Theoretical Optimization of Base Doping Concentration for Radiation Resistance

of InGaP Subcells of InGaP/GaAs/Ge Based on Minority-Carrier Lifetime

Dalia Elfiky�, Masafumi Yamaguchi, Takuo Sasaki, Tatsuya Takamoto1, Chiharu Morioka2, Mitsuru Imaizumi2,

Takeshi Ohshima3, Shin-ichiro Sato3, Mohamed Elnawawy4, Tarek Eldesoky5, and Ahmed Ghitas6

Toyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468-8511, Japan1Sharp Corporation, 282-1 Hajikami, Shinjo, Nara 639-2198, Japan2Japan Aerospace Exploration Agency, 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japan3Japan Atomic Energy Research Agency, 1233 Watanuki, Takasaki, Gunnma 370-1292, Japan4Faculty of Science, Cairo University, Giza 12613, Egypt5Faculty of Women for Science and Culture, Ain shams University, Cairo 11361, Egypt6National Institute for Astronomy and Geophysics Research, Helwan, Cairo 11421, Egypt

Received April 7, 2010; accepted September 1, 2010; published online December 20, 2010

One of the fundamental objectives for research and development of space solar cells is to improve their radiation resistance. InGaP solar cells

with low base carrier concentrations under low-energy proton irradiations have shown high radiation resistances. In this study, an analytical model

for low-energy proton radiation damage to InGaP subcells based on a fundamental approach for radiative and nonradiative recombinations has

been proposed. The radiation resistance of InGaP subcells as a function of base carrier concentration has been analyzed by using the radiative

recombination lifetime and damage coefficient K for the minority-carrier lifetime of InGaP. Numerical analysis shows that an InGaP solar cell with a

lower base carrier concentration is more radiation-resistant. Satisfactory agreements between analytical and experimental results have been

obtained, and these results show the validity of the analytical procedure. The damage coefficients for minority-carrier diffusion length and carrier

removal rate with low-energy proton irradiations have been observed to be dependent on carrier concentration through this study. As physical

mechanisms behind the difference observed between the radiation-resistant properties of various base doping concentrations, two mechanisms,

namely, the effect of a depletion layer as a carrier collection layer and generation of the impurity-related complex defects due to low-energy

protons stopping within the active region, have been proposed. # 2010 The Japan Society of Applied Physics

DOI: 10.1143/JJAP.49.121201

1. Introduction

Solar cells have been used as the main power source ofsatellites in space. Solar cells in satellites are bombarded byfluxes of energetic particles (protons and electrons), and as aresult, their electrical performance degrade seriously. Inspace applications, the end-of-life (EOL) output power in aradiation environment is a major design consideration. EarlySi single crystalline solar cells have been used, although theydo not have good radiation tolerance. Then, GaAs solar cells,which are more radiation-resistant and highly efficient, havebeen used. Recently, multijunction (MJ) solar cells, partic-ularly InGaP/GaAs/Ge cells, have been used for spacebecause they have a high beginning-of-life (BOL) efficiencyof 29.2% for 1-sun AM0 and a high radiation tolerance.1)

The degradation behavior due to proton or electronirradiations on single-junction solar cells such as Si, GaAs,and InP cells, has been investigated strenuously.2) For InPmaterials, the damage constant (KL) is found to decrease asthe fraction of the In and P bonds increases. Dharmarasuet al.3) have determined that the damage coefficients for theminority-carrier diffusion lengths (KL) of 3-MeV-proton-irradiated InGaP, InGaAsP, and InGaAs are 6:7� 10�5,8:8� 10�5, and 1:01� 10�4, respectively. These valuesare higher than that of the 3-MeV-proton-irradiated InP(1� 10�5). This can be illustrated by the migration energiesof VIn (0.26 eV) and Vp (1.2 eV) in InP that are lower thanthose of VGa (1.79 eV) and VAs (1.48 eV) in GaAs. Thissuggests that InP-related materials are more radiation-resistant than GaAs-related materials.

On the other hand, few studies about the degradationbehavior of MJ solar cells are reported.4–6) The radiation

effects on solar cells differ according to the type of solar cellmaterial and the type and energy of radiation because ofvariations in the formation of radiation-induced lifetime-limiting defects. In Si, radiation-induced point defectsinteract with dopants to form lifetime-limiting traps, result-ing in a higher lifetime degradation with an increasedbase doping concentration. In InP, the Frenkel pair defectconsisting of a phosphorus vacancy and an interstitial isthought to be the main radiation-induced lifetime-limitingdefect and shows nonradiative recombination-enhanceddefect annealing.7) This results in a lower net concentrationof radiation-induced lifetime-limiting defects in InP. Someof the radiation-induced point defects interact with dopantsto form complex defects, such as PIn–Zn.8)

Since the degradation behavior of MJ is limited by themost sensitive cell for radiation, it is important to improvethe radiation resistance of MJ by analyzing the radiationresistance of each subcell and by the optimum design for it.Previous studies reported that the optimum design for MJ isobtained by thinning the InGaP top cell and decreasingthe doping concentration of the GaAs middle cell.9) Theoptimum doping concentration of the p-InGaP subcell waspreviously investigated from the experimental results10)

indicating that InGaP with a lower base doping concen-tration is more radiation-resistant. However, the physicalmechanism behind this phenomenon is ambiguous. Fromthis point, we try, in this study, to clarify the physicalreasons for this phenomenon.

The most important physical parameters affected by irra-diation are minority-carrier lifetime (�) and carrier con-centration (�). In order to determine the radiation damage,we need a model based on minority-carrier lifetime andcarrier concentration. The radiation effect is incorporatedinto an analytical model based on a fundamental approachfor radiative and nonradiative recombination lifetimes. The

�On leave from National Authority of Remote Sensing and Space Science,

Cairo 1564, Egypt.

Japanese Journal of Applied Physics 49 (2010) 121201 REGULAR PAPER

121201-1 # 2010 The Japan Society of Applied Physics

radiative recombination lifetime as a function of the dopingprofile prior to irradiation was calculated and then usedas input in the one-dimensional optical device simulator(PC1D)11) program used to calculate quantum efficiency(QE), short circuit current (Isc), open circuit voltage (Voc),and maximum power (Pmax) before and after irradiation theirvalues, we can calculate damage parameters, such as thedamage constants for minority-carrier diffusion length (KL)and carrier removal rate (Rc). In addition, the effects of basecarrier concentration on the radiation resistance of InGaPsubcells and the optimal design of base carrier concentrationfor a higher radiation resistance have been discussed.

2. Experimental and Analytical Procedures

2.1 Experimental procedure

The InGaP subcells analyzed in this study were n-on-pdouble-heterostructure and heteroface structures. The n-emitter (0.05 mm) was Si-doped at a level of 2� 1018 cm�3

and the p-base (0.4 mm) was Zn-doped at levels of 4� 1016,1:6� 1017, and 6:4� 1017 cm�3 with an area of 1� 1 cm2.InGaP solar cells were grown on GaAs or Ge substrates bymetal–organic chemical vapor deposition. An antireflectioncoating was not formed on the cells. The InGaP solar cellswere irradiated with 30 keV protons using fluences of1� 1010, 1� 1011, and 1� 1012 cm�2 at the Japan AtomicEnergy Agency (JAEA) in Takasaki.

Current–voltage (I–V) and spectral response measure-ments were taken for each cell and fluence. The QE andremaining factor for Isc, Voc, and Pmax were obtainedexperimentally as functions of proton fluence and basecarrier concentration, as shown in Fig. 1.10)

2.2 Analytical modeling for minority-carrier lifetime

changes with irradiation

To demonstrate the impact of base carrier concentration inan InGaP subcell on radiation resistance, we analyzed theradiation damage of InGaP solar cells by using radiativerecombination lifetime (�R) and damage coefficient (K) forthe minority-carrier lifetime of InGaP. The effective minor-ity-carrier lifetime (�eff) of InGaP is determined by the radi-ative recombination lifetime (�R) and nonradiative recombi-nation lifetime (�NR) affected by radiation-induced defects:

1

�eff¼

1

�Rþ

1

�NR

: ð1Þ

The radiative recombination lifetime (�R) is given by

1

�R¼ BN; ð2Þ

where B is the radiative recombination probability and Nis the carrier concentration of p-InGaP. The B-coefficient(cm3/s) for direct semiconductors in terms of effectivemasses, band-gap energy (Eg), dielectric constant ("), andtemperature (T) is12)

B ¼ 0:58� 10�12ffiffiffi"p 1

mp þ mn

� �1:5

� 1þ1

mp

þ1

mn

� �300

T

� �1:5

Eg2; ð3Þ

where mp and mn are the hole and electron effective masses,respectively, in units of the free electron mass. For InGaP,the B calculated using eq. (3) is 1:7� 10�10 cm3/s. Figure 2shows the radiative minority-carrier lifetime for InGaP as afunction of base carrier concentration before irradiation. Itsvalues were then used for modeling the radiation resistanceof cells.

The nonradiative recombination lifetime (�NR) affected byradiation-induced defects is expressed by13)

1

�NR

¼X

�i�thNri ¼1

���

1

�0

� �¼ K�; ð4Þ

where �0 and �� are the minority-carrier lifetimes beforeand after irradiation, respectively, �i is the minority-carriercapture cross section of the radiation-induced i-th recombi-nation center, �th is the minority-carrier thermal velocity, Nri

is the concentration of the i-th recombination center, K is thedamage coefficient for minority-carrier lifetime, and � is theproton energy fluence.

2.3 Analytical modeling for carrier removal with irradiation

The degradation of the output performance due to the changein carrier concentration after proton irradiation was calcu-lated using PC1D. The schematic diagram of the cellmodeled in this study is shown in Fig. 3. The default values

Fig. 1. (Color online) Experimental results of normalizing value of Pmaxchanges with 30 keV proton fluence for n-on-p InGaP single-junction cells

with various base carrier concentrations and a base thickness of 0.4 mm.

Fig. 2. (Color online) Radiative minority-carrier lifetime of InGaP be-

fore irradiation.

Jpn. J. Appl. Phys. 49 (2010) 121201 D. Elfiky et al.

121201-2 # 2010 The Japan Society of Applied Physics

of the physical properties used in PC1D simulation areshown in Table I.

In order to fit the external quantum efficiencies (EQEs) ofproton-irradiated InGaP solar cells, the values of minority-carrier diffusion length and carrier concentration in the n-type emitter and p-type base layers, and front (rear) surfacerecombination velocity were varied. Considering the param-eters described in Table I, the EQEs of radiation-degradedInGaP subcells were fitted to the experimental data. Then,Isc, Pmax, and Voc were estimated using the parametersobtained by fitting. Subsequently, the estimated results werecompared with experimental results (Isc, Pmax, and Voc). Inaddition, the carrier removal rate (Rc) (cm�1) and damageconstant (KL) for the minority-carrier diffusion lengths ofInGaP subcells were calculated from the proton fluencedependence of carrier concentration (�) and minority-carrierdiffusion length (L) using

�� ¼ �0 exp�Rc�

�0

� �; ð5Þ

where �0 and �� are the carrier concentrations before andafter irradiation, respectively, and � is the proton fluence.16)

The damage constant KL is also expressed by13)

�1

L2¼

1

L2��

1

L20

� �¼

X�i�thNri

D¼ KL�; ð6Þ

where L0 and L� are the minority-carrier diffusion lengthsbefore and after irradiation, respectively, and D is theminority-carrier diffusion constant.

3. Results and Discussion

3.1 Effects of base carrier concentration on proton

irradiation degradation of InGaP solar cell properties

Figures 4(a) and 4(b) show the changes in EQE for alow base carrier concentration (4� 1016 cm�3) and a highbase carrier concentration (6:4� 1017 cm�3), respectively,induced by 30 keV proton irradiation with fluences of1� 1010, 1� 1011, and 1� 1012 cm�2. Lines representPC1D simulation results; symbols represent the experi-mental results. A reduction in the carrier concentration ofthe emitter region from 2� 1018 to 1� 1018 cm�3 and areduction in the carrier concentration of the base region from4� 1016 to 8� 1015 cm�3 are found to occur by analyticalmodeling, in addition to reductions in the minority-carrierdiffusion lengths of the emitter and base to 0.3 mm tosimulate the slight degradation of the EQE in the short-wavelength region for the low base doping concentration(4� 1016 cm�3). Furthermore, the severe degradation ofEQE in the red region (long wavelength) for the high basecarrier concentration (6:4� 1017 cm�3) is simulated by

Fig. 3. (Color online) Schematic diagram of cell modeling in this study.

Table I. Physical parameters used in the analysis.

Surface reflectanceFitting with

experimental value

Electron mobility at 300 K �e

(cm2�V�1�s�1)2500 (min), 3000 (max)

Hole mobility at 300 K �h

(cm2�V�1�s�1)80

Emitter thickness (mm) 0.05

Base thickness (mm) 0.4

Dielectric constant 11.9

Band gap (eV) 1.86

Intrinsic carrier concentration

at 300 K (cm�3)1200

Absorption coefficient Refs. 14 and 15

Refractive index Refs. 14 and 15

(a)

(b)

Fig. 4. (Color online) EQE of InGaP cells irradiated with 30 keV

protons with fluences of 1� 1010, 1� 1011, and 1� 1012 cm�2. (a) For

base doping concentration of 4� 1016 cm�3. (b) For base doping

concentration of 6:4� 1017 cm�3. Symbols represent the experimental

results. Lines represent PC1D analytical results.

Jpn. J. Appl. Phys. 49 (2010) 121201 D. Elfiky et al.

121201-3 # 2010 The Japan Society of Applied Physics

decreasing the carrier concentration of the emitter regionfrom 2� 1018 to 1� 1018 cm�3, the base doping concen-tration from 6:4� 1017 to 3� 1017 cm�3, the minority-carrier diffusion length of the emitter to 0.3 mm, and theminority-carrier diffusion length of the base to 0.03 mm, andby increasing the rear surface recombination velocity to1� 107 cm/s (in our modeling, the back surface field layer(BSF) was not considered).

Figures 5(a) and 5(b) show the degradation curves of theexperimental and analytical values of the normalizing valuesof Isc, Pmax, and Voc as a function of 30 keV proton fluencefor the low base doping concentration (4� 1016 cm�3) andhigh base doping concentration (6:4� 1017 cm�3), respec-tively. Isc is found to degrade more rapidly with protonfluence in the higher base carrier concentration solar cells.Voc and Pmax follow a similar trend, and the subcell with thelowest base carrier outperforms the others. The resultsestimated by this simulation show good agreement with theexperimental data, indicating that radiation damage toInGaP solar cells can be evaluated by using the fundamentalproperties of radiative and nonradiative recombinationproperties in InGaP solar cells.

Figure 6 shows the calculated AM0 efficiency changeswith 30 keV proton fluence for n-on-p InGaP single-junction

cells with various base carrier concentrations and a junctiondepth of 0.4 mm. It can be seen from Fig. 6 that, at highirradiation fluences, InGaP cells with the high base carrierconcentration experience a more severe degradation ofefficiency. This is a very important result for optimallydesigning radiation-resistant space solar cells. In the follow-ing section, the mechanisms of the minority-carrier diffusionlength degradation are based on effects of base carrierconcentration in InGaP solar cells, because the efficiencydegradation shown in Fig. 6 is thought to be mainly dueto the minority-carrier diffusion length degradation in theInGaP base layer.

3.2 Effects of base carrier concentration on changes in

minority-carrier diffusion length and carrier removal

rate in p-InGaP with proton irradiation

Using the values of minority carrier diffusion length (L)obtained from PC1D simulation, we have investigated thechanges in the inverse square of diffusion length �ð1=L2Þ forthe p-type InGaP base layer as a function of 30 keV protonfluence for different base doping concentrations. In Fig. 7(a),symbols represent the analytical values obtained by PC1Dand lines represent the fitting curves obtained using eq. (6).Here, we note the severe degradation in minority-carrierdiffusion length in the case of the high base dopingconcentration. Using the values shown in Fig. 7(a), andeq. (6) the minority-carrier diffusion length damage constant(KL) for InGaP irradiated with 30 keV protons as a functionof base doping concentration was determined, as shown inFig. 7(b). The damage constant (KL) is found to increasewith initial base carrier concentration, which reflects theeffect of the mobility as a function of initial base carrierconcentration. As known, the diffusion constant (D) andmobility (�) are related with the Einstein relation D ¼ðkT=qÞ�,17) where � is a function of base carrier concen-tration. Consequently, as the carrier concentration increases,the diffusion constant decreases. Moreover, according toeq. (6) and at the same defect density, the damage constantis expected to increase.

Figure 7(c) shows the changes in the inverse square ofdiffusion length �ð1=L2Þ for the p-type InGaP base layer as afunction of base carrier concentration due to 30 keV protonswith a fluence 1� 1012 cm�2. We can observe a sever

(a)

(b)

Fig. 5. (Color online) Normalizing values of Isc, Pmax, and Voc of InGaP

cells irradiated by 30 keV proton with fluence 1010, 1011, and 1012 cm�2

(a) For base doping concentration 4� 1016 cm�3. (b) For base doping

concentration 6:4� 1017 cm�3. Symbols represent the experimental

results. Lines represent PC1D analytical results.

Fig. 6. (Color online) Analytical AM0 efficiency changes with 30 keV

proton fluence for n-on-p InGaP single-junction cells with various base

carrier concentrations and a base thickness of 0.4 mm.

Jpn. J. Appl. Phys. 49 (2010) 121201 D. Elfiky et al.

121201-4 # 2010 The Japan Society of Applied Physics

degradation of minority-carrier diffusion length in the caseof high base carrier concentration.

To understand the physical mechanisms behind the degra-dations of Isc and EQE with various base carrier concentra-tions, we have analyzed the quantum efficiency of the solarcells using standard analytical expressions18) and appropriate

models for the absorption coefficient14,15) after 30 keVproton irradiation with a high fluence of 1� 1012 cm�2.

The total EQE is obtained by summing the contributionsof the emitter, base, and depletion layers. Isc is obtained fromthe integral of the product of the EQE with the spectrum ofinterest.

The main mechanism behind the degradations of Isc andEQE is depletion region broadening. The standard analyticalmodel result indicates that a considerable contribution to thetotal EQE stems from the depletion region. This is becausethe broadening of the depletion region is due to the carrierremoval effect. The quantum efficiency from the depletionregion (QED) depends on the width of the depletion region(Wd) according to the following equations:19)

QED ¼ expð��xEÞ½1� expð��WdÞ�; ð7Þ

Wd ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2"s

q

1

Na

þ1

Nd

� �Vbi

s; ð8Þ

where � is the absorption coefficient, "s is the permittivity ofsemiconductors, xE is the emitter thickness, Na and Nd arethe acceptor and donor concentrations, respectively. Thewidth of the depletion layer (0.5 mm) in the case of lowbase doping concentration (8� 1015 cm�3) after irradiation(’ ¼ 1� 1012 cm�2) is five time greater than that of thedepletion layer (0.1 mm) in the case of high base dopingconcentration (3� 1017 cm�3). The minority-carrier diffu-sion length (lifetime) decrease with proton irradiations isfound to be a minor effect. Although it is a minor effect, thebase doping effect on diffusion length degradation has beenfound in this study, as shown in Fig. 7(b). The degradationof Isc with proton energy fluence is due to the reduction inminority-carrier diffusion length (L), which can be expressedby the damage constant (KL). KL is found to increase withinitial base carrier concentration, as we explained previous-ly, the minority-carrier diffusion lengths of the emitter andbase regions markedly decrease with proton energy fluenceto very small values. Consequently, the Isc values from theemitter and base regions are very small compared to thatfrom the depletion region.

By the same method of investigating (KL), we havedetermined the effects of base carrier concentration oncarrier removal rate (Rc) in the p-InGaP base layer.Figure 8(a) shows the degradation of base carrier concen-tration for the InGaP cell as a function of 30 keV protonfluence. Symbols represent the analytical values obtained byPC1D and lines represent the fitting curves obtained usingeq. (5). The carrier removal rates (Rc) of InGaP subcellswere calculated using Fig. 8(a) and eq. (5). Rc is found toslightly increase with base doping concentration, as shownin Fig. 8(b). This result is thought to be due to complexdefects composed of radiation-induced point defects andimpurities. Most low-energy protons may stop within theactive region of the solar cell, introducing a larger number ofpoint defects, and most defects tend to pile up in a layerlocated at a depth of 0.3 mm. Therefore, radiation-induceddefects are thought to react with impurity atoms and formimpurity-related complex defects. Such complex defects arethought to act as recombination centers that decreaseminority-carrier lifetime (diffusion length) and as majority-carrier trapping centers that decrease carrier concentration.

(a)

(b)

(c)

Fig. 7. (Color online) (a) Changes in the inverse square of diffusion

length�ð1=L2Þ for p-type InGaP base layer as a function of 30 keV proton

fluence for different carrier concentrations. Symbols represent the

analytical results obtained by PC1D. Lines represent the fitting curves

obtained using eq. (6). (b) Damage constant of minority-carrier diffusion

length (KL) for 30 keV-proton-irradiated InGaP as a function of base

doping concentration. (c) Changes in the inverse square of diffusion

length �ð1=L2Þ for p-type InGaP base layer as a function of base doping

concentration due to 30 keV protons with fluence of 1� 1012 (cm�2).

Jpn. J. Appl. Phys. 49 (2010) 121201 D. Elfiky et al.

121201-5 # 2010 The Japan Society of Applied Physics

In summary, as the doping concentration increases in thebase more radiation-induced complex defects are generated.Therefore, the damage coefficients for the diffusion length(KL) and carrier removal rate (Rc) of InGaP are thought toincrease with carrier concentration, as shown in Figs. 7(b)and 8(b), as a result of complex defect generation. However,further work is necessary to clarify this reaction.

3.3 Discussion about effects of carrier concentration on

damage coefficients for minority-carrier diffusion

length and carrier removal rate in InGaP

As described above, the damage coefficients for minority-carrier diffusion and carrier removal rate with low-energyproton irradiations have been observed to be dependenton carrier concentration in this study. For InP solar cells,Messenger et al.20) have found that the carrier removal rateof InP with high-energy proton (3 –10 MeV) and high-energyelectron (1 MeV) irradiations is independent of initial carrierconcentration, and it is directly proportional to the numberof defects created.

As one of the mechanisms considered for the differenceobserved between Messenger et al. results and ours, thegeneration of different defect species under low-energy(30 keV) proton irradiation in our case and high energy

(3 –10 MeV) proton irradiations in Messenger et al.’s caseis proposed. In low-energy proton irradiation, whose rangeis smaller than the junction depth of the solar cell, itis necessary to consider the nonuniform distribution ofradiation-induced defects in the cell (Bragg damage peak).21)

Figure 9 shows the distribution of vacancy concentrationinduced by incident 30 keV protons in the InGaP solar cellswith a junction depth of 0.05 mm calculated using SRIM2008 software (Stopping and Range of Ions in Matter).22) Inthe case of 30 keV protons, the project range is 0.3 mm andthe ions are stopped within the active region of InGaP solarcells. The Bragg damage peaks of proton ions will lie in theactive region and their energies will change notably acrossthe region (nonuniform damage distribution). Generally,proton-induced defect density increases with decreasingparticle energy.

The Rc in the case of 30 keV protons is very high (2:6�105 cm�1) compared with the carrier removal rate of 1-MeV-electron-irradiated InGaP (0.93 cm�1).23) This difference dueto proton irradiation has a high introduction rate of defects inInGaP. During electron radiation, defects are introduced bythe primary collision between the incident electron and thelattice atoms, and the resulting damage is spread out alongthe length of the electron trajectory. During ion or protonirradiation, high-energy ions are slowed by Columbicinteractions and the nuclear stopping that causes the majorityof the displacement damage to occur only for low-ionenergies.24) Accordingly, the radiation-induced defects in thecase of electron irradiation are simple defects, such as theFrenkel pair (phosphorus-vacancy-related defect),25) whilethe radiation-induced defects under low proton irradiationsare thought to react with impurity atoms and form impurity-related complex defects, such as PIn–Zn, in InP.8) Suchcomplex defects are thought to act as recombination centersthat decrease minority-carrier lifetime (diffusion length) andas majority-carrier trapping centers that decrease carrierconcentration.

4. Conclusions

In this study, an analytical model for radiation damage tospace solar cells based on the minority-carrier lifetime,damage constant for lifetime, carrier concentration, and

(a)

(b)

Fig. 8. (Color online) (a) Proton fluence dependence of carrier con-

centration in the InGaP base layer due to 30-keV-proton-irradiations.

Symbols represent the analytical results obtained by PC1D. Lines

represent the fitting curves obtained using eq. (5). (b) Carrier removal

rate Rc for 30-keV-proton-irradiated InGaP as a function of base doping

concentration.

Fig. 9. (Color online) Distribution of vacancy concentration induced by

incident 30 keV protons in the InGaP solar cells with junction depth of

0.05 mm.

Jpn. J. Appl. Phys. 49 (2010) 121201 D. Elfiky et al.

121201-6 # 2010 The Japan Society of Applied Physics

carrier removal rate of solar cell materials has beenproposed. Numerical analysis shows that InGaP solar cellswith low base carrier concentrations are radiation-resistant.The satisfactory agreement between analytical and exper-imental results shows that radiation damage to InGaP solarcells can be evaluated by using the fundamental propertiesof radiative and nonradiative recombination properties inInGaP crystals. The damage coefficients for minority-carrierdiffusion and carrier removal rate with low-energy protonirradiations have been observed to be dependent on carrierconcentration in this study. As the physical mechanismsbehind the difference in the radiation resistant properties ofvarious base doping concentrations, two mechanisms name-ly the effects of the depletion layer as a carrier collectionlayer and the generation of the impurity-related complexdefects due to low-energy protons stopping within the activeregion, have been proposed.

Acknowledgments

The authors would like to thank the Egyptian governmentand the Ministry of Education, Culture, Sports, Science andTechnology of Japan for the Private University AcademicFrontier Research Center Program ‘‘Super High-EfficiencyPhotovoltaic Research Center’’. The authors would also liketo thank Dr. Hae-Seok Lee and Dr. Nicholas J. Ekins-Daukes for their effort.

1) M. Yamaguchi, T. Takamoto, K. Araki, and N. E. Daukes: Sol. Energy 79

(2005) 78.

2) G. Augustine, A. Rohatgi, and N. M. Jokerst: IEEE Trans. Electron

Devices 39 (1992) 2395.

3) N. Dharmarasu, M. Yamaguchi, T. Takamoto, Y. Takashi, T. Tanabe, S.

Takagishi, T. Ohshima, H. Itoh, M. Imaizumi, and S. Matsuda: Proc. 17th

European Photovoltaic Solar Cell Energy Conf., 2001, p. 2159.

4) T. Sumita, M. Imaizumi, S. Matsuda, T. Ohshima, A. Ohi, and H. Itoh:

Nucl. Instrum. Methods Phys. Res., Sect. B 206 (2003) 448.

5) S. R. Messenger, E. A. Burke, R. J. Walter, J. H. Warner, and G. P.

Summers: Prog. Photovoltaics 13 (2005) 115.

6) M. Imaizumi, S. Matsuda, S. Kawakita, T. Sumita, T. Takamoto, T.

Ohshima, and M. Yamaguchi: Prog. Photovoltaics 13 (2005) 529.

7) K. Ando, M. Yamaguchi, and C. Uemura: Phys. Rev. B 34 (1986) 3041.

8) M. Yamaguchi and K. Ando: J. Appl. Phys. 63 (1988) 5555.

9) M. Yamaguchi, T. Takamoto, A. Khan, K. Ando, M. Adachi, N.

Dharmarasu, M. Imaizumi, and S. Matsuda: Proc. 3rd World Conf.

Photovoltaic Energy Conversion, 2003, Vol. 1, p. 685.

10) M. Yamaguchi, N. J. Ekins-Daukes, H.-S. Lee, T. Sumita, M. Imaizumi,

T. Takamoto, T. Agui, M. Kaneiwa, K. Kamimura, T. Ohshima, and H.

Itoh: Proc. 4th World Conf. Photovoltaic Energy Conversion, 2006, Vol. 2,

p. 1789.

11) Web site of the University of New South Wales [http://www.pv.unsw.

edu.au/links/products/pc1d.asp].

12) R. N. Hall: Proc. IEE, Part B 106 (1959) 923.

13) J. J. Loferski and P. Rappaport: Phys. Rev. 111 (1958) 432.

14) R. Ferrini, G. Guizzetti, M. Patrini1, A. Parisini, L. Tarricone, and B.

Valenti: Eur. Phys. J. B 27 (2002) 449.

15) http://www.ioffe.ru/SVA/NSM/Semicond/GaInP/optic.html

16) A. Khan, M. Yamaguchi, J. C. Bourgoin, and T. Takamoto: J. Appl. Phys.

91 (2002) 2391.

17) S. M. Sze: Physics of Semiconductor Devices (Wiley, New York, 1981)

2nd ed., p. 55.

18) S. R. Kurtz, J. M. Olson, D. J. Friedman, J. F. Geisz, A. E. Kibbler, and

K. A. Bertness: Mater. Res. Soc. Symp. Proc. 573 (1999) NREL/CP-520-

26494.

19) J. Nelson: The Physics of Solar Cells (Imperial College, London, 2003)

p. 163.

20) S. R. Messenger, R. J. Walters, M. A. Xapsos, G. P. Summers, and E. A.

Burke: IEEE Trans. Nucl. Sci. 45 (1998) 2857.

21) S. R. Messenger, E. A. Burke, R. Walters, J. Warner, G. Summers, J.

Lorentzen, T. Morton, and S. Taylor: Tech. Rep. NASA/CP 2007-

214494.

22) http://www.srim.org/

23) N. Dharmarasu, A. Khan, M. Yamaguchi, T. Takamoto, T. Ohshima, H.

Itoh, M. Imaizumi, and S. Matsuda: Proc. 12th Photovoltaic Specialists

Conf., 2001, Vol. 75, p. 683.

24) J. R. Dekker, A. Tukiainen, R. Jaakkola, K. Vakevainen, J. Lammasniemi,

and M. Pessa: Appl. Phys. Lett. 73 (1998) 3559.

25) A. Khan, M. Yamaguchi, J. C. Bourgoin, K. Ando, and T. Takamoto:

J. Appl. Phys. 89 (2001) 4263.

Jpn. J. Appl. Phys. 49 (2010) 121201 D. Elfiky et al.

121201-7 # 2010 The Japan Society of Applied Physics