Extraction of Doping Density Distributions from C-V Curves

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Christina Tate
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1 Extraction of Doping Dnsity Distributions from C-V Curvs Hartmut F.-W. Sadrozinski SCIPP, Univ. California Santa Cruz, Santa Cruz, CA 9564 USA 1. Connction btwn C, N, V Start with Poisson quation d V = N (1) dx and th quation for capacitanc of a paralll capacitor A C = () x. whr x is th thicknss of th dpltd rgion. W masur C-V, i.. th capacitanc as a function of voltag, which using q. can b turnd into V(x). According to q. 1, diffrntiating this function twic rsults in th dpltion voltag. Succssiv approximation works quit wll: divid th capacitor of thicknss d into slabs of qual thicknss t, which ach hav a capacitanc d Ct = Co. (3) t Th rciprocal of ths constant capacitancs can b addd up to mak up th capacitanc masurd and th corrsponding voltags Δ t V(x) across th capacitors ar adjustd to match th obsrvd C-V curv. Assuming that th doping dnsity dos not chang across th distanc t, th voltag Δ t V(x) can b xprssd in trm of th local doping dnsity x dv ( x) = N x dx dx ( ) (4) x+ t x ΔtV ( x) = N ( x) dxdx ' N ( x)(( x t) x )) N ( x)* x * t = + = x Nd good fits for C vs. V curvs for this, and a studnt is working on this.. Simulations using N distributions On approach is to assum a trial N distribution and adjust th paramtrs such that th simulatd C-V curvs fit th xprimntal ons. x dv ( x) = N ( x) dx = N (1)*( x xx) + E dx (5) E() = E E E c = N = + N (1)*( xx1 xx) + E (1)*( xx1 xx) + E c

2 V ( x) = N (1)*[( x) ( xx) ] N (1)* xx*[ x xx] + E *[ x xx] V For un-irradiatd dtctors or dtctors whr th doping dnsitis ar uniform or at last monotonic functions of th dpth, this is a straight forward procdur: on slowly incrass th dpltion dpth with a stp siz of about on micron, and calculats th corrsponding filds and voltags dpnding on th trial N distributions. For trial distributions, w follow th modl from Fig. 3.b of our Carml papr (M. Bruzzi t al.) shown in Tabl I and Fig. 1, whr thr rgions with constant N s ar dfind; on in front with N (front), a constant fild rgion in th cntr (N =) and on with th opposit sign in th back, N (back). Ths distributions wr drivd from TCT data of b-typ MCz dtctors irradiatd to highr fluncs. Th simulation varis th boundaris of ths thr rgions and th valu of th N s. Nutrons Tabl I: Trial N Distributions Protons x [um] E [V/cm] N [cm-3] x [um] E [V/cm] N [cm-3] E E E E E E E E+1 Elctric Fild [V/cm] 4x1 4 p + n+ 4 GV protons.1x1 15 cm - 3x1 4 x1 4 1x1 4 Ractor nutrons 5x1 14 cm - (b) x [μm] Fig. 1 Elctric fild profil as dtrmind by TCT in n-typ MCz silicon aftr irradiation with 4 GV protons up to x1 15 cm - and with 5x1 14 cm - 1MV nutrons. For irradiatd dtctors, which might xhibit a doubl junction (DJ), on can try to start dpltion from both sids. Th qustion is thn which stp siz to choos on th two sids. Th only choic of stp siz which lt to a rasonabl agrmnt btwn

3 simulation and data was that th stp siz at th back contact Δx b was rducd in th ratio of th rspctiv N s with rspct to th front sid Δx f : Δ x = N ( front) / N ( back) * Δx b Sinc in all cass considrd th back sid N was much largr, th rsults wr consistnt with starting th dpltion only from th front. In many cass, starting th dpltion from th front lads to bttr fits of th data, as shown in Fig.. Th xtractd distributions of th doping dnsitis ar qualitativly quit similar, and in th following w will considr th simulations starting from th front only. f 1.E-3 1/C n MCz (protons) 1.E-4 1/C^ 1.E-5 1.E-6 n MCz n(protons) -19C 4Hz sim Front sim Scald 1.E Bias Voltag Fig. Logarithmic plot of th 1/C V distribution of a n-typ MCz silicon dtctor aftr irradiation with 4 GV protons up to 1.4x1 15 cm - with simulations starting ithr at th front or both on th ftont and th back ( scald ). 3. Dvics W usd th C-V curvs of th six SMART SSD shown in Tabl II. Th un-irradiatd p- typ FZ SSD 68-1 was usd to vrify that th procdur rsultd in th xpctd distributions basd on a uniform N. Tabl II: SMART SSD usd SSD Wafr Flunc [nq/cm - ] 187- n MCz 1.4* μm protons 53-4 p MCz ~1.4* μm protons 66-8 p MCz ~4* μm nutrons n FZ ~4* μm nutrons 14-5 p FZ ~4*1 14 μm nutrons Tmpratur [ o C] Frquncy [Hz] CCE -1 4 Ys Ys -1 4 Ys - 5 Ys - 5 RT 1,

4 68-1 p FZ μm Pr-rad RT 1, 4. Rsults 4.1 C-V Normalisation: Fig. 3 shows that th normalization of th capacitanc is wll undrstood: w gt agrmnt btwn th diffrnt SSD at dpltion. Th two p MCz dtctors with roughly th sam flunc in nutrons and protons agr vry wll in th limitd voltag rang whr thy can b compard: this opns up th possibility to mak prdictions for dpltion profil vn for dtctors which show arly brakdown, onc w gain mor xprinc with th C-V curvs. Th p-typ FZ dtctors hav μm thicknss, and it will b intrsting to compar th LTLF data of 14-5 with th pr-rad data of E-4 1/C p&n -typ 1/C [pf - ] 1.6E-4 1.4E-4 1.E-4 1.E-4 8.E-5 6.E-5 4.E-5.E-5.E p MCz (- 1dg) 4Hz protons 66-8 p Mcz (-C) 5Hz nutrons n MCz (-1C) 4 Hz protons 156 n Fz (-C) 5 Hz nutrons 14-5 p FZ (RT) 1 khz 68-1 p FZ (RT) 1 khz Voltag Fig. 3 Masurd 1/C V curvs at th optimal frquncis for th tmpraturs slctd. 4. Simulation Rsults Fig. 4 shows th rsults on th simulations of th two MCz dtctors which could b fully dpltd. Th agrmnt btwn data and simulations ar quit good, and th fits could b improvd vn mor by using a doubl-junction modl with two non-uniform Ns. As control, th simulation of th un-irradiatd p-typ FZ dtctor 68-1rsults in a straight-lin 1/C bhavior and a constant doping dnsity of 3.*1 1 cm -3.

5 .E-4 1/C p MCz W66-8 (nutrons) & W53-4 (protons) 1.5E-4 1/C^ 1.E-4 5.E p MCz (- 1dg) 4Hz protons 66-8 p Mcz (-C) 5Hz nutrons sim.e Voltag.E-4 1/C n MCz (protons) 1.5E-4 1/C^ 1.E-4 5.E-5 n MCz n(protons) -19C 4Hz sim.e Voltag Fig. 4 Masurd and simulatd 1/C curvs. Th fits ar quit good, but could b improvd using a doubljunction modl with two non-uniform Ns, Th fits yild distributions of th ctiv donor concntration in th assumd doubl junction modl. Thy ar shown in Tabl III and Fig. 5. A comparison of th lctric fild profils for th two MCz dtctors is shown in Fig. 6. As in Fig. 1, a doubl junction is clarly sn with a rlativ low-fild rgion in th dtctor cntr, indicating a vry high rsistivity bulk. Th rlativ strngth of th front to back junctions is clarly diffrnt in th two sampls, and w hav to await th rsults on n MCz irradiatd with nutrons to dcid if this is a proprty of th matrial or du to th irradiating particl spcis as suggstd by th xtraction of th fild by TCT (Fig. 1). Th n-typ MCz dtctor shows a much largr xtnd and much lowr strngth of th lctrical fild in th intrinsic bulk. Tabl III: Simulatd N Distributions 187- n MCz (protons) 66-8 p MCz (nutrons) x [um] E [V/cm] N [cm-3] x [um] E [V/cm] N [cm-3] 18,.4E+13 44, 1.8E ,.4E ,5 1.8E , -.7E ,5-1.3E , -.7E , -1.3E+14

6 4.E+13 N vs. dpth N [cm^-3].e+13.e+ -.E+13-4.E+13-6.E+13-8.E+13-1.E+14-1.E E n MCz (protons) p MCz W68-8 (nutrons) x [um] Fig. 5 Extractd doping dnsity profil N vs. dtctor dpth for both n- and p-typ MCz dtctors. 5.E+4 E Fild n MCz W187-4 (protons) p MCz w68-8 (nutrons) 4.E+4 E [V/cm] 3.E+4.E+4 1.E+4.E Dpltd Dpth x [um] Fig. 6 Extractd lctric fild distribution vs. dtctor dpth for both n- and p-typ MCz dtctors. Th rlativ siz of th filds at front (x ) and back. (x 3) is diffrnt fro n-typ and p-typ. 4.3 Charg Collction From th fits th dpltion charactristics of th dtctors can d xtractd. Th dpltd dpth is proportional to th rciprocal capacitanc. Fig. 7 shows th dpth of th dpltd rgion as a function of voltag for th invstigatd p-typ n-typ, and dscribs th sam data as Fig. 3. Th most striking fatur is that th n-typ MCz has vry

7 diffrnt dpltion charactristics from all othr wafr typs. W will soon hav data from all dtctor typs, irradiatd with both nutrons and protons, which will allow us to dtrmin th dpndnc of th dpltion charactristics on wafr and particl typ. 3 Dpltd Rgion Dpltd Rgion x [um] 1 n MCz W187-4 (protons) P MCz W66-8 (n+p) p FZ W68-1 pr-rad n FZ W156- (nutrons) p FZ 14- (nutron) Bias Voltag [V] Fig. 7 Dpltion charactristics xtractd from th fits. Th dpltd rgion is proportional to th rciprocal capacitanc. A critical tst of th simulation procdur is th comparison of th C-V data with charg collction (CC-V). Good agrmnt of CC-V with th xpctation (Fig. 7) would allow substituting rlativly asy and fast lctrical masurmnts lik C-V for th much mor involvd charg collction procdur to charactriz th prformanc of irradiatd dtctors. Diffrncs btwn C-V and CC-V might b intrprtd as an indication for trapping.

8 4 n MCz W187- Mdian & norm 1/C Karlsruh ( 6 MV protons) 1.4*1 14 nq/cm Collctd charg [fc] 3 1 Sim 1/C -C, 5 Hz CCE 5 6C Sim Front Bias Voltag [V] 4 P MCz low 66-8 Mdian & Norm. 1/C Louvain nutrons 4*1 14 nq/cm 3 Mdian [fc] 1 CCE 1 -C, 5 Hz Bias Voltag [V] Fig. 8 Masurd mdian charg collctd vs. bias voltag (CC-V) and th prdiction from th fits to th C- V data. Th normalization btwn th diffrnt curvs is accurat to about 1%. Th diffrnc btwn th CC-V and rciprocal C-V curvs might b xplaind by trapping in th nutral bulk.

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n