characterization and failure analysis of x-ray detector diodes872307/fulltext01.pdf · this master...

Characterization and Failure Analysis of X-Ray Detector Diodes

EDOARDO REDAELLI

Master of Science Thesis Stockholm, Sweden 2014

TRITA-ICT-EX-2014:123

Contents

Introduction 9

1 Theory 131.1 Silicon diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 131.1.2 Current-Voltage characteristics . . . . . . . . . . . . . . . 161.1.3 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.2 Diodes for radiation dosimetry . . . . . . . . . . . . . . . . . . . 181.2.1 Interaction of radiation with diodes . . . . . . . . . . . . 191.2.2 E↵ective sensitive volume . . . . . . . . . . . . . . . . . . 211.2.3 Minority carrier lifetime . . . . . . . . . . . . . . . . . . . 22

1.3 X-ray detector parameters . . . . . . . . . . . . . . . . . . . . . . 251.3.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.3.2 Dose linearity . . . . . . . . . . . . . . . . . . . . . . . . . 271.3.3 Dose Per Pulse Dependency (DPPD) . . . . . . . . . . . . 271.3.4 Sensitivity Variation With Temperature (SVWT) . . . . . 281.3.5 Long term stability . . . . . . . . . . . . . . . . . . . . . . 291.3.6 Directional dependency . . . . . . . . . . . . . . . . . . . 29

2 Statistical analysis of previous batches 312.1 Theoretical model: Forward bias . . . . . . . . . . . . . . . . . . 33

2.1.1 Temperature influence . . . . . . . . . . . . . . . . . . . . 342.1.2 Doping concentration influence . . . . . . . . . . . . . . . 352.1.3 Minority carrier lifetime influence . . . . . . . . . . . . . . 37

3 Experimental 393.1 Samples description . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1.1 Normal diodes . . . . . . . . . . . . . . . . . . . . . . . . 403.1.2 Failing diodes . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2 Epoxy removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2.1 Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.2.2 Mixture of nitric and sulfuric acids . . . . . . . . . . . . . 423.2.3 Sulfuric acid . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3 Open-Circuit Voltage Decay . . . . . . . . . . . . . . . . . . . . . 433.4 Capacitance-Voltage measurement . . . . . . . . . . . . . . . . . 453.5 Current-Voltage characteristics and response to light . . . . . . . 46

3.5.1 Normal diodes . . . . . . . . . . . . . . . . . . . . . . . . 473.5.2 Failing diodes . . . . . . . . . . . . . . . . . . . . . . . . . 47

3

4 CONTENTS

4 Results and discussions 494.1 Epoxy removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.1.1 Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.1.2 Mixture of nitric and sulfuric acids . . . . . . . . . . . . . 494.1.3 Sulfuric acid . . . . . . . . . . . . . . . . . . . . . . . . . 504.1.4 IV characterization . . . . . . . . . . . . . . . . . . . . . . 514.1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2 OCVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.2.1 Normal diodes as processed . . . . . . . . . . . . . . . . . 524.2.2 Normal diodes after pre-irradiation . . . . . . . . . . . . . 524.2.3 Failing diodes . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3 CV measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 544.3.1 Doping concentration calculation . . . . . . . . . . . . . . 55

4.4 IV characteristics - In darkness . . . . . . . . . . . . . . . . . . . 564.4.1 Forward bias . . . . . . . . . . . . . . . . . . . . . . . . . 564.4.2 Reverse bias . . . . . . . . . . . . . . . . . . . . . . . . . . 584.4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.5 IV characteristics - IR-LEDs . . . . . . . . . . . . . . . . . . . . 614.5.1 Normal diodes . . . . . . . . . . . . . . . . . . . . . . . . 614.5.2 Failing diodes . . . . . . . . . . . . . . . . . . . . . . . . . 654.5.3 Light response: a simple model . . . . . . . . . . . . . . . 68

5 Conclusions 75

6 Future Work 77

Bibliography 78

Acknowledgements 81

List of Figures

1 Pre-Treatment detector . . . . . . . . . . . . . . . . . . . . . . . 11

1.1 Silicon crystal structure . . . . . . . . . . . . . . . . . . . . . . . 131.2 Silicon band structure . . . . . . . . . . . . . . . . . . . . . . . . 141.3 Silicon pn junction . . . . . . . . . . . . . . . . . . . . . . . . . . 151.4 Generic IV characteristics . . . . . . . . . . . . . . . . . . . . . . 161.5 Resistivity vs Doping concentration . . . . . . . . . . . . . . . . . 211.6 Carrier lifetime dependence on Si quality . . . . . . . . . . . . . 231.7 Non ideality in OCVD measurements . . . . . . . . . . . . . . . . 241.8 Sensitivity vs Pre-irradiation . . . . . . . . . . . . . . . . . . . . 26

2.1 Current distribution at -1 V . . . . . . . . . . . . . . . . . . . . . 322.2 Current distribution at 0,5 V . . . . . . . . . . . . . . . . . . . . 322.3 IV characteristics - Temperature influence . . . . . . . . . . . . . 352.4 IV characteristics - Doping concentration influence . . . . . . . . 362.5 IV characteristics - Minority carrier lifetime influence . . . . . . . 37

3.1 Sample diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2 Normal diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.3 Failing diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.4 OCVD - Experimental setup . . . . . . . . . . . . . . . . . . . . 433.5 OCVD - Electronic schematic . . . . . . . . . . . . . . . . . . . . 443.6 OCVD - Test diode . . . . . . . . . . . . . . . . . . . . . . . . . . 453.7 IV measurements - Experimental setup . . . . . . . . . . . . . . . 463.8 LED - Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.9 LED - Experimental setup . . . . . . . . . . . . . . . . . . . . . . 48

4.1 Epoxy removal - Acetone . . . . . . . . . . . . . . . . . . . . . . 504.2 Epoxy removal - Nitric and sulfuric acid . . . . . . . . . . . . . . 504.3 Epoxy removal - Sulfuric acid . . . . . . . . . . . . . . . . . . . . 514.4 OCVD - Normal diode as processed . . . . . . . . . . . . . . . . 524.5 OCVD - Normal diode after pre-irradiation . . . . . . . . . . . . 534.6 OCVD - Failing diode . . . . . . . . . . . . . . . . . . . . . . . . 544.7 CV - Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.8 CV - Doping concentration calculation . . . . . . . . . . . . . . . 564.9 IV characteristics - Forward bias . . . . . . . . . . . . . . . . . . 574.10 IV characteristics - Reverse bias . . . . . . . . . . . . . . . . . . . 584.11 IV characteristics - Response variations with LEDs for normal

diode as processed . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5

6 LIST OF FIGURES

4.12 IV characteristics - Response variations with LEDs for normaldiode after pre-irradiation . . . . . . . . . . . . . . . . . . . . . . 62

4.13 Responsivity versus Wavelength . . . . . . . . . . . . . . . . . . . 654.14 IV characteristics - Response variations with LEDs for failing

diode for PT applications . . . . . . . . . . . . . . . . . . . . . . 664.15 IV characteristics - Response variations with LEDs for failing

diode for AT applications . . . . . . . . . . . . . . . . . . . . . . 664.16 IV characteristics - Response variations with LEDs for pre-irradiated

working diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.17 Penetration depth vs Incident wavelength . . . . . . . . . . . . . 674.18 Schematic diode . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.19 Model - Interaction with visible light . . . . . . . . . . . . . . . . 694.20 Model - Interaction with IR-LED: case 1 . . . . . . . . . . . . . . 704.21 Model - Interaction with IR-LED: case 2 . . . . . . . . . . . . . . 714.22 Model - Interaction with IR-LED: case 3 . . . . . . . . . . . . . . 714.23 Light response model - Overall . . . . . . . . . . . . . . . . . . . 73

List of Tables

2.1 Average current values for previous batches . . . . . . . . . . . . 33

3.1 Light sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1 Minority carrier lifetime . . . . . . . . . . . . . . . . . . . . . . . 544.2 Breakdown voltage . . . . . . . . . . . . . . . . . . . . . . . . . . 594.3 Recombination - generation lifetime . . . . . . . . . . . . . . . . 604.4 Response variations for normal diodes . . . . . . . . . . . . . . . 634.5 Responsivity vs Incident wavelength . . . . . . . . . . . . . . . . 654.6 Penetration depth vs Incident wavelength . . . . . . . . . . . . . 684.7 Leakage current responses variations with LEDs . . . . . . . . . . 684.8 Light response model . . . . . . . . . . . . . . . . . . . . . . . . . 72

7

8 LIST OF TABLES

AbstractThis master thesis report consists in the characterization of silicon diodes

for radiation dosimetry and the investigation of their failure.

An overview on the semiconductor properties in radiation detectors is pre-

sented to give physical basis to the successive analysis. Then the experimental

setups are explained and the results discussed. The main point of the thesis work

is an accurate study of the minority carrier lifetime in photodiodes, in order to

verify that it can be seen as a crucial factor in failure mechanisms.

To give supplementary confirmations, interaction of di↵erent light sources (IR-

LEDs) are analyzed in details and suggestions for the development of a func-

tional test method are finally presented.

This thesis was done in cooperation with Acreo Swedish ICT and ScandiDos.

10 LIST OF TABLES

Introduction

Modern radiation therapy technologies are based on sophisticated mechanismsof dose delivery and every treatment is studied to fit perfectly to a single pa-tient. Therefore it is necessary to guarantee that the dose fits exactly with theplanned characteristics and spatial distribution, in order to avoid to damagehealthy tissues. The solution to this request is a quality assurance program thatis made possible thanks to the use of specific radiation detectors, like the oneso↵ered by ScandiDos. These systems may be divided according to their work-ing conditions into two families: detectors for Pre-Treatment or At-Treatmentapplications. The former consist in a body phantom to be placed in the linearparticle accelerator (LINAC) before the treatment is started, while the latteracts directly during the real treatment. Depending on their applications, thedi↵erent detectors have to fulfill determined prerequisites and therefore theywill have di↵erent shapes and properties.

Beginning with the PT device depicted in the following figure, it is made ofa cylindrical water equivalent phantom containing many silicon diodes imple-mented in two crossing arrays.

Figure 1: Schematic representation of a detector for Pre-Treatment application.

The image aims to give an explanation of the e�ciency of such a system.The phantom shape and the disposition of the diodes allow to achieve a 3D mapof the dose delivered from any beam direction. Indeed, every unit of the arraysmeasures independently the received dose assuring a high spatial resolution.

11

12 LIST OF TABLES

The AT solutions exhibit interesting advantages compared to the first detec-tor presented. First, measuring the dose directly during the treatments lowersthe total time needed by the quality assurance program. The simplicity of theoperations is also increased thanks to the possibility of performing the measure-ment in background during calibration or Pre-Treatment phases.

The problem from which this thesis work originates is failure in silicon diodesfor the radiation dosimetry applications mentioned above. In particular, it con-cerns diodes produced in Acreo and then implemented in detector systems inScandiDos. The first task is to increase the understanding of how semiconduc-tor parameters influence the final product, the detector indeed. The startingpoint is connected to lifetime analysis, since it is thought to be a fundamentalfactor in dosimetric applications; then the investigation has to focus on fail-ure mechanism. Therefore two kinds of marginally failing diodes are providedby ScandiDos to analyze and compare them with normal working diodes withthe same specifications. Lastly, it is required to suggest a test method thatis able to distinguish among working and failing diodes at early stages in themanufacturing process.

Here the contents are presented.

The base of every scientific work is the understanding of the studied phe-nomena starting from the basic knowledge about the theory behind them. Inthe first chapter we will go through the most elementary concepts regardingsilicon and pn junctions to use them in more complex discussions later in thiswork. Moreover, particular care is given to the relationship between semiconduc-tor properties and X-ray detectors parameters, in order to obtain an overviewabout the state of art of the topic.

In chapter 2 a statistical analysis of measurements on batches previouslycharacterized in Acreo is presented. A theoretical model describing the for-ward bias characteristics of silicon diodes is applied to analyze the obtainedresults. Additionally, the influences of di↵erent factors - temperature, dopingconcentration and minority carrier lifetime - are addressed, based on empiricalconsiderations done in ScandiDos.

Then, in the third chapter we will explain the experimental part of the thesiswork. Starting from the samples description, we will evaluate the convenience ofan epoxy removal treatment on the diodes covered with a glob-top. Three exper-iments are thus illustrated: Open-Circuit Voltage Decay, Capacitance-Voltagemeasurement and Current-Voltage characteristics, including light response.

Chapter 4 shows the results of the experiments held and the discussionsabout them. In particular, confirmations about minority carrier lifetime varia-tions are given and the characteristics of the studied didoes are fully discussed.Furthermore, a simple model describing diode-light interactions will be pre-sented.

Afterwards, the fifth chapter contains the conclusions of the thesis work andaims to remark the most important concepts discussed in the foregoing chapters.

Chapter 6 will give suggestions for further works and the basis for the devel-opment of an e�cient test method for failure identification in diodes for radiationdosimetry.

Chapter 1

Theory

1.1 Silicon diodes

1.1.1 Background

The semiconductor industry is dominated by the use of silicon as base material.The reasons are the electrical properties of this element that is located in thefourth group of the periodic table and belongs to the cathegory of the semi-conductors. The semiconductor term generally refers to a material that has anintermediate electrical conductance between conductor and insulator and there-fore may be used taking advantage of its variable conductivity. Particularly,when silicon is considered, it is worth mentioning that it has four valence elec-trons that are shared between each atom and its four nearest neighbours in thecrystalline structure, as shown in the following figure.1

Figure 1.1: Unit cell of the Si crystal structure, known as diamond structure.

When we consider a crystal structure, what is determined is not simply therelative position among the atoms, but all the electronical characteristics, too.

1CHENMING, HU, 2010. Modern Semiconductor Devices for Integrated Circuits. UpperSaddle River, N.J.; London: Pearson Education, Fig. 1-2, p. 3.

13

14 CHAPTER 1. THEORY

Indeed, a fundamental concept in the studies of electrons in crystals is the factthat from the discrete energy levels in the single atoms we obtain energy bands.The understanding of the electrons moving in these bands is at the base of theworking mechanism in any semiconductor device. It is thus necessary to analyzethe band structure depicted below.2

Figure 1.2: Silicon band structure with valence band (EV

), conduction band(E

C

) and the band gap (Eg

) between them.

Three parts are present: a valence band, a conduction band and a band gap,that is 1,12 eV in silicon. At equilibrium conditions and at 0 K temperaturethe electrons tend to stay in the lower band while the upper ones are all empty,but the small band gap in semiconductor materials allows several possibilities ofhole and electron motion among them. The aim of this thesis is not a completedescription of how the electrons and holes behave in the silicon band diagram,which may be easily found in di↵erent handbooks,3,4,5 but we will now shortlydescribe how silicon is modified to build a diode, that is instead the main focusof our investigations. The addition of atoms of a di↵erent element to pure siliconis the most common technique to achieve a modification of its characteristics ina process called “doping”. In particular, being Si in group IV, common dopingelements are the ones next to it in the periodic table, as Boron, Aluminium, In-dium, Arsenic and Phosphurus. The former three materials listed before exhibitan electronical configuration with one electron less than Si. The consequenceof adding them to silicon crystals and their substitutions to the original atomsis therefore the tendency to reach a balance between the numbers of electronsin the structure. This means that one of the nearest silicon atoms will donateone electron to B, Al or In, that are indeed called “acceptors”, while the voidleft behind by the electron is called “hole”. The net results is a large number

2SZE, S., 1981. Physics of Semiconductor Devices. Third edition. Wiley, p. 24.3LUTZ, G., 1999. Semiconductor Radiation Detectors. Device physics. Springer, Chapter

2.4CHENMING, HU, Op. cit., Chapter 1.5SZE, S., Op. cit., Chapter 1.

1.1. SILICON DIODES 15

of holes in silicon, which brings to the definition of a p-type Si, where the con-duction is mainly due holes motion. The opposite e↵ect is obtained with Asand P, that have one electron more, available to be given to the nearest siliconatoms. In this case the doping elements are called “donors” and the silicon isdefined as n-type. An important definition is that in p-type silicon the holesare called “majority carriers” and the electrons “minority carriers”, while theopposite obviously occurs for n-type.

The most interesting application of the doping process is the combination ofboth the doping types. Adding acceptors atoms to a region of n-type silicon isa way to obtain the so-called “pn junction”, the structure of which diodes aremade of.

If we consider the occupation probability of an energy state we can introducethe concept of “Fermi level”, i.e. the energy at which such a probability isone half. It is worth noting that, when doped, silicon band diagram changes,leading to a movement of the Fermi level closer to the conduction or valenceband, depending on the doping type. If a p-type doped silicon is put togetherwith a n-type, as in the pn junctions indeed, the Fermi levels will be aligned atthermal equilibrium conditions and the two bands will di↵er of a quantity qV

bi

,where V

bi

is called “built-in potential”, as explained in the following figure.6

Figure 1.3: Silicon pn junction and its band structure. E

C

= conduction bandenergy, E

i

= intrinsic Fermi level, EF

= Fermi level, EV

= valence band energy.

It is easy to distinguish three regions in the structure: p-, n-type regionsand an intermediate part, known as depletion layer (W) or space charge region(scr), which is depleted of carriers, i.e. electrons and holes. The definition of thisregion in pn junctions is fundamental, especially for what concerns our samplediodes, built for dosimetry application. Thus, it is now necessary to show howthe extension of this layer may be estimated and on which factor it depends.The depletion layer width is defined as follows.7

6LUTZ, G., Op. cit., Fig. 3.2 b, p. 40.7SZE, S., Op. cit., p. 83.


W =

s2✏

S

(Vbi

� V )

q

N

a

+N

d

N

a

N

d

(1.1)

Where ✏

S

is the electrical permittivity, defined as ✏

r

✏0, with ✏

r

= 11.9 forsilicon and ✏0 is the constant vacuum permittivity, V is the applied bias, q isthe elemental charge and N

a

and N

d

are respectively acceptor and donor con-centrations in the material.The dimension of this region varies depending on the materials properties, asdoping concentrations, but at the same time on the external conditions, likethe applied voltage V . So, changing the applied bias leads to di↵erent behav-iors of the same device and this principle is used in recording current-voltagecharacteristics of diodes.

1.1.2 Current-Voltage characteristics

Recording the current flowing for di↵erent voltages is the basic characterizationprocess in diode analysis, since it is easy to derive important information justlooking at the di↵erent parts of the curve. Here it is showed a schematic rep-resentation of such a curve for a generic diode, which is commonly called IVcharacteristics.8

Figure 1.4: IV characteristics for a generic silicon diode.

We can immediately distinguish three regions. Starting from the right, wherethe applied bias is positive, a current can easily flow through the pn junction.Going closer to zero voltage it decreases and reaches zero. Moving again to theleft a small current can still flow, the so-called “leakage current”, before it startsflowing freely after a certain particular voltage, known as “breakdown voltage”,usually set by carrier generation by avalanche. Each part of the curve gives usrelevant information about the diode, but they need to be evaluated singularly,since they all depend on several factors.

8CHENMING, HU, Op. cit., Fig. 4-10 a, p. 101.

1.1. SILICON DIODES 17

Forward bias

While the voltage increases, the depletion layer width decreases and the di↵er-ence between the bands - defined as qV

bi

in Fig. 1.3 - is lowered of a quantityequal to the applied bias, allowing an easier passage of carriers through thejunction. If we refer to a p-type silicon diode, which has electrons as minoritycarriers, the formula that describes the current density in forward bias condi-tions is the following:9

J

F

= q

rD

n

⌧

n

n

2i

N

a

exp

✓qV

kT

◆+

r⇡

2

kTn

i

⌧

n

E0exp

✓qV

2kT

◆(1.2)

where Dn

and ⌧

n

are the di↵usion coe�cient and the lifetime of electrons, ni

is the intrinsic carrier concentration and E0 is the electric field at the locationof maximum recombination.This formula consists of two parts: the first is the total di↵usion current and thesecond takes into account the recombination processes. The explanation of howto derive this relationship may be found in the already quoted Sze’s book, butin the next chapters it will be explained how it contains important suggestionabout how to interpret IV curves.

Reverse bias

Applying a reverse bias to the diode brings to a progressive increase in the spacecharge region and to an increase of the potential barrier; thus the resultinge↵ect is a more di�cult flowing of carriers through the junction. Ideally thereshould be no current in this region, but a leakage current exists, as mentionedbefore. Referring once again to Sze’s handbook,10 the reverse current density isexpressed as

J

R

= q

rD

n

⌧

n

n

2i

N

a

+qn

i

W

⌧

g

(1.3)

where ⌧

g

is the generation lifetime.Here it is worth noting the presence of two kinds of lifetime, recombination

and generation. In theory it is usually just said that ⌧

g

is larger than ⌧

n

, butlater in this thesis work it will be useful to analyze them more deeply.

1.1.3 Capacitance

Recalling Fig. 1.3, it can be noticed that a diode consists of two neutral partswith movable carriers (n and p regions) divided by a charged region, i.e. thedepletion layer. Therefore such a structure may be seen as an insulator betweentwo conductors, exactly like a parallel plate capacitor. This leads to a relation-ship between the capacitance and the distance between the n and p regions.11

C = A

✏

S

W

(1.4)

9SZE, S., Op. cit., Eq. 77, p. 98.10Ivi, Eq. 70, p. 97.11CHENMING, HU, Op. cit., p. 98.


From this simple equation it is possible to estimate the depletion layer widthwith a capacitance-voltage measurement. Moreover, if considering the depen-dence of the space charge region on the voltage and the doping concentration(see equation 1.1), the previous formula may be rearranged for a n+p diode toget:

1

C

2=

2

qN

a

✏

S

A

2(V

bi

+ V

r

) (1.5)

where V

r

is the applied reverse bias.This last formula suggests a plotting that allows a calculation of the doping

concentration in the diode from the slope in a graph 1/C2 versus Vr

.

1.2 Diodes for radiation dosimetry

Once we have described the basic physics in silicon devices as diodes, the issue ofhow the semiconductor parameters are actually involved in real systems can befaced. Diodes find application opportunities in many field, but we are focusedon radiation dosimetry application. To better understand how and why theyare used we can start considering that in several cases the cancer treatmentrequires a radiation therapy. Before the process is started is necessary to fulfilla series of tests and calculations in order to guarantee an e↵ective treatmentthat does not involve other tissues.12,13 One of the most crucial points in thesepreparation steps is that the beam will be focused correctly on the desired areaand with the exact amount of dose. Therefore a quality assurance program isunavoidable to find out eventual errors in the radiation distribution.

Di↵erent methods are possible to measure and analyze the dose that willbe delivered to the patient. The possibilities comprehend di↵erent setups: pre-treatment (PT), at-treatment (AT) and in vivo. In the first case the detectoris placed in the X-rays machine before the treatment is actually started, whilein the other two the radiation detector works directly during the therapy. Inparticular, in AT applications we are referring to the implementation of thephotodiodes in the beam path directly after the X-ray source, as it has beendeveloping at ScandiDos. In this thesis work we are not interested in in vivo

dosimetry applications; however, there is a large amount of papers investigatingin vivo systems, giving interesting overviews about them.14,15

Two of the mainly used tools for PT applications are ionization chambersand silicon diodes. The latter is increasingly preferred because it presents sev-eral advantages compared to the former. The greatest reason is related to thesensitivity, a fundamental factor in dosimetry application: a silicon diode ex-hibits a 18000 times higher sensitivity than an ionization chamber due to a 1800

12LI, C., LAMEL, L.S., TOM, D., 1995. A patient dose verification program using diodedetectors. Medical Dosimetry, 20(3), pp. 209-214.

13DESHPANDE, D., DHOTE, D., KINHIKAR, R., KADAM, S., CHAUDHARI, S., 2012.Dosimetric validation of new semiconductor diode dosimetry system for intensity modulatedradiotherapy. Journal of Cancer Research and Therapeutics, 8, p. 87.

14MEILER, R.J., PODGORSAK, M.B., 1997. Characterization of the response of commer-cial diode detectors used for in vivo dosimetry. Medical Dosimetry, 22(1), pp. 31-37.

15MARRE, D., MARINELLO, G., 2004. Comparison of p-type commercial electron diodesfor in vivo dosimetry. Medical physics, 31(1), pp. 50-56.

1.2. DIODES FOR RADIATION DOSIMETRY 19

times higher density and a 10 times smaller ionization energy.16,17 The directconsequence is that a smaller dosimetric volume is needed, in addition to an ob-vious better response to the incoming radiation. Another advantage in diodesapplication is that they can work without a bias, which simplifies the system ifa significant number of detectors is present.

Considering semiconductor devices, moreover, it is worth mentioning thatsilicon is more suitable for detector applications compared to other materialsdue to a high enough intrinsic carrier concentration, directly derived from theenergy band gap. Indeed other semiconductors usually exhibit a larger band gapthan Si; this causes a lower n

i

and, consequently, a smaller outgoing signal.18

Furthermore, using a semiconductor like silicon both detector and electronicsmay be built of the same material, giving the possibility of integration in a singledevice, which leads to better speed properties.19

A drawback in using a silicon diode concerns the presence of the so-called “darkcurrent” produced by the diode and caused by thermally generated carriers.This phenomenon leads to an intrinsic noise in the device that may a↵ect themeasurements.20

In any case the implementation of silicon diodes in detector systems guaran-tees better operative conditions, although several parameters have to be consid-ered. Indeed the sensitivity depends on di↵erent fabrication and measurementconditions in a significant way. Thus a full understanding of how the sensitivitychanges depending on doping type, energy, dose per pulse and other parame-ters is required and the research is pointing to the definition of some generalguidelines to be followed in further applications.

1.2.1 Interaction of radiation with diodes

Before going through the sensitivity dependencies and variations in details, apreliminary introduction on how a diode interacts with the radiation is neces-sary. As explained already in the previous section, a silicon diode is simply apn junction, i.e. a silicon crystal with two doped regions, n-type and p-type.When irradiated, a diode absorbs a certain energy that will be involved in thecreations of an electron-hole pair - around 3,6 eV - and phonons.21 The carrierscreated in such a way can undergo a recombination process, but this is veryunlikely to happen directly from band to band. Thus the carrier lifetime de-pends strongly on the presence of imperfections in the crystal, which providestrapping sites where the carriers can recombine. However, if these charges reachthe pn junction without recombining, they will contribute in the creation of asignal. Therefore the detected signal comes from those carriers that originatein the ionization volume of the diode, consisting in the depletion layer and the

16ROSENFELD, A.B., 2006. Electronic dosimetry in radiation therapy. Radiation Mea-surements, 41, Supplement 1(0), p. S136.

17Diode in Vivo Dosimetry for Patients Receiving External Beam in Radiation Therapy.Aapm Rep 87. 2005. Medical Physics Pub, p. 3.

18REHAK, P., 2004. Silicon radiation detectors. Nuclear Science, IEEE Transactions on,51(5), p. 2494.

19LUTZ, G., 1995. Silicon radiation detectors. Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equip-ment, 367(13), p. 22.

20DIXON, R.L., EKSTRAND, K.E., 1982. Silicon diode dosimetry. The Internationaljournal of applied radiation and isotopes, 33 (11), p. 1172.

21LUTZ, G., 1999. Op. cit., p. 46.


material within one di↵usion length from the depletion layer border.22,23 Inparticular, the di↵usion length is defined as the measure of the distance thatthe carriers are allowed to travel into the p and n regions before they undergo arecombination process. Such a mechanism is also a good explanation of how thesignal varies linearly with the dose absorbed by the detector. Indeed the recom-bination rate exhibits a linear dependence on the concentration of free chargesin the ionization volume and this means that the same kind of relationship willbe present between the delivered dose and the signal.24

The linearity is one of the most important parameters to monitor in dosi-metric analysis because it dramatically a↵ects the results. A complete compre-hension is thus needed to allow a good control of the detector properties.

Later in section 1.3.2 the dose linearity will be further discussed, but firstwe have to consider a key element in the determination of the diode behavior,i.e. the doping type. In semiconductor physics it is well known that dopingconcentration regulates all the diode characteristics, but the doping type inparticular is the responsible of how the recombination processes take place and,hence, how the diode will answer to the incident radiation. Now the mechanismjust mentioned above will be analyzed more deeply to see how the physicalcharacteristics of the diodes are significant in determining the outgoing signal.

The starting point of the recombination phenomenon is the displacement ofsome silicon atoms, in our discussion after a high enough energy transfer fromthe incoming radiation. The movement of an atom creates a vacancy in thesemiconductor crystal, which can combine with another vacancy or impuritiesleading to the creation of a stable defect. As already stated, this imperfectionacts as a trap for the free carriers in the semiconductor.25 A minority carriermay be indeed captured by an empty trap and there recombine with a majoritycarrier. In the first place we consider n-type silicon diodes that have holes asminority carriers. In this case the cross section for the trapping of a hole islarger than the one for the capture of an electron in a filled trap site. As aconsequence the traps will tend to be filled and the concentration of the emptyones decreases if a large number of holes is present. Thus with high dose rate thedetector presents a decrease in recombination processes, which means more freecharge able to reach the pn junction and generate the signal. The conclusion isan increase in sensitivity with the dose rate for n-type diodes.

Examining a p-type silicon diode the scenario is di↵erent. The minoritycarriers are the electrons and the probability of capturing one of them in anempty trap is less than the one for the trapping of a majority carrier. Thee↵ect of this behavior is that the traps will be mainly not filled with electronssince as soon as it happens holes will interact with them and the recombinationprocess is completed. Hence the number of available traps is proportional tothe minority carrier concentration, i.e. the dose rate. In opposition to theprevious doping type, the response is linear. This is an advantage because itwill guarantee a constant sensitivity with changes in the dose per pulse and thus

22RIKNER, G., 1983. Silicon diodes as detectors in relative dosimetry of photon, electronand proton radiation fields. PhD Thesis, University of Uppsala, Sweden, pp. 14-16.

23LUTZ, G., 1999. Op. cit., pp. 91-93.24GRUSELL, E., RIKNER, G., 1993. Linearity with dose rate of low resistivity p-type

silicon semiconductor detectors. Physics in Medicine and Biology, 38(6), p. 789.25Ibidem.


a better reliability of the device.26

The doping type is just one of the several semiconductor factors that maybe varied in order to achieve certain diode characteristics. This is clearly anadvantage since tunable properties mean degrees of freedom and more operativeoptions, but at the same time it demands a complete comprehension of how toassure a proper detector behavior.

1.2.2 E↵ective sensitive volume

A first necessary observation is obviously related to the region in the diode fromwhich the signal can come out. The so-called e↵ective sensitive volume is indeedthe already mentioned ionization volume, consisting of the depletion region andthe material within one di↵usion length from its borders. Now the definition ofthese regions will be examined in details.

The depletion layer width has been presented with equation 1.1, where itcould be seen that two parameters can a↵ect it, one operative and the otherone processing related. The first is the already mentioned bias: applying aforward or reverse bias will decrease or increase the space charged region and,consequently, the sensitive volume. Taking into account processing influence, in-stead, we always refer to doping concentration. This point is crucial in practicalapplication since the producers provide wafers with a certain range of resistivityvalues, i.e. doping concentration values; the smaller the range is the easier willbe to predict the diode characteristics. The relationship between resistivity anddoping concentration in silicon is shown in Fig. 1.5.27

Figure 1.5: Relationship between resistivity and doping concentration in siliconat room temperature.

26RIKNER, G., Op. cit., p. 19.27CHENMING, HU, Op. cit., Fig. 2-8, p. 45.


What it can be easily noticed is that low resistivity values correspond tohigh doping level and this can be understood considering that the resistivity isby definition the reciprocal of the conductivity, a quantity directly proportionalto the carrier density.

The issue is to understand if in semiconductor detectors application is pre-ferred a high or low doping level. Grusell and Rikner28 tried to give an answerbasing their observation on two fundamental parameters, namely dose linear-ity and sensitivity variation with temperature (SVWT). The importance of thedose linearity in dosimetry has been already discussed in the comparison be-tween p and n-type diodes, but now the authors are referring to two di↵erentdoping levels in two p-type diodes. Both linearity and SVWT exhibit a morepronounced variation with accumulated dose in the case of highly doped silicon.This behavior may be wrongly seen as a defect while instead is an advantagefor the detector. Indeed, after the first significant variation, the highly dopedsilicon diodes have a longer stable dependency on the dose, guaranteeing betterlinearity and measurement conditions.

Addressing the issue of how the sensitive volume is a↵ected, it was said thatthe signal comes from the depletion region, but also from the material withinone di↵usion length from its borders. Therefore is necessary to explicate thedependency of that distance on semiconductor parameters. Firstly, the di↵usionlength is calculated with the following formulas:29

L

p

=pD

p

⌧

p

(1.6)

L

n

=pD

n

⌧

n

(1.7)

for minority holes and electrons, respectively in n and p-type semiconductor.Here it can be noticed the presence of the di↵usion coe�cient of carriers D,

directly proportional to temperature and mobility, and especially the minoritycarrier lifetime ⌧ . The latter is one of the most important parameters in thesemiconductor industry and is as important as it is di�cult to measure withprecision. Indeed the carrier lifetime is related to silicon quality, temperature,accumulated dose and other factors that will be explained in details in thenext sections. All these connections can’t be considered singularly since thelifetime in a diode is a combination of all the operative conditions and processingcharacteristics. However it can be intuitively stated that a large carrier lifetimeis a good starting point for a detector, since more carriers can contribute to thesignal and this increases the response to the incident radiation.

1.2.3 Minority carrier lifetime

As said above, the minority carrier lifetime is crucial in radiation dosimetry.This is why the factors that are involved in changes in lifetime or that aresomehow a↵ected by it will be analyzed in the following paragraphs.

A preliminary observation has always to be done regarding the silicon qual-ity. Lattice imperfections and impurities in the crystal are responsible of hugevariations in the minority carrier lifetime, also of three orders of magnitude, asshown in Fig. 1.6.30

28GRUSELL, E., RIKNER, G., Op. cit., pp. 785-792.29CHENMING, HU, Op. cit., Eq. 4.7.6 and 4.7.8, p. 108.30http://www.siliconsultant.com/SIlifetime.htm


Figure 1.6: Carrier lifetime in low, moderate and high quality silicon.

The di↵erences between the three qualities of crystal are less pronounced athigh doping concentration, because at that point the scattering due to acceptoror donor atoms will be predominant compared with the one related to siliconlattice imperfections.

Once the material quality is known, several other factors are involved in thelifetime determination. A first one is the temperature, which easily a↵ects mostof the physical properties in semiconductors. In particular, concerning silicondiode detectors, an increase in temperature leads to two opposite e↵ects. It iswell known in materials science that in crystals higher temperature means moreatoms agitation; as a consequence the number of scattering phenomena becomeslarger and the carrier mobility decreases. Moreover, the lifetime is changed aswell, but in a di↵erent way. Indeed once a minority carrier is trapped in arecombination-generation center, as described in section 1.2.1, it can recombinewith a majority carrier and this represents the end of that specific electron-holepair. Now, considering an increasing temperature, thus a general excitementof the lattice atoms, the probability of escaping from a trapping site raises,bringing to a longer lifetime compared to lower temperature conditions.

Furthermore, not only the instantaneous working conditions play a relevantrole in lifetime variations, but also the “history” of the detector itself influencesit. The crucial point in every carrier lifetime study is to understand the re-combination process in the diode. Considering the working life of a radiationdetector it receives a certain amount of dose every time it is used; in otherwords, the accumulated dose always increases. It has been deeply studied thatthe radiation damages the diode,31 depending on incident energies, radiationquality or dose rate, but a general trend can be defined. In fact, accumulateddose causes an increasing number of recombination-generation centers and, ascould be easily expected from this, a decrease in the carrier lifetime.

Due to these several dependencies of the minority carrier lifetime on di↵erentfactors its importance in dosimetric applications is underlined once again andthe di�culties to evaluate it with precision are justified, at least in part.

31RIKNER, G., GRUSELL, E., 1983. E↵ects of radiation damage on p-type silicon detec-tors. Physics in Medicine and Biology, 28(11), pp. 1261-1267.


Open-Circuit Voltage Decay

Several methods of evaluation of the minority carrier recombination lifetimeexist, although depending on the chosen method there could be some di↵erencesin the results due to even slightly di↵erent experimental conditions.

An old -but still working- strategy is the Open-Circuit Voltage Decay (OCVD).The principle is based on a first accumulation of carriers within the diode dueto an applied forward voltage. When the circuit is opened, it is possible to cal-culate the voltage decay caused by the progressive recombination of the excesscarriers. The strict relationship between voltage and carriers’ concentration isat the base of the theory of the OCVD technique, well explained in details bySchroder.32 Taking into account the recombination having place in the spacecharge region and the quasineutral region of the diode we can write a formulathat describes how the lifetime may be derived by the slope in a voltage versustime graph.

⌧ = �n

kT/q

dV/dt

(1.8)

Where the factor n can vary between 1 and 2, depending on the conditions:under high-level injection the ideality factor n has to be taken as 2, while forlow injection as unity.

When observing an OCVD curve, the shape of the voltage decay may beusually divided into two parts. The first is an abrupt decrease in the voltagedue to the ohmic drop in the diode when the current flow ceases. The secondpart is the one that can be used for lifetime calculation and is characterizedby a slope, the dV/dt term in equation 1.8. The determination of this slopeis thus a priority in such a measurement setup and we should pay particularattention to likely deviations from ideality that could be present in the curves.The possible variations can lead to a shorter or longer lifetime, depending onjunction capacitance or shunt resistance, as shown in Fig. 1.7.33

Figure 1.7: Deviations from ideality in a voltage decay curve.

These contributions add di�culties to the practical measuring and readingoperations. This is why the author’s suggestion is to use the OCVD results notas an absolute truth about the samples’ lifetime, but as a measure that needsfurther investigation to be fully validated.

32SCHRODER, D.K., 2006. Semiconductor Material and Device Characterization. Wiley-Interscience, Section 7.5.3.

33Ivi, Fig. 7.2, p. 422.

1.3. X-RAY DETECTOR PARAMETERS 25

1.3 X-ray detector parameters

After this brief overview on the physics of silicon diodes, we have the instru-ments to analyze in details the parameters that have to be taken into accountconsidering radiation detectors, and particularly X-ray detectors that are di-rectly involved in this thesis work.

The state of art of semiconductor radiation detector is generally based ontests on real products, without taking into account the physical explanation ofthe obtained results. This chapter is aiming to the definition of a general trendin silicon detectors, obtained through an overview on the available literature.For this reason the following statements are not directly tested by us, but theyare based on several experimental studies carried out on di↵erent kinds of diodes.Therefore, the next sections will be more qualitative and descriptive than anexposition of data analysis. The main points on which the following sectionswill be focused are:

• Sensitivity

• Dose linearity

• Dose Per Pulse Dependency (DPPD)

• Sensitivity Variation With Temperature (SVWT)

• Long term stability

• Directional dependency

1.3.1 Sensitivity

The sensitivity is a measure of how e�ciently the detector answers to the deliv-ered dose and the used unit is usually nC/Gy, where Gy refers to Gray, the unitfor the adsorbed dose defined as 1 J of adsorbed energy per 1 Kg of matter. Itis not always specified in the publications about this topic if it is considered theabsolute or the relative sensitivity, but in general the di↵erence is that in thelatter it is common to compare the diode detector response with the one of anionization chamber with the same settings.

As already explained, the advantages of the implementation of silicon diodesin radiation dosimetry are related to a high sensitivity, but new issues show up.Among them the most important is certainly the sensitivity variation.

Sensitivity variation

We presented in Fig. 1.6 that a high doping level is the reason for a decreasein the minority carrier lifetime in silicon of any quality.34 The consequences onthe sensitivity of the detectors are straightforward: short lifetime means smallsensitive volume and thus a lower sensitivity. The main issue is anyway not alow sensitivity, but an eventual change in it. Indeed for any small variation insensitivity the reliability of the instrument is modified, forcing a constant checkand, if needed, recalibration processes.

34RIKNER, G., GRUSELL, E., 1987. General specifications for silicon semiconductors foruse in radiation dosimetry. Physics in Medicine and Biology, 32(9), pp. 1112-1113.


In his paper, Rosenfeld proposes a method to reduce the sensitivity varia-tion.35 It consists in the addition of recombination active centers by introductionof materials like platinum or gold to achieve a better stability in the diode. Thissolution works fine with silicon, but the implementation in the industrial pro-cesses is more complicated to the additional requirements derived by these kindof metals. For this reason a good result is generally obtained by pre-irradiatingthe detector.

Pre-irradiation

The pre-irradiation of a detector diode is well known to be a mandatory pre-liminary phase before every dosimetric measurement. Indeed, in all the studiesof these systems a graph is usually presented: sensitivity as a function of thedose. In Fig. 1.8 it is shown an example from Rikner and Grusell, in which ispresented a comparison between the behaviors of p and n-type diodes.36

Figure 1.8: Sensitivity vs pre-irradiation dose for p-type (circle) and n-type(cross) diodes.

What can be deduced from the observation of Fig. 1.8 is first a repetitionof the already explained concept of a better linearity in p-type diodes in whichthe sensitivity drop is less pronounced. The second thing to point out is thatthe first part of the curve exhibits a very good sensitivity, but the changeswith the dose are immediate and dramatic. Therefore, what is actually done inradiation detectors processing is to avoid that part of the curves with a su�cientpre-irradiation. This means surely a lower sensitivity, but at the same time asignificant gain in stability and linearity.

35ROSENFELD, A.B., Op. cit., p. S136.36RIKNER, G., GRUSELL, E., 1983. Op. cit., Fig. 2, p. 1264.


A further consideration is the quality of the radiation used in the pre-irradiation treatment. Due to di↵erent interactions with matter, there is asubstantial di↵erence between, for example, protons and X-rays damage in sili-con: Rikner demonstrates that a 70 Mev proton beam causes a 40 times higherdamage than a 8 MV X-rays.37

Energy dependence

The diode response may be expected to vary with di↵erent photon energies andthis idea is the base of a specific test conducted by Djouguela et al..38 Comparingmeasurements held at di↵erent incident photon energies with the results of anionization chamber with the same conditions, the trend is a small increase inthe response when the energy decreases. Such an energy dependency is causedespecially by the high atomic number materials that surround the silicon.39,40

When considering the energy influence, moreover, the physical phenomenainvolved, like scattering of secondary electrons, are connected to the relative po-sition between detector and photon beam. Thus in within the same detector theenergy dependence is not invariant and it has been reported a more significante↵ect along the diode axis.41

1.3.2 Dose linearity

The linear response of the diode to the incident radiation is a requirement thathas always to be fulfilled to assure the correct working of the detector and re-liable results. How the doping type and the pre-irradiation a↵ect the linearitywas already discussed in the previous sections, but an additional comment couldbe done about the recombination process which is said to strongly depend onthe presence of trapping sites and their occupation probability changes if con-sidering a p-type or an n-type diode. Grusell and Rikner42 added to the processdescription the possibility that various kinds of traps are involved and thattheir di↵erent production rates are related to the radiation quality. Thus theoverall description of the recombination mechanism comprehends several vari-ables and it represents the first step to achieve good prediction on the detectorperformances and its linearity.

1.3.3 Dose Per Pulse Dependency (DPPD)

The Dose Per Pulse Dependency is not a secondary parameter in X-ray detec-tors because the delivered dose can vary significantly depending on the kind oftreatment required and this leads to obvious variation in the diode response.

37RIKNER, G., Op. cit., pp. 24-25.38DJOUGUELA, A., GRIEßBACH, I., HARDER, D., KOLLHOFF, R., CHOFOR, N.,

RUHMANN, A., WILLBORN, K., POPPE, B., 2008. Dosimetric characteristics of anunshielded p-type Si diode: linearity, photon energy dependence and spatial resolution.Zeitschrift fur Medizinische Physik, 18(4), p. 303.

39Diode in Vivo Dosimetry for Patients Receiving External Beam in Radiation Therapy.Op. cit., p. 14.

40SAINI, A.S., ZHU, T.C., 2007. Energy dependence of commercially available diode de-tectors for in-vivo dosimetry. Medical physics, 34(5), p. 1711.

41EVELING, J.N., MORGAN, A.M., PITCHFORD, W.G., 1999. Commissioning a p-typesilicon diode for use in clinical electron beams. Medical physics, 26(1), p. 103.

42GRUSELL, E., RIKNER, G., Op. cit., p. 789.


The basic idea that rules the research in radiation detectors is to minimizethe sensitivity dependency on all the operative parameters in order to guar-antee a stable device, avoiding recalibration or correction factors.43 Thus thepre-irradiation treatment is again encouraged, since it reduces the DPPD,44,45

although it can’t eliminate it.46

The explanation of this unavoidable dependency is related to the genera-tion of minority carriers. If the dose per pulse increases, the minority carriers’generation rate increases, causing a larger number of excess carriers. If theconcentration of trapping sites and recombination centers is thought to be thesame during the process, the resulting situation is an increase in sensitivity duea higher number of carriers that contribute in the signal creation.

A last aspect to consider about DPPD is that it is a↵ected also by the longterm use of the detector. Jursinic has observed its variation in a period of 4years on a monthly basis.47 The results show that the DPPD increases withaccumulated dose and radiation damage, but how it changes depends on thediode type involved.

1.3.4 Sensitivity Variation With Temperature (SVWT)

It’s easy to monitor the temperature in a device, but not so simple to understandhow it can influence the detector behavior. A temperature increase causes twoopposite phenomena, as described earlier in section 1.2.3. It brings to a decreasein carrier mobility due to a higher probability of scattering events in the crystal,but, on the other hand, it leads to a longer carrier lifetime because of an easierrelease from recombination centers and trapping sites. The final e↵ect is a trade-o↵ between those two di↵erent trends and most diodes exhibit an increase insensitivity with temperature.48 However, it has been also reported a decrease insensitivity with increasing temperature, even if it was only a small variation.49

The issue is anyway complex because it involves also a dependency of SVWTon DPP. Saini et al.50 have carried out a study on the temperature dependenceof several diode detectors in order to find some guidelines to better predictand limit sensitivity variations. The research was done both on n and p-type -unirradiated and pre-irradiated - diodes and it shows how the SVWT dependson DPP; an e↵ect that is more marked in n-type devices. It is worth noting thatpre-irradiation is again encouraged since it reduces, and eventually eliminates,the dose rate dependence of the SVWT, due to the introduction of defects inthe diode and the consequent decrease in the minority carrier lifetime.

43OMAR A., 2010. Silicon Diode Dose Response Correction in Small Photon Fields. MasterThesis, Stockholm University, Sweden.

44SAINI, A.S., ZHU, T.C., 2004. Dose rate and SDD dependence of commercially availablediode detectors. Medical physics, 31(4), p. 922.

45JURSINIC, P.A., 2009. Angular dependence of dose sensitivity of surface diodes. Medicalphysics, 36(6), p. 2167.

46SAINI, A.S., ZHU, T.C., 2002. Temperature dependence of commercially available diodedetectors. Medical physics, 29(4), p. 630.

47JURSINIC, P.A., 2001. Implementation of an in vivo diode dosimetry program andchanges in diode characteristics over a 4-year clinical history. Medical physics, 28(8), p. 1722.


49RIKNER, G., GRUSELL, E., 1987. Patient dose measurements in photon fields by meansof silicon semiconductor detectors. Medical physics, 14(5), p. 873.

50SAINI, A.S., ZHU, T.C., 2002. Op. cit., pp. 622-630.


1.3.5 Long term stability

It was already mentioned that the detectors properties change with the delivereddose and these variations have to be considered also on a long term perspective.The material of which the diode is made is indeed a↵ected by repeated radiationinteractions. In section 1.2.3, the accumulated dose was said to influence theminority carrier lifetime due to an increase in the number of recombination-generation centers. This is easily understandable considering a defect generatedinside the crystal: if no annealing process is performed, such an imperfectionwill last.

Therefore, accumulated dose means addition of an increasing number ofcenters that limit the carrier lifetime leading to a resulting smaller sensitivity.This kind of sensitivity reduction has not to be thought as the pre-irradiationsensitivity drop, since it is a slight variation, although it may be a di↵erenceof several percent.51 Anyway, as usual the pre-irradiation step allows reducingthis e↵ect and helps to guarantee a more predictable behavior.52

1.3.6 Directional dependency

The working mechanism of a radiation detector is based on interactions betweenincident photons and diodes, thus the relative position between them has to beconsider since it may a↵ect the outgoing signal, as explained in the followingparagraphs, where a brief overview on the question is given. Two di↵erent kindsof directional dependency can be considered: axial and radial.

Axial dependency

Taking into account the scanning direction and the diode and the beam axes,it is possible to evaluate two opposite situations, as explained by Beddar et

al..53 They consider the diode axis perpendicular to the scanning directionand parallel to the central beam axis and vice versa, in order to see whichconfiguration can be defined as the best. The used criterion is based on theobservation of the dose profile and in the determination of the distortion causedby the directional dependence. The results show that to minimize the distortionin radiation profile the best configuration is to set the diode axis perpendicularto the scanning direction and parallel to the central beam axis.

Radial dependency

The geometry of the diode itself leads to a directional dependency since it has thedepletion layer close to the surface. Indeed this means that the silicon detectorhas an inherent anisotropy that causes di↵erent responses depending on the

51WILKINS, D., LI, X.A., CYGLER, J., GERIG, L., 1997. The e↵ect of dose rate de-pendence of p-type silicon detectors on linac relative dosimetry. Medical physics, 24(6), p.881.


53BEDDAR, A.S., MASON, D.J., O’BRIEN, P.F., 1994. Absorbed dose perturbationcaused by diodes for small field photon dosimetry. Medical physics, 21(7), pp. 1075-1079.


incident angle.54,55,56 The physical reason of this influence is related to interfacephenomena that involve also multiple scattering e↵ects at the borderline betweensilicon and the materials around the die.

A way to reduce the angular dependency is to design a diode with a highersymmetry, as proposed by P. Norlin et al..57 The suggested geometry exhibitsa cubic diode with pn junctions on the six sides and it allows achieving a goodisotropic behavior, reducing directional dependence e↵ects.

54JURSINIC, P.A., 2009. Op. cit., pp. 2167-2168.55WESTERMARK, M., ARNDT, J., NILSSON, B., BRAHME, A., 2000. Comparative

dosimetry in narrow high-energy photon beams. Physics in Medicine and Biology, 45(3), p.691.

56WONG, J.H.D., KNITTEL, T., DOWNES, S., CAROLAN, M., LERCH, M.L.F.,PETASECCA, M., PEREVERTAYLO, V.L., METCALFE, P., JACKSON, M., ROSEN-FELD, A.B., 2011. The use of a silicon strip detector dose magnifying glass in stereotacticradiotherapy QA and dosimetry. Medical physics, 38(3), p. 1232.

57NORLIN, P., OBERG, O., JUNIQUE, S., KAPLAN,W., ANDERSSON, J. Y., NILSSON,G., 2014. A cubic isotropic X-ray dose detector diode fabricated by DRIE of SOI substrates.Sensors and Actuators A: Physical, 213(0), pp. 116-121.

Chapter 2

Statistical analysis ofprevious batches

One of the aims of this thesis is a better knowledge of the diodes for radiationdosimetry, in particular those ones produced in Acreo. This is the reason forwhich the work started with a statistical analysis of di↵erent batches of diodesproduced in the last years, in order to have a guideline for the characterizationof our samples.The data sheets with the results of post-process characterization didn’t presentthe characteristics of all the diodes contained in every wafer, but just a limitednumber of them was analyzed to avoid a too time-consuming characterizationphase. Nevertheless, the uniform selection performed should give a valid statis-tical estimate of the entire population. Moreover, not the whole IV curve wasanalyzed, but just some fixed points were recorded to cover both reverse andforward bias sides.

To define a general trend from such data sheets one voltage for the forwardbias and one for the reverse were selected. Doing so, it was possible to calculatetwo averages and obtain statistical considerations on both the sides of the curve.

First the received data were from 10 batches with 12 to 24 wafers each.The batches had 6 di↵erent resistivity ranges, which are related to the dopingconcentration in the silicon. Additionally for every wafer there were data bothbefore and after the pre-irradiation process.

As said earlier two voltage values were chosen: -1 V and 0,5 V. Then, toobtain a reliable average, median values were calculated for the current distri-bution of every wafer. In conclusion, an average of these values was calculatedfor the wafers with the same resistivity, considering both before and after irra-diation process.

An example of the resulting current distributions is shown in the followinggraphs in Fig. 2.1 and Fig. 2.2.

31

32 CHAPTER 2. STATISTICAL ANALYSIS OF PREVIOUS BATCHES

Figure 2.1: Batch D039: current distribution at -1 V for wafers 1-25 (as pro-cessed).

Figure 2.2: Batch D039: current distribution at 0,5 V for wafers 1-25 (as pro-cessed).

After having performed the same calculation for all the available data sheetsall the results could be summarized, as it is possible to see in table 2.1.

At a first glance, it is easy noticing that the current changes after the irra-diation process follows a common trend: the currents generally increase. Thisis expected, inspecting equations 1.2 and 1.3, where the current density was ex-pressed in the forward and reverse bias, respectively. In both cases, the minoritycarrier lifetime stays at the denominator position. It was already said how in-teractions between diodes and radiation introduce defects in the crystal which

2.1. THEORETICAL MODEL: FORWARD BIAS 33

Batch Date ⇢ (⌦cm) Wafer Average I at 0,5 V (A) Average I at -1 V (A)ID irradiated irradiatedD014 2008 0,1-0,2 1-24 2,84E-06 7,57E-06 -1,84E-10 -1,07E-10D019 2008 0,4-0,6 1-24 5,96E-06 1,62E-05 -1,47E-11 -3,37E-11D038 2009 0,4-0,6 1-24 4,03E-06 1,69E-05 -6,23E-11 -4,23E-11D039 2009 0,4-0,6 1-25 2,81E-06 1,32E-05 -1,64E-12 -1,66E-11D063 2010 0,4-0,6 1-24 2,45E-06 1,64E-05 -4,54E-12 -1,60E-11D064 2011 0,4-0,6 1-24 3,27E-06 1,99E-05 -8,54E-12 -1,55E-11D142 2011 0,13-0,15 1-12 1,77E-06 1,07E-06 -5,68E-12 -2,96E-11D142 2011 0,4-0,45 13-24 2,57E-06 2,43E-05 -5,06E-12 -2,59E-11D143 2012 0,13-0,15 1-12 2,31E-06 2,52E-05 -5,94E-12 -3,33E-11D143 2012 0,4-0,45 13-24 2,09E-06 5,98E-06 -2,81E-11 -6,33E-11D255 2012 0,13-0,15 1-16 3,41E-06 5,52E-06 -3,57E-11 -5,91E-12D255 2012 1-4 17-24 1,83E-05 8,81E-05 -2,43E-11 -9,21E-12D305 2013 1-2 1-12 7,85E-05 7,85E-05 -2,81E-11 -1,90E-11

Table 2.1: Average current values for di↵erent batches, recorded at -1 V and0,5 V for not- and irradiated wafers.

causes an increase in the scattering events. Therefore, after the pre-irradiationtreatment, the same wafer exhibit a higher current due to a shorter lifetime.

Another information present in this set of measurements is the position ofthe failing diodes on the wafers. Therefore it has been possible to count thesingle failing diodes related to their positions in order to draw maps for allthe batches. This approach was based on the idea that a pattern could bepresent in the failure positions, which could have meant that the failure causewas processing related.

The results didn’t allow any pattern determination, besides the obvious con-sideration that the largest amount of failing devices was located at the wafersedges. The probable reason is that those zones are the ones with a likely highernumber of defects caused by the fact that they are the most involved parts inhandling and transporting.

2.1 Theoretical model: Forward bias

Coming back to the statistical results, a theoretical model for IV characteristicsthat corresponded to the found values was applied, in order to see how changingthe semiconductor properties or the temperature can a↵ect the measurements.The focus was in particular on the forward bias part of the curve, trying tofigure out the e↵ects due to changes in temperature, doping concentration andminority carriers’ lifetime. The ideal model we are referring to is the one ex-pressed in section 1.1.2, in particular with equation 1.2. Such a formula consistsof two parts: the first is the total di↵usion current and the second takes intoaccount the recombination processes. Just observing the presence of two di↵er-ent exponential terms in these two contributions one can expect that also thefinal curve will exhibit this di↵erence, if plotted in logarithmic scale.

For the theoretical model two diodes with di↵erent resistivities and, conse-quently, doping concentrations were considered. Recalling the graphs in Fig. 1.5and 1.6, considering the worst case of very low quality silicon, the characteristics


of the chosen diodes are the following:

• diode 1

– ⇢ = 0, 4� 0, 6 ⌦cm

– N

a

= 3, 5 · 1016 cm�3

– N

d

= 1019 cm�3

– ⌧

n

= 1, 5 µs

• diode 2

– ⇢ = 0, 13� 0, 15 ⌦cm

– N

a

= 2 · 1017 cm�3

– N

d

= 1019 cm�3

– ⌧

n

= 0, 1 µs

Since the average for one value in the forward and one in the reverse direc-tion was studied, the adopted reference point for the comparison between thetheoretical model and the real measurements was the current at 0,5 V. For boththe diodes the di↵erence was almost negligible, in the order of magnitude of10�7 A and this shows that the level of approximation is acceptable.

Having a model is an advantageous and easy way to see how variations inthe parameters lead to di↵erent characteristics because a simple plotting ofthe equation quoted before gives an immediate result. However, a guideline isneeded not to have just qualitative information about such variations. In thiscase, a statistical consideration done in ScandiDos suggested that a di↵erenceat 1 mA of more than 12 mV between the measured characteristics and theaverage ones means a higher failure probability, while in within this small rangethe same probability can be considered low enough. This is why it was neededto calculate two curves around the average one, with a di↵erence of plus andminus 12 mV.

The e↵ects of temperature, doping concentration and minority carriers’ life-time on the IV characteristics of the selected diodes in the forward bias arepresented in the following sections.

2.1.1 Temperature influence

Considering the IV measurement performed at room temperature, the aim wasto see how colder or warmer the experimental setup should be to reach the 12mV di↵erence at 1 mA. The results are illustrated in semi-logarithmic scale inFig. 2.3.

The first observation is the confirmation of the expectation of two di↵erentslopes due the presence of the exponential terms in equation 1.2. Looking at thelegend, the two curves that distance themselves from the middle one are definedwith all the parameters and conditions the same, besides a di↵erence of 6 K,and this is valid for both the diodes. Such a temperature variation is quite highand we think it can’t be involved in failure investigation. However, the diodesundergo a thermal excursion during processing operations like soldering, butthese kinds of phases are so localized in space and time not to be responsible ofconsiderable changes in the material properties.


(a) Diode 1 (b) Diode 2

Figure 2.3: Temperature influence on IV characteristics - forward bias - fordiodes 1 and 2.

A last comment about the graphs above is related to the observation of thethree curves at di↵erent temperatures together: the trend in changing temper-ature leads to a broadening of the characteristics for increasing voltages. Thus,for low voltages the temperature e↵ect is not remarkable and this is a guaran-tee for further measurements, since it is common to not to go too deep in theforward bias direction.

2.1.2 Doping concentration influence

A crucial point in the semiconductor industry is related to the doping concen-tration. Since silicon is a semiconductor and all its electrical properties aredominated by type and amount of doping atoms, the ideal case is to knowperfectly this quantity. Unfortunately the wafers are generally produced witha quite broad range of doping concentration, that actually is not directly ex-pressed. Indeed it is common to define a resistivity range in which that specificwafer lays.

Therefore the problems brought by such a definition are mainly two: it isnot so precise to determine the doping concentration from resistivity values (seeFig. 1.5) and then it is not possible to say precisely how far from the rangeborders the actual values stay.

This introduction should explain how the following considerations are morequalitative than quantitative and how this topic is important in silicon diodesstudies. The following graphs in Fig. 2.4 show the calculated results for the twodiodes.

The 12 mV di↵erence is the guideline for the three curves, but the waythey vary is di↵erent from the temperature influence. The characteristics now



Figure 2.4: Doping concentration influence on IV characteristics - forward bias- for diodes 1 and 2.

are changing almost in the same way in the two parts with di↵erent slopes,although the recombination contribution, i.e. the part closer to zero voltage, isless a↵ected by doping concentration. To confirm the naked eye observation, thedi↵erences in voltages at lower current values were calculated. Thus it can bestated that at current values of 10�10 A or 10�11 A the curves behavior followsthe same trend that they exhibit at 1 mA.

These graphs are not meant to give precise quantitative results, but anywaythey can suggest interesting conclusions about doping dependence. Examiningthe legends, it is possible to see that the doping concentration di↵erences aresmaller for the second diode compared to the first, but there is a remarkabledistinction among them. To understand it, the resistivity ranges of these diodeshave to be recalled: 0, 4� 0, 6 ⌦cm for diode 1 and 0, 13� 0, 15 ⌦cm for diode2. In the second diode the guaranteed range is so small that it is actuallydi�cult to achieve the values in the legend. Diode 1, instead, has more degreesof freedom and with Fig. 1.5 it is possible to figure out which kind of dopingconcentration range corresponds to these resistivities: approximately the dopinglevel goes from 3 to 4 ·1016 cm�3. Such values seem good enough to stay withinthe 12 mV reference distance from the average curve, but this may represent thefailure cause, since the doping concentrations are not so far from the calculatedborderline values.

This conclusion has to be taken into account as an aspect of the semicon-ductor material used for the diode that needs further investigations.


2.1.3 Minority carrier lifetime influence

The last parameter we are going to discuss now has already received special at-tention in the previous sections, but its importance in semiconductor industryneeds to be underlined once again. The minority carrier lifetime governs theelectrical properties and the interactions of any silicon device, such as the ana-lyzed diodes. It is worth noting that the di�culties in measuring this parameterare still to be considered when the issue of how the forward IV characteristicsdepends on lifetime changes is addressed. Here in figure it is shown in the graphshow the 12 mV range is obtained in the curves for diode 1 and 2 at a currentof 1 mA.


Figure 2.5: Minority carrier lifetime influence on IV characteristics - forwardbias - for diodes 1 and 2.

As in the case of the doping concentration discussed earlier, a distinctionbetween diode 1 and 2 is necessary. In the second kind of diode the lifetimeis much shorter than the first and hence the changes in the lifetime are muchlower. This can’t be taken as a reliable value in general cases because it isderived from statistical analysis and approximation, but it can be used to betterunderstand how the shape of the curves may change with di↵erent lifetimevalues. Indeed the curves here are closer to each others in the higher voltagepart, which means that lifetime variations a↵ect the IV characteristic in theopposite way of temperature.

Chapter 3

Experimental

In this chapter the analyzed samples and the chosen experimental setups arepresented.

All the measurements were performed at Acreo laboratories in Electrum,Kista - Stockholm.

3.1 Samples description

Failure analysis is not a common topic in a semiconductor handbook. Whentalking about detector systems, then, the electronic apparatus is generally con-sidered more than the basic unities, like diodes.1 Therefore the aim is an anal-ysis focused on the silicon diodes constituting the detector, produced in Acreoin Stockholm. They are all n+p diodes and their geometry looks like the oneschematized in the figure below.

Figure 3.1: Schematic representation of one sample diode (top view).

1SPIELER, H., 2005. Semiconductor Detector Systems. Oxford University Press, Chapter9.

39

40 CHAPTER 3. EXPERIMENTAL

Here it is possible to see the circular shape of the diode and the presence oftwo metallic pads used to contact the diodes with all the measurement tools.

The diode characteristics are listed here:

• Diameter = 1 mm

• Depth = 110 µm

• n+ region depth = 3 µm

• N

d

= 1019 cm�3

• ⇢ = 0, 4� 0, 6 ⌦cm

All these properties are common to all the studied diodes, but some di↵er-ences occur due to processing and packaging.

3.1.1 Normal diodes

The purpose of this study is to inspect failing mechanisms in diodes for radiationdosimetry. To achieve that, the starting point is the analysis of normal workingdiodes, which were measured as processed and after a pre-irradiation process.They were in small pieces of wafer, as shown in the following figure.

(a) As processed (b) After pre-irradiation

Figure 3.2: Normal diodes.

3.1.2 Failing diodes

During the diodes processing to implement them in the final radiation detectors,di↵erent tests are held to verify their e�ciency, which allows an early identifica-tion of failing devices and a prompt replacement. If a diode is completely failingfrom an electrical point of view it is easy to find it out at early stages and throwit away. The problem faced in this thesis work refers instead to diodes that arejust marginally failing in electronical characteristics, but that then in the endof the process will exhibit a not good enough sensitivity. This means that theydeviate from the average in IV measurements, exhibiting higher forward andleakage currents.

3.2. EPOXY REMOVAL 41

Two kinds of failing diodes were received: a set of them was meant for pre-treatment (PT) applications and the other one for at-treatment (AT) devices.The main di↵erence among them is that while the former is placed in a bodyphantom to be put in the linear particle accelerator (LINAC) in substitution tothe patient, the latter is located at the X-ray source and may be used duringthe treatment. In Fig. 3.3 two examples are shown.

(a) Pre-treatment applications (b) At-treatment applications

Figure 3.3: Failing diodes.

The samples are the same kind of diodes, but it is clear that they haveundergone di↵erent processing and the way they were discovered to fail wasdi↵erent, too.

The observation started with the diodes for pre-treatment devices. They arecovered by an epoxy layer on both sides, which hides the contact pads as welland the new contacts are the metallic edges. Their marginal failure has beendiscovered immediately after they were placed in the boards with all the otherdetector diodes. The diodes intended for at-treatment applications are insteadmore similar to the normal ones, although they are not in wafers, but dividedinto single unities.

3.2 Epoxy removal

In reverse engineering an ordinary problem to face is the presence of an epoxylayer that hides the circuits underneath and prevent them from contaminationor mechanical stress. In our case a set of diodes was encapsulated in a blackepoxy (see Fig. 3.3 a), since they were already assembled in the detector systemswhen their failure was discovered. Thus it was decided to see if a safe removalof such a protection may be done and if it can be considered convenient enoughfor our purpose.

Taking inspiration from the work of Muarali and Srikanth,2 di↵erent ex-periments were performed on some of the samples. The idea is to achieve the

2MURALI, S., SRIKANTH, N., 2006. Acid Decapsulation of Epoxy Molded IC PackagesWith Copper Wire Bonds. Electronics Packaging Manufacturing, IEEE Transactions on,29(3), pp. 179-183.


selective removal of the epoxy, without destroying or altering the diode. There-fore the tests proceeded in steps, from weak to more aggressive techniques.

Below is a list of the conditions of the tested methods:

• Acetone

• Mixture of nitric and sulfuric acids

• Sulfuric acid

3.2.1 Acetone

The first test made was with simple acetone and tweezers. Scratching the epoxysurface with the tweezers tip and dropping acetone on it, it was possible to re-move the glob-top in a few minutes. The idea of this test was to avoid chemicalcorrosion of the diode under the epoxy layer, although it could be expected astronger mechanical action of the tweezer tips compared to the other experi-mental conditions.

3.2.2 Mixture of nitric and sulfuric acids

Murali and Srikanth suggest the use of fuming nitric acid combined with con-centrate sulfuric acid in their paper.3 The operative conditions can be di↵erentdepending on the reagents percentages and the temperature. To begin with anot so violent process it was chosen to mix 80% vol of fuming nitric acid with20% vol of concentrated sulfuric acid (95%-97%) to obtain a total volume ofabout 20 ml. The selected temperature was 80�C and the samples were putinto the mixture just after that temperature was reached. Then, in order tohelp the reaction and the dispersion of the glob top, the tweezers were usedagain, but more gently compared to the first case. The overall duration of theepoxy removal strongly depended on how much strength was put in the tweezersapplication and if the sample was kept in motion.

3.2.3 Sulfuric acid

The last tested method consisted in the use of concentrated sulfuric acid (95%-97%) alone. In this case, the acid bath was brought to a temperature around100�C to balance the absence of the nitric acid and to try to speed the reactionup further. The acid volume was again about 20 ml.

As can be predicted, once the temperature was reached and the sample wasput into the acid, the reaction started immediately. The tweezers were againused to facilitate the removal of the epoxy layer.

The considerations done for the acids mixture are still valid. The concen-trated acid acts chemically, easily dissolving the glob-top, while the increasedtemperature accelerates the reaction. Particular care has to be taken since theprocess is highly aggressive and it must be monitored for the whole time.

3Ibidem.

3.3. OPEN-CIRCUIT VOLTAGE DECAY 43

3.3 Open-Circuit Voltage Decay

The experimental setup used for lifetime measurements, based on the OCVDtechnique, is presented in the following figure.

Figure 3.4: OCVD experimental setup: (a) oscilloscope, (b) power supply, (c)signal generator, (d) circuit on a breadboard, (e) computer to see the contactswith the diode and to save the curves, (f) manual probe station.

The characteristics of the elements in Fig. 3.4 are:

• Power supply: Kenwood Regulated DC Power Supply

• Oscilloscope: Tektronix TDS 754A

• Signal generator: hp 8116A Pulse/Function Generator

• MOSFET: IRFZ24NPBF by Elfa Distrelec

The electronic schematic of the circuit is shown in Fig. 3.5.Before starting any measurement there are some prerequisites that need to

be checked. First the two probes connecting the oscilloscope to the diode mustbe the same. In our case, they were Passive Probe P6139B from Tektronix, withthe following specifications:

• Attenuation: 10X

• Dynamic range: 300 V CAT II

• Bandwidth: 500 MHz

• Input impedance at the probe tip: 10 M⌦, 8 pF


Figure 3.5: OCVD experiment: electronic schematic.

Regarding these probes, moreover, a calibration phase is needed to guaranteea perfect shape of the pulse signal. Finally, the channels’ grounds have to bealigned before recording any decay.

With these settings it was possible to apply the OCVD method to the diodesto measure their recombination lifetimes. However, to have a guarantee of thesetup quality, it was decided to begin with a known test diode, i.e. the diode1N3595 from Fairchild Semiconductor.4

The parameters used for the measurements were the following:

• Power supply voltage: 9 V

• Pulse frequency f = 3, 5 kHz

• Pulse width w = 50 µs

The recorded voltage decay is depicted in Fig. 3.6.Having proved the e�ciency in visualizing the expected voltage decay with

this setup, it was possible to perform measurements on normal diodes as pro-cessed keeping the same parameter as in the test experiment. On the other hand,analyzing irradiated diodes, both functional or failing, the parameters had to bemodified. Indeed it is known from literature5,6 that the pre-irradiation processleads to a decrease in the recombination lifetime due to radiation generated de-fects. Since the expected lifetime was shorter than the preceding measures, the

4http://www.fairchildsemi.com/ds/1N/1N3595.pdf5GRUSELL, E., RIKNER, G., 1986. Evaluation of temperature e↵ects in p-type silicon

detectors. Physics in Medicine and Biology, 31(5), p. 530.6RIKNER, G., GRUSELL, E., 1987. General specifications for silicon semiconductors for

use in radiation dosimetry. Op. cit., p. 1112.

3.4. CAPACITANCE-VOLTAGE MEASUREMENT 45

Figure 3.6: Voltage decay for the test diode.

setup had to be adapted to maximize the possibility of visualizing the slope inthe voltage decay.

The new parameters were therefore:

• Power supply voltage: 1,7 V

• Pulse frequency f = 2, 5 kHz

• Pulse width w = 20 µs

3.4 Capacitance-Voltage measurement

The capacitance-voltage (CV) measurement is a standard test for analyzingsilicon diodes.7 The instrument used to measure the CV curves for our diodeswas a HP 4284A Precision LCR Meter, connected to a probe station to makecontact with the samples. The tool registers at the same time capacitance andconductance as the reverse bias increases and it stops when the conductancestarts to become too high.

Two samples per kind of diode were measured, to have measures of functionaldiode as processed and pre-irradiated and of failing diode with and withoutepoxy.

7HODGSON, M., 2010. An Investigation into Silicon PIN Diode Detectors for DosimetryApplications. Master Thesis, University of Surrey, England.


3.5 Current-Voltage characteristics and responseto light

All the IV measurements were performed using a HP 4156A Precision Semi-conductor Parameter Analyzer connected to a manual probe station (Karl Sussand Temptronic TermoChuck System Manual Probe Station PM 5, TP0314A).The parameter analyzer has several tunable parameters that may be adjustedto obtain the best results. ILXLightwave LDP-3811 Precision Pulsed CurrentSource was used as LED driver. The experimental setup appeared as in Fig.3.7.

Figure 3.7: Experimental setup for IV measurements: (a) computer used torecord the measurements, (b) parameter analyzer, (c) probe station, (d) currentgenerator.

Here the detailed description of the experimental settings chosen for ourwork is presented. The IV measurements were executed on 5 diodes per kind ofsamples in di↵erent conditions: in darkness or with light shining on the devices.In table 3.1 we present all the light sources used and the currents applied tothem, accordingly with the corresponding data sheets.

All the LEDs used in this thesis work were from Elfa Distrelec and they areshown in Fig. 3.8.

3.5. CURRENT-VOLTAGE CHARACTERISTICS AND RESPONSE TO LIGHT47

Light source Wavelength Applied current(nm) (mA)

Microscope light Visible light �IR-LED 840 200IR-LED 850 20IR-LED 880 200IR-LED 940 20IR-LED 950 100IR-LED 1020 20IR-LED 1060 20

Table 3.1: Light sources used and applied currents.

Figure 3.8: LED sources with di↵erent wavelengths: (a) 840 nm, (b) 850 nm,(c) 880 nm, (d) 940 nm, (e) 950 nm, (f) 1020 nm, (g) 1060 nm.

3.5.1 Normal diodes

It was decided to operate two kinds of measurements, depending on the samplesand the desired achievement. In the first case working diodes, not irradiatedand pre-irradiated, were handled and the aim was to see the electrical behavioraround 0 V, including observation of di↵erences in response with light irradia-tion. Therefore the microscope light and the IR-LEDs from 840 nm to 950 nmwavelength, were chosen as light sources, while the parameter analyzer was setas listed here.

• Voltage from 2 V to �0,5 V

• Step: 10 mV

• Integration time: the longest available


In the second series of measurements failing diodes were analyzed; thereforecurves until the breakdown voltage were recorded in order to get a generaloverview on their behavior. Once again, the variations in response to di↵erentlight sources were observed, repeating the measurement on working diodes withthe same setup to be able to compare the results. A more detailed analysiswas performed, compared to the previous measurements, using two additionalLEDs, namely 1020 nm and 1060 nm.


The new setup for the parameter analyzer was:

• Voltage from 1 V to �9 V

• Step: 20 mV

• Integration time: the longest available

A supplementary comment on the second setup regards the relative positionbetween samples and light sources. To have coherent results one should keepit always constant, although it was not possible due to the di↵erent packagingof the LEDs. In particular, this refers to the 840 nm and 880 nm sources, asone can easily notice in Fig. 3.8. For all the other LEDs, instead, was possibleto maintain a constant distance of 1,7 cm between them and the samples. Anexplicatory picture of this setup is showed here.

Figure 3.9: Zoom on LED and sample in the probe station.

Chapter 4

Results and discussions

The aim of this thesis is to investigate the failure in silicon diodes for radiationdetectors, an issue usually not faced in this field. Therefore the results explainedin this chapter can’t be considered as final, but they are a starting point forfuture analysis, due to the novelty of the problem studied.

4.1 Epoxy removal

Three di↵erent strategies were tried to selectively remove the epoxy glob topfrom the failing samples for PT applications.

Here the results will be showed and discussed, in particular evaluating theconvenience of this process for our investigation.

4.1.1 Acetone

The first tested method was simple acetone while the surface was scratched withtweezers and in Fig. 4.1 the results can be observed. After an analysis with theoptical microscope, it was noticed that the diode surface was destroyed by theinsistent scratching with the metallic tweezers, while no corrosion was found.Therefore it may be concluded that this method is not chemically aggressive, butthe stress induced by the mechanical removal of the epoxy layer could introducemore defects than the original situation.

4.1.2 Mixture of nitric and sulfuric acids

The result was once again observed at the optical microscope. The epoxy wascompletely removed from the diode surface, that seemed to be intact, althoughthe contact on the right appeared somewhat destroyed. A picture of the resultis reported in Fig. 4.2.

This process is clearly more chemically aggressive than the one explainedin the previous section, but this leads to some advantages. First it is possibleto avoid the manual removal of the epoxy, using the tweezers just to help theprocess, because the mixture of acids is even more e�cient than the acids alone.Then the temperature of 80�C speeds up the reaction, strongly reducing therequired time. Since the reactivity is quite high at this temperature it is easyto destroy part of the diode if the process is not carefully followed by naked-eye

49

50 CHAPTER 4. RESULTS AND DISCUSSIONS

Figure 4.1: Epoxy removed with acetone.

Figure 4.2: Epoxy removed with a mixture of nitric and sulfuric acid.

observation. Therefore, a key issue is to take the sample out from the acidsbath at the right moment.

4.1.3 Sulfuric acid

After the treatment with hot sulfuric acid, the naked diode was investigatedat the microscope to have a qualitative idea of the process quality. Comparedto the previous case, this setup exhibits advantages and drawbacks at the sametime. The advantage is a faster action of the acid on the epoxy resin that allows ashorter process time. On the other hand such a violent reaction is more di�cultto stop in the exact right instant and residual of epoxy may be found on thediode or some parts might be too corroded. In the following figure indeed, itis worth noting the change in colour of the sample edges, now more orange-brownish due to the violent action of the sulfuric acid at high temperature.

4.1. EPOXY REMOVAL 51

Figure 4.3: Epoxy removed with sulfuric acid.

4.1.4 IV characterization

From the previous paragraphs may be understood that the removal of the epoxyglob top is not suggested in order to preserve the diode in good conditions. How-ever, if the electrical characteristics could be defined as unchanged the processwould be taken into account for all the samples. Therefore a simple IV measure-ment was performed on the naked diodes to certify the quality of the treatmentfrom a practical point of view.

The results were generally not good enough, compared to the recorded graphwithout epoxy removal. In particular, the current was less stable and this sug-gested that for a large number of samples it was better not to risk to deterioratetheir electrical properties with such a chemical treatment.

4.1.5 Conclusions

In conclusion the strategies tested here show drawbacks and advantages at thesame time. If the removal is performed correctly, the advantage is related to thefact that the treatment allows an easier performance of further tests, since thediodes are left naked and with the direct contacts exposed. Moreover, in thiscase a better interaction between incident light and diodes is guaranteed andtherefore leads to more attractive experimental conditions when we would liketo test them with IR LEDs.

The drawback is first a question of time. The process to remove the epoxylayer is not really long, but it is not encouraged to try to do it on several samplesat the same time, since particular care is needed not to destroy them in anirremediable way. Thus a second issue comes from the first one: the reliabilityof repeating the process always in the same conditions. If this requirementscan’t be fulfilled, it is strongly suggested not to try it, because the results of thesuccessive experiments will not be comparable.

In the end, considering that the electrical measurements are not obstructedby the presence of the epoxy on the diode, we decided not to remove it and tokeep the samples as received.


4.2 OCVD

4.2.1 Normal diodes as processed

After having successfully tested the OCVD setup on the test diode, it waspossible to record a graph like the one depicted in Fig. 4.4 for the normaldiodes as processed.

Figure 4.4: Voltage decay for a not irradiated diode.

As it is shown in the graph the measured minority carrier lifetime is about10 µs. Such a value fits well with previous measurements performed at Acreo onthe same kind of samples and encourages further investigation on diodes with ashorter lifetime.

4.2.2 Normal diodes after pre-irradiation

The consecutive step was thus the measurement on functional irradiated sam-ples. As explained in section 3.3, a change in the setup was needed to obtain areadable graph, as in the following figure. The result exhibits a minority carrierlifetime of about 3 µs for the normal diode after pre-irradiation. As expectedthe value is smaller after the irradiation treatment, but it is still possible tomeasure.

4.2. OCVD 53

Figure 4.5: Voltage decay for an irradiated diode.


More challenging is to perform the experiment on failing diodes, since it issuspected that the failure is related to an even shorter lifetime. With the sameparameters as for the previous measure, but a shorter pulse width of about 13µs, it was possible to register a slope in the decay that allows an evaluation ofthe lifetime. The recorded decay is shown in Fig. 4.6.

The minority carrier recombination lifetime is now much shorter and froman average taken on 10 samples it can be stated a lifetime of about 14 ns for thefailing diodes for PT applications and 13 ns for the ones for AT applications.

The fundamental observation to do is that such a low value could be evenlower since we have to consider the time constant of the MOSFET used asswitch. Indeed, considering both the turn-on and turn-o↵ delay time we couldfind their values in the data sheet around 10 ns. Another possible influence to bechecked is the one of the oscilloscope. In this case however, the number of cyclesper second is large enough to guarantee measurements down to 2 ns. Anywaythe resulting values will have to be verified with other methods or calculations.

4.2.4 Conclusions

It is worth noting that what is measured is not the only lifetime in a semicon-ductor. Here the focus is on the recombination process in the diode, but to havea complete overview on the lifetime in silicon the generation lifetime has to beconsidered, but it is not measurable with this technique. In the following tablethe results of these measurements are summarized. They will be useful in thenext sections when further discussions about the lifetime are held.


Figure 4.6: Voltage decay for a failing diode.

Sample Normal Failingdiodes As processed Pre-irradiated PT application AT application

Minoritycarrier ⇠10 µs ⇠ 3 µs ⇠14 ns ⇠13 nslifetime

Table 4.1: Measured minority carrier lifetimes with OCVD method for normaland failing diodes.

4.3 CV measurements

In the following figure a comparison between CV curves for normal and failingdiodes is depicted.

It can be immediately seen how the behavior of failing diodes deviates fromthe working not irradiated and pre-irradiated ones. They indeed show a muchlower capacitance that may bring to the conclusion that failing diodes havea larger depletion layer (see equation 1.4). However a larger depletion layershould give also an enhanced sensitivity due to a larger volume of interactionwith radiation and this is not in agreement with the starting point of a lowersensitivity in failing diodes.

Therefore two possible explanations are proposed to describe the phenomenon.First it has to be considered the very short recombination lifetime in the failingsamples that lower the sensitivity more strongly than it can be increased by anincrease in the depletion layer width, since the di↵usion length is longer thanthe space charge region.

Thus a second hypothesis is that the depletion layer may be the same forfunctional and failing diodes, but the latter have defects in the contacts between

4.3. CV MEASUREMENTS 55

Figure 4.7: CV measurements: comparison between normal and failing diodes.

the diode itself and the pads of the chip. This could bring to a lower recordedcapacitance in a normal CV measurement.

4.3.1 Doping concentration calculation

As already mentioned in section 1.1.3, CV measurements represent a goodmethod to evaluate the doping level in silicon diodes. Plotting equation 1.5with the recorded data the graph in Fig. 4.8 is obtained.

Here just the functional diodes’ measurements are presented, since for thefailing ones it is not possible to derive reliable results from so low capacitancevalues. Thus, it is possible to calculate the doping concentration with the fol-lowing formula:

N

a

=2

slope · q✏S

A

2(4.1)

For normal diodes, as processed or irradiated, the obtained slope was practi-cally the same and substituting all the known values a doping concentration ofabout 1,2·1017 cm�3 was calculated. It could be actually expected a small dif-ference between the samples due to the irradiation process; however this seemsreasonably di�cult to be determined just by a linear fitting and we will discussthe issue further in section 4.4.1.

Nevertheless, the resulting value agrees ruther well with the expectationsand thus confirms the doping properties of the functional samples.


Figure 4.8: Doping concentration calculation for a normal diode (red line: linearfitting).

4.4 IV characteristics - In darkness

As already stated earlier (section 1.1.2), the IV characteristic of a diode isusually divided into two parts, depending on the bias that can be forward orreverse. Therefore in this section the two regions will be analyzed separately,although they are connected to each other since they derive from almost thesame material properties.

4.4.1 Forward bias

The forward bias curves of the samples, recorded in darkness, are depicted inFig. 4.9. To simplify the data analysis it is shown just one curve per sampletype.

At a first glance it is easy noticing that the curve for not irradiated workingdiodes lies on the right of the other two. This means longer lifetime consideringthe e↵ect of minority carrier lifetime on IV curves explained in section 2.1.3.Moreover, moving to the left the characteristic of irradiated working diodes isfirst present and, farther, the one of the failing samples.

Always focusing on the ⌧

n

parameter, it can be briefly stated that

⌧

n

(not� irradiated) > ⌧

n

(irradiated) > ⌧

n

(failing)

Such a result is perfectly in agreement with the previously calculated life-time values (see section 4.2) and once again leads to the understanding of twophenomena: the first is that the pre-irradiation process shorten the minoritycarrier lifetime due the introduction of an increased number of defects in thematerial; secondly a proof of our statement that the failure mechanism is relatedto an even shorter lifetime is found.

4.4. IV CHARACTERISTICS - IN DARKNESS 57

Figure 4.9: Forward bias curves for normal and failing diodes. Comparison withtheoretical model.

Now it is worth applying the theoretical model expressed earlier in this workthat predicts the forward bias IV characteristic for a certain diode, given all theparameters. The wafers from which our samples are taken present a resistivityrange of 0, 1� 0, 2 ⌦cm and so, referring back to Fig. 1.5, they have an averagedoping concentration of 1, 5 ·1017 cm�3. To achieve a more realistic situation, itwas selected a lower doping concentration for the irradiated samples, i.e. 1 ·1017cm�3.1 Moreover, the diode dimensions are the same as the ones used beforeand for the minority carrier lifetime the values found with the OCVD methodare used.

The results are shown in Fig. 4.9. The first observation to be done is thata better fitting is possible for the working diodes, while for the failing ones theshape and the current values are less comparable. This of course makes sensesince we are considering diodes which are deviating from a standard behavior,but anyway a guideline can be defined. Indeed here it is nicely notable how themeasured lifetimes lead to a good curve fitting and therefore we have anotherproof of the e�ciency of the IV characteristics in showing easily such small diodeproperties.

Another thing to point out is the deviation from the theoretical curves athigher voltages: the reasons may be an e↵ect of high injection level and seriesresistance.

1SPIELER, H., 2005. Semiconductor Detector Systems. Oxford University Press, p. 285.


In conclusion, it was verified if the empirical observation done in ScandiDoswas still valid. The prediction was that if at 1 mA there is a di↵erence ofat least 12 mV between the forward characteristics the analyzed diode will befailing. In our case, both for recorded and calculated values, a di↵erence of 14to 16 mV was calculated. Recalling the fact that the studied samples are notcompletely failing, but just marginally, the results are reliable. If 12 mV is asort of threshold value, 14-16 mV represents a small deviation from that limitand therefore a not so marked failure.

Doing so, it was achieved a physical explanation of what was simply derivedfrom statistical considerations. OCVD measurements, forward IV characteris-tics and a theoretical model give reason to believe that the recombination carrierlifetime is a crucial discriminating factor in distinguishing failing diodes in earlystages of the manufactory processing.

4.4.2 Reverse bias

The reverse bias side of IV curves is more complicated to analyze than theforward one, since it shows two particular factors in semiconductor devices: theleakage current and the breakdown voltage. Both of them represent deviationfrom the ideality since with negative voltage a diode should just not allow anycurrent to flow, as already mentioned in section 1.1.2. In this section, the reversebias characteristics in darkness conditions of normal and failing samples will bepresented and discussed. The graph with a summary of this set of measurementsis shown here.

Figure 4.10: Reverse bias for normal and failing diodes.

Compared to the forward bias region, here the situation is more challengingand requiring a deep investigation. As done before, it may be useful to facethe graph analyzing the general trends in the curves. Now two properties are

4.4. IV CHARACTERISTICS - IN DARKNESS 59

clearly visible: the breakdown voltage and the leakage current, already explainedin details in the theoretical section.

We can witness three di↵erent voltage values depending on the sample typeconsidered and the numerical values are presented in the following table.

Sample Normal Failingdiodes As processed Pre-irradiated PT application AT application

BreakdownVoltage 6, 8� 6, 84 7, 78� 7, 8 7, 26� 7, 28 7, 26� 7, 28(V)

Table 4.2: Breakdown voltages of normal and failing diodes.

Here it may be noticed that the functional diodes without pre-irradiationtreatment exhibit the lowest breakdown voltage.

In the previous section it was stated that to make the theoretical modelmore realistic and adaptable to the real measurements it was needed to selecta lower doping concentration for the irradiated diodes, as a consequence of thepre-irradiation process. The breakdown voltage is inversely proportional to thedoping density2 and so it is easily understandable how all the irradiated samples- both working and failing - have a larger voltage for the breakdown to start,compared to the normal diodes as processed.3

The leakage current is a property easy to measure that can be used for severalobservations, depending on the diode characteristics and the experiment condi-tions. In Fig. 4.10 it is worth noting the changes in leakage currents dependingon the type of sample considered, although all the curves were measured in thesame way in darkness conditions. To explain the curves shapes and to analyzethem equation 1.3 has to be recalled. What could be expected before such ameasurement is that the samples with the longest minority carrier lifetime, i.e.the not irradiated functional ones, should exhibit the lowest leakage current,while above them we should find in sequence the irradiated and failing diodes,with the lowest lifetime. The graph depicted in the previous figure however isnot following this prediction and thus an explanation has to be found.

Di↵erently from the forward bias side of the IV curves, where the minoritycarrier lifetime led to a simple behavior prediction, now the data analysis ismore confusing and requires a better examination. Looking at the known rela-tionship for the leakage current, another lifetime term can be noticed, alreadymentioned before and related to the generation of carriers in case of paucity.This value can vary considerably depending on the generation mechanism. Arough approximation of such a lifetime may be performed by taking an averageof the leakage current I

R

in a range close to 0 V and then applying the followingformula.4

⌧

g

=qn

i

WA

I

R

(4.2)

2SZE, S., Op. cit., pp. 106-107.3VAVILOV, V.S., UKHIN, N.A., 1995. Radiation E↵ects in Semiconductors and Semi-

conductor Devices, Springer. p. 228.4SCHRODER, D.K., 1982. The concept of generation and recombination lifetimes in

semiconductors. Electron Devices, IEEE Transactions on, 29(8), Eq. 10, p. 1337.


The approximated generation lifetime values found are reported in the fol-lowing table, compared with measured recombination lifetimes.

Sample Normal Failingdiodes As processed Pre-irradiated PT application AT application⌧

n

⇠10 µs ⇠ 3 µs ⇠14 ns ⇠13 ns⌧

g

⇠11 µs ⇠ 17 µs ⇠ 3,16 µs ⇠1,11 µs⌧

g

/⌧

n

⇠1 ⇠ 6 ⇠ 226 ⇠ 86

Table 4.3: Comparison and ratio between generation and recombination life-times.

Generally in silicon it is expected that the generation lifetime is higher thanthe recombination lifetime,5 but from a first glance at table 4.3 significant ob-servations can be added. Indeed it is interesting to see that the ratio between⌧

g

and ⌧

n

is almost 1 for not irradiated working diodes - the samples withthe longest lifetime - but then it increases with irradiated and especially failingdiodes. This trend seems quite random, but a physical explanation was searchedbasing on the analysis of the samples characteristics. There are in particular twofactors to take into account: the pre-irradiation and the annealing processes.

The pre-irradiation phase has been said several times bringing defects inthe diodes and therefore causing a shortening in recombination lifetime, andour measurements confirmed it. However, the generation lifetime should beconsidered as well. Changes in ⌧

n

indeed obviously a↵ect the di↵usion lengthand they will consequently modify the generation mechanism itself.

Schroder clarifies how the complex carriers generation depends on several fac-tors and it consists of two contributions: space charge region (scr) and quasineu-tral region (qnr) generations.6 The relative domination of one mechanism on theother is fundamental for a fully comprehension of the generation phenomenon.In normal conditions at room temperature the quasineutral region generation isnegligible. Nevertheless it is proportional to n

2i

/L

n

and thus may change con-siderably if variations in n

i

or Ln

occur. Indeed with an increase in temperaturethe dependence on the intrinsic carrier concentration will lead the qnr term todominate in the generation, but, more interestingly, a reduction in the di↵usionlength may do the same.

Referring back to our table, considering the dependence of the di↵usionlength on the recombination lifetime, the conclusion is straightforward: a shorter⌧

n

, like for pre-irradiated and failing samples, causes a decrease in L

n

and there-fore an increase in the contribution of the quasineutral region to the generationprocess. This means a larger generation contribution in equation 1.3 and thusa smaller leakage current after the irradiation process. The failing samples donot lie below the not irradiated curves due to a significantly lower lifetime (twoorders of magnitude) than the working diodes.

The annealing process is also helping the described trend in the balancebetween generation and recombination lifetimes e↵ects on the IV characteristics.Schroder recorded a remarkable increase in the ratio ⌧

g

/⌧

r

after annealing and

5Ivi, Table I, p. 1338.6SCHRODER, D.K., 1997. Carrier lifetimes in silicon. Electron Devices, IEEE Transac-

tions on, 44(1), p. 168.

4.5. IV CHARACTERISTICS - IR-LEDS 61

oxygen precipitation in the silicon crystal.7 One cause of the phenomenon isthe expected decrease of the recombination lifetime due to precipitation, but afurther reason was an enhanced generation lifetime due to gettering of metalimpurities. Once again it is clear the di↵erence between the not irradiated andnot annealed diodes compared to the annealed irradiated and failing ones.

The foregoing discussion started on an approximated formula to define thegeneration lifetime in the di↵erent samples. Nevertheless, the main point tomark here is the influence of the generation lifetime in the curves shape, other-wise impossible to understand just referring to the minority carrier recombina-tion lifetime.

4.4.3 Conclusions

Here it is underlined how simple IV measurements in darkness can broaden ourcomprehension about several semiconductor properties. A special care has tobe taken talking about the minority carrier lifetime, the concept that lies at thebase of the thesis since the beginning. The influence of this simple factor onthe forward bias characteristics gives validity and support to the observationof small deviations from the average to identify possibly failing diodes at earlystages of the production.

On the other hand, the analysis of the reverse bias characteristics has broughtnew issues to the topic. The failure mechanism can’t be related just to a shorterrecombination lifetime, but also to an increased ratio between generation andrecombination lifetimes. With this first analysis, the failure investigation isextended from a semiconductor perspective.

4.5 IV characteristics - IR-LEDs

So far, the focus has been on current-voltage curves in darkness condition andsome important conclusions could be achieved. To go further in the samplescharacterization we will now take advantage of the diodes’ sensitivity to light.Indeed, being devices meant to be used in radiation detectors, their responsecan vary significantly depending on the type and intensity of the incident light.

To first understand the interactions involved in order to exploit them con-sciously, it was decided to begin with an analysis of working diodes - as processedand pre-irradiated - to later test the failing samples.

4.5.1 Normal diodes

The experimental setup used for this set of measurements was explained insection 3.5.1 and two examples of the resulting graphs are reported in Fig. 4.11and Fig. 4.12.

7Ibidem.


Figure 4.11: Response variations with LEDs for normal diode as processed.

Figure 4.12: Response variations with LEDs for normal diode after pre-irradiation.


From these graphs, three main comments may be done.The first observation is related to the curves recorded in darkness. As it can

be easily seen in the reverse bias side, all curves present noise. The noisy signalhere may be due to thermally generated carriers and low current values that arecomparable with the noise limit of the parameter analyzer used.

The second comment concerns the leakage current. Comparing the curvesrecorded in darkness with the ones under light irradiation, it can be immediatelystated that the starting point of the leakage current “moves” toward the forwarddirection. This e↵ect is due the overall modification of the IV characteristics,similar to the case of the solar cell application.8

The last thing to remark is still related to the leakage currents: for both not-and irradiated samples it can be noticed how the response changes in di↵erentways according to the light that is shining on the sample. What can be doneis to calculate the di↵erences between the reference curve and the responses forevery diode and then to take an average in order to define a general trend.The results are summarized in the following table.

Incident NormalLight As processed Pre-irradiated

Visible light 2,521E-05 A 2,229E-05 A840 nm 9,024E-05 A 1,469E-05 A850 nm 4,876E-05 A 3,354E-06 A880 nm 8,660E-06 A 3,920E-06 A940 nm 1,070E-05 A 1,243E-06 A950 nm 6,088E-06 A 2,065E-06 A

Table 4.4: Response variations to di↵erent light sources for normal diodes.

The comparison between these current values leads to two main conclusions.First, the microscope light results in almost the same response for not and

irradiated diodes. Second, the responses are much higher for the not irradiateddiodes than the irradiated ones, considering the di↵erent wavelengths. Thus thereasons of this behavior will be now explained.

As mentioned already in section 1.2.2, the e↵ective sensitive volume of in-teraction in a diode can be described as the sum of its depletion region andthe material within one di↵usion length from its borders, as explicated in thefollowing formula, which is referring to lengths instead of volumes, since thediode section may be taken as constant.

V

eff

= W + L

n

+ L

p

Where Ln

and L

p

are proportional to the square root of the carriers’ lifetime,accordingly to equations 1.6 and 1.7.

The e↵ect of the visible light from the microscope of the probe station isrelated to the interactions between the light and first surface layers of the diodes.So, looking at the formula and reminding that we are dealing with n+p diodes,it can be assumed that the part of the e↵ective volume that is generating thesignal is not including the factors a↵ected by the carriers’ lifetime, i.e. the

8FONASH, S.J., 2010. Solar Cell Device Physics. Second Edition. Boston: AcademicPress, Fig. 4.4, p. 135.


di↵usion length. Indeed, the incident beam causes an increase in the generationrate of the minority carriers in the silicon and therefore an increase in theresponse which is not connected to the lifetime in the silicon. Coming back tothe di↵erence between the irradiated and not irradiated samples, the di↵erentlifetime values were respectively about 3 µs and about 10 µs (see table 4.2.4).As stated, the response to visible light is not depending on the carriers’ lifetimeand thus both the samples will exhibit the same behavior.

In the light of the foregoing physical explanation, it can be addressed thequestion of the larger increase in the response with IR-LEDs in the not irradiateddiodes, compared to the irradiated ones. The IR-LEDs exhibit the property ofpenetrating into the material more than visible light. This phenomenon leads toa di↵erent interaction with the light, since now the signal comes from the bulksilicon. Looking at the formulas 1.6 and 1.7 it is possible to say that a longercarrier lifetime corresponds to a longer di↵usion length. Therefore the normaldiodes as processed, with a lifetime of about 10 µs, have a longer di↵usionlength that allows them to generate the signal from a larger volume than theirradiated samples. As a consequence, under the same irradiation conditions,the not irradiated diodes exhibit a higher response di↵erence.

Such a phenomenon was already found in literature and reported while dis-cussing about the sensitivity reduction due to a pre-irradiation process, as saidin section 1.3.1 and showed in particular in Fig. 1.8. Therefore, light interac-tion studies are a good way to analyze responses variation in radiation detectordiodes, since they are simpler than X-rays experiments and give reliable results,confirming once again how the minority carrier lifetime a↵ect dramatically thiskind of devices.

Further works in this direction may include a more detailed calculation ofthe response variations. Here the instrument to do it will be given. First westart considering the di↵erent values in the leakage current. It is intuitive tounderstand that di↵erent wavelengths bring to di↵erent responses, but it is alsopossible to predict how this new current will be, just applying the followingformula:9

I

P

= R

�

P

where R�

is the responsivity of the considered material, i.e. a measure of itssensitivity to light, and P is the power of the incident light.

The responsivity can vary depending on the material and the type of diode,besides obviously the incoming light wavelength, as shown for example in Fig.4.13,10 from which the numerical values listed in table 4.5 are derived.

To predict correctly the response variations using the equation showed beforeit’s necessary to know precisely the power of the incident light as well, due to theslight current di↵erences to be recorded. Therefore, the suggestion for furtheranalysis based on this physical concept is to use a tunable laser source insteadof single LEDs to have all the parameters perfectly under control.

9http://www.osioptoelectronics.com/application-notes/AN-Photodiode-Parameters-Characteristics.pdf

10WERNER, L., FISCHER, JOHANNSEN, U,. HARTMANN, J., 2000. Accurate deter-mination of the spectral responsivity of silicon trap detectors between 238 nm and 1015 nmusing a laser-based cryogenic radiometer. Metrologia, 37(4), Fig. 1, p. 280.


Figure 4.13: Responsivity variations as a function of the incident wavelengthfor one kind of silicon detector.

Wavelength Responsivity(nm) (A/W)840 ⇠ 0,66850 ⇠ 0,68880 ⇠ 0,71940 ⇠ 0,75950 ⇠ 0,76

Table 4.5: Responsivity values depending on the incident wavelengths for onekind of silicon detector.


In order to get the best results from the failing samples, the experimental setupwas modified as described in section 3.5.2. In the following figures one exempli-fying graph per kind of sample is presented.

At a first glance, we can see how Fig. 4.14, Fig. 4.15 and Fig. 4.16 exhibitboth similarities and di↵erences at the same time.

A common feature to all the graphs is the response to the LED with awavelength of 1060 nm: it perfectly overlaps with the reference curve recordedin darkness conditions. The reason is that with the selected wavelength theabsorption depth exceeds the dimension of the diode itself, and thus there isalmost no e↵ect of light absorption in the IV characteristics.


Figure 4.14: Response variations with LEDs for failing diode for PT applica-tions.

Figure 4.15: Response variations with LEDs for failing diode for AT applica-tions.


Figure 4.16: Response variations with LEDs for pre-irradiated working diodes.

It seems reasonable here to see more in details where the di↵erent wave-lengths will stop inside the sample, as showed in Fig. 4.17 from which derivestable 4.6.

Figure 4.17: Penetration depth vs Incident wavelength. The arrows correspondto the di↵erent LED sources.


Wavelength Penetration depth(nm) (µm)840 ⇠ 15850 ⇠ 16880 ⇠ 25940 ⇠ 50950 ⇠ 601020 ⇠ 1801060 ⇠ 900

Table 4.6: Penetration depth values depending on the incident wavelengths.

Now it is worth noticing that even the failing diodes present a response vari-ation as in the case of the normal ones, already discussed in the previous section.Therefore the idea is to compare the values to see if the lifetime considerationsdone before are still valid.

The starting point was the calculation of the response di↵erences dependingon the wavelength and the results are presented in table 4.7.

Wavelength Response Variations Ratio(nm) Normal Irr (I

irr

) Failing AT appl. (Ifail

) I

irr

/I

fail

(A) (A) �840 3,14E-05 1,33E-05 2,361850 8,52E-06 3,85E-06 2,213880 3,92E-06 2,21E-06 1,774940 2,98E-06 1,64E-06 1,817950 1,65E-06 8,08E-07 2,0421020 7,35E-07 3,17E-07 2,319

Table 4.7: Leakage current responses variation with LEDs.

It seems of immediate comprehension how the response is always higher inthe case of irradiated working diodes than in the failing ones. Moreover, theratio stays around the value 2 for all the used wavelengths.

The results just presented state again the centrality of the lifetime in thisthesis work. The shorter lifetime for the failing diodes is responsible of sucha behavior. The interaction with light is primarily governed by the e↵ectivevolume of interaction and the latter is related to the minority carriers lifetime,as discussed earlier.

Therefore, it is worth to summarize the observations done in the next section,where a simple model for the interaction between photodiodes and incident lightwill be proposed.

4.5.3 Light response: a simple model

After having performed IV measurements on all the samples and in di↵erentconditions, an overview on the physical explanation of these phenomena may bedone. Furthermore, a simple model can be developed to describe the interactionof di↵erent light sources with the diodes and its changes depending on the sample


characteristics. Schematically, the sample diodes look like the one depicted inFig. 4.18.

Figure 4.18: Diode scheme with highlighted depletion layer (W) and di↵usionlength (L

n

). Cross section view, not in scale.

It was repeated several times in this thesis discussion that the analyzedsamples exhibit three di↵erent minority carrier lifetimes and it was also showedhow this a↵ects the di↵usion length (see equations 1.6 and 1.7). Therefore, nowwe will discuss three di↵erent conditions of light interaction with the three kindof samples, i.e. normal diodes as processed and pre-irradiated and failing ones(the di↵erence between PT and AT application diodes here is negligible). Thescheme presented above is still valid, with the only modification of the di↵usionlength, keeping in mind that from the di↵erent lifetimes it can be stated that

L

n

(not� irradiated) > L

n

(irradiated) > L

n

(failing)

where not irradiated and irradiated are clearly referring to working diodes,while failing corresponds to both PT and AT application devices.

Interaction with visible light

The first scenario consists in visible light shining on the sample and experi-mentally it was represented by microscope light in tests on normal diodes. Theschematic representation of this experiment is the one presented in the followingdrawing.

Figure 4.19: Schematic representation of interaction with visible light (orangearrows). White rectangle = Volume of interaction.

As discussed in section 4.5.1, the microscope light does not penetrate intothe diode enough to be influenced by di↵erences in the di↵usion length. Thus,the ratio between the responses irradiated and not irradiated working diodesand failing ones will be always around 1, as indeed previously showed.


Going further with a longer wavelength light source the interaction volumeis extended deeper into the diode, following the curve in Fig. 4.17. Thereforeany change in the incident light source may be seen by observation of responsevariation in the reverse bias side of the IV characteristics. Let us examine howthe diodes’ responses will change according to di↵erent irradiation situations.

Interaction with IR-LED - case 1

Using IR-LED allows an analysis that goes from the visible light region to thewavelength for which silicon becomes transparent. In the presented model, therole of reference point is occupied by the di↵usion length and the e↵ective volumeof interaction, directly derived from the former. The first case is in fact the useof a light source that overcomes the di↵usion length in the failing diodes, butnot the ones for the normal ones, as described in the following figure.

(a) Not irradiated (b) Irradiated

(c) Failing

Figure 4.20: Interaction with IR-LED - case 1. The white rectangle representsthe volume of interaction and the red arrow represents the incident LED light.

In this case, the e↵ective volume is the same for the working diodes, whilefor the failing samples it occurs to be smaller, in particular its depth is limitedby the di↵usion length. Thanks to the measured carriers’ lifetime with theOCVD method and the penetration depth values presented in table 4.6, thisfirst scenario is expected to always happen for failing diodes with the availableIR-LED sources.


The successive step is the case in which the incident light overcomes both thedi↵usion lengths of pre-irradiated normal diodes and failing ones, but with apenetration depth still shorter than the not irradiated samples’ di↵usion length.The model now looks like in Fig. 4.21.

The failing devices will have now the same behavior as in the previous case.the light will penetrate even deeper in the material, but the signal will continuecoming from the same portion of the silicon diode, still limited by its very shortdi↵usion length. In addition, the same event is verified in normal diodes afterthe pre-irradiation process: the wavelength of the incident LED is longer than



(c) Failing

Figure 4.21: Interaction with IR-LED - case 2.

before, but the threshold is overcome and the interaction is governed by thevolume delimited by L

n

(irradiated). The only kind of sample that is able totake the maximum advantage from the incident light entering in it is the one ofthe normal diodes as processed: image a) in Fig. 4.21.


The last situation proposed exhibits a LED source with a wavelength longenough to exceed the di↵usion length of the not irradiated working diodes,as presented in the following sketch.


(c) Failing

Figure 4.22: Interaction with IR-LED - case 3.

At this stage, all the samples’ responses are governed by their di↵usionlengths and further increasing the incident wavelength will not modify the out-going signal.


Discussion

The simple model just explained is based on elementary concepts as di↵usionlength, recombination lifetime and e↵ective volume of interaction, but it is farfrom being easy to develop properly. Indeed, what theoretically is linear andpredictable in reality hides several variable parameters that are strongly involvedin the final results.

First, to have coherent outcomes all the LED parameters have to be perfectlyunder control. As mentioned in advance, a tunable laser source would guaranteeperfectly repeatable experimental conditions. Moreover, a delicate point in thediscussion is the power of the light source. The recorded di↵erences in theresponse are directly caused by the light power and thus, if it is not well knownand controlled, it may lead to misunderstanding of the results, mixing di↵usionlength e↵ects with the power ones. For example, if particular care is not taken,it is possible to predict a larger response due to a longer wavelength althoughit may be simply caused by a more powerful source.

A second issue is the fact that what is analyzed here are failing diodes,i.e. something inherently unpredictable and di�cult to describe with models.The central point that requires in-depth studies is related to the variationsin recombination and generation lifetimes. While for normal diodes after pre-irradiation the e↵ects of the combination of the two di↵erent lifetimes are notdramatic, in failing diodes the di↵erences are larger (see table 4.3). So it happensto be di�cult to base reliable calculations on response variations if they are notalready fully understandable. This is the reason for which a model with thedata obtained from working diodes will be studied first.

Conclusions

Merging together the data derived from IV measurements under irradiationfor normal diodes and the considerations done in the previous paragraphs, it ispossible to prepare a graph to see the theoretical model applied in real measures.The idea is to plot the ratio between the responses in normal diodes as processedand pre-irradiated to visualize the three di↵erent irradiation conditions.

To plot the resulting curve presented in Fig. 4.23 we based on the followingtable.

Wavelength Penetration depth Ratio(nm) (µm) I

notirr

/I

irr

Visible light ⇠ 0,1 - 5 1,131840 ⇠ 15 2,865850 ⇠ 16 1,292880 ⇠ 25 2,209940 ⇠ 50 3,590950 ⇠ 60 3,6891020 ⇠ 180 6,568

Table 4.8: Penetration depth and responses ratio for normal diode as processedand pre-irradiated.


Figure 4.23: Schematic representation of the light response model.

Ideally three regions are expected: two with a horizontal line related toa fixed ratio between the responses and one that connects them with all theintermediate situations.

Starting from the lowest penetration depth the part of the spectrum of thevisible light has to be considered. As already discussed, microscope light causesthe same response variation independently from the minority carrier lifetime.Therefore the first region of the studied plot will exhibit a ratio equal to 1 andthe experimental data fit relatively well this first expectation (see table 4.4).

The passage to di↵erent behaviors in the two kinds of diodes should occurwhen the penetration depth of the incident light reaches the di↵usion length ofthe shortest lifetime sample, i.e. the pre-irradiated samples. The limited amountof data due to a limited number of light sources does not allow a perfect curvefitting: the changes in ratio seems suggesting a di↵usion length for irradiatedsamples much shorter than it could be expected.

After having exceeding the longest di↵usion length of the not irradiateddiodes a fixed ratio between the responses can be expected, until the wavelengthis not high enough to pass through the device without being absorbed. Althoughthe graph depicted above is not describing the real situation numerically, thisapproach stands on a good base. Taking the ratio between di↵erent responses,indeed, it is possible to neglect the responsivity variations due to the use ofdi↵erent wavelength, previously expressed in Fig 4.13 and table 4.5. Thereforeall things considered suggest that the proposed model represents a promisingway to define the interactions between several light sources and samples withdi↵erent minority carrier lifetimes.

Chapter 5

Conclusions

To summarize, in the thesis work the issue of failure in silicon diodes for radia-tion dosimetry applications was investigated. The theoretical background aimedto introduce correlations between semiconductor properties and detectors char-acteristics. In particular, from the literature search, the minority carrier recom-bination lifetime was found to play a central role in sensitivity determination.

A statistical analysis of previously produced diodes was performed to achievea definition and validation of a theoretical model of the forward bias region inIV characteristics. The influences of parameters such as temperature, dopingconcentration and minority carrier lifetime were investigated according to sta-tistical considerations about deviations from average values, done at ScandiDos.

The experimental section regarded four types of samples: normal diodes asprocessed and pre-irradiated, failing diodes for at-treatment and pre-treatmentimplementations. The samples intended for the last application were coveredwith an epoxy glob top. Thus the convenience of its removal was analyzed afterhaving tested three strategies, namely immersion in acetone, mixture of sulfuricand nitric acids and sulfuric acid alone. The results were not encouraging tobe applied to all the samples, although these technique were working well. Themain problem was the di�culty in repeating the experiment in the same wayfor all the diodes.

The next experiments involved a capacitance-voltage measurement, useful toconfirm the doping concentration of the working samples and to see di↵erencesin behavior among functional and failing devices.

The fundamental concept of the minority carrier recombination lifetime wasthe starting point of the main parts of the experimental chapter: Open-CircuitVoltage Decay and current-voltage measurements were performed to investigatedi↵erences in lifetime between normal and failing samples. The former exper-iment showed how the pre-irradiation process caused a shortening in lifetimeand a further reduction was found in failing diodes. In fact, it was possible tomeasure a recombination lifetime of about 10 µs, 3 µs and 13 ns respectivelyfor normal diodes as processed, pre-irradiated and failing.

The lV analysis allowed a better comprehension of how the lifetime param-eter changes the IV curves shape. In the forward bias side it can be seen as a“translation” of the curve to higher current values due to a decreased recombi-nation lifetime induced by defects. A 12 mV di↵erence from the average at 1 mAwas confirmed as not only a statistical consideration, but also as a physically

75

76 CHAPTER 5. CONCLUSIONS

explained phenomenon due to a shorter lifetime in failing diodes. A furtherstudy in IV curves was done with the addition of light sources, i.e visible lightand IR-LEDs. In this particular case, in the reverse bias side it was possible towitness response variations depending on the incident light type. The resultsbrought to the understanding of how a longer lifetime led to larger changessince the e↵ective volume of interaction was strongly dependent on the di↵usionlength. Therefore normal diodes after pre-irradiation showed less pronouncedleakage current modifications and the failing samples even less, due to their veryshort lifetime compared to the functional ones as processed. An additional issuecame to light in this section, regarding the leakage currents recorded in dark-ness condition. The recombination lifetime was not enough to explain alone thebehavior of pre-irradiated and failing devices compared to the normal ones. Sothe introduction of the concept of generation lifetime was necessary. It seemedreasonable that the the pre-irradiation process was responsible of an increasedratio between generation and recombination lifetime and it could be stated thatfailing samples had an even larger ratio.

All the arguments outlined above may be merged together to define anoverview on silicon diodes for radiation dosimetry and their failure. This thesiswork has described the characteristics and properties of failing devices. Withoutconsidering the failure causes, all the experiments and discussions were aimedto put the basis for the definition of a functional test method for failure identi-fication at early stages in the processing phases.

Chapter 6

Future Work

The aim of the thesis work is an investigation of failures in silicon detectordiodes. Since there is no large availability of publications regarding the topic,the main task consists in building the basis for further analysis. Thereforedi↵erent suggestions are possible for future works.

First a comparison with other kinds of failing diodes seems useful to completethe overview on the problem. Indeed, in addition to the marginally failing diodespresented in the previous sections, at ScandiDos some diodes were also foundperfectly working in all the electrical tests performed, but they were failing insensitivity measurements in the LINAC, at the last stage of the production.Thus studies on that kind of devices could allow to extend our understandingabout failure mechanisms in silicon diodes.

Another technique that may be taken into account in order to describe thereasons of failure is the characterization with the electron microscope. Cleavingone sample as the ones for AT applications would expose the cross section of thediode. Thus, with a SEM it is possible to search for particular imperfections thatmight be related to the lifetime shortening verified in the previous discussions.Although such imperfections are usually on the atomic scale, and therefore notvisible with a SEM, what can be searched could be a combination of defects,which may constitute a valid failure cause.

Furthermore, next studies should include the development of a test method.The simple idea is to take advantage of the lifetime di↵erence between workingand failing diodes, as expressed earlier in this thesis work. Several strategies arepossible; particularly two of them come directly from our measurements.

An easy suggestion is to perform OCVD measurements on the diodes atearly production stage. Doing so, it is immediate the distinction among longand short lifetime diodes and, consequently, it is possible to select just the diodesthat will guarantee a good enough sensitivity. The drawback is the addition ofa new measurement to the production chain and an increase in the time neededfor the testing phases.

Another method is related to the variation in response due to light interac-tions. After having completed the data collection with a tunable light source asmentioned earlier, we should be able to define a certain trend in changes of theleakage current, at a particular voltage value. Therefore the test method mayconsist in recording the leakage current for a given voltage - for example -1 V- with a light source shining on it. The chosen light source has to be able to

77

78 CHAPTER 6. FUTURE WORK

penetrate into the diode material enough to exhibit the di↵erences in responsesdescribed in our experiments. To define without doubts this behavior, it is firstfundamental to initiate a deeper investigation about recombination and gener-ation lifetime e↵ects in the reverse bias for failing diodes. So, a good testingsetup should consist of an IR-LED at a fixed distance from the diodes to beanalyzed and a probe station, better if automatic, in order to contact them tothe voltage source.

Moreover, a good way to control the devices quality was already defined inScandiDos, where a di↵erence of at least 12 mV at 1 mA seemed to be reason-able to predict a failure. Our studies suggest that this is not just a statisticalconsideration, but a direct consequence of a shorter lifetime and therefore it hasto be used as control parameter in the processing steps.

In conclusion, on the basis of the foregoing considerations OCVD methodand IV measurements under irradiation conditions combined together will al-low an early identification of failing diodes, avoiding a subsequent removal andreplacement.

Bibliography

[1] BEDDAR, A.S., MASON, D.J., O’BRIEN, P.F., 1994. Absorbed dose per-turbation caused by diodes for small field photon dosimetry. Medical physics,21(7), pp. 1075-1079.

[2] CHENMING, HU, 2010. Modern Semiconductor Devices for Integrated Cir-

cuits. Upper Saddle River, N.J.; London: Pearson Education.

[3] DESHPANDE, D., DHOTE, D., KINHIKAR, R., KADAM, S., CHAUD-HARI, S., 2012. Dosimetric validation of new semiconductor diode dosime-try system for intensity modulated radiotherapy. Journal of Cancer Researchand Therapeutics, 8, pp. 86-90.

[4] Diode in Vivo Dosimetry for Patients Receiving External Beam in Radiation

Therapy. Aapm Rep 87. 2005. Medical Physics Pub.

[5] DIXON, R.L., EKSTRAND, K.E., 1982. Silicon diode dosimetry. The Inter-

national journal of applied radiation and isotopes, 33 (11), pp. 1171-1176.

[6] DJOUGUELA, A., GRIEßBACH, I., HARDER, D., KOLLHOFF, R.,CHOFOR, N., RUHMANN, A., WILLBORN, K., POPPE, B., 2008. Dosi-metric characteristics of an unshielded p-type Si diode: linearity, photon en-ergy dependence and spatial resolution. Zeitschrift fur Medizinische Physik,18(4), pp. 301-306.

[7] EVELING, J.N., MORGAN, A.M., PITCHFORD, W.G., 1999. Commis-sioning a p-type silicon diode for use in clinical electron beams. Medical

physics, 26(1), pp. 100-107.

[8] FONASH, S.J., 2010. Solar Cell Device Physics. Second Edition. Boston:Academic Press.

[9] GRUSELL, E., RIKNER, G., 1986. Evaluation of temperature e↵ects in p-type silicon detectors. Physics in Medicine and Biology, 31(5), pp. 527-534.

[10] GRUSELL, E., RIKNER, G., 1993. Linearity with dose rate of low resistiv-ity p-type silicon semiconductor detectors. Physics in Medicine and Biology,38(6), pp. 785-792.

[11] HODGSON, M., 2010. An Investigation into Silicon PIN Diode Detectorsfor Dosimetry Applications. Master Thesis, University of Surrey, England.

79

80 BIBLIOGRAPHY

[12] JURSINIC, P.A., 2001. Implementation of an in vivo diode dosimetry pro-gram and changes in diode characteristics over a 4-year clinical history. Med-

ical physics, 28(8), pp. 1718-1726.

[13] JURSINIC, P.A., 2009. Angular dependence of dose sensitivity of surfacediodes. Medical physics, 36(6), pp. 2165-2171.

[14] LI, C., LAMEL, L.S., TOM, D., 1995. A patient dose verification programusing diode detectors. Medical Dosimetry, 20(3), pp. 209-214.

[15] LUTZ, G., 1995. Silicon radiation detectors. Nuclear Instruments and

Methods in Physics Research Section A: Accelerators, Spectrometers, De-

tectors and Associated Equipment, 367(13), pp. 21-33.

[16] LUTZ, G., 1999. Semiconductor Radiation Detectors. Device physics.

Springer.

[17] MARRE, D., MARINELLO, G., 2004. Comparison of p-type commercialelectron diodes for in vivo dosimetry. Medical physics, 31(1), pp. 50-56.

[18] MEILER, R.J., PODGORSAK, M.B., 1997. Characterization of the re-sponse of commercial diode detectors used for in vivo dosimetry. Medical

Dosimetry, 22(1), pp. 31-37.

[19] MURALI, S., SRIKANTH, N., 2006. Acid Decapsulation of Epoxy MoldedIC Packages With Copper Wire Bonds. Electronics Packaging Manufactur-

ing, IEEE Transactions on, 29(3), pp. 179-183.

[20] NORLIN, P., OBERG, O., JUNIQUE, S., KAPLAN, W., ANDERSSON,J. Y., NILSSON, G., 2014. A cubic isotropic X-ray dose detector diodefabricated by DRIE of SOI substrates. Sensors and Actuators A: Physical,213(0), pp. 116-121.

[21] OMAR A., 2010. Silicon Diode Dose Response Correction in Small PhotonFields. Master Thesis, Stockholm University, Sweden.

[22] REHAK, P., 2004. Silicon radiation detectors. Nuclear Science, IEEE

Transactions on, 51(5), pp. 2492-2497.

[23] RIKNER, G., 1983. Silicon diodes as detectors in relative dosimetry of pho-ton, electron and proton radiation fields. PhD Thesis, University of Uppsala,Sweden.

[24] RIKNER, G., GRUSELL, E., 1983. E↵ects of radiation damage on p-typesilicon detectors. Physics in Medicine and Biology, 28(11), pp. 1261-1267.

[25] RIKNER, G., GRUSELL, E., 1987. General specifications for silicon semi-conductors for use in radiation dosimetry. Physics in Medicine and Biology,32(9), pp. 1109-1117.

[26] RIKNER, G., GRUSELL, E., 1987. Patient dose measurements in photonfields by means of silicon semiconductor detectors. Medical physics, 14(5),pp. 870-873.

BIBLIOGRAPHY 81

[27] ROSENFELD, A.B., 2006. Electronic dosimetry in radiation therapy. Ra-diation Measurements, 41, Supplement 1(0), pp. S134-S153.

[28] SAINI, A.S., ZHU, T.C., 2002. Temperature dependence of commerciallyavailable diode detectors. Medical physics, 29(4), pp. 622-630.

[29] SAINI, A.S., ZHU, T.C., 2004. Dose rate and SDD dependence of commer-cially available diode detectors. Medical physics, 31(4), pp. 914-924.

[30] SAINI, A.S., ZHU, T.C., 2007. Energy dependence of commercially avail-able diode detectors for in-vivo dosimetry. Medical physics, 34(5), pp. 1704-1711.

[31] SCHRODER, D.K., 1982. The concept of generation and recombinationlifetimes in semiconductors. Electron Devices, IEEE Transactions on, 29(8),pp. 1336-1338.

[32] SCHRODER, D.K., 1997. Carrier lifetimes in silicon. Electron Devices,

IEEE Transactions on, 44(1), pp. 160-170.

[33] SCHRODER, D.K., 2006. Semiconductor Material and Device Characteri-

zation. Wiley-Interscience.

[34] SPIELER, H., 2005. Semiconductor Detector Systems. Oxford UniversityPress.

[35] SZE, S., 1981. Physics of Semiconductor Devices. Third edition. Wiley.

[36] VAVILOV, V.S., UKHIN, N.A., 1995. Radiation E↵ects in Semiconductors

and Semiconductor Devices, Springer.

[37] WERNER, L., FISCHER, JOHANNSEN, U,. HARTMANN, J., 2000. Ac-curate determination of the spectral responsivity of silicon trap detectorsbetween 238 nm and 1015 nm using a laser-based cryogenic radiometer.Metrologia, 37(4), pp. 279-284.

[38] WESTERMARK, M., ARNDT, J., NILSSON, B., BRAHME, A., 2000.Comparative dosimetry in narrow high-energy photon beams. Physics in

Medicine and Biology, 45(3), pp. 685-702.

[39] WILKINS, D., LI, X.A., CYGLER, J., GERIG, L., 1997. The e↵ect ofdose rate dependence of p-type silicon detectors on linac relative dosimetry.Medical physics, 24(6), pp. 879-881.

[40] WONG, J.H.D., KNITTEL, T., DOWNES, S., CAROLAN, M., LERCH,M.L.F., PETASECCA, M., PEREVERTAYLO, V.L., METCALFE, P.,JACKSON, M., ROSENFELD, A.B., 2011. The use of a silicon strip de-tector dose magnifying glass in stereotactic radiotherapy QA and dosimetry.Medical physics, 38(3), pp. 1226-1238.

82 BIBLIOGRAPHY

Acknowledgements

I would like to thank Acreo Swedish ICT and ScandiDos for o↵ering me theopportunity of doing the thesis work.I am particularly grateful for the assistance given by Kjell Lundgren andPeter Norlin who gave me all the information and support in defining thework to do. Great thanks to Peter that has been a good supervisor and areally helpful source of answers to all the problems I had to face in these sixmonths.I would also like to express my gratitude to Professor Jan Linnors, withseveral useful comments that have allowed to improve the final report.I wish to thank all the Nanoelectronics department members for making mefeel welcome in the company. For sure I have to mention Ingemar, with hiseveryday help, and Reza, for the football discussions.Coming to the less scientific support, I would like to thank my family forthe constant encouragement not only in the thesis period, but in the lasttwo years in Sweden. Then my special thanks to Lisa, that was always withme, every single day. A great thanks to all my flatmates for the good timetogether. In particular Etche, Andrea and Mika for the fika time in Acreo;Alfredo, Gerard, Fernando and Valerio for the casa mediterranea great mo-ments. Last but not least, thanks to my italian friends, especially Simo, Fedeand Gaia, that are still there for me after two years.

83

characterization and failure analysis of x-ray detector diodes872307/fulltext01.pdf · this master...

Documents