Bachelor Thesis - Institute of Particle and Nuclear Physics
Contents
1. Donor level Eg Acceptor level oe bi o a CD D D GS oS G amp S amp amp Valance band Valance band Valance band a Intrinsic semiconductor b n type semiconductor c p type semiconductor Fig 1 Energy level diagrams for a intrinsic b n type c p type semiconductors When two different conductivity semiconductors or same conductivity semiconductors with different concentration of impurities are joined together a pn diode is created Because of a higher concentration of holes in p region they start to diffuse to n region Similarly electrons from n region diffuse to p region This effect results in imbalanced volume charges in both p and n parts of diode n p creating an electric field It is because of this field that nia a charge carriers start moving in directions opposite to the ones caused by diffusion this movement is called drift Finally drift and diffusion currents compensate each other n Na diode comes to equilibrium and a potential difference Ux b in junction is created Concentrations of electrons and holes ionized impurities concentrations and volume charges distributions dependance on coordinate is shown in figures 2 a b and c respectively 1 Because of this field charge carriers gain potential IT energy thus their conductivity and valance bands shift and R Fig 2 a Concentration of e and h can be written as b concentr2. stands for number of pixels in matrix N number of photons hit the detector PDE photodetection efficiency Even this expression fails when the length of pulse is longer than detectors recovery time 2 Gain The gain can be written as c c CoA U 12 px From this equation we can see that G can be increased whether with increasing capacitance bias voltage or breakdown voltage 3 Bias voltage Ubias Adjusting this parameter 1s the easiest way to adjust the gain coefficient It can be shown that lee Ny Upas Una EN re U G A bias bd 0 X iis bd 2 V U bias 2 si V U sias 13 If the capacitance is 50pF Upa 57 V Ubias 60 V then we have G 1 2 10 However with increasing bias voltage the influence of some side effects is also increased 9 Breakdown voltage Upa This parameter is dependant on temperature the dependance coefficient 1s negative usually in range of 10 100 mV K 9 Upa dependance on temperature can be analyzed as electrons scattered by phonons Energy gained by a charge carrier in electric field is proportional to its free path along the direction of field This energy has to be higher that the width of energy gap so the atom can be ionized If the length of free path is limited by phonons then it can be written as A 2N 1 where Ag free path in T 0K N phase space of phonons The later can be expressed as 10 11 hv j N exp T
3. 14 14 where v stands for the effective energy of phonons in scattering Then the breakdown voltage can be written Usa 040 Ed ol fons 15 where E stands for energy gap width and d depleted layer thickness PDE Q E E wE Photodetection efficiency PDE can be expressed in 4 terms 2 9 16 pl E Geig Epav fill factor becouse of electronics not all the surface of detector is active photons hitting the inactive areas will not be registered Ep permeability factor photons reflected from surface or absorbed in dead layer will not be detected Q E quantum efficiency the ratio of photons that created a pair of charge carriers to the ratio of photons that got into active area EGeig probability for a charge carrier to start avalanche process 2 4 Noise Every single charge carrier to get into avalanche region creates a signal same as incident photon Such a signal generated by thermal charge carriers is usually in range of 100kHz up to few MHz per mm There are few ways to reduce the noise 9 Cooling the detector number of carriers decreases by a factor of 2 for every 8K Reducing the charge colection area Reducing the Up as gain also reduces Apart from termal noise there are some other unwanted effects 9 Optical cross talk Afterpulses Optical cross talk is the effect when one charge carrier escapes from a cell and is cought in another ce
4. Waveform smoothening Because of noises in detector and electronics measured signal has a lot of local disorders that need to be removed To achieve this the response of every single cell is averaged in a window of 10 nearby cells 2ns Mathematically this can be written As 17 n0 4 10 ani dj i d n i 5 T d n i 5 gt i 5 1019 18 Waveforms before and after smoothening are shown in figures 12a and 12b 20 a Waveform before processing 10 15 20 0 20 40 60 80 100 120 140 160 180 200 220 Fig 12a Raw oscilloscope data Noise is visible at 30ns nue signal is registered at 170ns shift from OmV is seen b Waveform after smoothening gt 2 E 2 0 2 f k 4 6 8 10 12 14 16 0 20 40 60 80 100 120 140 160 180 200 220 Re t ns Fig 12b Waveform after smoothening Noise peak at 30ns is eliminated c Waveform after pedestal subtraction gt 4 E gt 2 0 A LY 2 4 6 8 10 12 14 KA EE E ae tiles ici asili 0 20 40 60 80 100 120 140 160 180 200 220 t ns Fig 12c Waveform after smoothening and pedestal subtraction Shift from OmV position is removed 21 Pedestal subtraction All the cells in each waveform share a common shift from OmV amplitude This shift called pedestal applies to the peak measured as well therefore 1t must be removed Oscilloscope starts recording the signal after receiving a trigger however response from detector can be shifted
5. strong enough to accelerate charges to cause avalanche the secondary electrons are collected in this well and the field becomes insufficient to cause another avalanche In this case quenching resistors are not needed the well suppresses its activity itself The cell remains inactive until it discharges The advantages of such a detector are high sensitivity to visible and UV light high dynamical range and as mentioned above fill factor with values up to 100 5 13 11 ia Db n Si wafer cc Fig 5 Schematic views of three MAPD types a MAPD with individual surface resistors b MAPD with surface transfer of charge carriers c MAPD with individual micro wells 1 Common metal electrode 2 buffer layer of silicon oxide 3 p n junctions micro pixels 4 individual surface resistors 5 individual surface channels for the transfer of charge carriers 6 drain region contact 7 epitaxial silicon layer of p type conductivity 8 a high doped silicon layer of p type conductivity 9 a region with micro wells 10 local avalanche regions 1 1 individual micro wells 5 12 2 3 Properties Every single element of MAPD is connected to the voltage source via a quenching resistor and the response of all the elements are collected in one electrode The output of detector is the sum of all individual micro cells The operating voltage of every cell is a little higher than the breakdown voltage and the di
6. ul LA 3 where Nx lower concentration of impurities Depleted zone is the active area of pn detector where the incident particles create e h pairs which are later collected by corresponding electrodes and thus create a signal 1 A diode with a depleted zone of area S and thickness D operates like a planar capacitor with capacity Cah EE EN y 4 D 2 U To achieve a better energy resolution capacity has to be reduced thus the external voltage has to be increased 3 Leakage currents Even if the detector is not exposed to any radiation a small current lt 14A will be registered if detector is reverse biased This current can be both volume and surface type There are two sources for volume leakage currents e Minority charge carriers in p and n regions having diffused from neutral to depleted zone will be exposed to electric field and will drift to the corresponding part of diode Since these charges are continuously generated in both sides of junction and are free to diffuse a small constant current will be registered Usually generation of such carriers is small and do not have much influence on signal registered e Another source for leakage current is thermal pair generation in depleted zone Apparently number of such charges will grow with increasing thickness of depleted region therefore to avoid this detector has to be constantly cooled For silicon such a generation in room temperature is small on the
7. delay for second pulse was in range of 50ns 230ns were used for analysis Absolute values of suppressed amplitude and its ratio to ordinary one cell response are given in figures 20a and 20b respectively Amplitude spectra for delay time t 100 and all three powers are given in figure 21 32 a Full second pulse amplitude b Second pulse amplitudes ratio to first pulse amplitude 6 0 65 5 5 0 6 0 55 gt 5 E S A 0 5 34 5 T d Q 0 45 z 4 Pulse power a 0 32 uw 3 5 4 35 uw 0 35 7 35 uW gt 40 60 80 100 120 140 160 180 200 220 240 a 40 60 80 100 120 140 160 180 200 220 240 Time between pulses ns Time between pulses ns Fig 20 a absolute amplitude value of suppressed one cell response to the second pulse and b suppressed amplitudes ratio to ordinary one cell response versus time between two pulses in three different pulse powers With an increasing time between absolute value of suppressed amplitude grows for the cells recharge level raises within time after first pulse The ratio decrease in power range of 0 32uW to 4 35uW is due to the increase of first pulse amplitude while the suppressed remains constant With pulse power increased to 7 35uW there seems to appear a shift of 1 2mV in suppressed amplitude value This shift remains constant in the time range measured This shift is possibly due to charge sharing between few cells 33 0 32 uW 1st pulse Entries 20000 2200 Mean 8 599 RMS
8. eisi ania a a i bea 27 Be CONG IS ia 35 JK OO 101 1011 1111 111112 36 GAD ici 37 0 1 Data Anal YSIS S0LLW ATC 5 sa aaa aa i o a a a r a a i a a 37 S a iii 40 1 Introduction Micro pixel Avalanche Photo Diodes MAPD also known as Silicon Photomultipliers SIPM are a novel type photon detectors with a potential to replace the traditional photomultiplier tubes A MAPD is a matrix of avalanche photodiodes working in Geiger mode on silicon substrate The efficiency of these detectors is dependant on wavelength of photon being registered and is greatest in UV IR region therefore they are usually coupled with scintillators or Cherenkov counters The main advantages of SiPM compared to traditional PMTs are their rigid size low production costs low bias voltage and most important capability of working in strong electric and magnetic fields Therefore such detectors can be used in areas like Positron Emission Tomography EM calorimetry in particle accelerators etc where registering single photons becomes a main task However a lot of research is still needed before such photomultipliers are ready to be used at their full potential Thus it is the purpose of this paper to analyze the response of one of silicon multipliers MAPD S60 when exposed to 682nm wavelength laser pulses simulating scintillators output In particular it is of importance to check its response linearity over surface area as well as its behavior when exposed to diffe
9. in time due to delays in detector electronics and laser itself To find the exact position in time when detectors response is registered we draw 100 waveforms in a same graph Fig 13 Then the timing of response becomes apparent Big time interval before the response is an advantage when calculating pedestal from a bigger number of cells we can more accurately evaluate their mean value Mathematically this operation can be written 19 ni ni n 20 th Li i N l PN M li Li IO M di L j bi AN i i vl Whi Lili r li il NNT I ji IN pEr i i HS 20 40 60 80 100 120 140 160 180 200 ee Fig 13 100 waveforms on same graph It is clearly visible that detectors response is in time window from 160ns to 185ns 22 here n stands for waveform number i cell number k number of cells that are used for pedestal evaluation ani n th waveform i th cell amplitude An n th waveform first k cells mean value a n th waveform i th cell amplitude with pedestal subtracted already Signal waveform after smoothening and pedestal removal is shown in Fig 12c When measuring double pulse response the response to first pulse is at the very end of oscilloscope s measured range thus registering a second response would become impossible To avoid this a trigger delay in oscilloscope is set Increasing the delay value we broaden the possible measuring window for double pulse response however we re
10. is focused by a lens to detectors surface The focusing lens is fixed on a stage which is able to move in three directions Both the 3D stage and optical attenuator are controlled by a PC Detector under test is connected to oscilloscope DRS4 Evaluation Board v4 via a preamplifier The preamplifier is sourced by external power source while oscilloscope is powered by PC over USB Oscilloscopes external trigger is connected to the generator The triggers for oscilloscope and impulses for laser are generated simultaneously Having received the trigger signal oscilloscope reads the selected input channels and records collected data on PC hard drive for later analysis 17 3 2 Measurements description For measurement a MAPD with individual surface resistors MAPD S 60 was used This model has a matrix of 30 30 APDs distributed on 1 1 mm of surface Its full surface and a close up picture are shown in figure 10a and 10b respectively Fig 10a MAPD S 60 full surface Fig 10b close up photo of MAPD S 60 surface Surface scan First of all a small area on detectors surface is scanned to check the linearity of detector The scanning is done in 20 20 steps with a step size of 3 75um providing a total of 75 75 um area Full power of 3ns laser pulse was measured to be 7 8uW Considering attenuation a factor of 0 04 is introduced yielding a power of 0 32uW or 1 10 J pulse Pulse freguency is chosen to be 1 kHz 1000 samples per point a
11. the place where photon hits the surface with extreme assumption that the pulse consists of only one photon the best estimations still give an upper limit of fill factor eg lt 20 30 Single point response in different powers Obtained amplitude spectra for three pulse powers are given in figures 19a b and c Entries Y Mean E RMS O O 1000 0 cell response 1 cell response 800 2 cell response 600 400 200 Fig 19a Detector response to 0 32uW pulse amplitude spectra when laser is focused to the middle of a cell Red line represents zero cell response green line one cell blue line two cell response As expected most of events are one cell cases Calculating the ratio of two cell events versus one cell we find N gt ceit Nicen 0 15 Most probable amplitude values and their standard deviations are given in table 4 One cell response makes a fraction of 71 of all the events Entries Mean RMS 1 cell response 2 cell response 400 3 cell response 300 200 100 Fig 19b Detector response to 4 35uW pulse amplitude spectra when laser is focused to the middle of a cell There are no events resulting in zero cell response as the number of incident photons in each pulse is high enough to cause at least one avalanche The mean values of amplitudes and their standard deviations are higher than in 0 32uW case and are given in table 4 The higher amplitudes are mos
12. 4 573 2000 1800 0 cell response 1600 1 cell response 1400 2 cell response 1200 o 51000 800 600 400 200 Entries 20000 1200 Mean 14 98 RMS 6 79 1 cell response 1000 2 cell response 3 cell response 800 3 600 o O 400 200 0 0 7 35 uW 1st pulse Entries 20000 600 I Mean 20 23 RMS 8 979 1 cell response 500 2 cell response 3 cell response 400 4 cell response N 3300 o O 100 Counts 0 32 uW 2nd pulse Entries 20000 oa Mean 4 669 RMS 4 219 2000 1800 0 cell response 1600 1 cell sup response 1 cell response 1400 N 21200 3 51000 800 600 400 200 Entries 20000 Mean 11 6 RMS 7 45 1 cell sup response 2 cell sup response 2 cell mixed response Entries 20000 600 Mean 17 29 RMS 9 288 1 cell sup response 500 2 cell sup response 2 cell response 3 cell response 400 2 cell sup 1 cell response 100 20 30 50 60 U mV Fig 21 Detector response to both 1 and 2 pulse amplitude spectra in three different pulse powers when time between pulses is 100ns When pulse power is 4 35uW a suppressed two cell and mixed one suppressed one ordinary two cell response becomes visible In case of 7 35uW laser pulse power peaks overlap too much to be clearly distinguished thus the legend gives only possible combinations 34 4 Conclusions In this experiment response of Micr
13. Ionization coefficient a 1s written N 6 il i I N TTT PT T A iii iii La ia i ii Li A L i Li ii La i Li i lu where Nen number of e h pairs 0 01 0 02 0 03 0 04 0 05 006 0 07 0 08 0 09 0 1 x10 created by initial charge carriers drift WE cm V Fig 4 typical MAPD ionization coefficient path Typical MAPD ionization coefficient dependance on applied electric field 2 a f 1 E is shown in figure 4 4 Because of their low mobility holes create much less free charges therefore an lt Qe and process can be classified into two modes e Proportional mode in relatively low electric fields ap lt lt Ge therefore we can neglect the secondary charges generated by holes Average number of impact ionization events caused by a single photon can be written as n Nie 7 where L is mean drift path It is apparent from this expression that the response signal is dependant on No initial photoelectrons Gain factor in such case 1s 2 O x e Geiger mode in stronger electric fields holes must also be accounted for They create electrons nearby the edge of depleted layer which later drift through the entire zone and extend the avalanche Process continues until the external resistors suspend it The charge created in such a case is not influenced by the number of initial photoelectrons but rather by capacity of junction and current suppression mechanism Should such a detector be exploited impr
14. VILNIUS UNIVERSITY FACULTY OF PHYSICS SEMICONDUCTOR PHYSICS DEPARTMENT Vytautas Vislavicius ANALYSIS OF SILICON PHOTOMULTIPLIER RESPONSE Bachelor Thesis Study Program APPLIED PHYSICS Student Vytautas Vislavicius Supervisor RNDr PhD Peter Kodys Reviewer Habil Dr Eugenijus Gaubas Consultant Dr Vincas Tamo i nas Head of Department Prof Habil Dr Gintautas Tamulaitis Experimental part of work was done in the Institute of Particle and Nuclear Physics Faculty of Mathematics and Physics Charles University in Prague Czech Republic Prague Vilnius 201 1 I declare that I wrote my bachelor thesis independantly and exclusively with the use of cited sources I agree with lending and publishing the thesis PripaZistu kad darb para iau pats nepriklausomai naudodamasis pamin tais literat ros altiniais Sutinku kad is darbas b t publikuojamas ar naudojamas kaip literat ros altinis Vytautas Vislavi ius Prague Vilnius 26 May 2011 Table of contents Lincei 4 Ds SCMUICONGUCIOV QCLCCIONS a iais i ii i i a tack en i i i a i a a 5 2 1 Semiconductor detector Mode Lisinskas a 5 2 Wee Ly Pes Ol MAPD er a ai a a a is 10 DR ELO DE 61 S ici 13 Da Gs Isis een REN Tee a a E Ie a a Een ASS 15 IMAP DESOO TEPO ns E AA VSS sdraiarsi 17 Sie Measurement sehe mal S a sis ai a ai ia iai o k a a a a a ai o k a a a a a 17 3 2s Measurements descrip oDi a A A 18 Jo Data GAY SIS sena a a a i i a i a rere a 19 I REW
15. a run described above and thus are given in table 1 Laser frequency is 1 kHz width of each laser pulse 3ns 20000 samples for each time and power combination are taken 3 3 Data analysis Data collected from oscilloscope is saved in raw format The structure of a file is described in table 2 12 Byte Content 0 LSB Ist channel Ist cell 16 bit value 0 0 5 V 1 MSB 65535 0 5 V 2 LSB Ist channel 2nd cell 16 bit value 3 MSB 2048 LSB 2nd channel Ist cell 16 bit value 2049 MSB Table 2 Structure of a raw data file created by an oscilloscope For data processing ROOT environment was chosen 14 To calibrate the oscilloscope a 60MHz built in internal clock was used Period of such a clock is T 17ns its measured waveform is shown in fig 11 In this graph on abscissa axis we have cell number corresponding to particular time and on ordinate axis response amplitude in milivolts It 1s seen from this graph that one period corresponds to approximately 85 cells therefore we deduce time intervals between cells 19 T T U0 2ns 16 Nr Built in 60MHz clock waveform U mV 100 200 300 0 20 40 60 80 100 120 140 160 180 200 220 t ns Fig 11 60MHz built in clock waveform with a period 17ns used for oscilloscopes calibration Data processing can be classified into three stages 1 Waveform smoothening 2 Pedestal subtraction 3 Amplitude search and identificaition
16. ation of ionized impurities and c volume charges distribution E E 00 dependance on coordinate when pn Cc Cc junction is in equilibrium E E e 1 b Uo lt O X X Fig 3 Energy levels of pn junction when a no external voltage is applied b external reverse voltage is applied Since g is dependant on coordinate energy levels also become dependant on coordinate Moreover because of differences in potentials in junction charges moving from one side of diode to another have to overcome potential barrier e Ux Fig 3 Applying external voltage this barrier can be either increased or decreased 1 In the region of volume charge concentration of free charge carriers 1s dramatically lower than in neutral areas therefore resistance in this region is much higher than in neutral one In such a case all the electric field falls in this high resistance zone which is called depleted zone Thickness of depleted zone can be expressed as J 2ee N No y U 2 eN Np where Na stands for acceptor concentration Np donor concentration Ux potential of junction Uo external voltage Uo gt 0 if direct biased Uo lt 0 if reverse biased and eg dielectric permeability in matter and vacuum respectively Usually concentration of some type of impurities is much bigger than of the other type moreover U A gt gt U in case of reverse biased Then 2 can be simplified to _ 2
17. cited by 682nm 3ns laser pulses of 0 32uW 4 35uW and 7 35uW powers and its output signal was recorded with oscilloscope DRS4 Evaluation Board From the data obtained the estimated detectors fill factor is less than 20 Number of SiPM cells fired is dependant on pulse power in case of 0 32uW one cell response is dominating 71 of all the events while in cases of 4 35uW and 7 35uW one cell response makes up fractions of 38 and 18 of all the events Amplitudes from cells in recovery mode show dependances only on time elapsed after an excitation when pulse powers are 0 32uW and 4 35uW With a pulse power of 7 35uW 1 5mV shift in output signal is registered indicating an additional dependance of amplitude on power in range of 4 35uW to 7 35uW 40
18. ctions in analysis software void LoadWFAIlI const char If loads waveforms from the data file found at path f void Smoothen void smoothens the loaded waveforms void Pedestal Int t Iavg 800 calculates and removes pedestal from waveforms loaded Pedestal is calculated from first Javg cells If not specified default value of Javg is 800 Note Use only after smoothening void DrawWFFull Long64_t nr Int_t sk 1 char par AL draws a graph of unmodified sk waveforms starting with nr th waveform Parameter par specifies drawing options default AL removes the old graph and draws a new one to draw few waveforms on single graph parameter A has to be emitted To draw the points without connecting lines L has to be replaced with P void CropPeaks char fPar wb Int_t beg 800 Int t inter 200 find the peak in the interval inter starting from cell number beg and save it to a file defined by a global variable AmpFile 29 66 99 Parameter fPar provides some writing options and should be chosen between wb and a W stands for write meaning that the existing file will be replaced by a new file a stands for append meaning that the new data will be appended to the end of the file Note in both cases b binary is needed as the other functions read data in binary format void LoadAmps void loads amplitudes from a data file defined by global var
19. duce the available number of cells to calculate pedestal value In experiment a delay of 110ns was chosen Measured double pulse waveforms before processing after smoothening and after pedestal removal are shown in Fig 14a b and c respectively Amplitude search and identification Amplitude search in single pulse case is trivial in a preset interval we search for a lowest value The search interval is chosen accordingly to fig 13 When the minimum is found it is averaged in 1 2ns window 23 a Waveform before processing ass ee pr LA 1 i 1 O 00 o A Oo L N N 20 40 60 80 100 120 140 160 180 200 220 t ns b Waveform after smoothening gt E gt 0 20 40 60 80 100 120 140 160 180 200 220 t ns 0 20 40 60 80 100 120 140 160 180 200 220 t ns 24 Histogram of amplitudes 500 Entries Mean RMS 400 a 300 c 5 o O 200 100 0 E pee ees pel e _ 5 0 5 10 15 20 25 U mV Fig 15 histogram of amplitudes in position where 1 cell response is biggest To identi the amplitudes we draw their r J D Pixel fired Amplitude histogram There the amplitudes should distribute their interval mV selves around some particular values each of these If the pedestal removal is done correctly the first if Table 2 Amplitude intervals and corresponding number of pixels fired values correspond to some number of cells fired Fig 15 maximum should be near OmV On the othe
20. e amplitude spectra In 2 pulse amplitude spectra b a fraction of suppressed one cell response is visible emerging from zero cell signal However their overlapping is too great for it to be Histogram of amplitudes 2nd pulse 1000 Counts possibleto distinguishe between them Entries 20000 Mean 3 721 RMS 3 223 900 0 cell response 800 700 Suppressed 1 cell response 600 Ordinary 1 cell response 500 Superposition of all three 400 300 200 100 2 12 U mV Fig 17 2 pulse amplitude spectra laser power 0 32uW time between pulses 80ns with Gauss functions fitted Using Gaussians it becomes possible to separate zero from one cell response 26 3 4 Results Surface scan After 75 75 um area of surface scanning zero one two and three and more cells response maps were obtained They are shown in fig 18a 18b 18c and 18d respectively a 0 cell response MatLego Entries 260867 Mean x 36 57 Mean y 38 41 RMS x 21 38 RMS y 21 54 90C 80C 700 60C 50C 400 70 X um 10 40 50 60 20 30 Fig 18a 75 75um surface area map indicating number of zero cell response events at different surface spots Red regions indicate areas where detection efficiency is lower than 10 This histogram is in good confirmation with an actual pixel matrix shown in fig 10b low activity areas correspond to aluminum electrodes and the big i
21. exports the histograms under the path SavePath Form variable definition see DrawAmpHisD void Split Int t kk 0 char na part Int_t offset 0 if the file is too large to be processed it can be splitted into kk pieces The file name then is na offset offset kk 1 dat File is saved in directory ext Data void daryt Int t fSk 1 char ComPart data bool SplitNeeded false Int t offset 0 a combination of previously defined functions Basically if needed splits a file named ComPart dat into fsk piecies then loads them one by one performs smoothening pedestal subtraction and crops peaks If SplitNeeded 1s false file splitting is skipped Files that are processed must be in directory ext Data and named ComPart _ offset offset fSk 1 dat void DoublePulseAmps Int t AttVal 4950 loads double pulse waveforms from directory ext Data Double AttVall and crops peaks Files must be named 2Ons dat 30Ons dat up to 38 250ns dat The output file with cropped amplitudes is defined by global variable PeakAmps Files processed are starting from 20ns up to 250ns in 10ns steps To change this changes have to be done to the for loop inside the function void ReadPeaksGaus Double_t mas 19 Int t AttVal 4950 reads AmpExt AztVal dat file and saved the data into array mas for later processing void DPRG void loads three files AmpExt4950 dat AmpExt2800 dat and AmpE
22. fference U Upias Uba is called overvoltage If a pair of charge Carriers 1s created in detectors depleted area then the avalanche process starts and the pixel with capacity Cpx will start to discharge The generation of secondary charge carriers will stop when cells voltage drops down to U lt Upa Then the whole charge can be written as 2 Q C x U pias a U 9 For a short period of time after the discharge another avalanche process may not happen because the guenching resistors will limit cells recharge time The recovery Une time of one element can be written TE Cat eM Ubias where R is the resistance of quenching resistor One cell voltage dependance on time can be seen in fig 7 at t 0 cell is fully charged its bias e e Urva voltage Upias 1s usually 3V higher than the breakdown voltage T D T3 t At time T a pair of charge carriers l l Fig 7 One cell voltage dependance on time is created in the depleted area The avalanche process starts and the cell discharges very fast At time tz the avalanche stops cell is fully discharged and begins its recovery If at time t t2 lt t lt t3 another pair of charge carriers is created in the same cell it results in lower amplitude response 9 When the flux of photons is not big the output of detector is directly proportional to the number of pixels per detector The dependance can be written as PDE N 11 N N x l exp px 13 where N
23. iable AmpFile 37 void DrawAmpHis Int t first 0 Int t last 1000 const char nam NULL Int_t bins 525 draws a histogram of amplitudes starting with first and finishing with Jast 1 If variable nam is specified the histogram is saved in gif format in the path defined by global variable SavePath under the name nam bins number of bins per histogram with a default value of 525 void DrawAmpHisD Int t tim bool saugot false Int t yAx 2000 Float_t FitIntl NULL Float_t FitInt2 NULL Int t MaxNr 1 Int t MaxC1 3 Int t MaxC2 3 draws amplitude histograms for time tim If saugot is true the histogram is saved under the path SavePath with a name tim png yAx maximum value of y axis Fit nt and FitInt2 Double t type arrays defining intervals for each Gaussian to be fitted to for 1 and Die pulse responses MaxNr defines the number of a Gaussian corresponding to suppressed one cell response MaxC1 and MaxC2 number of Gaussians to fit to 1 and 2 pulse amplitude histograms When runing this function two new files are created under the path ext Data AmpPar dat yielding the parameters of fitted Gaussians and AmpExt dat yielding values of x corresponding to the maximum y of suppressed one cell response Gaussian void ExportHistogramsD Int t yAx 1700 Float_t FitIntlh NULL Float_t FitInt2 NULL Int t cnr 0 Int t MaxC1 3 Int_t MaxC2 3 goes through histograms with timing from 20ns to 250ns and
24. l response is also registered in case of laser pulse hitting the aluminum areas which can be a result of either laser beam spread or photons being reflected to active areas 30 40 50 60 10 20 29 d 3 and more cells response MatLego Entries 683 Meanx 40 97 Meany 35 08 RMS x 22 52 RMS y 21 1 9 Y um 70 X um 60 10 20 30 40 50 Fig 18d 75 75um surface map indicating number of three or more cell response events at different surface spots Apparently only a small fraction 0 2 of all events measured result in more than two cell response The highest rate yielding spots seem to cluster at random places most likely due to detector defects The highest number of three and more cell response on one spot is registered to be 9 standing for 0 9 of all the flux hitting the spot Comparing all the histograms given in fig 18 the following conclusions can be made Registered number of photons reflected from aluminum areas is small otherwise there would be other than 0 responses in the area of electrode grid Considering the conclusion mentioned above the main reason for more than 1 cell response comes to be signal sharing between few cells optical crosstalk In small photon flux 0 1 and 2 cell responses are dominant histogram 18d has a total of 683 entries standing for only 0 17 of all the flux activating more than 2 cells Detectors efficiency is strongly dependant on
25. ll where it starts another avalache process Fig 8 On the other hand in strong 15 electric fields electrons can be accelerated enough so the photons they radiate becouse of bremstralung can cause avalanches in other micro cells On average in every 10 electrons 30 of them create avalanche in nearby cells To avoid this pixels have to be isolated this however reduces detectors active area on the other hand lower electric fields mean less acceleration as well as less electrons to escape 2 9 Afterpulses During the avalanche process charge carriers might get trapped in lattice defects If the trapping time is long enough charge carrier might be released when the cell is recharging or has already recharged In this case a fake photon will be registered The number of charged carriers cought in traps is dependant of the total number of charge carriers therefore it can be reduced by decreasing the electric field 9 Fig 8 Optical cross talk between two cells 9 16 3 MAPD S60 response analysis 3 1 Measurement schematics Measurement schematics are shown in figure 9 on 3D stage Fig 9 Measurement schematics Generator Hewlet Packard 81101A Pulse Generator creates a 10ns width voltage pulse which is then sent to a laser A 3ns 682nm laser pulse is generated which then is transferred via optical cables to optical attenuator OZ Optics Motor Driven DD 100 MC In Line and later to a black box where the beam
26. nactive spot on top right is the area where cells discharge to electrodes via the quenching resistors Assuming that every avalanche was caused by only one photon the best estimation of fill factor gives a value of gp 20 Y um 27 b 1 cell response MatLego Entries 126557 Mean x 39 2 Mean y 35 83 RMS x 21 95 RMS y 21 66 700 Y um 60C 50C 400 30C 20C 100 10 70 X um Fig 18b 75 75um surface area map indicating number of one cell response events at different surface spots The red spots yielding highest rates of one cell responses indicate middles of cells Assuming that every avalanche is caused by only one photon the efficiency in case when photon hits the middle of a cell is 70 Areas with aluminum also yield a small detection efficiency 10 25 depending on alumina width mainly due to spread of laser spot or photon reflection 40 50 60 20 30 28 c 2 cell response MatLego Entries 11887 Meanx 39 49 Meany 35 38 RMS x 22 03 RMS y 21 78 Y um s 70 X um Fig 18c 75 75um surface area map indicating number of two cell response events at different surface spots As it is seen the highest rate for two cell response is yielded by events when photon flux hits the middle of a cell This is due to optical cross talk since it is the only available mechanism for signal sharing in the middle of the cell On the other hand two cel
27. o pixel Avalanche Photodiode with individual surface resistors MAPD S 60 was investigated After data evaluation following conclusions can be made Probability for photon to be registered is strongly dependant on place where it hits the surface best estimations of fill factor give an upper limit of efu lt 20 Fraction of photons reflected from aluminum area and then registered is no more than 3 Optical cross talk is the main reason for more than one cell response Amplitude of one cell response increases with increasing pulse power Number of cells responded is dependant on pulse power and increases with increasing power In pulse powers of 0 32uW and 4 35uW response amplitude of a cell in recovery is dependant only on the time passed from previous pulse In high radiation intensities 7 35uW pulse power response of cell in recovery shows dependance on the intensity itself however to clearly understand this effect thorough measurements in pulse power range of 4 3 7 6 uW are needed 35 5 References 1 A Po kus Atomo fizika ir branduolio fizikos eksperimentiniai metodai Vilnius Vilniaus universiteto leidykla 2008 2 H G Moser Progress in Particle and Nuclear Physics 63 2009 211 214 3 G F Knoll Radiation Detection and Measurement Third Edition John Wiley 2000 4 R van Overstraeten and H de Man Solid State Electronics 13 p583 1970 5 Z Sadygov A Olshevski I Chirikov I Zheleznykh A No
28. operly i e the avalanche is not suppressed the detector would suffer irreversible damage 2 Avalanche photodiodes are used to register a low intensity light Usually they operate in proportional mode however if so external amplifiers are still needed for gain is not large enough to distinguish between signal and noise The disadvantages of a detector working in proportional mode are following e Gain dependance on temperature e Gain dependance on bias voltage e Insufficient signal discrimination 2 To overcome the last problem detector should be used in Geiger s mode Then single photon registration efficiency would increase dramatically however the diode would only be usable with low intensity radiation In order to extend its dynamic range a number of avalanche photodiodes APDs can be joined together into one single matrix 2 2 2 Three types of MAPD Micro pixel Avalanche Photodiode MAPD is basically a number of ordinary avalanche photodiodes joined into a single matrix Each of APD all connected to a single common electrode is working in Geiger s mode The realization of APDs matrix however is not unambiguous various models of such a detector yield different parameters Currently there are three types of MAPD Fig 5 5 e MAPD with individual surface resistors Fig 5a consists of pn junctions on the surface These junctions are connected to a common electrode via individual quenching resistors which are
29. other hand germanium has to be constantly cooled by liquid nitrogen for its energy gap width is narrow 3 Surface leakage currents originate on the surface of detector nearby the junction where potential barrier is big These currents are influenced by many factors such as humidity dirty surface and basically anything that could change conductivity on surface 3 Leakage currents not only influence detectors energy resolution but also reduce Up To isolate signal reversed voltage is usually applied via series of resistors Thus Uo then becomes U 2U i Ro 5 where i stands for leakage current and Ro resistance of all the resistors connected to detector 3 Avalanche amplification Internal amplification processes in previously described detector do not occur Therefore even having the noise reduced to the minimum it is impossible to identify one photon response using just external amplifiers In such case avalanche effect can be exploited in very strong electric fields 200keV cm charge carriers can be accelerated to energies 800 00 500 300 E ker sufficient to ionize other atoms of lattice alpha 1 cm via collisions process is called impact ionization Newly created electric particles can also be accelerated to sufficient energies to ionize even more LI T T atoms As a result the signal can be amplified up to measurable values electrons _ _ __ _ holes nl DI Pa
30. r hand such a peak is missing this could be a result of absence of 0 cell response Intervals and corresponding number of cells are given in table 2 In case of double pulse the same method as mentioned above is used What should be noted however is that in case of double pulse response we have both ordinary 1 cell response amplitudes and suppressed ones appearing from not fully recharged cells The later can be very similar to ordinary 1 cell amplitude therefore sometimes they overlap and become indistinguishable Fig 16 When amplitudes overlap just partly means to evaluate their mean value and number can be taken Since amplitude distribution 1s Gauss function we can approximate whole spectra into a superposition of a number of Gaussians F x X o ae 21 25 where each fi x corresponds to a Gaussian representing the distribution of some particular amplitude Fig 17 Their mean value can be used as a mean value for an amplitude and an integral of such a function yields a total number of events when 7 cells have been fired a Histogram of amplitudes 1st pulse b Histogram of amplitudes 2nd pulse Amp_His2 Entries 20000 Entries 20000 1400 Mean 8 515 1400 Mean 4 059 RMS 4 545 RMS 4 21 1200 1200 1000 1000 800 800 600 600 400 400 200 200 0 ERA ras RE ESE oe La L Pe I EY PE QU 0 Se Boni a is SR Rcs ae TE a 5 0 5 10 15 20 25 30 5 0 5 10 15 20 25 30 U mV U mV Fig 16 a 1 and b 2 puls
31. re taken If the results from this measurement match the actual surface seen in fig 10b it would confirm that measurement setup is successful Detector response vs power After a surface scan the laser beam is focused to a Pulse power Pulse energy point where the number of one cell response events is the uW J highest This point represents the middle of a cell Full pulse power was measured to be 21dBm standing for Table 1 pulse powers and energies 7 9uW Then using optical attenuator pulse power is ited in exveriment 18 changed by factors of 0 04 0 55 and 0 93 Pulse powers and corresponding energies are given in table 1 Pulse frequency is set to kHz the width of pulse remains 3ns 20000 samples are taken for each pulse power Detector response to double pulse vs time in different powers To check cell in recovery behavior generator is set to generate two pulses with time between them varying from 20ns to 250ns in steps of 10ns Trigger for oscilloscope is generated only for the first pulse Laser is set to the middle of a cell where a number of one cell response events is highest This is done to reduce the influence of unwanted effects like cross talk few cell activation because of laser beam spread etc In ordinary oscilloscope configuration first pulse response is at the very end of oscilloscopes measured time window thus a trigger delay of 110ns is set Pulse powers used in this run are the same as in
32. rent intensities of radiation and most important its ability to register several photons when timing between them is comparable with detectors recovery time 2 Semiconductor detectors Some general requirements have to be met when choosing a material for a semiconductor detector for electromagnetic radiation In particular the material is required to be as dense as possible so the interaction cross section of initial radiation with matter is high On one hand excitation energy of atoms in matter has to be low so there are more charge carriers created on the other hand low excitation energy results in a higher number of thermal charge carriers To achieve good time characteristics mobility of charge carriers in matter has to be high so they are collected before they can recombine So far the best materials fulfilling these requirements are germanium and silicon 1 2 1 Semiconductor detector model Operating principle Energy levels of atoms in a solid state body combine to make energy bands The highest filled energy band is called valance band and the one above it conductive band the gap between those two is energy gap fig la Electrons in valance band are bound to atoms however provided sufficient energy they can transit to conductivity band where they are free to move and drift along the electric field When temperature is above OK a fraction of all the atoms is already excited and there are some electrons in conductivi
33. seperated from silicon wafer by a layer of S105 6 High resistivity resistors limit the avalanche processes and discharge the cells to a common electrode This type of MAPD are sensitive to UV light Big gaps between each cell result in small probability of short 10 circuit moreover only a small fraction of the surface 1s covered by low transparency layer The main disadvantage of such a diode is low number of micropixels availabe usually 1000 px mm 5 MAPD with surface channels for charge transfer Fig 5b basically the same as the one mentioned before the difference is that the charge is collected via thin surface channels formed between waffer and S10 layer 7 MAPD with deep micro wells Fig 5c have one common pn junction The surface of such a diode is not covered at all thus theoretically it can reach a p contact layer gt S__ photons efficiency up to 100 The 4 epitaxial layer n pixels inside avalanche and quenching Kan _ epuazia ayer regions are created in the n layer volume of waffer These n silicon wafer zones are usually 3 5um bE Avalanche region under the surface and their pe V Micro wells for electron collection density can reach up to 4 10 px mm 8 Schematics of charge avalanche and collection is shown in fig 6 when the well is empty the Fig 6 Charge avalanche and collection schematics 13 electric field it created 1s
34. t likely a result of a higher flux creating charge carriers in a bigger volume One cell response makes a fraction of 38 of all the events 31 Entries 20000 Mean RMS c 7 35uW 300 Counts 250 1 cell response 2 cell response 3 cell response 200 4 cell response 150 100 50 05 40 Fig 19c Detector response to 7 35uW pulse amplitude spectra when laser is focused to the middle of a cell Most of the signals result in more than one cell responses Fitted Gaussians overlap and it is hard to distinguish between three four and more cells Response amplitudes have increased even more due to a larger volume that charge carriers are created in and are given in table 4 One cell response makes a fraction of 18 of all events Pulse power Number of cells AmV AAmV o mV Ao mV uW responded O0 120 00104 061 0 0061 _ 1 8 31 0 0097 1 12 0 0085 0 32 735 23 16 0 2952 2 07 0 2379 Table 4 Mean amplitude values their standard deviations and errors obtained from fitting Gaussians oO Detector response to double pulse vs time in different powers During this experiment it was noticed that when timing between pulses are T lt 50ns suppressed amplitude of the second pulse is indistinguishable from zero cell response moreover measurements with timing between the pulses more than t gt 230ns are out of oscilloscopes measured time window Therefore only those events where
35. ty band already In such case width of energy gap is of great importance since it influences the initial amount of free charge carriers 1 In case of intrinsic semiconductor number of initial free charge carriers is small thus to increase it impurities are introduced Also called dopants they can be of two types donor or acceptor Impurities create discrete energy levels in the energy gap of intrinsic semiconductor and these levels are close to either valance or conductivity band Donor type impurities donors create an energy level just below the conductivity band and therefore they can easily ionize fig 1b In such a case donor remains stationary in crystal lattice while the electron enters the conductivity band and becomes free Similarly acceptor type impurities acceptors create discrete energy levels just above valance band and thus can ionize an intrinsic atom fig Ic Such a case results in a generation of a positively charged free quasi particle a hole which is also free to move If the concentration of donors is higher than the one of acceptors a 5 semiconductor is called n type semiconductor and its majority carriers are electrons In opposite case where the concentration of acceptors is higher than the one of donors a semiconductor is called p type semiconductor and its majority carriers are holes 1 Conductivity band Conductivity band Conductivity band O O e 222202 D O
36. vikov Nuclear Instruments and Methods in Physics Research A 567 2006 70 73 6 Z Ya Sadygov Russian Patent 2102820 priority of 10 10 1996 7 Z Ya Sadygov Russian Patent 2086027 priority of 30 05 1996 8 Z Ya Sadygov Russian Patent Application 2005 108324 of 24 03 2005 9 S Korpar Status and perspectives of solid state photon detectors RICH 2010 10 R L Aggarwal I Melngailis S Verghese R J Molnar M W Geis L J Mahoney Solid State Communications 117 2001 549 553 11 F Capasso in R K Willardson A C Beer Eds Semiconductors and Semimetals vol 22 part D Academic Press New York 1985 12 Stefan Ritt DRS4 Evaluation Board User s Manual 2010 07 13 Z Sadygov A F Zerrouk A Ariffin S Khorev J Sasam V Zhezher N Anphimov A Dovlatov M Musaev R Muxtarov N Safarov Nuclear Instruments and Methods in Physics Research A610 2009 381 383 14 http root cern ch drupal Last checked 2011 05 25 15 http root cern ch download doc Users Guide 5 26 pdf Last checked 2011 05 26 36 6 Appendix 6 1 Data analysis software Software has been written for data analysis and can be found on CD or online http www ucif troja mff cun1 cz kodys works mapd thesis V ytautas FinalAnalysisS W_ V Vislavicius z1 To run the software ROOT framework is required http root cern ch drupal To modify the program a useful reference is ROOT manual 15 List and detailed description of main fun
37. xt1200 dat reads its contents calculates the ratio of suppressed one cell amplitude to ordinary one cell amplitude and draws two graphs one containing the absolute values of the suppressed amplitudes and the other one containing the ratio calculated void simts Int t pr 0 Int t gal 100 const char ch ext Data M20000 dat loads data file ch and draws gal pr waveforms in a single figure First waveform 1s defined by pr last one gal void DrawLegoPlot Float t min Float t max Int t matsk Int t xBin Int t yBin Float t xStep Float_t yStep draw a surf1 type 3D histogram surface map Variables min and max define the minimum and maximum values for an amplitude to be accepted to histogram matsk number of measurements per point xBin yBin x and y bining values and xStep yStep step sizes in x and y axes The function uses data from LoadAmps function this has to be done manually 39 7 Summary SiPM Silicon Photomultiplier is a novel type of a detector with a potential to replace traditional vacuum photomultiplier tubes in particle accelerators medical industry and other areas where magnetic fields are present or detector size is important However a very few experiments have been done so far and to use SiPM at its full potential more investigation is needed During the experiment the response of one of such a multipliers in particular MAPD S60 was analyzed Detector under test was ex
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