USING SRIM TO CALCULATE THE RELATIVE DAMAGE COEFFICIENTS FOR SOLAR CELLS

Scott R. Messenger

SFA, Inc., Largo, MD 20774

Edward A. Burke Consultant, SFA, Inc., Largo, MD 20774

Robert J. Walters and Jeffrey H. Warner

Code 6818, Naval Research Laboratory, Washington, DC 20375

Geofffey P. Summers Code 6818, Naval Research Laboratory, Washington, DC 20375

Department of Physics, UMBC, Baltimore, MD 21250

ABSTRACT It is shown how the widely available computer code SRIM can be used to calculate proton relative damage coefficients (RDCs) for solar cells. This approach is essential in the case of crystalline Si cells where the incident proton energy is reduced significantly in traversing the active volume of the cell. However, the same approach can be used in other cases such as GaAs-based multi-junction cells where the active region consists of several different material layers. In the case of Si cells analytic calculations of the non-ionizing energy loss (NIEL) are not satisfactory for calculating the energy dependence of the RDCs in contrast to technologies such as single junction GaAs and thin films such as CIGS, for which the NIEL approach has been extremely successful. In the SRIM approach it is assumed that the RDCs are proportional to the number of total vacancies formed. The calculation involves integrating the vacancy.txt files produced by SRIM over the active depth of the cells and normalizing the results to the number of vacancies produced by 10 MeV protons. The RDCs calculated from SRIM are found to agree well with experimentally measured values for both Si and MJ cells. In particular the “double hump” structure in the measured RDCs for several kinds of MJ technologies can be reproduced.

INTRODUCTION

Relative damage Coefficients (RDCs) are needed to estimate solar cell degradation in the complex proton and electron environment found in space. The most straightforward way to determine the RDCs is to measure them directly. In a typical case such an undertaking involves measuring cell degradation curves for various photovoltaic parameters for a range of incident proton and electron energies. Anspaugh [1] produced an excellent data set of this kind for single junction GaAs cells. The RDCs for normal incidence monoenergetic particles can be converted to the corresponding RDCs for an isotropic environment, from which the RDCs for shielded cells can be derived using the widely used approach developed at JPL and described in the Solar Cell Radiation Handbooks and elsewhere [2,3]. The problem with this approach is that acquiring the necessary data is extremely labor intensive and consequently expensive. In a series of papers over the last decade NRL showed that in many cases the energy dependence of the RDCs could be determined analytically using calculations of the nonionizing energy loss for particular particles and cell materials [4 and references therein]. These calculations have become progressively more sophisticated for electrons and protons, and have been recently extended to incident heavy ions [5]. When the NIEL is multiplied

NASA/CP—2005-213431 217

by a particle fluence a quantity called displacement damage dose is obtained, which plays the same role for displacement damage that ionizing dose plays for ionization effects. When Anspaugh’s data for GaAs was converted to displacement damage dose it was found that the curves for E >10keV collapsed to a single characteristic curve. Indeed it was primarily the availability of Anspaugh’s excellent data set that enabled the displacement damage dose approach to cell degradation to be developed. The NIEL approach works well when the particle energy can be assumed to be constant across the active region of the device. This is the case for GaAs-based cells, where the active region can be considered thin for proton energies >~100 keV. In these cases the energy dependence of the NIEL and the relative damage coefficients (RDCs) are similar [4]. However, this is not true for very low energy protons incident on uncovered GaAs cells, and deviations between the energy dependence of the NIEL and the RDCs are observed at proton energies < 100 keV [1]. The reason for the deviation is that protons with these energies slow down significantly or stop in the active region of the cell. For silicon cells, where the active region in typical cells is 100 times greater than is the case for GaAs, the problem is exacerbated. In GaAs cells, the active region is typically on the order of a few micrometers in depth from the front surface of the cell, as opposed to ~100 µm for crystalline silicon cells. This means that protons with relatively high energy will slow down significantly or reach the end of their tracks in the critical silicon cell regions more so than is the case in GaAs cells. The slowing-down effects complicate the analysis. What is more, experiments show that, for normally incident protons of a given energy, the damage per incident proton is a maximum when the particle track terminates in the active device region. Whereas for GaAs [1,6] the energies where this is a problem exist only for protons below a few hundred keV, it extends to several MeV in the case of silicon [2,3].

RDCs FOR CRYSTALLINE Si CELLS The observations made above can be quantified by analyzing actual experimental results. Figure 1 shows data for the degradation of Pmax for Si cells taken from the Solar Cell Radiation Handbook [2,3]. Results are shown for incident 100,and 300 keV, and 1 and 9.5 MeV protons. The two most striking features of these data are firstly that the curves are not similar in shape and secondly the curves do not come in any obvious order with increasing

109 1010 1011 1012 1013

Proton Fluence (p+/cm2)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

No

rmal

ized

Max

imu

m P

ow

er

100 keV300 keV1 MeV10 MeV

Si

Proton Energy

Figure 1. The degradation of the maximum power point of Si cells as a result of proton irradiation [2,3]. The points of the curves are for identification only and are not measured data.

NASA/CP—2005-213431 218

proton energy. The data for Si cells is in contrast to similar data for the degradation of Pmax in GaAs cells taken from Anspaugh and shown in Fig. 2. In this case the curves are similar in shape except for the two lowest energies (50 and 100 keV) and there is a clear trend with energy, with the lowest energy protons causing the most damage as would be expected from the interaction cross sections. It is the behavior of the 50 and 100 keV curves in Fig. 2 that suggests the cause of the results shown in Fig. 1. As noted above 50 and 100 keV protons do not completely traverse the active region of single junction GaAs cells so that the damage is done in these cases differently than for higher energies. Once the proton energy is > ~200 keV the damage is done uniformly and the degradation curves become similar in shape. For the data shown in Fig. 1 only in the case of the 9.5 MeV curve do the incident protons traverse the active region of the Si cell. For the other energies the protons stop in different parts of the active region.

109 1010 1011 1012 1013

Proton Fluence (p+/cm2)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

No

rmal

ized

Max

imu

m P

ow

er

50 keV100 keV200 keV300 keV500 keV1 MeV3 MeV9.5 MeV

GaAs

Proton Energy

Figure 2. The degradation of the maximum power point of GaAs cells due to proton irradiation [1]. The points on the curves are for identification only and are not measured data.

There is an added complication that arises when the degradation curves are not similar in shape and that is in the determination of the RDCs. In the JPL approach, the RDCs are determined by comparing the fluences of different energy protons that cause the same relative damage. Typically the 75% degradation point is used. If the curves are not parallel obviously the RDCs will vary if a different degradation point is chosen. Figure 3 shows the RDCs for Si cells determined from the kind of data shown in Fig .1. For comparison the energy dependence of the calculated NIEL for protons in Si is also plotted on the figure [7], with the two curves normalized at 10 MeV. It is clear that the NIEL only tracks the measured RDCs for energies where the slowed down energy in the active region Eso is comparable to the incident energy (Einc). It is reasonable to assume that the active region of the cells that produced the data shown in Fig. 1 ranged from ~0.8 – 80 µm from the front of the cell. SRIM [8] runs then put the discussion above on a more quantitative basis as can be seen in Fig. 4. Figure 4 was obtained from the vacancy.txt output of SRIM, which has been converted to NIEL using the Kinchin-Pease approximation. The SRIM studies show that at energies below about 3 MeV the proton stops within the active region.

NASA/CP—2005-213431 219

10-1 100 101 102

Proton Energy (MeV)

10-1

100

101

102

Rel

ativ

e D

amag

e C

oef

fici

ents

Proton NIELJPL Damage Coefficients

*All data normalized to 10 MeV protons

ESD<EINC ESD≈EINC

Si

Figure 3. Comparison of the calculated NIEL for protons in Si [7] with the measured RDCs for maximum power degradation [2,3 ]. In the figure, Einc refers to the incident proton energy and Eso refers to the slowed down energy.

10-1 100 101 102 103

Depth (µm)

10-3

10-2

10-1

100

NIE

L(k

eV/µ

m)

400 keV1 MeV4 MeV10 MeV

SiProton Energy

Figure 4. SRIM derived NIEL as a function of the depth for an incident proton in Si [8] . The simplest approach to quantitatively account for the spatial nature of the damage is to assume that the RDC changes in direct proportion to the total damage produced within a minority carrier diffusion length of the junction. The energy deposited to displacements at low energies can be estimated by numerically integrating the SRIM-derived NIEL over the particle track. The adjusted NIEL is then calculated by dividing the total deposited energy

NASA/CP—2005-213431 220

by the width of the active region (80 µm). At high energies, where the protons traverse the cell with little change in energy, the damage factor is assumed to be proportional to the displacement damage energy deposited. This is given by the product of NIEL and the width (approximately 80 µm). The NIEL for 10 MeV protons in silicon is 7.885x10-3 MeVcm2/g [5]. This can be expressed as 1.829x10-3 keV/mm or 3.33x10-2 vacancies/mm [5]. The latter units are convenient for direct comparison to SRIM results, which are usually expressed as vacancies/mm The low-depth tail of the 10 MeV SRIM-derived NIEL indeed agrees with the analytical value obtained in [7]. The results obtained by applying this procedure (and normalizing at 10 MeV) are given in Fig. 5 and are compared with the data given in [3]. Inspection of Fig. 5 shows reasonable agreement between the calculated and the experimentally determined RDCs. The general shape of the calculated curve is not very sensitive to the exact value used for the diffusion length. As shown in the Fig. 5, an active depth value of 100 µm does not alter the shape or the curve significantly.

10-1 100 101

Proton Energy (MeV)

100

101

102

Rel

ativ

e D

amag

e C

oef

fici

ents

Proton NIELJPL Damage CoefficientsSRIM Results (80 µm)SRIM Results (100 µm)

*All data normalized to 10 MeV protons

Si

Figure 5. Comparison of the SRIM-derived RDCs for Si cells and the experimentally determined values, (see Fig. 3). 100 µm and 80 µm refer to the active depth assumed in the calculation.

.

RDCs FOR MULTI-JUNCTION CELLS A similar analysis can be performed for the case of multi-junction cells. In this case the added complexity comes from the fact that the active region of the cells extends over several different materials; InGaP, GaAs and Ge. Figure 6 shows the degradation curves for Pmax for a three junction InGaP/GaAs/Ge cell technology [ ]. It can be seen that for E >400 keV the curves have similar shapes and follow the expected variation with energy. For lower energies the curves show the familiar variation that occurs when the incident protons slow down or stop in there active volume of the cells. Figure 7 shows experimentally determined [10,11] RDCs for Pmax degradation for several kinds of MJ cells compared to calculations of the NIEL for protons in GaAs. It should be noted that the energy dependence of the NIEL for GaAs is almost identical to that for Ge, and very close to that for InGaP. An obvious feature of the experimental data is the double hump structure seen ~0.1 MeV where the data starts to fall below the NIEL. At higher energies there is good agreement between the experimental data and the calculated NIEL.

NASA/CP—2005-213431 221

108 109 1010 1011 1012 1013

Proton Fluence (p+/cm2)

0.5

0.6

0.7

0.8

0.9

1.0

No

rmal

ized

Max

imu

m P

ow

er

50 keV100 keV200 keV400 keV1 MeV5 MeV10 MeV

InGaP/GaAs/Ge 3J Solar Cell

Proton Energy

Figure 6. The degradation of the maximum power point of InGaP/GaAs/Ge triple junction cells due to proton irradiation [ ].

10-1 100 101 102

Proton Energy (MeV)

10-1

100

101

102

Pm

ax R

elat

ive

Dam

age

Co

effi

cien

ts

NIELSL 2JSL 2J EOLTEC 3JSL3JSL 3J EOLEmcore 3J

MJ

*Data from Marvin 2000

Figure 7. Comparison of the calculated NIEL for protons in GaAs with the experimentally determined RDCs for several multijunction InGaP/GaAs/(Ge) cell technologies [9,10,11].

It is reasonable to assume in light of the discussion above for Si cells, that the deviation of the experimental data from the NIEL in the double hump region in Fig. 7 is due to slowing down of the incident protons in the active volume of the cell. This is confirmed by SRIM runs as shown in Fig. 8. The analysis that follows is aimed at using these SRIM runs to try to reproduce the double hump structure in the energy dependence of the RDCs as shown in Fig.7.

NASA/CP—2005-213431 222

10-2 10-1 100 101 102 10310-2

10-1

100

101

102

103

Penetration Depth (µm)

15.8 keV25.1 keV39.8 keV63.1 keV126 keV199 keV316 keV501 keV794 keV1.26 MeV1.99 MeV3.16 MeV5.01 MeV7.94 MeV12.6 MeVV

acan

cy P

rod

uct

ion

Rat

e (#

/µm

/p+ )

InGaP GaAs Ge

Proton Energy

Figure 8. SRIM-derived vacancy introduction rates for protons on an InGaP/GaAs/Ge triple junction cell.

In the case of a cell technology consisting of one material such as Si, it was shown above that a good representation of the energy dependence of the RDCs could be found by determining the total number of vacancies produced over the active volume. When the cell consists of several different materials it is necessary to take into account the fact that incident protons will usually affect the electrical properties of the junctions differently. For example InGaP cells are more radiation resistant than GaAs cells. The different radiation resistance could be due to a greater level of defect annealing in InGaP than in GaAs, for example, or it might be due to the different electrical properties of the defects produced. The result in InGaP/GaAs cells is that the degradation of the overall cell is largely determined by the softer GaAs subcell. This result is confirmed by measurements of the quantum efficiency (QE) of each of the junctions following irradiation with the same fluence of protons of different energies. A fluence of 1 x 1012/cm2 of 50 keV protons, which stop in the top surface of the InGaP region, decrease only the blue part of the QE of the InGaP junction, whereas 100 keV protons, which stop in the back region of the InGaP junction decrease the QE of the red part of the InGaP junction. In both cases the change in the QE measured was quite small. However, the same fluence of 400 keV protons, which stop in the GaAs junction, produces a large drop in the GaAs QE even though 400 keV protons are less damaging than 100 keV protons In light of these results the following approach was taken. Using the SRIM results in Fig. 8, the vacancy.txt files for energies up to 126 keV were used to calculate the total number of defects produced in InGaP over the whole range of the slowed down protons. These results were normalized to the total number of vacancies produced by 10 MeV protons. For energies >126 keV only the defects produced in the GaAs layer were counted since these appear to be much more effective in degrading the operation of the cell than those in either the InGaP or Ge layers. The results of this analysis can be seen in Fig. 9 where the SRIM-derived RDCs are compared to the experimentally determined values. It can be seen in Fig. 9 that the SRIM analysis produces the double hump structure seen in the experimental data, although the calculated RDCs in this energy region are slightly higher than the measured values. It should be noted that SRIM does not include contributions from inelastic proton interactions, which are responsible for the flattening out of the total NIEL for protons in GaAs at E > 10 MeV. The SRIM-derived RDCs are therefore expected to fall below the experimental determined values at these higher energies.

NASA/CP—2005-213431 223

10-1 100 101 102

Proton Energy (MeV)

10-1

100

101

102

Pm

ax R

elat

ive

Dam

age

Co

effi

cien

ts

NIELJPL RDCs (SP 2J)SRIM RDCs

MJ

Figure 9. Comparison of SRIM-derived RDCs, experimentally determined values [10], and the calculated NIEL for protons [7] in GaAs, normalized at 10 MeV.

CONCLUSIONS

It has been shown that calculations of the total number of vacancies formed in active regions of solar cells using the Monte Carlo code SRIM can be used to calculate proton RDCs, which agree quite well with experimentally determined values. The approach is particularly useful in two cases. Firstly, in crystalline Si cells where because of the large active region of the cell protons in the MeV range slow down significantly or stop. Secondly, in multijunction cells such as InGaP/GaAs/Ge where the active volume consists of several monolithic layers of different materials. The ability to reproduce RDCs in this way is very useful because. from this basic curve for unidirectional, monoenergetic incident proton beams a family of RDC curves can be generated for isotropic protons traversing different amounts of shielding using the approach described in detail in references [3]-[6]. The performance of Si or multijunction solar cells can then be predicted for any defined space radiation environment. Comparison of predictions made for specific space missions using SRIM-derived RDCs and those experimentally determined are found to agree closely. This gives confidence in the reliability of SRIM-derived RDCs for developmental cells where experimental values are not yet available.

REFERENCES [1] B.E. Anspaugh, Proc. 22nd IEEE Photovoltaic Specialists Conf., Las Vegas, NE, 1593, (1991). [2] Y. Tada, J.R. Carter, Jr., B.E. Anspaugh and R.G. Downing, Solar Cell Radiation Handbook, 3rd Edition

JPL Publication 82-69, 1982. [3] B.E. Anspaugh and R.G. Downing, Radiation Effects in Si and GaAs Solar Cells Using Isotropic and

Normally Incident Radiation, JPL Publication 84-61, 1984. [4] S.R. Messenger, G.P. Summers, E.A. Burke, R.J. Walters, and M.A. Xapsos, Prog. Photovolt.: Res.

Appl., 9, 103-121 (2001).

NASA/CP—2005-213431 224

[5] S.R. Messenger, G.P. Summers, E.A. Burke, M.A. Xapsos, R.J. Walters, E.M. Jackson, and B.D. Weaver, IEEE Trans. Nucl. Sci., 46-6, 1595-1602 (1999).

[6] B.E. Anspaugh, GaAs Solar Cell Radiation Handbook, JPL Publication 96-9, 1996. [7] G.P. Summers, E.A. Burke, P. Shapiro, S.R. Messenger and R.J. Walters, IEEE Trans. Nucl. Sci. 40, 1372

(1993). [8] J.F. Ziegler, J.P. Biersack, and U. Littmark, The Stopping and Range of Ions in Solids, Volume I, New

York: Pergammon Press, 1985. (SRIM is freely available at http://www.srim.org.) [9] D.C. Marvin and J.C. Nocerino, Proc. 26th IEEE Photovoltaic Specialists Conf., Anchorage, AK, 1102 -

1105 (2000). [10] D.C. Marvin, Aerospace Report TOR-2000(1210)-1. [11] P.R. Sharps, D.J. Aiken, C.H. Thang, and N.S. Fatemi, Proc. 17th EUPVSEC, Munich, Germany, (2001).

NASA/CP—2005-213431 225