than natural space radiation rates. In space, the damage and annealing processes occur simultaneously, with the annealing rate much closer to the damage rate than in the laboratory. For laboratory electron irradiation, ambient annealing as high as 10% in short circuit current has been observed in a few days to a month, predominantly in 10 ohm cm cells. For laboratory proton irradiation, ambient annealing of as high as 20% of short circuit current has been observed after 22 months.

Radiation effects on shielding materials

The degradation due to radiation effects on solar cell coverglass material in space is difficult to assess. The different radiation components of the environment act individually and synergistically on the elements of the shielding material and also cause changes in the interaction of shielding elements.

The radiation effects observed in cover materials can be characterised as ionisation damage rather than displacement damage. In general, ionisation effects are usually dependent upon the absorbed dose and to that degree are independent of particle type or energy. Some exceptions to this rule occur in the case of highly charged massive particles. In such cases, the ionisation effects may be concentrated along the particle track rather than uniformly distributed. It is reasonable to assume that the ionisation damage produced in cover materials by space electrons and protons is related to the total absorbed dose. This assumption allows the various radiation components of the space environment to be reduced to a total dose, without a laborious detemrination of degradation constants for each energy and particle. It also allows the use of experimental data from a single ionising environment such as 1 MeV electrons.

The most significant radiation effects in cover materials involve changes in the transmission of light in the visible and near infrared region. These data can be reported by means of so-called 'wide-band' transmission loss. In this method, solar cell short circuit currents are measured under sun simulated conditions, with coverglasses attached. The coverglasses are attached with a thin liquid film with an index of refraction similar to that of silicone adhesive. The 'wide-band' transmittance is defined as the solar cell Isc with an irradiated coverglass in place divided by the solar cell Isc with the unirradiated coverglass in place. Such measurements are influenced by solar cell spectral response. Results determined with unirradiated solar cells will not be representative of those for irradiated solar cells. This error is probably negligible compared to the uncertainty of the available experimental data.

Since the 'wide-band' transmission loss is a measure of the loss light transmitted, it directly affects the light generated current and likewise the short circuit current. It is desirable to use the 'wide-band' transmission data to estimate the change in solar cell Pmax. As seen above, Pmax is proportional to the product of Isc and Voc. Because Voc is proportional to ln Isc, the following relation can be developed to estimate the change in Pmax due to coverglass darkening from transmission data:

Pmax/Pmax0 = T [ln(T Isc) / ln Isc]

where Pmax/Pmax0 is the fractional change in Pmax, T the 'wide-band' transmission of irradiated coverglass, and Isc the short circuit current with unirradiated coverglass.

To aid in the estimation of solar array losses due to reduced transmission from radiation effects in coverglass materials, data relating transmittance to absorbed dose is required. In Fig. 7, 'wide-band' transmittance is shown for various absorbed doses. The absorbed doses were produced by 1 MeV electron irradiations in a room temperature, air environment which included no ultraviolet illumination. This electron radiation is sufficiently penetrating to produce a relatively uniform dose through the entire coverglass, coating, and filter. The Pmax/Pmax0 data shown in Fig. 7 were calculated from the 'wide-band' transmittance value by use of the equation above. The data include 0.0152 cm (0.006 in) 7940 fused silica and 0211 Microsheet coverglass with antireflecting coating and blue filter. It has been established that Corning 7940 fused silica exhibits little or no radiation darkening in the visible region. Since the transmission loss for 7940 coverglass must be assumed to be due to changes in the filter, the data can also be used for thicker coverglasses. For thicker 0211 Microsheet coverglass, the data in Fig. 7 cannot be used.

[Variation of coverglass transmittance]
Figure 7. Variation of coverglass transmittance with absorbed dose

Relative damage coefficients for space radiation

A large volume of experimental data is available for normal incidence irradiation of unshielded solar cells. These data are not directly applicable in the prediction of space radiation effects because of the omnidirectional nature of the space radiation and because of the energy degrading effects of coverglass shielding. The damage effectiveness of space radiation is calculated relative to normal incidence 1 MeV electrons and 10 MeV protons on unshielded solar cells. This concept of the damage effectiveness or relative damage constant D is an extension of the previously discussed concept of equivalent fluence. It will allow the reduction of all components of the space radiation to an equivalent laboratory (normal incidence, mono-energetic) irradiation. In this way, laboratory data can be used to predict the behaviour of shielded solar arrays in space. In addition, the similar problem of calculating energy deposition at various depths in shielding will be discussed.

Geometrical aspects of radiation fluences

The expression for the effectiveness or relative damage constant, weighted for all angular components of an omnidirectional mono-energetic flux, and assuming infinite back shielding, is:

where D(E,t) is the relative damage coefficient of omnidirectional radiation particles with energy E, relative to unidirectional 1 MeV electrons or 10 MeV protons for a cell protected by a coverglass of thickness t; D(E0,theta) is the damage coefficient of unidirectional radiation particles with angle of incidence theta and energy E0 relative to unidirectional 1 MeV electrons or 10 MeV protons; E0 is the proton energy as it enters the solar cell (when t=0, E=E0). The quantity 2pi sintheta dtheta is an increment of solid angle. The above equation must be further modified to reflect the energy degradation in the coverglass shields used on silicon solar cells.

Effect of shielding on radiation

A common solar cell configuration involves infinite back shielding and an optically transparent finite shield covering the front surface of the cell. The assumption of infinite back shielding is not always valid, and the differences in both shield thickness and material require separate treatments for front and back radiation. If an omnidirectional flux of radiation particles with energy E is incident on a solar cell shield of thickness t, the particles not stopped in the shielding will exit the shielding (i.e. enter the silicon) with energy E0, which is a strong function of the angle of incidence because of varying path length in the shield. The particle track length in the shield is equal to t/costheta. By subtracting the particle track length in the shield from the range R(E) of the particle in the shield material, one can determine the residual range R(E0) of a particle with energy E0:

E0(E,theta,t) = R-1 [R(E) - t / costheta] ,

where R-1 is a convenient form used to represent an inverse function of the range-energy relation R.

Electron space radiation effects

The evaluation of D(E,theta) is necessary to complete the integration of the equation for D(E,t). Data regarding the experimental evaluation of the relative damage coefficient for n/p silicon solar cells D(E) for various electron energies at normal incidence is presented in Fig. 8. Electrons in the MeV energy range penetrate silicon solar cells thoroughly enough that the damage produced by an electron can be considered uniform along its track. For this reason, the amount of displacement damage produced by a high energy electron is proportional to the total track length produced in the cell. The length of an individual electron track in a solar cell is proportional to sectheta, hence:

D(E0,theta) = D(E0,0) / costheta .

The number of electrons intercepted by the cell is proportional to its project area normal to the direction of the radiation [the costheta factor in the equation for D(E,t)]. The net result of these two factors is a cancellation of the cos terms so that the damage induced in the solar cell is independent of the angle of incidence theta.

[Relative damage coefficients]
Figure 8. Relative damage coefficients for space electron irradiation of shielded n/p silicon solar cells

The equation for D(E,t) for the case of electron space radiation can be modified as follows:

This equation can be evaluated with the aid of the equation for E0 and the data in Fig. 8 to evaluate D(E0,0). The results are also plotted in Fig. 8. Because of electron straggling, there might be some question regarding the suitability of the equation for E0. However, use of alternate Monte Carlo methods yielded results identical to those in Fig. 8.

The evaluation of ionisation dose in solar array materials due to omnidirectional space electron fluences is analogous to that just completed for silicon solar cell degradation. In the case of absorbed dose, the energy deposited by the radiation in the shielding is determined in terms of rads. To evaluate this energy deposition at various depths in the shielding, an expression similar to the equation for D(E,t) can be used. This equation is modified to the extent that the electron stopping power together with the flux-to-dose conversion factor (see the dose equation above)

1.6x10-8 (1/rho dE/dx)collision

replaces D(E0,theta), and D(E,t) becomes the absorbed dose per unit fluence. The results of this integration are shown in Fig. 9.

[Absorbed dose]
Figure 9. Absorbed dose per unit fluence of space electrons for various depths in planar fused silica shielding

The data of Fig. 9 may be used to estimate the energy deposition in coverglasses and their subsequent darkening. The data must be used with caution and somewhat differently than the plotted solar cell damage coefficient data. For example, an omnidirectional fluence of 0.5 MeV electrons incident on 0.152 cm (0.06 in) thick coverglass material shows no energy deposition at a depth of 0.152 cm. This does not mean, however, that there is no energy deposition in this thick coverglass. Rather, there is a relatively constant energy deposition to a depth of approximately 0.0764 cm (0.030 in) in the glass and it will be darkened fully as much as though it were only 0.0764 cm thick. Thus, for irradiation by monoenergetic electrons, one has a coverglass which is either totally exposed or exposed to some depth relatively uniformly, and a corresponding transmission loss can be easily determined from existing experimental data. In an actual space application, however, the data in Fig. 9 has to be integrated with the expected electron fluence-energy spectrum to determine the actual dose-depth profile in the coverglass. For typical trapped eletron spectra, this integration will produce a dose-depth profile in which the absorbed dose decreases monotonically through the thickness of the coverglass. If this profile shows that sufficient exposure over a significant depth has occurred, an average energy deposition over that depth may also be estimated. This value may then be used in conjunction with the curves in Fig. 7 to estimate the transmission loss.

Proton space radiation effects

For proton space radiation, the evaluation of the equation for D(E,t) is more complex than for electrons. Two problems arise in the treatment of space protons with energies less than about 10 MeV, because of their limited penetration and increased damage production. One problem exists because the relative damage constants based on silicon solar cell Isc, Voc, and Pmax are different and diverge at low proton energies. The second problem is that low energy proton damage has been experimentally characterised only for normal incidence irradiation, and basic considerations indicate that the damage is a strong function of the angle of incidence. The normal incidence proton coefficients for energies of 10 MeV and greater can be assumed to be independent of the angle of radiation incidence for the same reasons discussed for electron irradiation.

The physical distribution of low energy proton damage was discussed above. The most significant aspect of the low energy proton damage is the fact that most of the displacements are produced at the end of the proton track, as illustrated in Fig. 6. The high damage concentration near the end of the proton track allows the construction of a simple damage model for the prediction of the effect of angle of incidence on low energy proton damage in silicon solar cells. It is assumed that the effect of a low energy proton, of arbitrary angle of incidence and energy, is roughly equal to that of a normally incident proton with a range equal to the perpendicular penetration of the non-normally incident proton. To partially correct the inaccuracies of this proposed model, a factor is employed which relates the ratio of the total displacements produced by the non-normally incident proton to those of a normally incident proton which would penetrate to the same depth in the cell. The total number of displacements may be computed using the Kinchin and Pease [1955] model as discussed above. The low energy proton relative damage coefficient given by the above model can be expressed as follows:

D(E0,theta) = D(En,0) Ntd(E0) / Ntd(En) ,

where D(E0,theta) is the relative damage coefficient for protons entering a silicon solar cell with energy E0 at an angle theta; D(En,0) is the relative damage coefficient for a proton of normal incidence (theta=0) with energy En [range equal to R(E0) costheta]; Ntd(E0) the total number of silicon displacements created by a proton entering the silicon with energy E0; costheta the projected cell area; En = R-1[R(E0)costheta]; E0 the proton energy as it emerges from the coverglass and enters the solar cell.

When the range of a proton of energy E0 incident on a solar cell at angle theta exceeds (cell thickness)/costheta, the proton will penetrate the cell. This case is entirely analogous to the case previously discussed for high energy electrons so that:

D(E0,theta) = D(E0,0) / costheta .

The two equations above allow the evaluation of the equation for infinite backshielding as follows:

where thetap is the angle of incidence for which a proton of energy E will just penetrate both the coverglass and the solar cell.

The first term in this equation represents the case when the proton completely penetrates the coverglass and the solar cell, while the second term applies when the proton penetrates the coverglass but stops in the cell. This integration has been done using the D(E0,0) values shown in Fig. 5. Separate integrations were done for D(E0,0) values based on Isc and on Voc, Pmax. D(E,t) Values calculated by the equation above unfortunately are a function of solar cell thickness. However, evaluation of this equation for cell thicknesses ranging from 0.0457 cm (0.018 in) to 0.005 cm (0.002 in) has shown that the dependence on cell thickness is very slight, and for practical purposes the results can be considered independent of cell thickness. The results of the numerical integrations for several coverglass thicknesses are shown in Figs. 10 and 11.

[Relative damage coefficients]
Figure 10. Relative damage coefficients for space proton irradiation of shielded n/p silicon solar cells (based on Isc)

[Relative damage coefficients]
Figure 11. Relative damage coefficients for space proton irradiation of shielded n/p silicon solar cells (based on Pmax or Voc)

The values of relative damage constants for omnidirectional fluences of protons on shielded solar cells allow a space proton environment to be reduced to an equivalent fluence of normally incident 10 MeV protons on unshielded silicon solar cells. Experimental studies of silicon solar cells have indicated that a fluence of normally incident 10 MeV protons produces damage that can be approximated by a fluence of 1 MeV electrons, which is 3000 times that of the 10 MeV proton fluence.

The evaluation of the absorbed dose in shielding materials due to space protons requires an analysis similar to that for space electrons. For this evaluation an expression similar to the equation for D(E,t) is used. The quantity D(E0,0) is replaced by the stopping power times the flux-to-dose conversion factor for protons of energy E0, and the quantity D(E,t) becomes the absorbed dose per incident omnidirectional flux proton of energy E at shielding depth t. The results of this integration for several shielding thicknesses of fused quartz are shown in Fig. 12. The same cautions discussed above regarding the use of electron dose calculations also apply here.

[Absorbed dose]
Figure 12. Absorbed dose per unit fluence of space protons for various depths in planar fused silica shielding

Solar array degradation calculations

The methods for estimating solar cell degradation in space are based on the techniques described by Brown et al. [1963] and Tada [1973ab]. In summary, the omnidirectional space radiation is converted to a damage equivalent unidirectional fluence at a normalised energy and in terms of a specific radiation particle. This equivalent fluence will produce the same damage as that produced by omnidirectional space radiation considered if the relative damage coefficient (RDC) is properly defined to allow the conversion. When the equivalent fluence is determined for a given space environment, the parameter degradation can be evaluated in the laboratory by irradiating the solar cell with the calculated fluence level of unidirectional normally incident flux. The equivalent fluence is normally expressed in terms of 1 MeV electrons or 10 MeV protons. In the presence of a cover shield, angular dependence of both effective shield thickness and damage effectiveness (or stopping power for dose calculations) is integrated over 2pi for a given energy, assuming semi-infinite planar geometry. As a result, the RDC for a given shield thickness is computed only once. Subsequent equivalent fluence calculations simply involve an integration of the omnidirectional fluence times the appropriate damage coefficients as discussed below.

The three basic input elements necessary to perform degradation calculations are:

  1. degradation data for solar cells under normal incidence 1 MeV electron irradiation;
  2. effective relative damage coefficients for omnidirectional space electrons and protons of various energies for solar cells with various coverglass thicknesses;
  3. space radiation environment data for the orbit of interest.

General procedure, equivalent fluence

The effective relative damage coefficients allow the conversion of various energy spectra of space electrons and protons into equivalent fluences. The equivalent fluences are based on normal-incidence monoenergetic irradiations for which the degradations of the solar cells of interest are characterised. The process of weighting an integral energy spectrum of electrons can be described as follows:

Phi1MeV e = Sum [Phi(>E) - Phi(>E+Delta E)] D(E,t) ,

where Phi1MeV e is the damage equivalent 1 MeV electron fluence, Phi(>E) - Phi(>E+Delta E) the isotropic particle fluence in the energy range [E,E+Delta E] (difference spectrum), and D(E,t) the relative damage coefficient for isotropic fluences of energy E incident on solar cells shielded by coverglasses of thickness t.

This equation can also be used for space protons with the exception that D(E,t) values for protons are based on 10 MeV proton fluences rather than 1 MeV electrons. The calculated equivalent fluence will therefore be a damage equivalent 10 MeV proton fluence. The equivalent 10 MeV proton fluence can be converted to equivalent 1 MeV electron fluence as follows:

Phi1MeV e = 3000 Phi10MeV p .

This relationship is an approximation which must be made for the purpose of combining electron and proton damage. The differences between electron and proton degradation were discussed above. Since the slope of the degradation curve (the constant C in the equation for Isc) is different for 1 MeV electron and 10 MeV proton irradiations, the constant in the equation above will differ depending on the level of degraded cell output at which this constant is determined. A value of 3000 is indicated when cell output parameters are degraded by 25%. In cases when the cell degradation is entirely dominated by proton damage, the cell degradation could be estimated more accurately by calculating the equivalent 10 MeV proton fluence and using 10 MeV proton cell damage data, than by using the equivalent 1 MeV electron fluence and electron data.

An additional problem arises in calculating equivalent fluences for proton environments. The results shown in Figs. 10 and 11 reveal that different values of D(E,t) for proton irradiation are found when this damage constant is based on cell Isc or Pmax and Voc. The Pmax, Voc damage coefficients are higher in the low energy region, which accounts for the much higher damage produced in these parameters by low energy protons. This differs from the results of electron irradiation where one value of D(E,t) describes the behaviour of all cell output parameters. Because of the two sets of D(E,t) values for proton irradiation, two different equivalent 10 MeV proton fluences must be considered: one will describe the variation of solar cell Pmax and Voc, the other the variation of Isc.

The values of D(E,t) have been calculated assuming infinite back shielding. Although this condition is often approached by the body-mounted solar arrays of spinning spacecraft, it is not generally true. The designer must also evaluate the contribution of equivalent fluence resulting from radiation incident on the back side of the solar cells. The result is a front and a back component of equivalent fluence. A question arises as to the values of D(E,t) to be used for back irradiations. In the case of trapped space electron irradiation, it is reasonable to use the same values of D(E,t) for both front and back irradiations. The only problem in this case is to convert the backshielding of the panels, satellite, etc., to an equivalent planar shielding.

The case for space protons is considerably more compelex because of the non-penetrating nature of low energy protons. Low-energy proton irradiation from the rear not only increases bulk resistivity, thereby decreasing the fill factor, but also greatly changes the forward dark I-V characteristic curves. These phenomena, peculiar to rear irradiation, must be considered and included in the evaluation of D(E,t). In case D(E,t) cannot be properly evaluated, the only alternative is to use the front irradiation data, assuming that both front and back irradiations produce the same results as long as all protons penetrate through the junction. However, the use of the Pmax, Voc coefficients, which were designed to account for the high junction damage by low energy protons, is not considered proper for protons incident on the rear cell surface. Therefore, only the Isc proton damage coefficients are used for rear incidence protons. To allow for the self-shielding effect for cells irradiated with protons from the rear, the back contact solder thickness (approximately 0.01 to 0.08 mm) plus the thickness of the substrate and the substrate adhesive should be included in the total back shielding.

Effect of reduced light transmission on solar cell response

To use coverglass darkening data, a procedure is necessary to evaluate the absorbed dose produced by the various radiation components of the space environment. The procedure is similar to that used for equivalent fluence, with the exception that the absorbed dose is a point function and therefore varies with depth in the cover material. To calculate the absorbed dose at a particular depth in the cover materials, the following expression is used:

Dose(d) = Sum [Phi(>E) - Phi(>E+Delta E)] I(E,d) ,

where Dose(d) is the absorbed dose in the cover material at depth d, and I(E,d) the absorbed dose per unit fluence for isotropic space radiation particles of energy E at depth d in the shielding material (see Figs. 9 and 12).

The absorbed dose must be calculated at several depths in the cover material, and the electron and proton portions of the environment must be summed to determine the dose-depth profile. The necessity of including contributions from back radiations must also be considered. In practice, the dose deposited will decrease greatly with increasing depth into the cover materials. The greater dose near the surface is due largely to low energy trapped protons, and contributes little to the average dose deposited in the cover materials. Because of the uncertainties in evaluating cover materials transmission loss in space, there is little to be gained in making an extremely accurate evaluation of the surface dose. When the average dose deposited in the cover material is known, the degradation in transmission can be estimated from data such as those presented above. These loss factors may then be applied to the estimated solar cell output parameter values.

Implementation in SPENVIS

The EQFLUX program, developed by the Jet Propulsion Laboratory (JPL) calculate 1 MeV and 10 MeV damage equivalent electron and proton fluences, respectively, for exposure to the fluences predicted by the trapped radiation and solar proton models, for a specified duration. The conversion to damage equivalent fluences is based on the damage ratios D(E,t) determined for Si [Tada and Carter, 1982], GaAs [Anspaugh, 1996] and multijunction [Marvin, 2000] cells, respectively, using the method described above.

The damage produced by back radiation is, to first order, regarded as the same in nature and magnitude as that produced by the front radiation provided only Isc damage coefficients are used. An equivalent fluence attributable to the back radiation can be added to the front contribution by estimating an effective thickness of back shielding. This assumption is not valid when higher order effects are considered. If a composite backshielding material is similar to the coverglass, only a density correction is required to compute the effective shielding thickness. This is done by comparing shield thicknesses in units of g cm-2. If the atomic number and/or density of the substrate is vastly different from that of glass, the equivalent fluence should be computed using effective damage coefficients specifically developed for the new shielding material. However, the uncertainty contributed by an improper Z correction is probably much less than the uncertainty introduced by applying these damage coefficients to rear incidence calculations.

The process of calculating an equivalent 1 MeV electron fluence reduces the space radiation environment to a laboratory electron environment for which solar cell degradation has been evaluated. When the damage equivalent fluence is known, the estimation of solar array degradation is almost completed. The next step in estimating array degradation is to make use of such variables as base resistivity, cell thickness, front surface treatment (such as AR coating and texturing), and rear surface treatment (such as back surface fields and back surface reflectors) to choose proper solar cell radiation data. The equivalent fluence then allows the estimation of solar cell output parameters through the use of the appropriate data.


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Berger and Seltzer, NASA SP-3036, 1966.

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Kinchin, G. W., and R. S. Pease, The Displacement of Atoms in Solids by Radiation, Report Prog. Phys., 18, 1, 1955.

Marvin, D. C., Assessment of Multijunction Solar Cell Performance in Radiation Environments, Aerospace Report No. TOR-2000(1210)-1, 2000.

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This page is based on the Jet Propulsion Solar Cell Radiation Handbook, Third Edition [Tada et al., 1982].

Last update: Mon, 12 Mar 2018