R*
^*SHf]«n^ f > J ^ ^ w-t#J
fö
TR diss
wwfr.
Proefschrift
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus,
Prof.dr. J.M. Dirken,
in het openbaar te verdedigen
ten overstaan van een commissie door
het College van Dekanen daartoe aangewezen
op dinsdag 17 november 1987 te 16.00 uur
door
Warner Rudolph Theophile ten Kate
geboren te Leiden
elektrotechnisch ingenieur
TR diss
1587
man muss sie für fertig erkldren, wenn man
nach Zeit und Umstdnden das Möglichste getan hat. Johann Wolfgang von Goethe.
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 OVERVIEW 7 2.0. INTRODUCTION 7
2.1. HISTORY 7 2.2. DETECTOR OPERATION 9
2.2.1. Radiant - electrical signal conversion 9
2.2.2. Signal processing 11 2.2.3. Noise 13 2.2.4. Radiation damage 16 2.3. DETECTOR TYPES 16 2.3.1. Application 17 2.3.2. Material 18 2.3.3. Fabrication process 19 2.3.4. Lay-out 20 2.4. CONCLUSIONS 23 CHAPTER 3 FABRICATION 25 3.0. INTRODUCTION 25 3.1. PART I - THEORY 25 3.1.0. Introduction 25 3.1.1. The leakage current 27
3.1.2. Carrier generation 33 3.1.3. Characterization 36 3.1.3.1. Temperature dependence 36 3.1.3.2. Lifetime measurement 38 3.2. PART II - EXPERIMENTAL 39 3.2.0. Introduction 39 3.2.1. /F-characteristic 41 3.2.2. Temperature 43 3.2.3. Lifetime 44 3.2.4. Radiation 47 3.2.5. Other processes 48 3.3. CONCLUSIONS 50
CHAPTER 4 OPERATION 53 4.0. INTRODUCTION 53 4.0.1. POSITION PRECISION 53 4.1. PART I - THE PULSE RESPONSES ON A DETECTOR'S STRIPS 55
4.1.0. Introduction 55 4.1.1. Theory 56 4.1.1.1. The equations 56 4.1.1.2. Discussion 60 4.1.2. Results 62 4.1.2.1. The model 63 4.1.2.2. The pulses 65 4.2. PART II - THE INFLUENCE OF THE STRIP WIDTH 71
4.2.0. Introduction 71 4.2.1. Numerical model 73 4.2.2. Surface charge 76 4.2.3. Field plates 79 4.2.4. Bias dependence 81 4.2.5. Disturbance voltages on the strips 83
4.2.6. Experiments 87 4.3. CONCLUSIONS 97 CHAPTER 5 READOUT 101 5.0. INTRODUCTION 101 5.1. READOUT SCHEMES 101 5.1.0. Introduction 101 5.1.1. The passive readouts 102
5.1.2. The active readouts 106 5.2. CCD READOUT . . 108 5.2.0. Introduction 108 5.2.1. Injection time I l l 5.2.2. Experimental results 114 5.3. CONCLUSIONS 118 CHAPTER 6 CONCLUSIONS 121 REFERENCES 125
SAMENVATTING - DE SILICIUM MICROSTRIPDETECTOR . . . . 137
ACKNOWLEDGEMENT 140
Semiconductor materials have found a widespread use in nuclear physics for radiation-detection purposes. At the beginning of this decade (1980), recognition of their usefulness in radiation detection for experiments in high-energy physics led to a renewed interest in this type of sensor and stimulated internationally the initiation of many research programs in this field. Position-sensitive detectors, in particular, received a great deal of attention, as current microelectronics fabrication techniques enable the production of detectors with a very high position resolution. In other fields of science (e.g. medicine and nuclear physics) as well, solid-state position detectors are attracting an increasing amount of interest and are finding more and more applications [1.1].
Fig.1.1. A typical event in a high-energy-physics experiment.
In high-energy physics an experiment can proceed as follows. Stable particles, such as protons, are accelerated in a cyclotron. When they have enough energy, they are directed towards a so-called target (see Fig. 1.1.), usually a slice of beryllium. The idea is for the protons to collide with the beryllium atoms. Upon collision, all kinds of reactions can occur, as long as they obey physical laws such as the conservation of energy, preservation of quantum number, etc. In high-energy physics this collision is referred to as
an event. Because of the high initial energy of the proton other, less stable particles can be generated at the event. By studying the events which have occurred, the theory describing the possible reactions can be verified, new particles (predicted by theory) can be discovered, or, last but not least, the properties of known particles can be studied.
The experiment as outlined above is called a fixed-target experiment (Fig. 1.1.). In another type, the so-called collider experiment [1.2], the initial particle (the proton above) is not directed towards a non-moving slice of material, but is allowed to collide with an identical particle (commonly its anti-particle) of the same energy moving in the opposite direction. In this way, the center of mass is not moving, and all of the energy is available for generating new particles.
Many other kinds of experiments are, of course, performed in h i g h -energy physics as well (e.g. studying photon-photon interaction). What is relevant at the moment is to understand where the position detectors come in. This will be explained by returning to a fixed-target experiment, in which the properties of a resulting unstable particle have to be measured, see Fig. 1.1. Because the particle is unstable, it will decay to other particles before it can be measured. Consequently, its properties have to be deduced from those of the resulting secondary particles. The existence of the unstable particle can be proven by showing that its secondary particles originate from another point than all the other particles generated at the event (Fig. 1.1.). (In addition, the lifetime of the short-lived particle can be deduced from the distance between these points [1.3].) Such a point is called a vertex, and the detectors which measure that vertex are referred to collectively as the vertex detector.
A vertex detector measures the position of the resulting particles generated during an event at different places, enabling their tracks to be reconstructed. If this reconstruction is carried out sufficiently accurately, the vertex of the secondary particles can be distinguished from that of the primary (the intersections of the solid and dashed lines in Fig. 1.1., respectively), thereby proving the existence of the short-lived particle. For a whole class of particles nowadays under study, the required accuracy for the vertex determination can be achieved when the position detectors have a position resolution on the order of a few micrometers [1.2,1.3].
As silicon is a suitable material for the detection of radiation, it is a likely candidate for the fabrication of such position detectors. Only the well-known IC-fabrication techniques are used. The silicon microstrip detector was the very first semiconductor detector to be made in this way [1.4]. It constitutes the subject of this thesis. Other detectors made with IC-fabrication techniques include the CCD-based detector [1.5] and the silicon drift chamber [1.6].
When an ionizing particle traverses through silicon, it loses energy by creating electron-hole (eh) pairs and heat; on the average 3.6 eV will be lost for every eh pair created [1.7]. The particle is measured by collecting this charge. This can be achieved by making a reverse-biased diode. The detector
is made position sensitive by integrating an array of strip-like diodes (henceforth to be referred to as a strip detector), because only that strip through which the particle traverses will give an output signal.
Due to their high energy the particles in a high-energy-physics experiment move so fast that they barely interact with the silicon. However, due to this high speed the way they interact is nearly the same for all of them, despite their diversity in physical properties. Therefore, no distinction has to be made when discussing them in relation to silicon detectors. In that sense, these particles are usually referred to as minimum ionizing particles.
Minimum ionizing particles generate about 85 eh pairs per micrometer when traversing silicon [1.8]. This means that a depletion layer of a few hundred micrometers is needed to achieve a satisfactory signal-to-noise ratio (the preamplifier noise has to be accounted for as well). Collection by diffusion is not efficient and fast enough to contribute to the signal of the required detector. A detector is depleted by raising the reverse bias voltage. However, the breakdown phenomenon limits this voltage and consequently the maximum size of the depletion layer. The only way to achieve large depletion layers is to use high-purity silicon (HP-Si). To deplete a wafer (of about 400 nm thickness) completely the silicon has to have a (net) doping concentration on the order of 10 cm (or one dopant to every 50 billion silicon atoms!).
Such h i g h - p u r i t y ("detector-grade") silicon is available nowadays [1.9]. Due to the low doping concentration, some device parameters have unusual dimensions. The Debye length, for example, is about 6 ym. Similarly, the depletion layer width at zero bias is about 27 ^m. As a consequence, the current behavior of diodes fabricated on this material will be greatly governed by the generation-recombination in the depletion layer, instead of by the usual diffusion outside this layer.
Likewise, there are some unusual aspects in the fabrication of microstrip detectors. Firstly, an entire wafer is covered with strip diodes in order to obtain one device. It is still possible, nevertheless, to achieve a reasonable yield, as the structure of the microstrip detector is relatively simple (except the strip length-to-width ratio of a few thousands) [1.10]. The malfunctioning of one or a few strips will moreover not prevent the device from being useful as a position detector. Secondly, the wafer is processed on both sides (masking is only needed for the strip side of the wafer; the processing on the rear covers the entire surface). Two junctions are needed for a low leakage current, which in turn is required for a low noise. A detector is a kind of wafer-thick pin-diode, except that the latter, with a higher doping level, but also with an intrinsic layer even smaller in size, can be modeled as being totally depleted at every bias voltage, with a (nearly) zero gradient of the electric field, whereas a detector clearly cannot. Finally, due to their large size, strip detectors require their own "packaging" strategy [1.1,1.11].
This thesis deals with the silicon microstrip detector as it is applied in a high-energy-physics experimental environment (measurement of the position
of minimum ionizing particles). Experimental devices have been made on silicon having a resistivity of about 2000-5000 Ccm (n-type). The strip pitch is on the order of 20 /mi. ("Pitch" refers to the repetition length of the strip pattern, i.e. the distance between the axes of two neighboring strips. Similarly, the interspacing between the strips is referred to as the "gap".) The total area of the devices was made much smaller than the wafer size. This was done to save material as well as to be able to use standard DIL-housings for packaging. Clearly, the same amount of knowledge can be gained from a device having a few strips which are also shorter in length. Only when performing measurements in a real high-energy-physics experimental environment (such as the many that have been carried out at CERN, Geneva) is a smaller area disadvantageous. Throughout the thesis, the detectors are assumed to be of the junction type. Surface barrier detectors, which are based on Schottky diodes, exhibit higher leakage currents and are made with a lower reproducibility (especially with large areas). They are therefore of less interest.
Briefly, the thesis is organized as follows. Chapter 2 presents an overview of semiconductor radiation detectors. This paves the way for a discussion of the fabrication (Chapter 3), the operation (Chapter 4) and the readout (Chapter 5) of the microstrip detector. In the thesis less attention will be directed towards such topics as radiation damage, yield and reliability, noise, packaging, and electronics.
Chapters 3 and 4 constitute the main chapters of this thesis. They are devoted to the two attractive characteristics of a semiconductor detector: its potential high energy resolution and its potential high position resolution.
Chapter 3 deals with the first aspect. It is divided into two parts. The first offers a theoretical description of the leakage current, as a high energy resolution requires a low leakage current. The second part presents the experimental results obtained on detectors (diodes) processed in different ways, showing the influence of the process on the detector's leakage current and thus on the energy resolution.
Chapter 4 takes up the second, positional, aspect of the microstrip detector. This chapter is likewise divided into two parts, which are preceded by a short discussion of the position precision of microstrip detectors. In the first part the output pulses on the detector's strips when generated charge carriers are collected by the detector are calculated. A new calculation method has been developed to obtain these pulses. The second part analyzes the influence of the strip width on the detector's performance. This is carried out theoretically by numerical calculation of the potential and electric field distributions in the neighborhood of the strips, and experimentally by measurements on fabricated test structures.
Chapter 5, treating the readout of a strip detector, begins by evaluating the existing readout methods. These are divided into two categories: the passive and the active readouts. Passive readouts are based upon resistor-capacitor networks, whereas active readouts include some active components. Subsequently, the use of JCCDs for readout will be considered in some more
detail. In particular, the transit time needed for the signal charge to flow from the detector strip into the CCD channel will be examined. Some experimental results are presented as well.
Chapter 6 closes the thesis by offering a short summary of the conclusions reached in the previous chapters.
2.0. INTRODUCTION
In this chapter an overview of semiconductor radiation detectors is presented [2.1]. Compared to the gaseous one the solid-state detector has many advantages, the most important being the high energy resolution obtainable [2.2]. In a semiconductor detector about 3 eV is needed for the creation of one electron-hole pair, whereas a gaseous detector needs about 30 eV [2.2]. This means that the same radiation will generate much more charge in the semiconductor detector and consequently that the energy of this incident radiation can be estimated much better (see also Sec.2.2.3.).
Some other advantages of solid-state detectors are their linearity of response over a large range, their fast pulse rise time and their high density, which lowers the range of the radiation particles, thereby also enabling the more energetic ones to be stopped [2.2]. Finally, special configurations can possibly be made with semiconductor detectors by using the fabrication technologies known from microelectronics.
In the next section, Sec.2.1., the history of the semiconductor detector is briefly reviewed. In the subsequent section, Sec.2.2., some general considerations concerning the detector operation are given. It is divided into four subsections, which treat successively the interaction of semiconductor material with radiation, some signal processing, the noise aspects and the radiation damage. Sec.2.3. deals with the various kinds of detectors which can be made with a semiconductor. It is also divided into four subsections, in which the detector application, the detector material, the fabrication process and the lay-out are successively discussed.
2.1. HISTORY
The history of the semiconductor detector starts in 1951 when McKay observed that in a point-contact germanium diode measurable signals were produced by impinging a-particles [2.3]. At that time semiconductor materials had been investigated for particle detection [2.4], but the detection principle had been based upon modulation of the crystal conductivity by the radiation. The reverse-biased diode, having a lower noise level and a faster response time, is clearly a much better device.
At the end of that decade the semiconductor detector had become the center of interest. Different groups were doing research on this subject in a friendly spirit of competition, which is nicely described in [2.4]. The 7t h
Annual. National Meeting (USA) in October 1960 was entirely devoted to "Solid-State Radiation Detectors", that being the "most timely theme" [2.5].
[2.6], but Schottky diodes (Au-Si or Au-Ge) were soon being investigated [2.7]. The possibility of detecting radiation by these devices was first reported in 1955 [2.4]. Because these surface barrier detectors, as they are usually called, do not have high temperature steps incorporated in their fabrication process, lower leakage currents could be achieved on these devices. Moreover, the dead layer was much smaller.
At this stage, only a-particles could be detected and the research was headed in the direction of lower noise levels and larger depletion layers to enable the detection of /3- and minimum ionizing particles. The technologies springing from this research consist of Li-drifted silicon, h i g h - p u r i t y germanium, surface passivation and guard ring structures. The development of the ion-implantation technique also enabled a new processing technique for detectors [2.8,2.9]. This technique combined the advantages of the former two (junction-type detectors - which means low leakage current, better reproducibility and yield - low temperature process and thin dead layers) and led in the end to the state-of-the-art as set by Kemmer [2.10].
Not only the energy of the impinging particle, but also its position can be measured by a semiconductor detector (and both with a high resolution). The first position-sensitive radiation detectors were based upon resistive charge division [2.11]. The charge division was done in the undepleted bulk. As the characteristics of this layer could not be controlled well, the resistive part was soon made by evaporating or implanting the division resistors [2.12].
Along with the development of these detectors gains were made in the theory behind their operation, and it became clear that with resistive charge division good position resolutions could only be achieved with high energetic radiation [2.12]. As a result the strip and checkerboard detectors were invented [2.13], which were able to measure both the energy and the position (in respectively one and two dimensions) of low energetic radiation. The disadvantage of these detectors is the necessity of having an amplifier chain for every strip; clearly, some multiplexing scheme had to be developed. Matrix addressing [2.14] and resistive charge division (by external resistors) [2.15] resulted.
At the beginning of this decade there was a revival of interest in the semiconductor radiation detector, due to the need in high-energy physics for detectors with a very high position accuracy. A resolution of a few micrometers was needed, and this led to the introduction of the microstrip detector [2.16]. Its much more complicated readout problem demanded and got more attention and more sophisticated solutions were under study [2.17,2.18,2.19,2.20] (see Chapter 5). Due to the more mature state of microelectronics, other types of detectors were also invented, namely the CCD detector [2.21] and the solid-state drift chamber [2.22]. Today's state-of-the-art is depicted well by [2.23].
2.2. DETECTOR OPERATION
In this section some general considerations concerning the operation of a
semiconductor detector are given. Firstly, the way in which the material interacts with radiation is reviewed; secondly, the signal processing, mainly the preamplifier configuration, is discussed; thirdly, the various contributions to the noise in a whole detection system are considered; and finally, some remarks about radiation damage are made.
2.2.1. Radiant - electrical signal conversion
Roughly speaking, there are three sorts of radiation: charged particles, uncharged particles and photons. To be detected by a semiconductor detector they should liberate electron-hole (eh) pairs in the semiconductor, which, upon collection, will produce an electric output pulse, enabling further processing. In this generation process the particle will lose energy and will eventually be stopped in the detector. The amount of generated eh pairs is a measure of the energy deposit by the particle. In silicon each eh pair represents 3.6 eV, and in germanium 3.0 eV [2.24].
RADIATION ON SILICON
IONIZATION
hot electrons (few keV)
& l a t t i c e vibrations (heat) IONIZATION
1
f r e e electrons (1.12eV) & heatUltimately, 3.6 eV used per generated electron-hole pair
Fig.2.1. The interaction between radiation and silicon in general.
The first sort of radiation, the charged particle, is stopped mainly by means of the Coulomb interaction (other effects can be elastical scattering, the Cerenkov effect and Bremsstrahlung [2.24]). At such an interaction, Fig.2.1., a bound electron is liberated and brought into the conduction band; the semiconductor is being ionized. (For this reason this sort of radiation is often referred to as ionizing radiation.) According to the laws of conservation of energy and momentum, the freed electron will have an energy of a few keV. However, it will lose this energy very quickly by creating other eh pairs. Because in the course of this whole process, which takes only a few
picoseconds [2.2], energy will also be lost in the form of optical phonons [2.2], the mean energy ultimately represented by each created eh pair will be larger than the band-gap width.
In the second sort of radiation the neutron is the main representative. Because the particle is uncharged it cannot be detected by electromagnetic interaction. Therefore, it first has to create a charged particle, which then can be detected. For this purpose a coating can be deposited on the detector, which interacts with neutrons in such a way that charged particles will be created [2.24]. For example, the coating may be a polyethylene layer; the neutron can knock out a proton from this layer. (Because the proton has the same mass, it is even possible that all the neutron's energy will be transferred to the proton.) Another solution is to let the neutron initiate some kind of nuclear reaction in which charged particles arise [2.24].
The last sort of radiation, the photon, is characterized by the fact that it reacts only once and disappears after that reaction. A photon is not slowed down as a charged particle is. There are three types of interaction, every type significant in a special range: the photoelectric effect, Compton scattering and pair production [2.2,2.24].
The first effect dominates at the lower energies, from visible light up to about 100 keV. Upon a reaction a hot electron is created, and the photon is lost. The electron, falling down to the conduction band edge, will behave as a charged particle by creating other eh pairs, thereby enabling the photon to be detected. (In the case of visible light only one eh pair (of the energy of the band-gap width!) is created per photon. Therefore only a continuous flow of light, resulting in an output current instead of an output pulse, can be measured, whereas at the higher energies each photon can be detected separately.)
From 100 keV up to 10 MeV the Compton scattering dominates [2.24]. In this type of reaction not only a hot electron, but also a new photon is generated. If this photon escapes out of the detector, too low an energy estimate will be made of the primary photon. As a result, instead of a single peak a broad spectrum ending at the photon's energy will be seen in the energy spectrum.
At the highest energies the production of electron-positron pairs will occur. The energy of the photon should be at least 1.022 MeV, the rest energy of such an electron-positron pair. The remaining part is converted into kinetic energy of the generated pair. After their generation, the electron and positron will be slowed down as charged particles. The positron will be annihilated along with an electron from the crystal, thereby generating two 511 keV photons. If one or both are not absorbed, too low an energy estimate will again be made. Now, instead of a broad spectrum, two extra peaks will be seen in the energy spectrum: the single and double escape peak [2.2].
The probability of an interaction depends strongly on the kind and energy of the impinging particle [2.24]. Heavy ions of low energy have a high such probability and are stopped in the surface region of the semiconductor crystal (cf. ion implantation), whereas elementary particles at
relativistic velocities hardly interact at all. (In fact, these minimum ionizing particles, as they are usually called, generate in silicon about 85 eh pairs per micrometer [2.25], which means an energy loss of only 300eV//mi and for a 300/im thick detector a generation of only 4 fC signal charge.) Photons of low energy a r e also more likely to interact with the semiconductor than those of higher energies [2.24]. The required detection volume therefore depends on the radiation to be detected.
2.2.2. Signal processing
By collecting the generated eh pairs the particle is detected. This can best be achieved by making a reverse-biased diode. To ensure fast and total charge collection the device has to be fully depleted (of course, this is not necessary for the detection of low-range particles). Besides the fact that collection by diffusion is not fast enough, partial depletion will not guarantee a complete charge collection, which can result in a wrong estimate of the deposited energy, or, due to the noise level, in particles remaining undetected. Moreover, the chance of trapping is larger in the undepleted part. This will also reduce the amount of collected charge, because, compared with the filtering time constant of the electronics, the trapped charge will not be collected in time. Typical collection times in fully depleted detectors are on the order of 10 ns [2.25].
BIAS radiaton ^
~L
detector & amplifier pulse PULSE HEIGHT ANALYZER (A.O.C.1 M.C.A. MEMORY countst
ENERGY SPECTRUM channel no(Enercjy)J
Fig.2.2. The method of measuring an energy spectrum.
The total amount of collected charge is a measure of the energy deposited by the particle. As a detector has a capacitive impedance, this charge can be measured by measuring the height of the detector's output pulse. This is done in a multi-channel analyzer (M.C.A.), see Fig.2.2.: The detector is irradiated with particles, and the heights of the subsequent output pulses are measured. The whole spectrum of possible pulse heights (the window) is divided into channels. Each pulse from the detector is counted by the channel corre sponding to it. In this way an energy spectrum of the radiation is obtained.
The signal from a detector is too small for direct processing and some amplification is needed. There are three main types of preamplifiers, Fig.2.3.: the charge-sensitive, the voltage-sensitive and the current-sensitive one. They will be discussed below.
Q6(t) a) f CD 1 "Cf Q6(ö
e
v
* A N y 1 R2 * | V o u t |f
'W
Q6(t)e
c)n ^
vo u t : R , 6 ( t )Fig.2.3. Basic amplifier configurations: a) charge-sensitive amplifier, b) voltage-sensitive amplifier and c) current-sensitive amplifier.
Usually, the preamplifier is of the charge-sensitive type (Fig.2.3a.). As a result of its large input capacitance all the generated charge will flow from the detector onto the feedback capacitance. The output voltage is therefore linear to the amount of charge generated, the feedback capacitance being the proportionality factor.
The disadvantage of this type of amplifier is its speed. Its rise time increases linearly with the detector's capacitance [2.26,2.27]. The voltage-sensitive amplifier (Fig.2.3b.) doesn't have this drawback. The rise time is independent of this capacitance [2.26]. However, as the output signal now depends on the capacitance of the detector, this capacitance should have a high stability. This demand is met in totally depleted detectors.
For very fast applications the current-sensitive amplifier (Fig.2.3c.) can be used [2.28]. Here, the pulse from the detector still has to be integrated, which in fact is done by the filtering system [2.28]. In the case of reading out a multi-electrode detector such as a microstrip detector, this type of amplifier is even preferred over the voltage-sensitive one, because, by virtue of its low input impedance, it will decouple the contiguous electrodes [2.26],
Because semiconductor detectors have no internal amplification the preamplifier should be a low-noise one, especially in those cases where the signal from the detector will be low (e.g. detection of minimum ionizing particles). First of all, the input transistor is responsible for the amplifier's noise, and therefore has to be of the low noise type. Normally, a junction FET is used for this purpose, but when short filtering times are used, such as in high-speed situations, a bipolar (microwave) transistor can be advantageous [2.27,2.29,2.30].
In the second place, the feedback resistor contributes to the noise. This favors the use of the charge-sensitive configuration, in which this resistance is very large or even left out altogether. However, in the case of the voltage-sensitive amplifier the feedback resistors can be chosen in such a way that their noise contributions are not of primary importance [2.27]. The noise contribution from the feedback resistor in the current-sensitive amplifier can also be greatly reduced by the use of short processing times [2.27]. It has been demonstrated that comparable results can be obtained with all three configurations [2.31].
2.2.3. Noise
The effect of the noise will be a reduction in the energy resolution, seen as a broadening of the peak in the energy spectrum (Fig.2.2.). The energy resolution is expressed by the FWHM-value (Full Width at Half Maximum). As the whole noise process has a stochastic nature, the individual noise contributions have to be added quadratically:
A£t2ot = AEÏ + A£22 + A£32 + (2.1)
The contributions to the noise can be attributed to three main sources: noise in the radiation itself, noise from the detector and noise from the preamplifier. These will now be discussed successively.
The first main source of noise is attributed to the stochastic nature of the energy loss process of an impinged particle. Being a Poisson process, the resulting widening in the energy spectrum is proportional to the square root of the number N of generated electron-hole pairs, or relatively [2.2,2.24]:
where E is the energy deposited by the particle and e the creation energy for one electron-hole pair (3.6 eV in the case of silicon). Eq.(2.2a) demonstrates why semiconductor detectors have a better energy resolution than gaseous detectors or scintillators: Because the creation energy e is smaller, more charge will be generated, resulting in a lower intrinsic widening.
In practice, the observed fluctuations appear to be less than predicted by Eq.(2.2a) and a correction factor F (the Fano factor [2.24]) has to be added:
AE, = Ijf-. (2.2b)
The reason for this smaller width of the peak is due to the fact that the total amount of energy loss is fixed; the particle is completely stopped in the detector [2.24]. For silicon F is on the order of 0.1 - 0.2 [2.32].
On the contrary, when the particle is not stopped in the detector, but traverses through it (e.g. minimum ionizing particles), the peak will be broadened. A tail will appear on the right side (the higher energies) of the energy distribution. This effect is known as the Landau distribution [2.33]. It is due to the fact that the particle has only a few interactions with the semiconductor. At each interaction an electron of a few keV will be created (Fig.2.1.); therefore a reasonable signal will result and the particle can be detected. However, fluctuations in the small number of these collisions will have a significant effect on the energy distribution, resulting in the Landau broadening [2.24]. When the detector becomes very small an even wider spectrum results [2.34].
Noise from the detector is the second main source contributing to the total noise. It is mainly due to current noise. In a usual pn-diode, where the current-voltage characteristics are governed by the diffusion process in the quasi-neutral regions, this noise is equated for the reverse bias case as [2.35]
ID = 2qIAf, (2.3) where / is the value of the leakage current and the other symbols have their
usual meaning.
However, in the case of a detector, the generation-recombination in the depletion layer is the main source of leakage current and noise (Sec.3.1.). It appears that in this case Eq.(2.3) can still be used, albeit with the introduction of a small correction factor [2.36]. Eq.(2.3) clearly demonstrates that a lower leakage current will result in a lower noise contribution from the detector.
Other contributions to the noise from the detector can be attributed to the series resistance (not depleted bulk or contact resistance), \/f noise, surface noise, and noise due to other leakage sources. All these are negligible when the detector is made under the customary circumstances.
Fig.2.4. Detector-amplifier circuit with noise sources.
the bias resistor and the input stage of the preamplifier. When the bias resistance is high, its contribution to the (current) noise is negligible compared to the other noise sources, as they are depicted in Fig.2.4.
The noise from the amplifier is usually described by a series voltage and a parallel current noise source (Fig.2.4.). It stems mainly from the input transistor (its bias and gate or basis currents) and the feedback resistor, Sec.2.2.2., [2.29,2.37].
Usually, the effect of all of the noise sources is expressed by the ENC (Equivalent Noise Charge), i.e. the amount of charge which the detector should generate in order to give the same output signal. The effect of the series voltage noise source can be translated via the detector capacitance (differentiation) to a parallel current noise source and then all the noise contributions can be added [2.29]. In this way an optimum filtering time constant for a large signal-to-noise ratio can be estimated [2.29,2.37].
This procedure also shows that the detector contributes to the noise through its capacitance. A low capacitance is favorable, because it reduces the contribution from the amplifier's series voltage noise source. This constitutes, next to that of obtaining large signals (Chapter 1), a second reason for requesting large depletion layers (however, not in the case of microstrip detectors, as their interstrip capacitance is much larger than their junction capacitance, Sec.4.2.6.). A drawback of a large depletion layer is the accompanying increase in the leakage current (Sec.3.1.) and thus noise. Therefore, depending on the shaping time constant, the noise level of the preamplifier and the actual height of the detector leakage current, an optimum depletion layer can exist for a given set-up, where the noise will be the lowest (vice versa, given a fixed bias voltage, an optimum shaping time constant will be found for minimum noise) [2.38].
2.2.4. Radiation damage
As damage by radiation is inherent in the use of detectors, radiation detectors will always have a limited lifetime. Except in generating electron-hole pairs, the radiation will displace some atoms in the crystal [2.39]. The amount and kind of displacements (clusters, etc.) depend on the kind of radiation: whether or not it is charged, its mass, its energy, etc. [2.24]. The resulting crystal defects will create levels in the band gap [2.39,2.40], which means that the leakage current (noise) will increase (besides a change in the effective doping concentration). There will also be more trapping of
generated eh pairs, which will result in pulse broadening or inefficient charge collection [2.41]. (Especially in the case of the silicon drift chamber, where the collection time of the generated charge carriers is on the order of microseconds, charge can be lost by the increased recombination velocity [2.42].) With respect to the microstrip detector there is another radiation effect which occurs when the detector is inhomogeneously irradiated (such as
in fixed-target experiments): due to the local change in the effective doping concentration a transversal electric field will arise in the detector, which will consequently disturb the detector's position linearity [2.43].
Usually, the effect of radiation damage will be noticed after some critical dose has been exceeded. The level of this critical dose depends on the purity of the crystal and on the kind of radiation [2.39,2.40,2.41]. Commonly, a temperature treatment will anneal the radiation damage, allowing the detector to be used for an extra amount of time [2.40].
Whereas crystal damage is the effect of radiation in the bulk, in the oxide layers it will be charge buildup [2.39,2.42]. As a result, MOS circuitry is more sensitive to radiation damage than its equivalent made in junction technology (e.g. JFETs and JCCDs [2.42,2.44,2.45]). Charge buildup is due to the fact that those holes created by the ionizing radiation that escape initial recombination will stay trapped in the oxide layer, while their counter electrons will be swept out of it [2.39]. Consequently, the threshold voltage will change, ending in a malfunction of the circuitry. (Logically, these considerations concern only the electronics placed in the neighborhood of the detectors, especially in the case of a collider experiment, where the circuitry will be more subject to radiation than in the case of a fixed-target experiment [2.42].) As for the microstrip detector, there are also some effects which can result from the charge buildup in the oxide layer [2.42]: the surface leakage current can increase and the interstrip resistance can decrease, both of which affect the noise performance.
2.3. DETECTOR TYPES
All semiconductor detectors are based upon the principle of a reverse-biased diode; the impinging particle generates electron-hole pairs, which are collected by the electric field. However, within this base a large diversity of detectors is still possible. The semiconductor material, the geometry, the
lay-out and the fabrication process have to be chosen. These will depend on the application for which the detector is to be used. These considerations will be discussed in the following subsections.
2.3.1. A p p l i c a t i o n
First of all, it is important to know what kind of radiation has to be detected. As heavy ions and low energetic particles have a short range, the detector should have a thin dead layer. (The diode structure can even be designed horizontally, if necessary, to enable the radiation to enter the (sensitive) depletion layer directly.) Minimum ionizing particles and 7-photons have a long range and absorption length, respectively. The window thickness is less crucial, but a large collection volume is required for these particles.
Secondly, the purpose for which the detector will be used has to be determined. That can be for energy measurement, position measurement, timing and particle identification.
When the particle is completely stopped within the detector a very high resolution energy measurement can be performed, due to the low ionization energy of the electron-hole pairs, Sec.2.2.3. [2.24]. When the particle cannot be stopped by the detector, either a telescope or a so-called calorimeter construction can be made. In a telescope several detectors are stacked on top of each other, thereby effectively increasing the stopping volume. Moreover, the signals from the different detectors can be used for correlation, etc. (rejecting wrong data) [2.46]. In a calorimeter several detectors are likewise stacked, although in this case there is h i g h - Z material (e.g. plumbum, uranium) in between them, thereby enlarging the stopping power of the whole system [2.47].
Fig.2.5. Two ways to make a detector position sensitive: a) by integrating an array of strip-like detectors; and b) by contacting the detector on two opposite sides, enabling resistive charge division.
A position-sensitive detector is made by integrating an array of detectors (strip and checkerboard detectors) or by contacting the detector on two opposite sides, thereby enabling resistive charge division [2.12], see Fig.2.5. Two-dimensional position measurement can be achieved by two one-dimensional position detectors in the case of particles which traverse the
detectors. In the other case, however, the detector should indicate both dimensions at once. This occurs, for example, in tomography (medicine), where the xy-position of ^-photons has to be measured. The first case occurs, for example, in high-energy physics, where the particles traverse the detectors. (It is even important to have small detectors there, in order to avoid scattering.)
One way to identify a particle is by measuring its energy loss over a short distance dE/dx together with its total energy E. The product of these two identifies the particle [2.24,2.48]. Another possibility, only useful for non-relativistic particles, is to measure the energy and the time of flight between two detectors [2.24]. The mass can be calculated from the (kinetic) energy and the velocity, measured by the time of flight.
Because semiconductor detectors have a fast response, they can also be used for timing purposes, one of these being the time-of-flight measurement. The triggering function is another clear example. In coincidence or anti-coincidence measurements the timing aspect is implicitly used [2.24]. 2.3.2. Material
The most important materials for semiconductor detectors are silicon and germanium, as, due to the electronics industry, they are available in large quantities with a high purity and in monocrystalline form. As silicon can be oxidized, its surface is easy to passivate, thereby reducing surface leakage currents. Because silicon has a larger band gap than germanium, silicon detectors can be operated at room temperature, whereas germanium detectors will exhibit too large a current at such temperatures and will need cooling. A silicon detector has the extra advantage of having some electronics potentially integrated along with the detector [2.49,2.50].
Due to their higher density, solid-state detectors have a much better stopping power than gaseous detectors [2.4]. In this respect germanium is even preferable to silicon. Its higher atomic number (Z) implies a much better stopping power, as most of the stopping processes are proportional to a power of Z [2.24]. Therefore, research has also been done on other semiconductor materials with even higher Z [2.51,2.52,2.53]. The main problem is to fabricate these materials monocrystalline and with a high purity. For example, Hgl2 is a soft material, needing special care during cleaving and
sawing to avoid mechanical damage [2.51].
Another material which has been studied is diamond [2.51,2.52]. Since this material is an insulator, it will have a low "leakage current", which means a low intrinsic noise level. However, its low Z , small size and high price prohibit wide-spread use. "Materials" with a very small band gap (and therefore possibly a high energy resolution) are found in the superconductors [2.54].
To achieve large depletion layers the net doping level of the bulk material should be as low as possible. This means that high purity or compensated material has to be used.. Compared with compensated material,
better diodes can be made on high-purity material, as this type of material contains fewer impurities, which means fewer generation-recombination centers and thus lower leakage currents (Sec.3.1.). Moreover, there is no chance of a redistribution of the doping (compensating) atoms, which would of course deteriorate the detector's performance. However, the fabrication of high-purity material is more sophisticated, and, due to the lower impurity level, it is also less radiation-resistant. Therefore, the purity grade should not exceed the needed level. Nowadays, nearly all desired levels of purity can be achieved. Only for really large depletion layers must lithium-compensated material be used.
H i g h - p u r i t y silicon is fabricated by using starting material which already has a high purity grade. The final crystal is grown from these selected pieces. Then by zone refining the impurity content is diminished until the required purity grade is achieved [2.55]. As boron remains in the silicon during zone refining, p-type silicon will have a lower compensation level than n - t y p e silicon of the same doping concentration [2.55]. The state-of-the-art is a doping concentration on the order of 1.10 cm (which means one dopant atom per cubic micrometer!). Lower concentrations are available, but difficult to achieve. As stated in [2.55], "business in this range is more like gambling."
Instead of using purifying techniques to achieve low doping levels, compensation techniques can also be used. In this way a net low doping level will result. The most successful method is based upon the lithium-drift process [2.2,2.24]. As an interstitial, lithium has a donor character. In the process it is brought into p-type silicon by a deposition step as in a normal diffusion process. In this way a pn-junction is formed. Then by reverse biasing and by heating, the lithium will drift to those places where boron atoms are left [2.24]. A perfect intrinsic region will result and a large depletion layer of several millimeters can be formed [2.55]. Due to the larger depletion layer (and higher impurity level) the leakage current will be higher, thereby increasing the detector noise. As a consequence, these detectors must be operated at low temperatures. Lithium-drifted germanium detectors even have the drawback of having to be maintained continuously at liquid nitrogen temperatures to prevent the. lithium from further diffusion and precipitation [2.2].
Another way, only suitable for silicon, is based upon neutron transmutation [2.24,2.56]. The (high-purity p-type) silicon is irradiated with neutrons. In this process some silicon atoms will get heavier because of absorbing these neutrons. When their atomic weight has grown to 3 1 , they will disintegrate into a phosphorus atom by means of y9-decay [2.56]. In this way high resistivity uniformly doped n-type silicon can be fabricated. 2.3.3. Fabrication process
Based upon the different existing fabrication processes, it is possible to classify the detectors into three main types, Fig.2.6., namely the diffused
3|lm boron diffusion 30nm gold evaporation n-Si n-Si 3|!m phosphorus diffused detector 100nm aluminum surface-barrier detector
.tLim boron implantation
S3 £SS
n-Si
3u.m arsenic ion-implanted detector
Fig.2.6. The three main types of detectors: a) the diffused detector, b) the surface-barrier detector and c) the ion-implanted detector.
detector, the surface-barrier detector and the ion-implanted detector.
Diffusion was the first technique available for detector fabrication. The high temperature steps necessary for the processing, however, degrade the material in such a way that the carrier lifetime is reduced, resulting in higher leakage currents (cf. Sec.3.2.). Moreover, due to the diffusion, the detector will have a reasonable dead layer.
Surface barrier detectors, on the contrary, are made in a low temperature process and can have extremely thin windows [2.57]. Instead of using a pn-junction, they are based upon the rectifying properties of the Schottky barrier. In practice, however, this metal-semiconductor interface is difficult to control, so that it is hard to make such detectors in a way easy to reproduce. Moreover, the (theoretical) leakage current of these devices is higher than that of the junction ones (made by implantation).
The ion-implantation technique offers the advantages of both techniques combined. Junction detectors can be made in a process with hardly any high temperature steps (cf. Sec.3.2.). Thin dead layers can also be made [2.10,2.58]. 2.3.4. Lay-out
The most straightforwardly designed detector is the planar one, either square or circular in form. Using photolithography a guard ring can be designed around the detector area in order to lower the leakage current [2.59]. p n-type /' bulk )) /
To achieve larger detection volumes, the detector can be made transversal. The best form in which this can be achieved is the coaxial detector, Fig.2.7. [2.60]. The surface in the hole forms one of the contacts, and the outer side of the crystal the other. In this way active volumes on the order of 100 cm3 can
be achieved [2.60]. As the stopping power of these large volume detectors is of primary importance, these detectors are usually made of lithium-drifted or high-purity germanium.
A more refined lay-out is needed for position-sensitive detectors. The first detectors of this kind were based upon resistive charge division (Sec.5.1.1.), but, as it soon appeared, a better performance could be achieved by using array-type detectors [2.12], the checkerboard detector being the first of this kind [2.13].
strip detector drift chamber CCD detector
Fig.2.8. The three main types of high precision position detectors: a) the microstrip detector, b) the drift chamber and c) the CCD detector.
In high-energy physics detectors with a very high position resolution, on the order of a few micrometers, are needed (see Chapter 1) [2.41,2.42]. Up to the present three kinds of silicon detectors which have such a high position resolution have been invented, Fig.2.8.: the microstrip detector, the silicon drift chamber and the CCD detector. Another solution which also uses silicon consists of the scintillating fiber with silicon readout (e.g. photodiodes or CCD camera) [2.25,2.42]. As this detector is not a full-silicon device, it will not be discussed here. Additionally, based upon the drift chamber, a lot of other silicon detector types have been derived by implementing microelectronics technology [2.61].
The first of these to be invented, the so-called microstrip detector (Fig.2.8a.) [2.16], is made by the same process as the planar detectors, except that another masking set has to be used. The strip pitch of these devices is on the order of 20 /zm, resulting in a position resolution of a few micrometers [2.62].
Every strip has to be read out (see Chapter 5, which is the subject of this topic). This means that a lot of amplifier chains are required. Furthermore, the connection between the electronics and all those strips poses a technical problem. The easiest way to overcome these is to use charge division, either resistive or capacitive [2.12,2.25,2.42]. A more sophisticated approach is to use a second metalization layer, so that capacitive multiplexing can be performed [2.63]. The solutions based upon the full electronic multiplex
systems which have been invented so far are based on sample-and-hold principles [2.19,2.20] or on the use of CCDs [2.17,2.18,2.44]. These systems, however, do not eliminate the interconnection problem. Solutions to this problem are based on either the use of sophisticated bonding schemes [2.20,2.64] or on the integration of the electronics on the detector wafer [2.49,2.50].
A completely different approach for detectors with a high spatial resolution has resulted in the so-called drift chamber (Fig.2.8b.) [2.22]. In this case strips are made on both sides of the detector (which thus requires a double sided masking technique). Their doping is opposite that of the bulk material. There is only one strip (or point) having the same doping, which serves as bulk contact. To operate, the detector has to be fully depleted and a drift field towards the bulk contact has to be created. This is achieved by first reverse biasing the structure into full depletion and subsequently imposing different voltages on all the strips (increasing to the outer strips). It is also possible to bias only the outermost strips and let the others float [2.65]. (When, during the depletion process, the expanding depletion layers on both sides meet, the capacitance will decrease dramatically [2.22]. In this way, large sized, low-noise photodiodes can be made [2.22,2.25,2.66].) When electron-hole pairs are generated in the silicon, the ones will be collected by the strips directly, and the others will drift to the bulk contact. When the latter enter the neighborhood of that contact a pulse will be induced. The time difference between this pulse and the one from the strips indicates the drift time and therefore the position of the impinged particle [2.22]. With respect to the timing aspects fast, low noise electronics are required for a high performance of this type of detector. Moreover, the temperature should be stable, as the mobility of the charge carriers and thus the drift time depends on it.
Finally, the CCD detector (Fig.2.8c.) can be used for high-precision position measurement [2.21]. It is a two-dimensional position-sensitive detector which exploits the achievements of microelectronics. It functions in the same way as the CCD camera [2.41,2.67]: the electron-hole pairs generated by a particle are collected by a pixel (picture element) and the position is determined by successive readout. Due to its low noise, this type of detector doesn't need a large signal and therefore not a large depletion layer (this is still in reference to the detection of minimum ionizing particles, i.e. the particles in high-energy physics) [2.41,2.68]. However, cooling to liquid nitrogen temperatures is a prerequisite. Due to the development of fabricating and processing high-purity silicon for microstrip detectors, research has been started to investigate the properties of CCDs made on this type of silicon [2.45]. Because they have a large depletion layer, there can be no smear out of generated signal charge collected by diffusion, which would deteriorate the measurement. The output signal will clearly be larger.
In comparing the strip detector, the drift chamber and the CCD detector (Table 2.1., [2.25,2.41,2.42,2.69]), it can be concluded that the strip detector has the highest resolution and is the fastest device. However, the readout is
Table 2.1. Comparison of the strip detector, drift chamber and CCD detector.
properties
position precision (/jm) two-particle resolution (/im)
readout time active area (cm2) fabrication technology notes strip detector 2.5 60 (using cap. charge
division) 10 ns (without multiplexing) 50 relatively simple one-dimensional drift chamber 4.5 200 2 /is 50 complicated needs uniform doping of bulk CCD detector 4.3 40 40 ms 1 very complicated needs cooling; thin active region
complicated and a lot of electronics are needed. The CCD detector, on the other hand, fits in well with the electronics and the interconnection. Besides, it provides two-dimensional position information. Drawbacks, however, are the long readout time, which doesn't allow high event rates (especially when the CCD remains active as a detector during readout), and the complicated technology, which doesn't allow the fabrication of large detection areas. When made in MOS technology the radiation resistance will also be lower [2.45] (Sec.2.2.4.). The drift chamber stands somewhere in the middle with respect to the other two devices (Table 2.1.). Which detector is going to be used depends strongly on the experiment (event rate, multiplicity of decays, etc.) for which it has to be used.
2.4. CONCLUSIONS
An overview of semiconductor radiation detectors has been presented. After a brief sketch of their history, the principles by which they can detect radiation were outlined. First, the interaction with radiation, which enables the semiconductor to be used for radiation detection, was summarized. Thereafter, the signal processing, mainly the preamplifier, was taken into consideration. And finally, the noise aspects of an entire detection system were discussed, followed by some remarks about radiation damage.
Next, the various types of semiconductor detectors came up for discussion. Even though the principle of operation is the same for all of them, there is still a large diversity among the detectors, depending on the application for which the detector has to be used. The crucial parameters which have to be selected in order to achieve that purpose are the semiconductor material, the geometry, the lay-out and the fabrication process. The large variation in these parameters leads directly to the large variety of semiconductor radiation detectors to be found in the literature today.
3.0. INTRODUCTION
Once the HP-Si is available, the manufacture of detectors appears to be straightforward. Only two junctions (a pn- and a hi-) have to be made, so that the processing sequence is relatively simple. Moreover, compared to VLSI-circuitry the mask requirements for microstrip detectors are seemingly less stringent; a micrometer variation in the strip's dimensions can easily be tolerated. On the other hand, however, a wafer-scale device has to be made with a reasonable yield, and, what is more, it appeared that the resulting detector quality (denoted by its leakage current) is strongly dependent on the processing sequence used.
There are many conceivable processing sequences resulting in the required junctions. Some of these protocols have been selected and used at the IC-Workshop of the Delft University of Technology for the fabrication of test diodes. As stated in Chapter 2, Sec.2.2.3., for a low noise contribution the detector should have a low leakage current. Therefore, the process resulting in diodes with the lowest currents should be selected. Extra processing steps, needed for, say, integrating some (multiplexing) electronics with the detector, however, may influence the leakage current and thus the choice of the proper process. It is therefore important to know their influence as well.
In this chapter the effect of the processing is discussed. As the leakage current is the most important quality indicator in a detector, the measurements are strongly related to this parameter. In order to interpret the measurement data, one needs a model describing the reverse bias behavior of the junction diode. Because the diodes discussed here are made on HP-Si some care has to be taken when simply adapting the usual formulas. Therefore, the theory of the leakage current as applied to these diodes has been reexamined.
The chapter is divided into two parts. P a r t i , Sec.3.1., reviews the theory of the leakage current and related subjects. In Part II, Sec.3.2., the measurement results obtained on differently processed diodes are presented and discussed. They will show the dependence of the leakage current on the choice of process.
3.1. PARTI - THEORY 3.1.0. Introduction
The quality of a detector is characterized by its leakage current. A low leakage current means a low noise and thus a good quality. Measurement of this parameter is therefore an inevitable tool in detector research and development. In this part the theoretical basis on which this and related
Table 3.1.1. List of symbols. Q e k "i n,p N An, Ap A» D L W W» Wgen Wlh T G ■^HL ^HL.norm T EK E,<0) EF £r Ei V J subscripts: elementary charge permittivity Boltzmann's constant
intrinsic carrier concentration electron, hole concentration doping concentration
deviation of the electron, hole concentration from its equilibrium value
carrier mobility
carrier diffusion constant diffusion length layer width depletion-layer width generation-layer width wafer thickness lifetime
net generation rate
effective surface generation velocity of the high-low junction
normalized effective surface generation velocity absolute temperature
activation energy
band-gap width at 0 K (1.2 eV) Fermi energy level
trap energy level intrinsic Fermi level bias voltage
current density
I, II, m , IV indicating region I, II, III, IV of the diode (Fig.3.1.1.) depl
QN n, p dep,indep
indicating region II (the depleted part)
indicating region III (the undepleted, quasi-neutral part) indicating electrons, holes
measurements are interpreted is outlined. First, in the next section, the theory of the leakage current is formulated and then investigated further in the subsequent section .with respect to the carrier generation. In the final section, the temperature dependence and lifetime measurement will be discussed.
Before going into more detail about the analytical description let us shortly analyze the leakage current qualitatively. In a reverse biased diode this current is due to [3.1,3.2]:
- thermal generation in the depletion layer,
- thermal generation outside this layer (in all three directions) until typically one diffusion length away,
- surface generation,
- injection from the (metal) contact.
Optical generation and (avalanche) multiplication are assumed not to occur. These four leakage sources can be reduced by:
- using high-purity material (a low number of impurities and thus of generation - recombination centers),
- contacting the bulk by a high-low junction (diminishing the effective diffusion length and avoiding injection from the contact),
- designing guard rings (automatically included in strip detectors; suppressing the contribution by surface generation and lateral diffusion), - passivating the surface (usually by oxidation; reducing the surface states
and thus the surface generation).
As the generation is a thermal process a further reduction can be achieved by cooling the device. Finally, a proper processing sequence has to be chosen, as will be shown in Sec.3.2.
In the following theoretical description ideal junctions, i.e. those without pinholes etc., are assumed. The analysis is kept 1-dimensional, as the geometry of most detectors is such that this restriction is allowed. Calculations of the depletion layer of a diode with a surrounding guard ring made on HP-Si showed that the electric field beneath the diode obeyed 1-dimensional theory, as long as the guard ring had a width of at least 300 /zm. However, measurements on 20 /im-pitch strip detectors showed that the leakage current through an arbitrary number of strips was already proportional to that number of strips when they were guarded by their nearest two neighboring strips (i.e. a total of four strips needed for guarding; see also Sec.4.2.6.). 3.1.1. The leakage current
To calculate the current in a fixed area, one has to solve the current and continuity equations, which are, for the sake of completeness, given respectively below [3.3] (See Table 3.1.1. for the meaning of the symbols):
n+
T
in
IV
Fig.3.1.1. Subdivision of the diode structure into four regions, according to which the leakage current is calculated.
Jn = qnnnE + QDn-^,
J
p= q
HpE - qD
pjg,
dt " + q dx '32 _
rL^s
dt GP q dx (3.1.1a) (3.1.1b) (3.1.2a) (3.1.2b) To derive an expression for the leakage current the diode structure is divided into four regions as shown in Fig.3.1.1. The outer two regions represent the high-doped regions, and the inner two the depleted and undepleted parts of the low-doped bulk (the abrupt depletion approximation [3.3,3.4] is assumed to be valid). The bulk is assumed to be of n-type behavior (in the case of p-type behavior the theory holds analogously). Therefore, the interface of regions I and II forms a pn-junction, while that of regions III and IV forms a high-low (hi-) junction. As explained by Gunn [3.5], the former junction may be made nearly impermeable to majority carriers, while remaining completely permeable to minority carriers, whereas the latter may be made the reverse (nearly impermeable to minority and permeable to majority carriers), and thus together they will lower the leakage current [3.6]. A reverse bias voltage which is applied will appear across the pn-junction. The potential drop across the hl-junction is negligible [3.5,3.6]; region II is the depleted (space-charge) part and region III the undepleted (quasi-neutral) part. WD represents the thickness of the depletionlayer, which is proportional to the square root of the applied bias voltage (Eq.(3.1.12) below). Wth stands for the thickness of the wafer (about 450 /mi).
In each region there is thermal generation of electron-hole pairs, which, when collected at the contacts (either by diffusion or drift), contributes to the total leakage current. This current can therefore be written as the sum of the currents of each separate region:
J = JY + Ju + J1U + 7I V. (3.1.3)
Region I is an undepleted (quasi-neutral) region. Its contribution to the leakage current is therefore determined by diffusion of the minority carriers in this region. When an infinite surface generation velocity, a constant doping profile and no degeneracy effects are assumed, the contribution of this region to the leakage current can be calculated as the standard solution of the current and continuity equations (the electron concentration at the edge of the depletion layer is taken to be zero, C = An/r, and L = v^Jr):
Jj = qül D (3 .L 4 )
N L tanh(H^L)
All coefficients are, of course, those of region I (for electrons).
In most cases it will be sufficient to use Eq.(3.1.4) for an estimate of the current contribution from region I. However, for very thin layers this equation will have too large a current, due to the assumption of an infinite surface generation velocity. In these cases the real value of this parameter has to be accounted for, or the equation might even be replaced by that of the Schottky barrier.
Region II is the depleted part of the diode. Usually, the generation rate is assumed to be the same over the entire layer [3.7]. This assumption can be used in a first approximation, but, as will be outlined in the next section, some caution must be exercised [3.1,3.8]. Still, when this assumption is applied, the current contribution of region II can be denoted as the standard (thermal) generation current [3.3,3.4,3.7]:
Jn = g^WD. (3.1.5)
rdepl
Like region I, regions III and IV are undepleted. So, once again the diffusion of the minority carriers (which are now holes) determines the contribution of these regions to the leakage current. Because of the different doping levels it is convenient to model the contributions of these regions independently. At the interface the continuity of the carrier concentration and current have to be introduced as boundary conditions. The interface is chosen to lie just on the lowly doped side. When the current contribution of the third region is modeled the continuity condition is fulfilled by
introducing an effective surface generation velocity SJJL defined by [3.3,3.4]
J(x0 = qLpfxOS^, (3.1.6)
where X; denotes the interface on the lowly doped side.
With this parameter region IV is modeled by (cf. Eq.(3.1.4)) [3.9]
>HL D N,
L tanh(H^L) WIV
III. (3.1.7)
Here W is the width of region IV and the coefficients are those for holes in region IV. Similar to region I, the surface generation velocity (at the metal contact) is taken to be infinite, as constant doping and no degeneracy are also assumed. Of course, these effects can be included in the model [3.10]; however, as will be shown below, the contributions of the first and the fourth region to the leakage current are negligible, and therefore no corrections for these effects have to be made.
When calculating the contribution to the leakage current of region III it is convenient to normalize the parameter S^.
SHL.norm = ^HL I 7 (3.1.8) Mil
Then the contribution of region III can be calculated by again solving the current and continuity equations (in fact, the contribution of region IV is included in this expression) [3.2,3.8]:
s i n h ( ^ ) + W o r mc c * h ( ^ )
C O S h ( ^ h _ D ) + SH L i n o r mS i n h ( _ Ü ! _ _ D )
where the coefficients are those for holes in region III and Ap(WD) is the
deviation of the hole concentration at the interface of regions II and III from its equilibrium value, which increases with increasing bias voltage from 0 up to its maximum
*P(WD) = - £ l . (3.1.10)
Nm
Table 3.1.2. Data [3.11] chosen to estimate the influence of regions I and IV on the leakage current.
Q = " i = NY =
A =
L, = W1 = #111 A l lAv
^ i n LI Vw
lv 1.6 1 0 "1 9C 1.5 1 01 0c m -3 1 01 8c m -3 2 10 cm /s 32 nm (T = 1 /is) 2 jum 1 10 cm i i n2 0 "3 1 10 cm = 12.5 cm /s = 2.0 cm2/s = 0.11 cm (r = 1 ms) 9 /zm (r = 0.4 /zs) = 2 /xm -Ji = 1.8 1 0 "1 2A / c m2W ™ =
8-
9 10"
7reduces to an expression similar to Eq.(3.1.4).
The contribution of region II is the most important one. Ju is on the order
of nanoamps per cm2 when rd e p l is about 1 ms. It can now be shown that the
contribution of region I is negligible so that high doping effects in this region do not have to be accounted for: As can be seen from the data in Table 3.1.2. (taken from [3.11]), the current from this region is on the order of picoamps per cm2.
The order of influence of the hl-junction can also be estimated with the aid of Table 3.1.2.: ^HL,norm *s about 10" , which is merely due to the large
ratio of N1U versus Nw (Eq.(3.1.7)). Therefore, it is not necessary to account
for high doping effects in this fourth region either.
Now the importance of the hl-junction can also be demonstrated. The n+-doping on the back side is not only necessary for a good ohmic contact
between the metal and the semiconductor, but also for reducing the leakage current part due to diffusion [3.6,3.8]. Because of the low effective surface generation velocity 5H L n o r m, the current contribution of region III will be
lowered, as can be seen' from Eq.(3.1.9). The effect, known in the field of solar cells as the Back Surface Field [3.6,3.10], is more pronounced for
