Beam Profiling

8/10/2019 Beam Profiling

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Spatial Cross Section Intensity of Purdues Rare

Isotope Measurement Laboratory Particle BeamProfessor: Matthew Jones

Author: Samuel Higginbotham

December 19, 2014

Abstract

The focus of this project is the analysis of a proton beam incident on an array of Commercial

BPW34FS silicon p-i-n Diodes to profile a particle beam. The goal of the experiment was to obtain

values of the forward voltage and compare the results before and after irradiation in order to map a

spatial intensity distribution to the cross-section of the beam based on the forward voltage. The prospect

of even equivalence in the beam for an arbitrary part is discussed. Further investigation and the start

of the analysis used Equivalence Fluence of 5 1014neq/cm2 and the diodes were read out at room

temperature in both reverse bias and forward bias regions up to a compliance limit of 1mA.

1 Introduction

The effect of radiation on silicon diodes isrecorded well, and their properties examined in greatdetail even at higher radiation dosages/higher equiv-alent fluences [1]. When Silicon Diodes are radiatedtheir dark current - an intrinsic current that is mea-sured at different voltages when there is no excita-tion of the diode - increases. This phenomena canbe attributed to a damage of the crystal lattice,or for a more thorough explanation, the radiationdamage produces traps that cause the semiconduc-tor to have high resistivity and dense generation-

recombination centers, visit the sources listed for fur-ther information[1] & [2]. Radiation and Semiconduc-tors is a rich study with copious amounts of material;however, this study is interested in the before andafter behavior of the diodes in order to map an inten-sity distribution. The BPW34FS silicon p-i-n diodesin use are extremely stable semiconductors with wellknown distributions that follow solid-state semicon-ductor theory. The forward and reverse bias regionsare invariant under measurement assuming same tem-perature and other environmental conditions. Oncethe diodes are irradiated they can be measured atthe same temperature as they were before irradiationto observe the changes that the radiation caused inthe dark current. Room temperatures may be used ifthe experimentalist is careful to measure voltage ator under 1mA of current for fluences on the order of1 1015neq/cm2 [1].

The sensitivity of radiation and the ease of useprovides enough motivation to use these silicon p-i-n diodes as a measurement tool for the beam profileat the location where dosage parts would be placed.

This study will also be useful for seeing how siliconsemiconductors behave in a beam that is mostly usedfor rare isotope measurement. The prospect of futureresearch and development at Purdues beam line canbe entertained.

2 Measurement

The diodes have been fixated to a circuit boardin an array of 20 with a separation of 6.72mm in thehorizontal direction and 4.20mm in the vertical direc-tion.

Array of Diodes No Pitch and Spacing:6.724.20mm

The IV curves of each diode are measured before andafter dosage in a temperature controlled room with alight sealed testing area. A Keithley 2410 Source me-ter was used to precisely measure the dark current atdifferent bias voltages. To be thorough, the forward

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4 ANALYSIS

10

5

0

5

10

10

5

0

5

10

0.51

0.512

0.514

0.5160.518

0.52

Foward Voltage at 100e-6A

Array 2: All 20 Diodes Z Axis is Forward Voltage

Note: The bin widths dont directly correlate to the

dimensions of the diode

Unfortunately the data for irradiated parts wasnot found in time, so the formula below can be usedto generate theoretical data. The forward voltage rel-ative to the fluence can be described in the followingway[1]:

V0 = eq

Thus data can be generated by assuming that thebeam would die off over a Gaussian distribution. In[1] the and parameters were found to be:

= 4.27 1018

= 1.289The forward voltage as a function of fluence can becomputed assuming the fluence dies off radially likea 2D gaussian. Hereeq = 5 10

14 Note: Gaussianmay be more skewed and sharper in practice.

105

05

10

105

05

10

0

5

10

15

20

25

30

h4Entries 20Mean x 3.037Mean y 2.078RMS x 3.744RMS y 2.606

h4Entries 20Mean x 3.037Mean y 2.078RMS x 3.744RMS y 2.606

Simulation of Radiation

Array 2: All 20 Diodes Z Axis is Forward Voltage

Simulation with Fit

4 Analysis

As the diodes of have been mapped out to a 2Dcross section it is natural to calculate a Bivariate Nor-mal Distribution to fit to the array of diodes in orderto calculate the probability density function that can

be used later for contour analysis and fitting for evenequivalence flux.

p.d.f=fp(x1, x2,...,xn) =

1(2)n||

e(1

2(x)T1(x))

Where is the covariance matrix:

ij =cov(xi, xj) = Exp[(xii)(xj j)]

Thus for the analysis here the bivariate case isthe function that should describe an x-y spatial in-tensity distribution with weights of the intensity ateach point corresponding to the dark current readout.The bivariate case is as follows[3]:

f(x, y) = B

2xy

12eA

A= 1

2(12)

(xx)

2

x2

+(yy)2

y2

2(xx)(yy)

xy

Where x is the Standard deviation of the forwardvoltage in x, and similar for the y direction. ThusROOT can be used to find the spatial distributionon the diode. The fitting function in the data sec-tion can have parameters returned and the contourmapped effectively:

10 5 0 5 10

10

5

0

5

10

Fitting Function Simulation

Array 2: All 20 Diodes Simulation with Fit

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REFERENCES

It has been shown that if the forward voltages canbe measured a bivariate distribution can be fitted andthe values of the means and standard deviations canbe obtained. The fitting function can then be usedas a guide to place a sensor for a particular amountof fluence. The parameters for this simulation would

be:***********************************X Mean -3.0825X Standard Deviation 14.743Y Mean -2.08Y Standard Deviation 6.71281Correlation Parameter Sig.xy 3.38e-05***********************************

5 Discussion

It must be restated that the actual data given isindeed hypothetical. The measurements for the for-ward voltage were real for the unirradiated diodes,but because of time constraints, the data gener-ated from the equivalence fluence was purely ficti-tious. Even though the data is generated, the anal-ysis should work in a real run, and there is enoughmotivation to complete this analysis.

The science and relationships behind these semi-conductors are well known to the point where if theparticle beam can be used to dose these diodes thenthe chance in the voltage and the equivalence flux canbe measured, because both can be easy measured as

shown in the study [1].Given that the relationships themselves are likely

in a real run, there is reason to believe that the distri-bution should be similar to what is seen here, whichmeans that the analysis is quite plausible for the realscenario. This analysis has quite a few advantagesover other techniques which should be discussed.

Using an array of diodes to calibrate or profilea beam has some advantages to other methods. Thediodes are placed where a silicon sensor may be placedif the beam is being used for new physics, whichmeans that the radiation would be extremely simi-lar to what parts place in the beam would see. The

accuracy of a beam profiler up the beam line is dif-ferent because there may be dispersion of the beamas it comes to the part. Also using the diodes createsvital experience for those who havent been familiar-ized with silicon sensor lingo and technology, not tomention that the array of diodes is probably less ex-pensive than a beam profiler.

6 Even Equivalence

In a real exercise, an experimenter is most likelyinterested in an even dosage. After mapping out theforward voltage to the spatial cross section of thebeam, the fitting parameters may show exactly where

the experimenter should place the sensor for the de-sired equivalence fluence.If the experimentalist was very ambitious then a

contour on the fitting function can be picked to findthe equivalence fluence of interest and the part can betraced along the contour to over the dosage time toobtain an even amount of radiation. In practice thiswould be rather difficult, because a motor would haveto be constructed to traverse the contour effectively.

7 Conclusion

The idea of using silicon p-i-n diodes as a beamprofiling tool was explored. The diodes are invari-ant before irradiation at room temperature, in a lightsealed environment. Due to time constraints, the ir-radiated data had to be simulated; however, with thevaluable fitting parameters obtained from [1] the datacould be simulated rather easily. The irradiated for-ward voltage can then be fitted with a bivariate dis-tribution, which will indicate where the desired flu-ence or dosage can be obtained, assuming the beam isnot moved between subsequent runs. Therefore usingCommercial BPW34FS silicon p-i-n Diodes to profilePRIME Labs particle beam seems completely feasi-

ble. Further investigation and further study with realdata should be implemented.

References

[1] J. Mekki, M. Moll, M. Fahrer, M. Glaser, and L.Dusseasu, Senior Member, IEEE. Prediction ofthe Response of the Commercial BPW34FS Sil-icon p-i-n Diode Used as Radiation MonitoringSensors up to Very High FluencesIEEE Transac-tions on Nuclear Science, Vol. 57, No. 4, August2010.

[2] H. Spieler, Chinese Physics C 33.7. Semicon-ductor detectorsNovember 2013. Vol. 38, No. 9,September 2014.

[3] Hamedani, G. G.; Tata, M. N. (1975). On the de-termination of the bivariate normal distributionfrom distributions of linear combinations of thevariables. The American Mathematical Monthly82 (9): 913?915. doi:10.2307/2318494

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8 ROOT CODE

[4] All About Circuits(2014).http : //www.allaboutcircuits.com/vol3/chpt3/1.html

8 ROOT Code

double func(double *x,double *p) {

double a = p[0];

double ux = p[1];

double uy = p[2];

double sx = p[3];

double sy = p[4];

double sxy = p[5];

double det = sx*sy-sxy*sxy;

double wx = sy/det;

double wy = sx/det;

double wxy = -sxy/det;

double arg = (x[0]-ux)*(x[0]-ux)*wx+

2*(x[0]-ux)*(x[1]-uy)*wxy+

(x[1]-uy)*(x[1]-uy)*wy;return a*exp(-0.5*arg);//(2*3.141592654)/sqrt(det);//took out the normalization factor...

}

/*****************************************************************************************

***********************************************************************************/

double fit1(double *x, double *p){

double a = p[0];//the saturation current for the reverse bias region.

double k = 1.3806488e-23;

double T = p[1];

double q = 1.60217657e-19;

return a*(exp(x[0]*q/(k*T)) - 1);

}

/********************************************************************************

*******************************************************************************/

void parsegraph2(){

//This program attemps to read multiple files

//based on the input file as the following convention:

//array#.diode#.biasDirect.ext

//The following doubles and constants are for reading out each diode//...find the iv curve fit it, then use the inverting function in

//ROOT to obtain the forward Voltage.

Double_t SpatCur[20];

Double_t SpatVol[20];

Double_t Posx[20] = {1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4};

Double_t Posy[20] = {1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5};

Double_t VD[20];

//The current that will correlate to a forward voltage for the fit1 function

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8 ROOT CODE

double ID = 100e-6;

double Is = 2.5e-10;//2.5e-6;//The saturation current for the diodes.

double Temp = 283;//The temperature in kelvin...Room temp here at 20 degrees celcius.

//Graphing each of the IV Curves

TCanvas *c1 = new TCanvas("Diode Readout","Diode Readout",200,10,600,400);

//c1->Divide(3);

TGraph *g[20];

TMultiGraph *mg = new TMultiGraph();

//Declaring the fitting function to fit the iv curves

TF1 *f1 = new TF1("f1",fit1, 0, 0.6, 2);

f1->SetParameters(Is,Temp);

/*************************************************************************************/

for(int fo = 1; foSetPoint(n,-x,-y);

n++;

//mg->Add(g[n++]);

}

}

g[fo-1]->SetLineColor(fo);

mg->Add(g[fo-1]);

g[fo-1]->Fit("f1");

g[fo-1]->GetXaxis()->SetTitle("Voltage V");

g[fo-1]->GetYaxis()->SetTitle("Current A");

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8 ROOT CODE

//"Inverts" the function for us...

VD[fo-1] = f1->GetX(100e-6,0.4,0.6,1e-11,100,false);

cout


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9 SUMMARY OF PROJECT: A STUDENTS POINT OF VIEW

Double_t VS[20];

for(int i = 0; iDraw("surf1");

//h4->Draw("lego2");

h4->Fit("fn");

fn->Draw("cont");

fn->SetTitle("Fitting Function Simulation");

//Getting the fitting paramters:

cout

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