Activation energies of the In Si -Si i defect transitions obtained by carrier lifetime measurements

Transcription

1 Phy. Statu Solidi C 14, No. 5, (2017) / DOI /p Ativation energie of the In Si -Si i defet tranition obtained by arrier lifetime meaurement urrent topi in olid tate phyi Kevin Lauer *,1, Chritian M oller 1, Chritopher Teßmann 1,2, Dirk Shulze 2, and Nikolay V. Abroimov 3 1 CiS Forhungintitut f ur Mikroenorik GmbH, Konrad-Zue-Str. 14, Erfurt, Germany 2 TU Ilmenau, Intitut f ur Phyik, Weimarer Str. 32, Ilmenau, Germany 3 Leibniz-Intitut f ur Kritallz uhtung, Max-Born-Str. 2, Berlin, Germany Reeived 29 April 2016, aepted 1 February 2017 Publihed online 21 February 2017 Keyword arrier lifetime, light-indued degradation, ilion * Correponding author: klauer@imt.de, Phone: þ , Fax: þ Light-indued degradation (LID) i invetigated in indium doped ilion by time and temperature dependent arrier lifetime meaurement. Different tranition rate and ativation energie were meaured and interpreted within the A Si -Si i defet model. The ae of indium aeptor i ompared to the ae of boron. Reult are diued within the frame of a omparion between A Si -Si i and A Si -Fe i defet. It wa found that reported dependenie of the tranition rate of the A Si -Si i defet on the hole denity upport defet model whih are baed on defet onfiguration hange. An in-depth explanation of the A Si -Si i defet model i given and poible error related to the meaurement of tranition rate are diued. 1 Introdution The phenomenon of light-indued degradation (LID) [1], whih our in boron-doped ilion, wa found to our in indium doped ilion a well [2, 3]. For the ae of boron, it wa propoed that oxygen trimer [4] or dimer [5] are loated in the viinity of thi aeptor atom and are reponible for the LID phenomenon. Conidering ab initio imulation of one aeptor and one ilion atom haring one lattie poition in ilion [6 9], an A Si -Si i defet wa propoed a an alternative origin for LID [2] and a defet model wa developed [10]. Thi defet model an alo explain the kineti of a photolumineene peak in indium doped ilion alled P line [10]. Exiting experimental data with repet to the boron intertitial defet and oxygen lutering during rytal ooling are in agreement with the aumption of an A Si -Si i defet [11]. Hene, the defet underlying the LID phenomenon i denoted by A Si -Si i defet throughout thi work. Our A Si -Si i defet i modeled throughout the manuript by a onfigurational-oordinate () energy diagram to interpret the kineti of the LID phenomena. In thi ontribution, we further invetigate the ae of indium. We report on the ativation energie of the different tranition within the A Si -Si i defet model. The ativation energie are obtained by time- and temperature-dependent harge arrier lifetime meaurement on one indium doped ilion ample. 2 Defet model 2.1 Level heme The A Si -Si i defet model, whih wa developed in Ref. [10], i extended by a third onfiguration to inlude a more likely mehanim for the generation of the fat reombination enter (ee Fig. 1). The hape of the total energy urve i dedued from ab initio imulation of the ilion intertitial [12]. It i preumed that a poible A Si -Si i defet inherit the propertie of a free ilion intertitial atom. The diagram reported in thi ontribution i a uggetion, whih i ued to exemplify the explanation of the LID phenomenon uing thoe diagram. There are even poible tate of the defet within thi model, whih are denoted by number. The total energy, whih inlude the elati and eletroni energy, i plotted for eah harge tate a a funtion of the defet onfiguration oordinate. An introdution to the appliation of diagram an be found, e.g., in Ref. [13, 14]. The eletroni energy i indiated with repet to the interation of the defet with the valene band. Thi i uffiient to explain the kineti of the LID phenomenon in p-type ilion. If a hole i emitted into the valene band

2 p (2 of 8) K. Lauer et al.: Ativation energie of the In Si -Si i defet tranition Figure 1 Configurational-oordinate energy diagram propoed for the A Si -Si i defet. In omparion to the earlier propoed A Si -Si i defet model [10] a third onfiguration i added. (e.g., from tate 1), the total energy of the defet and the hole ((A Si -Si i ) 0 þ h þ ) inreae due to the energy gain of the emitted hole. After relaxation, tate 2 i reahed. The energy gain i the hole emiion ativation energy and i the ditane of the energy level from the valene band edge. If the hole emiion an be oberved, thi energy an be obtained from meaurement of the hole emiion rate a a funtion of temperature a done, e.g., by DLTS meaurement. An eletron hole reombination event via a defet take plae by an eletron apture from the ondution band and a hole apture from the valene band. The harge tate of the defet hange during the reombination event. Suh a mehanim i alled Shokley Read Hall (SRH) reombination. It an be deribed by the SRH tatiti uing one energy level in the band gap and two apture ro etion for eletron and hole, repetively [15]. The preent A Si -Si i defet model ha four poible SRH reombination hannel, whih are aued by the tranition between tate 1 and 2, 2 and 3, 4 and 5 a well a 6 and 7. If the diagram (ee Fig. 1) i ued to diu arrier reombination it ha to be notied that the defet i able to interat with either the ondution or the valene band. Thi mean that the harge tate hange, e.g., from tate 7 to 6 an be due to an eletron apture from the ondution band, a well. The energie plotted in the diagram with repet to the valene band are valid irrepetive of the proe, whih ha led to the harge tate hange. The type of tranition, whih aue the harge tate hange, depend on the experimental ondition. Stritly peaking, it ha to be noted that in the preent A Si -Si i defet model the energy minima in the negative harge tate (tate 3, 4, and 6) lie at different onfiguration oordinate ompared to the repetive energy minima in the neutral harge tate (tate 2, 5, and 7). Thi mean that during the eletron hole reombination event light onfiguration hange take plae. In ae of uh proee one of the implifying aumption made in the tandard SRH tatiti i invalid. In tandard SRH tatiti, it i aumed that the energy poition of the defet level i table and doe not depend on the harge tate of the defet. If onfiguration hange of the defet appear during a reombination event the ativation energy of the eletron emiion (e.g., from tate 6) and the ativation energy of the hole emiion (e.g., from tate 7) annot be deribed with only one energy level within the band gap. It ould be poible, that in uh a ae an appropriate fit of meaured arrier lifetime uing the tandard SRH formula require two tandard SRH defet level. A detailed deription of the tatiti whih ould deribe eletron hole reombination via uh reombination hannel i beyond the ope of the preent ontribution. Irrepetive of the exat reombination tatiti the reombination rate mut be a linear funtion of the defet denity. For impliity the reombination hannel within the A Si -Si i defet model are approximated by the tandard SRH tatiti in the following. The LID phenomenon exhibit two main reombination hannel, whih an be eparated by the timeale of their appearane and are denoted by the fat reombination enter (FRC) and the low reombination enter (SRC). Within the A Si -Si i defet model, the FRC i the reombination hannel related to the tranition between the tate 4 and 5 and the SRC i related to the tranition between the tate 6 and 7. The other two reombination hannel in the A Si -Si i defet model (tranition 1 to 2 and 2 to 3) are aumed to have reombination parameter whih reult in a negligible reombination ativity. Thi aumption an be made ine the initial tate of the LID phenomenon after annealing wa found to be le reombination ative. An eletron trap, whih i related to the defet underlying the LID phenomenon, wa oberved by minority arrier tranient petroopy (MCTS) with an eletron emiion ativation energy of E C E t ¼ ( ) ev. An eletron apture ro etion of n m 2 wa found [16]. E C E t denote the ditane of the level from the ondution band. Within the frame of the A Si -Si i defet model, thi ativation energy an be identified with the eletron emiion from tate 6 to 7. The energy level at E C E t ¼ ( ) ev and the eletron/hole apture ro etion ratio of n / p ¼ 9.5, whih are determined from temperature- and injetiondependent lifetime petroopy (TIDLS) uing tandard SRH tatiti [17], are aoiated in the A Si -Si i defet model with the tranition from tate 6 to Defet kineti The kineti of the LID phenomenon i explained within the frame of the A Si -Si i defet model by harge tate hange indued onfiguration hange. The

3 Contributed Artile Phy. Statu Solidi C 14, No. 5 (2017) (3 of 8) initial tate, whih i formed after the uually applied 200 8C anneal, i tate 1. If exe harge arrier in the valene and ondution band are generated (e.g., by illumination), the harge tate of the A Si -Si i defet hange from poitive to negative (tranition 1 to 2 to 3). In ae of the neutral and negative harge tate, there are three tate, repetively, whih are eparated by energy barrier. In the negative harge tate of the A Si -Si i defet, whih prevail under arrier injetion, tate 6 ha the lowet total energy and thermally ativated hange of the atomi onfiguration between S 1 to S 3 take plae. Firt the energy barrier E 34 mut be urmounted to generate the FRC (tranition between tate 4 and 5). Subequently, the energy barrier E 46 mut be urmounted to generate the SRC (tranition between tate 6 and 7). If the arrier injetion i turned off then the neutral harge tate of the A Si -Si i defet prevail. The defet remain in tate 7 until enough thermal energy i upplied to hange the onfiguration from S 3 to S 1. The energy barrier E 75 mut be urmounted to annihilate the SRC and energy barrier E 52 mut be urmounted to annihilate the FRC. Finally, the eletron i releaed to reah the initial tate 1. The analyi of the LID kineti within the frame of the A Si -Si i defet model i exemplified in the following by the tranition from tate 4 to 6. Thi tranition i aoiated with the generation of the SRC. State 6 i the lowet in total energy due to the lowet elati energy in the negative harge tate. To reah tate 6 from tate 4 the energy barrier E 46 ha to be urmounted. The l proe underlying thi tranition i a thermally ativated onfiguration hange. The rate k 46 of the tranition from tate 4 to 6 an be deribed by the Arrheniu law: k 46 ¼ v 46 e E 46 k BT ; ð1þ with the prefator n 46 and the ativation energy E 46. T i the temperature and k B i the Boltzmann ontant. If it i aumed that all defet are in tate 4 at the beginning of an experiment and only the tranition to tate 6 our, the temporal hange of the denity of defet in tate 4[Z 4 ](t) i deribed by the rate equation: The temporal evolution of the defet denity [Z 6 ](t) an be meaured by the time dependent harge arrier lifetime a explained in the following. The arrier lifetime i the average time interval an exe harge arrier pend in the valene or ondution band before an eletron hole reombination event. In the SRH tatiti the invere arrier lifetime, whih an be alulated for a peifi defet with given energy level and apture ro etion for eletron and hole, i proportional to the denity of the defet. In ae of the tranition between tate 6 and 7, the SRH arrier lifetime t 6$7 and the time dependent defet denity in tate 6 [Z 6 ](t) are related via: 1 t 6$7 ðtþ ¼ C 6$7½Z 6 ŠðtÞ: ð4þ C 6$7 i the SRH prefator, whih depend in the tandard SRH tatiti on the poition of the energy level and the apture ro etion. A imilar equation hold for the SRH arrier lifetime t 4$5, whih i aued by the tranition between the tate 4 and 5. The meaured arrier lifetime t m i the um of all reombination hannel: 1 t m ðtþ ¼ 1 t 6$7 ðtþ þ 1 t 4$5 ðtþ þ 1 ; t other ð5þ with t other being the arrier lifetime due to all other reombination hannel. If the invere lifetime meaured at t ¼ 0 i ubtrated from Eq. (5), it follow with Eq. (3): 1 t m ðtþ 1 t m ðt ¼ 0Þ ¼ðC 6$7 C 4$5 Þ½Z 6 ŠðtÞ: ð6þ If the arrier lifetime t m i meaured a a funtion of time (ee Fig. 2 or Fig. 3), the funtion [Z 6 ](t), whih i aoiated with the generation of the SRC, an be obtained. An exponential fit of the invere arrier lifetime then reveal the generation rate of the SRC, whih i denoted by k 46 and i plotted a a funtion of temperature in Fig. 4. The energy d½z 4 ŠðtÞ dt ¼ k 46 ½Z 4 ŠðtÞ: ð2þ The denity of defet in tate 6 [Z 6 ](t) i given by: ½Z 6 ŠðtÞ ¼½Z 4 Šðt ¼ 0Þ ½Z 4 ŠðtÞ: ð3þ The olution of the rate equation Eq. (2) reveal a mono exponential inreae for [Z 6 ](t) until the overall defet denity [Z 6 ](t!1) ¼ [Z 4 ](t¼0) ¼ N t,src i reahed. The time ontant of thi exponential funtion repreent the invere tranition rate k 46 from tate 4 to 6. If the aumption that all defet at t ¼ 0 are in tate 4 and only the tranition from tate 4 to 6 our, are not valid, the mathematial deription beome more omplex a diued later. Figure 2 Carrier lifetime a a funtion of time during tranition 3 to 4 and 4 to 6.

4 p (4 of 8) K. Lauer et al.: Ativation energie of the In Si -Si i defet tranition Figure 3 Invere arrier lifetime a a funtion of illumination and annealing time during a omplete In Si -Si i defet yle. The exponential fit and the tranition rate for the tranition 3 to 4, 4 to 6, and 7 to 5 are given. Figure 4 Arrheniu plot of the In Si -Si i defet tranition rate. The ativation energie for eah tranition are denoted a well. barrier E 46 between tate 4 and 6 i then obtained by a linear fit of the Arrheniu plot of the tranition rate, whih are meaured at different temperature (ee Fig. 4). It ha to be noted that above evaluation approah a diued for the tranition from tate 4 to 6 (generation of SRC) i baed on two aumption a hown previouly. It i aumed that at the beginning of the meaurement all defet are in a peifi tate, e.g., tate 4 for the ae of SRC generation. It i further aumed that only the tranition from tate 4 to 6 i allowed. Other tranition, e.g., from tate 6 to 4 or from tate 7 to 5 (annihilation of SRC) are not taken into aount. In general, all poible eletroni tranition a well a poible onfiguration hange our during an LID experiment. Hene, to aount for all tranition it would be neeary to olve a rate equation ytem for the denity of defet [Z i ](t) in eah tate i (i ¼ ): d½z i ŠðtÞ dt ¼ k ji ½Z j ŠðtÞ; ð7þ k ji are the rate of all poible tranition (ee Fig. 1). For example, the olution of thi rate equation ytem for [Z 6 ](t) and [Z 7 ](t) would deribe the defet denity N t,src (t) ¼ [Z 6 ] (t) þ [Z 7 ](t), whih i ued in the tandard SRH approah and i a linear funtion of the meaured invere arrier lifetime. The deiion to explain the generation of FRC by a thermally ativated onfiguration hange i diued in the following. In the firt A Si -Si i defet model propoed in Ref. [10], the generation of the FRC wa an eletron apture proe. One l mehanim to releae the energy of the eletron i by emiion of multiple phonon ([18] and referene therein]. The temperature dependene of the tranition rate of thi proe an be deribed by an Arrheniu law (ee Eq. (1)) a well. If the eletron apture proe would be reponible for the generation of the FRC, it i neeary to aume a apture ro etion for eletron in the range of n ¼ k 34 /(v th n) m 2. v th i the thermal veloity of eletron and n i the eletron denity aued by illumination. A thi apture ro etion i everal order of magnitude below reported apture ro etion for defet in ilion [18] thi proe eem to be unlikely. On the other hand tranition rate for onfiguration hange depend on the ratio between the partition funtion in the tranition tate and the partition funtion in the initial tate (ee in Ref. [19]). To alulate a tranition rate, for example for the FRC (tranition 3 to 4 in Fig. 1) the partition funtion of tate 3 and of the tranition tate mut be known. The tranition tate in ae of the FRC i the defet onfiguration at the maximum total energy between tate 3 and 4. Thee partition funtion an be deribed laially but an ontain quantum mehanial proee like tunneling a well [19]. In the laial piture, the tranition tate between tate 3 and 4 would be a tate where the aeptor atom, the ilion atom of the A Si -Si i defet and the urrounding ilion atom of the lattie all have a defined poition, veloity and diretion of the veloity. Depending on the probability of the oupany of thi tranition tate, the tranition rate may vary over order of magnitude. Hene, an explanation of the FRC generation via a thermally ativated onfiguration hange eem to be more likely ompared to the apture of eletron. It ha to be noted that a meaured tranition rate alo depend on the oupany probability [20] of the initial tate [21]. To enable thermally ativated onfiguration hange for the FRC tranition it i neeary to introdue two new eletroni level in omparion to the previou model. Two oneutive eletron apture from tate 1 hange the harge tate of A Si -Si i defet to negative. After thee eletron apture onfiguration hange in the negative harge tate take plae. A eond reaon, whih ha led to the introdution of the two level, i the reported diagram of two ilion atom haring one lattie poition [20]. Within thi diagram three table onfiguration are reported. The exat hape of the diagram for eah type of A Si -Si i defet, e.g., the B Si -Si i defet i not reported in the

5 Contributed Artile Phy. Statu Solidi C 14, No. 5 (2017) (5 of 8) literature. To ugget the A Si -Si i defet model depited in Fig. 1, we followed a a firt etimate the reported diagram for the ilion intertitial [12]. Thi way eem to be feaible ine the reported onfiguration for the B Si -Si i defet with lowet total energy in the negative harge tate [6] i indeed imilar to orreponding onfiguration of two ilion atom haring one lattie poition, whih i the plit intertitial onfiguration [12]. 3 Experimental The ample ued for thi tudy were ut from an intentional indium-doped 2 inh <100> Czohralki rytal, whih wa grown at Leibniz-Intitut f ur Kritallz uhtung (IKZ). The ample ued for the arrier lifetime meaurement wa ethed with potaium hydroxide to remove the aw damage, tandard RCA leaned and urfae paivated by a PECVD ilion nitride layer [22]. A hiny ethed ample of 2 mm thikne wa ued for FTIR meaurement. Detail of the FTIR etup an be found in Ref. [23]. The intertitial oxygen onentration wa [O i ] ¼ m 3 [24]. Low temperature FTIR meaurement revealed a boron onentration of [B ] ¼ m 3 and [B ] ¼ m 3 uing the alibration fator of Ref. [25, 26], repetively. The indium onentration i [In ] ¼ m 3 and [In ] ¼ m 3 with the alibration fator of Ref. [26, 27], repetively. The meaurement were arried out under bia illumination to remove the ompenation effet of the thermal donor. The peifi reitivity of r ¼ ( ) Vm (p-type) wa meaured by a 4-point-probe etup [24]. The peifi reitivity inreaed unexpetedly to r ¼ ( ) Vm after the thermal donor anneal of 600 8C for 20 min. Carrier lifetime meaurement were done on a ample without thermal donor anneal. The mirowave-deteted photoondutane deay (MWPCD) after laer exitation wa meaured uing the Semilab WT-2000 devie. To extrat the arrier lifetime at a fixed exe arrier denity of Dn ¼ m 3 the photoondutane deay wa evaluated after the method deribed in Ref. [28]. A temperature ontrolled hot plate wa ued to invetigate the arrier lifetime hange during the defet reation at different temperature. The defet tranition within the A Si -Si i defet model from tate 3 to 4, 4 to 6, and 5 to 2 were monitored while the ample wa tored on the hotplate, whih wa plaed in the MWPCD devie. For the tranition from tate 7 to 5, an external hot plate wa ued. The illumination during the tranition 3 to 4 and 4 to 6 wa done with the MWPCD exitation laer, whih ha an average intenity of I av ¼ 8.5 kwm 2. The error of the arrier lifetime i etimated by alulating the tandard deviation of the arrier lifetime during the LID experiment of the gallium doped ample in Ref. [2]. The tandard deviation from the mean value during thi LID experiment i found to be 0.2%. For the meaurement of the tranition from tate 7 to 5, the ample wa taken out of the devie. Depite areful poitioning of the ample mall lateral variation of the meaurement poition may our. Thee variation may lead to an additional error a the arrier lifetime varie laterally, a well. An example of the evolution of the arrier lifetime during the tranition 3 to 4 (generation of FRC) and 4 to 6 (generation of SRC) i hown in Fig. 2. The meaurement under illumination tarted after annealing the ample at 200 8C for 10 min to adjut tate 1. For the arrier lifetime meaurement during tranition 5 to 2 (annihilation of FRC) the illumination wa turned off after ompletion of tranition 3 to 4. For the LID experiment plotted in Fig. 3, tranition from tate 3 to 4 i aumed to be ompleted after Tranition 7 to 5 wa monitored after illumination for about 1dat508C. A omplete In Si -Si i defet yle i hown in Fig. 3. Reported tranition rate are the invere time ontant of a monoexponential fit to the time dependent invere lifetime. The meaured rate of the different In Si -Si i defet tranition a a funtion of the invere temperature are depited in Fig. 4. Ativation energie are obtained from a linear fit to the Arrheniu plot of the tranition rate. The error bar of the tranition rate repreent the tandard error from the leat quare fitting method. An auray of the temperature meaurement of 1 K i aumed. The ativation energie for the different tranition are ummarized and ompared to the boron ae in Table 1. 4 Diuion In Table 1, the ativation energie for the generation and annihilation of the FRC and the SRC are given, repetively. The denotation follow the A Si -Si i defet model with tranition from tate 3 to 4 and 5 to 2 Table 1 Ativation energie of A Si -Si i defet tranition. tranition In Si -Si i (LID) E A (ev) In Si -Si i (Pline) E A (ev) B Si -Si i (LID) E A (ev) 3 to b 5 to to a b 7 to d a Ref. [11]. b Ref. [40]. Ref. [10]. d Ref. [41]

6 p (6 of 8) K. Lauer et al.: Ativation energie of the In Si -Si i defet tranition aoiated with generation and annihilation of the FRC and tranition 4 to 6 and 7 to 5 aoiated with generation and annihilation of the SRC. The ativation energie, whih are obtained in thi work for the ae of indium, are ompared to the literature data in Table 1 for the ae of boron. Additionally, one ativation energy, whih wa meaured by low temperature photolumineene petroopy, i inluded a well. For the tranition from tate 3 to 4 and 5 to 2, a differene between the ae boron and indium i oberved. For the tranition from tate 4 to 6 and 7 to 5, the ativation energie are omparable within the error. For the SRC, thi i a imilar ituation a in the ae of the A Si -Fe i defet [29]. The ommon undertanding for the aoiation reation of the A Si -Fe i defet i that thi ativation energy i a meaure for the diffuion barrier of poitively harged intertitial iron. The loe relation between the LID phenomenon and the A Si -Fe i defet beome alo apparent in exiting model for the LID phenomenon [30], a imilar defet reation model a well a energy diagram [31, 32] were propoed. Both uggeted model are baed on a pairing proe inluding a long-range migration and three harateriti energie, whih are the dioiation energy, the binding energy and the migration energy. The migration energy i in eah ae related to a fat diffuing omponent of the repetive defet omplex. In Ref. [30], the fat diffuing omponent wa propoed to be the oxygen dimer. Thi loe relation between the LID phenomenon and the A Si -Fe i defet i diued in the following. The A Si -Fe i defet were omprehenively invetigated [31] and there are experiment, whih indiate that a dioiation proe indeed our [33, 34]. In that ae, the ubtitutional aeptor and the iron are fully eparated. It i known, that the A Si -Fe i defet itelf an be metatable [31]. Suh a behavior wa reported, e.g., for the Al Si -Fe i defet [35] but not for the B Si -Fe i defet [30]. In ae of the Al Si -Fe i defet for eah table onfiguration, the defet parameter for arrier reombination are different. Thi mean that a onfiguration hange of the Al Si -Fe i defet would indue a hange in the arrier lifetime. The dioiation of the iron from the aluminum would then lead to a further hange of the arrier lifetime. The reombination enter after dioiation i the free intertitial iron atom. A defet with uh propertie ould explain the two-tep propertie of the LID phenomenon. Thi would mean that the LID phenomenon i partly aued by a longrange migration proe rather than by onfiguration hange a aumed in the preent A Si -Si i defet model. Thi poibility i diued in the following. On the bai of urrent experimental data uh a mehanim for the A Si -Si i defet i till poible. Illumination would firt indue a defet onfiguration hange. After that the aeptor and the ilion intertitial dioiate a the Coulomb attration vanihe due to the eletron apture. Annealing in darkne would then lead to an aoiation of the aeptor and the ilion intertitial aued by the Coulomb attration. The ilion intertitial i imilarly to the intertitial iron poitively harged in p-type ilion [36]. The wide range of reported data on the diffuivity of the ilion intertitial [37] doe not allow to rule out uh a mehanim. Within thi idea it ould be poible that after the dioiation proe the ilion intertitial move to other ink like ubtitutional arbon C, intertitial oxygen O i [38], di-oxygen vaany omplex VO 2, or an oxygen dimer O 2i [39]. In thee ae, the tranition rate from tate 4 to 6 (generation rate of SRC) mut depend on the denity of the ink itelf, a the rate would be enitive to the diffuion ditane. In ae of arbon, no report of the dependeny of the rate on the arbon onentration are known to the author. In ae of intertitial oxygen, it wa found that the generation rate of the low LID omponent doe not depend on the intertitial oxygen onentration [40]. Hene, intertitial oxygen i unlikely a a ink for intertitial ilion or for intertitial boron, a propoed in Ref. [38]. The ame hold for the poibility that the oxygen dimer i the ink, a it onentration depend on the intertitial oxygen onentration a well. The bai quetion i: I the oberved LID phenomenon due to a onfiguration hange of a defet a propoed in Ref. [4, 10] or doe a long-range migration our imilar to the A Si -Fe i defet at leat for one omponent? One riterion would be, how the annihilation rate of the SRC (tranition 7 to 5) depend on the aeptor denity. If a long-range motion of the ilion intertitial away from the ubtitutional boron during defet generation would our, the annihilation rate hould inreae linearly with the aeptor denity [42]. Thi feature i ued in ae of the A Si -Fe i defet to meaure the aeptor denity in ompenated ilion [34]. For the LID, however, a dereae of the annihilation rate with inreaing hole denity i oberved [41]. It wa hown, that the annihilation rate i not related to the aeptor denity. Thi finding upport defet model, whih aoiate the annihilation of LID with onfiguration hange. If a longrange migration would our, the annihilation rate in unompenated and ompenated ilion in imilarity to the A Si -Fe i defet hould depend on the aeptor denity. The interpretation of the variou dependenie of the meaured defet tranition rate on parameter like eletron and hole denity, et. [43] i a omplex problem. In ae of a two-tate ytem, a aumed for the A Si -Fe i defet [29], the reation rate of the equilibrium reation an be extrated by olving the rate equation Eq. (7) for (i ¼ 1...2) and fitting the analytial olution to the meaured data. In that way, the aoiation and dioiation reation rate k 12 and k 21, repetively, for the A Si -Fe i defet ould be eparated [29]. In ae of the A Si -Si i defet, there are 7 tate with 16 poible reation rate (ee Fig. 1). An analytial olution of Eq. (7) for (i ¼ ) doe not exit. Hene, a eparation of a meaured tranition rate into the different reation path of the A Si -Si i defet model, whih our in an experimental etup, i hardly poible. It i neeary to make aumption a indiated in the theory etion, whih are reponible for a ytemati error in the obtained reult. Suh a ytemati error wa found for the ae of A Si -Fe i defet[29]. In that ae, the aeptor iron aoiation reation

7 Contributed Artile Phy. Statu Solidi C 14, No. 5 (2017) (7 of 8) wa monitored by arrier lifetime meaurement tarting from the fully dioiated tate. Then the ativation energie were obtained under two aumption. Firt, only the aoiation reation wa aumed to be preent, whih mean that the rate equation ytem Eq. (7) wa olved for i ¼ 1. Seond, the aoiation a well a dioiation reation wa aumed to be preent during the meaurement, whih mean that the rate equation ytem Eq. (7) i olved for i ¼ 1, 2. Both olution were fitted to the ame meaured data and the ativation energie were obtained. It wa found that the ativation energy for the aoiation reation i different in both ae. Thi ytemati error i due to the different aumption made for the extration of the tranition rate. In ae of the LID phenomenon, it wa found that generation a well a annihilation of the SRC our imultaneouly [44]. Thi mean that a imilar ytemati error a oberved in ae of A Si -Fe i defet may our for the ae of A Si -Si i defet. Suh a ytemati error mut be taken into aount, if the meaured ativation energie are ompared to energy barrier, whih ould be obtained by ab initio imulation. A detailed analyi of the ytemati error due to the aumption made for the evaluation of the meaured data i beyond the ope of the preent invetigation. A omparion of the ativation energie obtained in thi work with ativation energie reported in the literature i poible a the aumption made to olve Eq. (7), whih are made in thi work and whih are ued in the literature [40, 41, 45], are the ame. In our ample, the defet denity parameter N t i about a fator 5 larger than expeted if the ample would ontain no indium [40, 46]. Thi mean that the mall amount of boron, whih i preent in the ample, ha only a mall impat on the oberved LID phenomenon. But thi impat may lead to a mall error in the reported ativation energie a well. The onequene of the ourrene of all poible tranition in Eq. (7) during an LID experiment i that the meaured generation rate of the SRC i in priniple influened by all poible tranition rate k ji of the A Si -Si i defet model (ee Fig. 1). The following quetion exit: How doe the olution of the rate equation ytem Eq. (7) hange if a parameter like, e.g., the hole denity i hanged? Whih hange in a tranition rate due to variation of a parameter (e.g., hole denity) i the reaon for the hange in the meaured tranition rate? Experimentally, it i found that the meaured generation rate of the SRC and the defet denity, whih i orrelated to the equilibrium population of tate 6 and 7, depend on the hole denity [47]. It i poible that the tranition from tate 6 to 7, whih i indeed a hole apture, ha a large impat on the olution of the rate equation ytem and hene on the meaured generation rate and on the meaured defet denity. With inreaing hole denity the tranition 6 to 7 beome more likely and tate 6 i depopulated. Thi ha an impat on the equilibrium reation between tate 4 and 6 and ould in onequene inreae the meaured tranition rate a well a the number of defet whih are in tate 6 or 7. In Ref. [44], a defet ativation due to a harge tate hange a propoed in Ref. [2, 4, 10] wa expliitly ruled out. The experiment arried out in Ref. [44] are baed on the aumption that the harge tate of a defet under nonequilibrium ondition i exluively ontrolled by the quai-fermi level. Thi aumption i wrong. It i neeary to take into aount the apture ro etion for eletron and hole of a defet [20]. It i poible that the oberved temperature dependene of the V 50 value i aued by the temperature dependene of the apture ro etion of the defet. Hene, the reported experimental reult [44] are not uffiient to exlude a poible defet ativation by hanging the harge tate of the defet. Bothe et al. [48] built-up a ophitiated experiment to meaure the V 50 value. A forward voltage wa applied to degrade n-in-p CZ ilion olar ell until a teady tate i reahed. The applied forward voltage generate eletron in the p-type bae, whih indue the LID phenomenon. A imilar experiment wa arried out for the ae of A Si -Fe i defet [49]. In that ae, it wa neeary to hift the teady tate of the A Si -Fe i defet by illumination. The V 50 value define the applied forward voltage and in onequene the eletron denity for a teady tate of 50% of the maximal defet denity. Within the frame of the A Si -Si i defet model thi ituation our for example for the SRC if the rate k 46 equal the rate k Conluion The ativation energie of the different defet tranition of the In Si -Si i defet were determined by time and temperature dependent arrier lifetime meaurement. It wa found that the energie of tranition 3 to 4 and 5 to 2 are different ompared to the B Si -Si i ae. 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