SCIPP-00/48

SIMULATIONS OF THE SILICON MICROSTRIPDETECTOR FOR THE GLAST EXPERIMENT.

ClaudioPiemonte

INFN, Sezione di Trieste, Via A. Valerio 2, I-34127 Trieste, Italy

Abstract

Devicesimulationsof thesiliconmicrostripdetectorsthatwill equiptheTrackingSystemof theGLAST experimenthave beenperformed.Theinfluenceon theelectriccharacter-isticsof bothstrip pitch andwidth have beenevaluated.First, a DC calculationis doneto predicttherisk of breakdown within theworkingbiasconditions.Then,thebackplaneandinterstripcapacitancesareestimatedby meansof anAC analysis.

1 Introduction.

TheGLASTtrackingsystemusessiliconmicrostripdetectorsto tracktheelectron-positron

pairsresultingfrom gamma-rayconversionin thin leadfoils [1,2]. It consistsof a square�����arrayof nearlyidenticaltowermodules.Eachtowerhasascintillatorvetocounteron

thetop,followedby a ��� -layersilicon-striptrackerand,finally, acesiumiodidecalorime-

ter. Eachtrackinglayerusestwo planesof single-sidedsilicon strip detectorswith strip

orientedat � � degreeswith respectto eachother. Thedetectors,cut from � -inch wafers,

have a size of about � � �"!$#&% and are wire bondedinto ”ladders” ' �(!)# long. Four

of these”ladders”composea detectorplane.Whenoperatinga system,with sucha high

channelcount,in space,two limitationsappear: theavailability of powerfor theelectron-

icsandthedifficulty of dissipatingtheresultingheat.In orderto satisfytheseconstraints,

both the numberof channelsandthe readoutelectronicspower consumptionshouldbe

minimised.

Thebaselinedetectoris realisedon * -typewaferhaving a resistivity of �,+.-0/1!$# ,

anda thicknessof� ����23# . The readoutelectronicsis AC coupledto the 465 implants,

whicharebiasedby meansof integratedpolysiliconresistors.Thisdesignforeseesastrip

pitchof 7�� 892:# , andanimplantwidth of ; �92:# . Themetaloverhangstheoxide� 23# be-

yondtheimplantin orderto reducetherisk of breakdown. Theresultingnumberof strips

perdetectoris��� 8 , thus,usinga � � -channelreadoutelectronics,< chipsarenecessaryto

collectall theinformation.Recently, theconstraintson thepower consumptionhasbeen

revised,forcingareductionof thenumberof chips.It resultsin areductionof thenumber

of stripsperdetector.

In thispaper, theelectricalperformancesof thedetectorareevaluated,varyingboth

the strip pitch andwidth. First, a DC analysisis doneto estimatethe electric field in

thecritical region. Then,anAC analysisis appliedin orderto predictthe interstripand

backplanecapacitances.

2 Simulation technique.

Thesimulationis carriedout with ATLAS Device SimulationSoftwareproducedby Sil-

vaco[3]. A 2D approachis adoptedsince,for thesimulatedvalues,thepartialderivative

alongthe strip length is negligible. The lateralboundaryconditionsarea crucial point

whenselectingthe lengthof thestructureto besimulated.Mainly, therecanbetwo ap-

proaches.Oneis to build a very long cell in orderto keepthe lateralboundariesdistant

from the region of interest.Thedrawbackis a high numberof meshpointsand,conse-

quently, a long computationaltime. Theotherapproachis to choosea lateralboundary

2

1/2 implant widthfield plate length

pitch

depth

n-bulk

metal metalcathodes

p+ implant

n+ implant

p+ implant

anode

oxide

Figure1: Basiccell usedfor thesimulations.

whereonly theverticalcomponentof theelectricfield is present.As a result,we obtain

a very narrow cell having a lengthequalto thestrip pitch (fig. 1). This is optimalfor the

electricfield analysisbecausea high numberof pointscanbeusedto refinethemeshat

the edgesof the implantswithout exceedingthe computationaltime. Nevertheless,this

structureis not suitablefor the interstrip capacitanceevaluation,becausethe coupling

betweennon-adjacentstripsis neglected.As a matterof fact, this calculationrequiresa

lowernumberof meshpointswith respectto theDC analysis,thuswecanjoin morecells

without increasingthecomputationalcost.

TheDC solutionis obtainedsolvingbothPoissonandcarriercontinuityequations.

Thisanalysisallowsfor theevaluationof thebreakdown risk. It is known thatbreakdown

occurswhenfreecarriersareacceleratedup to a point wherethey have sufficient energy

to generatemorefree carrierswhencolliding with the atomsof the crystal. In orderto

acquiresufficient energy two conditionsmustbe met: the electricfield is enoughhigh

(morethanabout ' � ���>=@?"A�!)# ), andthe meanfreepathof the carriersis long enough

to allow accelerationto a sufficienthigh velocity. Only whenthegenerationrateof these

free carriersis sufficiently high this processleadsto avalanchebreakdown. In orderto

take into accounttheseparameters,animpactionizationmodelis includedin thesimula-

tion.

Beforestartingthe simulations,two parametersmustbe defined:the oxide charge den-

sity andthe 465 implantprofile. The former, for thesake of simplicity, is consideredall

localisedat the B3C@DEB�CGF % interface,while agaussianshapeis chosenfor thelatter.

It is worth noting that, in thesimulations,the 4 5 implanthasbeendirectly connectedto

3

themetal.Thisdoesnot introduceanappreciableerrorsincetheflat bandvoltage,related

to thethin AC couplingoxidelayer, is verysmall.

The AC analysisis performedjoining two elementarycells. It allows for the re-

Cback

1 2 3

bulk

oxide Cac

C"int

C’int

1 2 3

bulk

oxide Cac

Backplane capacitance Interstrip capacitance

Figure2: Structureadoptedfor theAC analysis.

constructionof thestripcapacitance,oneof theparametersdeterminingthenoiselevel of

the readoutelectronics.It is givenby the sumof two capacitances:one( HJILKNMPO ) derives

form thecouplingbetweenthe implantandthebackplanelayer, while theother( HJQSRUT ) is

dueto thecouplingbetweentheconsideredstrip andall theothers.We do not take into

accounta third tiny contributiongivenby theAC couplingcapacitor, sincethesimulation

is performedona structurein which themetalis connecteddirectly to theimplant.

Theprocedureadoptedfor thesimulationis thefollowing: first, thedevice is broughtat

a biasvoltagerising thepotentialof theanode.Then,in orderto evaluateHJILKNMPO , a small

signal(with a frequency of �UVXWZY ) is appliedto theanode,andthecapacitancebetween

thecentralstrip (strip n. 7 ) andtheanodeitself is checked. As far as HJQ[RUT is concerned,

a small AC signalis appliedto the cathoden. ' andthe capacitancesH]\Q[R�T and H]\ \QSRUT are

measured.In this way thecouplingto moredistantneighboursis neglected,andthetotal

capacitanceis givenby:

HJT�^_T�`aHJILKbMPO�cdHJQ[RUT9`eHJILKNMfO"cd7 �hg H \Q[R�T chH \ \Q[R�T_i (1)

Thecalculationof thebackplanecapacitanceasa functionof thebiasvoltagepermitsthe

reconstructionof thefull depletionvoltageby meansof the �UA�H]%ILKNMfO curve.

Thetablebelow shows thepitch/widthvaluesusedin thesimulations.

4

width pitch width/pitch23# 23#50 175 0.28650 208 0.24050 235 0.21350 265 0.18960 175 0.34360 208 0.28960 235 0.25560 265 0.226

Table1: Pitchandwidth valuesusedin thesimulations.

3 DC analysis.

First, a simulationis donein orderto estimatethe impactof the metaloverhangon the

electricfield intensityin thevicinity of thejunction. Fig. 3 shows themapof theelectric

203j

204j

205j

206j

207j

208j

209j

210j

211

-2

-1

0k1

2

3l4

Microns

Mic

rons

metal

n-type bulk

oxide

p+ implant

E Field (V/cm)

03.74e+047.48e+041.12e+051.5e+051.87e+052.24e+052.62e+052.99e+053.37e+053.74e+05

Figure3: Map of the electricfield strengthfor the 7 '�;(A ;�� structure(the biasvoltageis7�� �(? ).

field intensityfor the 7�'�;�A ;�� (pitch/width)structurewith a metaloverhangof� 23# , and

anoxidecharge mn^_o of � � �p�rq$qtsuA�!$#&% . In thesilicon, thehighestelectricfield is located

at the implant edgeand in the proximity of the metalborder. Without field-plates,the

5

lines of the electric field would be all accumulatedat the edgeof the implant. Fig. 4

shows theprofile of theelectricfield strength,takenalonga line crossingtheedgeof the

465 implant, for thesamestructure:gwv i with, and

gwx i without field-plate.Theusefulness

0.2 0.4 0.6 0.8 1 1.2

0

50000

100000

150000

200000

250000

300000

350000

Line crossing the junction edge (micron)

Elec

tric fie

ld (V

/cm)

(a)

(b)

Figure4: Electricfield profile alonga cut-linecrossingthe implantedgefor the 7�' ;(A ;��structure:

gwv i with, andgfx i withoutfield-plate.

of the field-plateis clearly visible: the peakheight is reducedby two times. Further-

more,thedevice without field-platepresentsa peakhigherthanthecritical value,hence

potentiallydangerous.Fig. 5, showing the electroncurrentdensity, demonstratesthat

thereis generationof free carriersin that region, but not high enoughto determinean

avalanchebreakdown. Accordingto thesimulations,it occursat a biasvoltageof about

��� �(? . Plainly, the calculationdoesnot take into accountthe presenceof local defects

whichcouldgenerateenoughfreecarriersto reachthebreakdown ata lowervoltagewith

respectto the ideal case.Thus,the useof the metaloverhangis advisablein a detector

with suchcharacteristics.

Now, let usanalysetheinfluenceof thepitch/widthsizeontheelectricfieldstrength.

Fig. 6 and7 display the maximumvalueof the electricfield asa function of the bias

voltagefor thestructureslisted in Table1. As expected,it dependsbothon the implant

pitchandwidth. Anyway, thepeakintensityis below thecritical valuefor all thestructures

up to abiasvoltageof '�� �"? .

6

208y

209y

210 211y

-2

-1

0

1

2y

Micronsz

Mic

rons

e- Current Magnitude (A/cm2)

0{1.73e-103.47e-10|5.2e-10}6.94e-10~8.67e-10�1.04e-091.21e-091.39e-091.56e-091.73e-09

Figure5: Theelectroncurrentdensityplot evidencesa carriergenerationat theedgeoftheimplant.

1.0e+05

1.5e+05

2.0e+05

2.5e+05

3.0e+05

100 150 200 250 300

Ele

ctr

ic f

ield

(V

/cm

)

�

Bias Voltage (V)

implant width = 50µm

full depletion pitch = 175µmpitch = 208µmpitch = 235µmpitch = 265µm

1.0e+05

1.5e+05

2.0e+05

2.5e+05

3.0e+05

100 150 200 250 300

Ele

ctr

ic f

ield

(V

/cm

)

�

Bias Voltage (V)

implant width = 60µm

full depletionpitch = 175µmpitch = 208µmpitch = 235µmpitch = 265µm

Figure6: Magnitudeof theelectricfieldpeakasa functionof theappliedvoltage,for structureshaving an implant ;���23#wide.

Figure7: Magnitudeof theelectricfieldpeakasafunctionof theappliedvoltage,for structureshaving an implant ����23#wide.

7

1.2e+05

1.4e+05

1.6e+05

1.8e+05

2.0e+05

2.2e+05

2.4e+05

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34

Ele

ctric

fiel

d (V

)

w/p

Bias voltage = 200V

implant width = 50µmimplant width = 60µm

Figure8: Electricfield peakasa functionof thewidth/pitchratio.

Also theoxidechargedensityplaysanimportantrole: thehighertheconcentration

thestrongertheelectricfield. As anexample,fig. 9 showstheeffectof varyingtheoxide

1.0e+05

1.5e+05

2.0e+05

2.5e+05

3.0e+05

3.5e+05

100 150 200 250 300

Ele

ctric

fiel

d (V

/cm

)

�

Bias Voltage (V)

235/50 structure

Qox = 1*1011 q/cm2

Qox = 2*1011 q/cm2

Figure9: Electricfield peakasa functionof thebiasvoltagefor differentoxidecharges.

charge densityfrom � � ���(q$q to 7 � ���(q$q�suA !)#&% for the 7�'�;�A ;�� structure. The higher

concentrationbrings the electricfield over the critical valuewhenwe apply more than

7�; �(? .

8

4 AC analysis.

In orderto verify the quality of the simulations,a comparisonbetweenthe calculations

andexperimentaldatais performed. The dataare taken from [4], wherea carefulex-

perimentalstudyregardingthecapacitancesis done.Oneof thetestedstructuresis very

similar to our detector, having a thicknessof� ����23# anda bulk resistivity of �"+�- . The

siliconis ��������� -type,leadingto ahigheroxidechargeconcentrationwith respectto the

��������� crystaltypeforeseenfor GLAST. Threestructureswith a constantwidth/pitch

ratio, equalto �(���p; , aremeasured.Figures10, and11 show a comparisonbetweenex-

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 50 100 150 200

Cback (

pF

/cm

)

pitch (µm)

Backplane capacitance

Bias Voltage = 500VSimulation

Experimental data

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 50 100 150 200

Cin

t (p

F/c

m)

�

pitch (µm)

Interstrip capacitance

Bias Voltage = 500VQox=1*1011 q/cm2

Qox=2*1011 q/cm2

Qox=3*1011 q/cm2

Experimental data

Figure10: Backplanecapacitanceof thetestdetector.

Figure11: Interstripcapacitanceof thetestdetector.

perimentaldataandsimulationresultsfor bothinterstripandbackplanecapacitance.The

agreementis foundto bequitegood,thusvalidatingthesimulationprocedure.It is worth

noting that the valueof the interstripcapacitancedependson the electronaccumulation

layer underthe B3C�DXB3C�F % surface,that in its turn dependson many parameter. In par-

ticular, suchparametersare: the fixed oxide charge density, the bias voltage,and the

environmentalhumidity. It is quite difficult to estimatenumericallythe influenceof the

lastparameter. In aqualitativeway, negativecharges(polarisedwatermolecules)arecol-

lectedon theuncoveredoxidesurface,partially compensatingthepositive oxidecharge

[5]. In our casetheeffective valueof m�^_o&`�7 � ���rq$qts�A�!$#&% is found to fit in a proper

way theexperimentaldata.

Let’snow simulatethecapacitancesof thestructureslistedin Table1.

9

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

180 200 220 240 260

Cba

ck (p

F/cm

)

pitch (µm)

GLAST detector - Backplane capacitance

Bias voltage = 250V

implant width=50µmimplant width=60µm

Figure12: Backplanecapacitanceasa functionof thepitch.

0

1

2

3

4

5

6

0 50 100 150 200 250 300

1/C

back

2 (cm� 2

/pF2 )

Ubias (V)

175/50208/50235/50265/50

Figure13: �UA H�%ILKbMPO asafunctionof thebiasvoltagefor structureshaving animplant ;���23#wide.

10

Fig. 12 shows the backplanecapacitancefor a biasvoltageof 7 ;��(? . It doesnot

changesubstantiallyvarying the width from ; � to ����23# , while, asexpected,increases

with thepitch. HJILKNMfO givesinformationconcerningthedepletionof thedetector. Fig. 13 is

a plot of ��A�H�%ILKbMPO asa functionof theappliedvoltagefor thestructureshaving animplant

;���23# wide. For eachcurve, the changeof the slopeindicatesthat the full depletion

voltageof thedetectoris reached.Increasingthepitch from ��< ; to 7�� ;92:# it risesfrom

��' � to �p<��(? . Thesevaluesdependslightly ontheoxidechargeconcentration;in thiscase

weusedmn^_o�`�� � ���(q$qGsuA�!$#&% .Theinterstripcapacitanceis plottedin figure14. As onecansee,thevaluedepends

consistentlyonboththeimplantwidth andpitch.

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

180 200 220 240 260

Cin

t (pF

/cm

)

�

pitch (µm)

GLAST detector - Interstrip capacitance

265/50

235/50

208/50

175/50

Bias voltage = 250V

implant width = 50µmimplant width = 60µm

Figure14: Interstripcapacitanceasa functionof thepitch usinga biasvoltageof 7�;��(?andanoxidecharge mn^�o�`�� � �p� q$q suA !)# % .

The total capacitanceasa function of the pitch is presentedin fig. 15. As it is

evidencedexperimentallyin [4], this valuedependsonly on the ratio betweenthe two

quantities,on thecontraryto theelectricfield behaviour (fig. 8). Thecapacitancegrows

linearlywith the ��A�4 ratio,asdemonstratedin fig. 16.

11

1

1.1

1.2

1.3

1.4

1.5

1.6

180 200 220 240 260

Cto

t (pF

/cm

)

�

pitch (µm)

GLAST detector - Total capacitance

implant width = 50µmimplant width = 60µm

Figure15: Total capacitanceasa functionof thepitch.

1

1.1

1.2

1.3

1.4

1.5

1.6

0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34

Cto

t (pF

/cm

)

�

w/p

GLAST detector - Total capacitance

f(w/p) = 0.89 + 1.3*(w/p)

implant width = 50µmimplant width = 60µm

Figure16: Total capacitanceasa functionof thewidth/pitchratio.

12

5 Conclusions.

The resultsof the capacitancestudy indicatethat the best-performingstructure,among

thoseanalysed,hasa pitch of 7���;�23# and an implant ;���23# wide. The DC analysis

performedfor this structuregivesa maximumfield underthecritical value,beingabout

7(��< � ��� = ?�A�!$# at a biasvoltageof '�����? . Still, having sucha high valueof theelectric

field, weconsiderapitchof 7 ��;�23# asa limit for animplantwidth of ;���23# . For a larger

pitch it is necessaryto increasealsotheimplantwidth.

6 Acknowledgements

The authorwould like to thank A. Vacchi for the continuousencouragementandsup-

port. Many thanksalso to V. Bonvicini, L. Bosisio,andA. Rashevsky for the fruitful

discussions.

References

[1] P. Michelsonet al., “GLAST LAT”, Responseto AO 99-OSS-03,StanfordUniv.,

(1999).

[2] E.D. Bloom et al., “Proposalfor GLAST”, SLAC-R-522(1998).

[3] SILVACO International,ATLAS User’s manual(1998).

[4] CMS Collaboration,Addendumto theCMS tracker TDR, CERN/LHCC2000-016

(2000).

[5] A. Bischoff et al., Nucl. Instr. andMeth.A326, 27-37(1993).

13