Single-grain Silicon Technology for Large Area X-ray Imaging

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Single-grain Silicon Technology

for Large Area X-ray Imaging

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Single-grain Silicon Technology for

Large Area X-ray Imaging

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus Prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op dinsdag 14 april 2015 om 10:00 uur

door

Aslıhan ARSLAN

Master of Science (M.Sc) in Electrical and Computer Engineering, Koç University, Turkey

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This dissertation has been approved by the promotor: Prof. dr. C. I. M. Beenakker and copromotor: Dr. R. Ishihara

Composition of the doctoral committee: Rector Magnificus

Prof. dr. C. I. M. Beenakker promotor Dr. R. Ishihara copromotor Independent members:

Prof. dr. E. Charbon EWI, TUDelft Prof. dr. ir. A. J. P. Theuwissen EWI, TUDelft

Prof. N. Teranishi Univ. of Hyogo and Shizuoka, Japan Dr. T. Poorter Philips Healthcare

Dr. ir. I. Peters Dalsa, Eindhoven

This research presented in this thesis was performed as a part of Hidralon project, which was financially supported by CATRENE.

Keywords:

Single grain PIN photodiodes, pulsed laser crystallization, flexible electronics, X-ray image sensor

ISBN: 978-94-6186-452-9

Copyright  2015 by Aslıhan ARSLAN,

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior written permission of the copyright owner.

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Chapter 1 Introduction

In this chapter, a novel single grain indirect X-ray image sensor is proposed after a brief background information is given in Chapter 1.1-1.3 about the requirements of the digital X-ray image sensors. The aim of the thesis is introduced in Chapter 1.4 and the outline is given in Chapter 1.5.

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1.1 History of X-ray Imaging

X-ray imaging starts with the discovery of X-rays by Röntgen in 1895. The first X-ray image was taken by him which was his wife’s hand wearing a ring, as shown in Figure 1.1(a). X-ray imaging can be simplified to a structure, as presented in Figure 1.1(b). X-ray beams pass through the object and the transmitted rays are collected at the image plane. The absorption of X-rays is dependent on the density of the object and its atomic number. For example, as the X-ray passes through the hand, it is attenuated in the bones more than the soft tissue. The metal ring absorbs even more X-rays; hence it is darker in the negative X-ray image.

X-ray generator Object Image plane (a) (b)

Figure 1.1: (a) Negative X-ray image of Bertha Röntgen’s hand, (b) simplified schematic of X-ray imaging.

In the beginning of analog imaging, photographic plates were located on the image plane and later photographic films were used instead. However, with the development of high quality digital detectors, analogue technology is replaced by digital radiography which has many advantages, such as wide dynamic range, image processing, better image quality, fast and real-time image acquisition and remote access [1].

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When X-ray imaging was first introduced, physicians had only a few tools for the diagnosis of diseases. Therefore, the clinical application of X-rays had a major impact in Western world. During its more than one hundred years of development, the image quality and the quantity of the diagnostic information have improved dramatically and allowed for the diagnosis of many diseases. However, the future of radiology not only depends on the technological development, but is also highly affected by economic and social influences. In fact, cost reduction is the main issue in the future of the clinical X-ray imaging. Cost efficient technologies with sufficient image quality will be more preferable than the ones with very high quality, but expensive [2].

1.2 Digital Radiography

Digital radiography systems basically convert the X-ray energy into digital signals using one of the two following conversion techniques. In direct conversion, a photoconductor material is used to capture the X-rays and generates charge carriers. Amorphous selenium (a-Se) is widely used as the photoconductor material as it has high X-ray absorption and high intrinsic spatial resolution [3]. When the photoconductor is exposed to X-rays, generated electron and holes are drawn directly to the X-ray charge collector and stored in a storage capacitor until the readout. Direct X-ray detectors have the advantage of low noise and high dynamic range, but they cannot detect hard X-rays (>20 keV) [4][5].

In indirect detection, which is depicted in Figure 1.2, a scintillator is used to convert the X-rays into visible light. The photons are then detected by the photodiode and the photo-generated carriers are collected by the detector. CsI as a scintillator material is an attractive choice for X-ray detection due to its high photon emission yield [6]. Its high density (4.53=g/cm3_{) and high effective}

atomic number (Z=54) provide high stopping power which enhances the conversion efficiency. CsI is resistant to thermal and mechanical shock [7]. In order to improve the luminescence efficiency, CsI is doped with impurity ions [8]. Na and TI doped CsI crystals are widely used. However, CsI(Na) scintillators are highly sensitive to moisture. They require special handling and integration conditions, and the scintillation performance degrades with the exposure under high humidity conditions. On the other hand CsI(TI) is more robust against humidity. Moreover, its overall light output is higher than CsI(Na) [9]. Light yield [photons/MeV] of CsI(Tl), CsI(Na) and undoped-CsI are 52-56x103_{, 38-44x10}3_{and 2x10}3_{, respectively [10]. CsI(TI) is grown in a}

columnar structure and has an emission peak at 550 nm. The micro-columnar structure of CsI(TI) works as waveguides. Photons are guided by the columnar structure of this scintillator. Thus, lateral spreading is reduced significantly

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which decreases the width of the point spread function and enables high spatial resolution without a loss of photons in thick scintillator layers. In [11], it has been shown that 20% of the MTF (modulation transfer function) value of the CsI(TI) film with a columnar structure is 6.5 lp/mm.

Detector

Scintillator

X-Ray

Figure 1.2: Schematic of indirect X-ray imaging.

1.3 Large Area Indirect X-ray Image Sensors

Two main X-ray detector technologies are used in indirect digital radiography; charge coupled devices (CCD) and CMOS. In comparison to CCD, CMOS image sensors have disadvantages such as low fill factor, low uniformity, high noise and image lag [12]. On the other hand, low power consumption and the processing compatibility of CMOS detectors are more convenient for X-ray detection [13], [14].

1.3.1 a-Si Flat Panel Imagers

In many medical applications of X-ray image sensors which require large area detection, such as mammography and chest radiography [15], a-Si thin film transistor (TFT) flat panel imagers based on passive pixel sensors (PPS) are used. Figure 1.3 shows a schematic diagram of a-Si imaging PPS pixels. A passive pixel has a photodiode and a transistor switch. In this architecture, row drivers address the gate lines sequentially to enable each row of TFTs and vertical lines carry the bias voltage. Datalines are connected to the charge

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amplifiers. Then, the signal is multiplexed onto the external analog-to-digital amplifier (ADC). Bias line Gate line D ata lin e

Charge amplifiers ADC

Row

dri

ve

rs

Figure 1.3: Array of a-Si PPS pixels.

Hydrogenated amorphous silicon (a-Si:H) is one of the first materials in the fabrication of TFTs with many benefits, such as low cost and a possibility for large area deposition. The main advantage of a-Si:H is the low temperature processing (200-250°C) [16]. Therefore, it is convenient for large-area glass substrates. a-Si:H TFTs meet the electrical requirements of LCD technology, yet a-Si:H TFTs are not sufficient for fast electronics applications due to its low electron mobility (< 1 cm2_{/Vs). Poly-silicon offers higher mobility and replaces}

a-Si for high quality display applications. Poly-silicon films can be produced either by high temperature (>600°C) deposition or by re-crystallization methods. Direct deposition of poly-silicon is cost-efficient. However, the film quality is low due to a high defect rate. In the phase transformation method, a-Si layer is crystallized to poly-Si by different methods [17][18][19]. Although bigger grains can be obtained, the grain boundaries are random. At the grain boundaries there are dangling bonds that trap the carriers and reduce the electrical performance of the devices.

1.3.2 CMOS-based APS Imagers

CMOS-based active imagers have many advantages in comparison to passive pixel a-Si flat panel X-ray imagers. It is known that the carrier mobility of single crystalline silicon (c-Si) is much higher than amorphous and polycrystalline silicon. The electron and hole mobility of c-Si are 1400 cm2_/Vs

and 480 cm2_{/Vs, respectively [20]. These values decrease to 1 cm}2_{/Vs and 0.005}

cm2_{/Vs for a-Si. Thus, the higher readout speed is the main advantage of the}

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CMOS imagers over a-Si imagers. The higher mobility of c-Si imagers also enables a smaller transistor size and the pixel size is much smaller in comparison to a-Si imagers. The minimum CMOS pixel size can be less than 3 µm while it is limited to 50 µm for a-Si imagers [20]. The size of the readout and drive electronics is reduced by designing smaller transistors. This allows for the integration of A/D converters in the pixel while passive pixel a-Si imagers have to be connected to the converters externally. a-Si flat panel imagers can also be designed in active pixel arrays [21]. However, despite the dataline noise is reduced, the instability of the in-pixel amplifier is a considerable problem for the imager. In addition, due to additional electronic components in the pixel, the pixel size increases and the fill factor reduces.

However, despite its advantages, CMOS imagers also have disadvantages over a-Si imagers. One of the main issues is the imager size. The size of the c-Si wafers is limited by the wafer size which is 300 mm currently. Thus, tiling is necessary for large area image sensor applications [22]. For example, a mammography imager size is ~24 cm x 18 cm [5][23], which is larger than a square shape imager cut from a 300 mm wafer. CMOS is an expensive technology due to the cost of a single crystalline silicon wafer and its processing. The cost of a larger wafer processing is even higher. When the single imagers are tiled, the price increases because of the expensive processing and also the yield reduces. In addition to the cost, the process of tiling is also a major concern. When each imager is tiled, there must be edges without electrical connections. The schematic of a DALSA imager is shown in Figure 1.4. This architecture enables extending one direction but the other direction is not possible (three sides butt-able) [24]. Tiling requires very precise alignment and at the attachments, the imaging lines can be lost. DALSA merged the row-driver into the pixel array to minimalize the gap between the arrays. However, this decreased the fill factor from 82% to 62%-74%. As an alternative, Suntharalingam [25] presented another method of tiling using 3D integration via bump bonding for back side illuminated imagers. This method enables increasing the fill factor, but, it also further increases the process complexity of imagers with large area and the cost. On the other hand, a-Si can be deposited on large area substrates and the imager size is not a limitation for a-Si image sensors [26].

Another disadvantage of c-Si is that the absorption coefficient of c-Si is more than 10 times less than a-Si at 550 nm [27]. In the indirect X-ray image sensor pixel, the photodiode should read the emission spectrum of the scintillator for the highest yield. The absorption layer of the c-Si photodiode must be thicker than a-Si at 550 nm to use a CsI(TI) scintillator and this increases the complexity of the pixel fabrication.

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Figure 1.4: CMOS tiling; three sides butt-able [24]

1.3.3 A New Approach: SG Technology

Electrical performance of a-Si is improved by single grain TFT technology which makes it a good candidate for large area flat panel X-ray imagers. Electron and hole mobility of the SG-TFT are 600 cm2_{/Vs and 200 cm}2_/Vs,

respectively [28]. The μ-Czochralski process has been developed in TUDelft [29][30] and enables 2D location-control of single grain using pulsed excimer laser crystallization of a-Si. The location of the grains is controlled by a mask. Therefore, the active area of the devices can be accurately positioned within the grains, avoiding the grain boundaries. As seen in Figure 1.5 random grain boundaries are only at the edge of the grains. Inside the grains, the only defects are the planar coincidence site lattice grain boundaries (CSL-GBs). Dominantly, Σ3, Σ9 and Σ27 CSL boundaries are formed. Their electrical activity is much smaller than random grain boundaries [31], [32].

Single grain technology also allows monolithic integration of the SG-lateral PIN photodiode and does not require any external drive electronics. Readout electronics and lateral PIN photodiodes are fabricated in the same process. PIN photodiodes are operated at reverse bias and since the width of the intrinsic region does not change, the junction capacitance is independent of the bias voltage. By increasing the width of the intrinsic region, the junction capacitance can be reduced to obtain high speed photodiodes, while at the same time the size of the light sensitive area increases. Furthermore, PIN photodiodes have low leakage current (1-10nA). These photodiodes are primarily suitable for the detection of the low wavelengths (<400 nm). SG-lateral PIN photodiodes are presented in [33],[34]. It was reported in [34] that 250 nm-thick lateral single grain PIN photodiodes have maximum absorption at 310 nm. The quantum

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efficiency (QE) of the photodiode at this wavelength is 60%, but, QE decreases to 15% in visible wavelengths. Because of the many mentioned advantages, in this study a CsI(TI) scintillator is planned to be used which has an emission peak at 550 nm. However, thin SG-photodiodes were not suitable for CsI(TI) integration; therefore, SG technology must be used to crystallize a thick silicon layer for deep-depletion photodiodes.

Figure 1.5: Top view of SG-TFT designed inside the grains. Only CSL-GBs are formed inside the grains.

Single grain technology also offers the ability to develop a flexible X-ray image sensor. Image resolution increases by wrapping the image sensor around the part or object under examination due to a closer inspection. Moreover, for dental X-ray imaging, there is an increasing demand of flexible, user friendly and fast sensors with good image quality [35]. However, there are some challenges in the fabrication of the devices on flexible substrates. Fabrication-induced stress causes bending and curling of the released layers and that causes difficulty for handling. During the transfer and gluing to a flexible substrate, the released layer should be kept smooth and air paths should be avoided. Yet, the major problem in the processing of the flexible electronics is that the process temperature is usually limited to 450ºC. Thus, LPCVD materials cannot be used in manufacturing the device layer. This limitation is resolved by the single grain technology by using the sputtered silicon which is deposited at 100°C [28]. SG technology was first applied to flexible TFTs by Zhang et al. In that work, only die-level devices were fabricated and transferred by mechanical peeling off which introduces stress. The effect of the stress on the electrical performance of the transistors is reported in [36], [37]. However, the processing and transferring of the flexible SG-photodiodes must also be investigated for the proposed flexible X-ray image sensor, especially to prevent the degradation of the photodiode dark current and the light on-off ratio.

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1.4 Aim of This Dissertation

In this thesis, single grain TFT technology is proposed for a novel large area X-ray image sensor. The main advantage of SG imagers over c-Si imagers is the fact that there is no size limitation and tiling is not needed. a-Si can be deposited and crystallized using the μ-Czochralski process on large area substrates. This significantly reduces the process complexity and imager cost. In addition, as stated in Chapter 1.3, the electrical performance of the single grain TFTs is much higher than in case of a-Si and poly-Si TFTs and is comparable to c-Si.

Photodiode Capacitor Readout ADC Scintillator Polyimide SiO2 Crystallized sputtered Si X-rays

Figure 1.6: Schematic of a flexible single-grain X-ray image sensor.

One of the aims of this work is to investigate the deep-depletion photodiodes in order to increase the QE of the photodiodes at 550 nm for optimum use of a CsI(TI) scintillator and then to monolithically integrate the photodiodes with the SG-TFT readout. Firstly the thickness of the crystallized silicon layer must be increased. An excimer laser and a green laser are used in the numerical analysis and in the experiments to compare the effects of the crystallization parameters. Secondly the doping depth of the SG-lateral PIN photodiodes must be increased. The photodiodes are integrated with the pixel electronics using a modified 3T-APS structure. A capacitor is added to each pixel. This structure enables sampling the column signal at any time during the exposure and store the signal. Using the single grain technology, the capacitor can be monolithically integrated in the same fabrication process without adding any

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process complexity. Since the data can be stored in the pixel using the sampling capacitor, an in-pixel ADC can also be integrated. Therefore, it is promising for a future single grain X-ray image sensor with digital pixels which offers many advantages, such as fast readout and high dynamic range while achieving large area detection thanks to the single grain technology.

Another aim of this thesis is to develop flexible lateral PIN photodiodes for a novel X-ray imaging system using the single grain technology (Figure 1.6). Release and transfer of the flexible photodiodes are investigated using two methods. The first method only uses polyimide as the sacrificial layer and that allows only die-level release and transfer as reported in [36], [37]. For the large area flexible electronics, a water assisted releasing technique is proposed by introducing a nickel layer which enables wafer-size release and transfer.

1.5 Outline

Chapter 2 discusses thick silicon crystallization with large grain formation for

lateral PIN photodiodes using excimer and green laser sources. The heat transfer simulations of the pulsed laser crystallization and experimental results are analyzed in this chapter.

In Chapter 3, thick SG-lateral PIN photodiodes are introduced. It is shown that by the deeper photodiode depletion region, the quantum efficiency at 550 nm is substantially improved. SNR, dark current and the light on/off ratio of the photodiodes are compared with respect to the design and fabrication parameters. Flexible lateral PIN photodiodes are presented in Chapter 4. Devices are fabricated directly on flexible substrates using the µ-Czochralski process. Silicon sputtered at 100°C is used as the device layer instead of LPCVD silicon due to the low temperature budget of the process. Two different techniques are evaluated for releasing. The details of the sputtered silicon crystallization experiments and releasing methods are discussed.

In Chapter 5, the integration of the SG-lateral PIN photodiodes and pixel electronics is shown. Each component of the pixel is characterized and the results are reported. Transient light response of the pixel is measured at readout, sampling and ADC outputs.

Finally in Chapter 6, the key conclusions of the thesis and the recommendations for the future work are given.

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Chapter 2 Laser Crystallization of Thick Si Film

with the μ-Czochralski Process

This chapter introduces a detailed analysis of thick silicon film crystallization for the SG-lateral PIN photodiodes that were explained briefly in Chapter 1. A pulsed excimer laser and a green laser are used for the crystallization and process parameters are investigated experimentally and numerically. First, single grain formation details are given. In the following section, the material constants and heat diffusion method are explained to understand the thick silicon film crystallization simulations better. The excimer laser and the green laser operate at 308 nm and 515 nm, respectively. The effects of the wavelength and the pulse duration are analyzed using COMSOL Multiphysics simulation tool. Pulse duration is varied in green laser experiments and the results agree with the numerical analysis. In the last part, the thermal behavior of the thick layer is evaluated by Raman spectroscopy and excimer laser experiments are analyzed in order to understand the stress factors which cause the cracks in the film.

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2.1 Introduction

In the previous work [1], a 250 nm-thick a-Si layer was crystallized for lateral PIN photodiodes using an XeCl excimer laser (308 nm) and the μ-Czochralski process. 6 μm Si grains were obtained at predetermined positions and the intrinsic area of the devices is placed inside the grains. However, it is known that, with a thin crystallized layer, only short wavelengths can be absorbed. Thus, the silicon thickness had to be increased in order to increase the depletion depth of the prospective photodiodes which are explained in detail in Chapter 3. In this chapter, in addition to the XeCl excimer laser, a green laser (515 nm) is introduced for the thick silicon layer crystallization to compare the effects of the source wavelength. The green laser also offers a maximum pulse duration of 1200 ns which allows us to understand the effects of the long pulse duration experimentally.

2.2 Single Grain Formation

Grain formation steps are shown in Figure 2.1. First a 100 mm Si-wafer is thermally oxidized and 1 μm x 1 μm size cavities are patterned in a 750 nm-thick-SiO2 layer (a). The cavity diameter is reduced to 100 nm by depositing

850 nm SiO2 by tetraethyl orthosilicate (TEOS) using plasma-enhanced

chemical vapor deposition (PECVD) at 350ºC (b). After defining the cavities, which later serve as the grain filter, amorphous silicon is deposited by low-pressure plasma chemical vapor deposition (LPCVD) and it fills the grain filters (c). The position and pitch of the grain filters defines the position and the size of the grains. Next, the wafer is crystallized with the pulsed excimer laser (d). Upon laser irradiation of the a-Si layer, crystallization occurs from the grain filter locations forming location-controlled Si grains.

Substrate SiO2 a-Si (a) Substrate SiO₂ Grain Filter Substrate SiO2 1 μm (c) GF mask Substrate SiO2 a-Si (d) Excimer Laser (308 nm) (b)

Figure 2.1: Fabrication steps of single grains with the μ-Czochralski process.

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Laser radiation is absorbed only at the surface, yet due to the propagation of the melt front through the depth of the silicon, thicker layers can be melted, as well. During laser radiation, the layer fully melts. However, as seen in Figure 2.2, since the cavity is deep, a very small amount of silicon stays solid at the bottom of the cavity. This solid silicon acts as a seed and guides the crystal growth during the solidification.

GF

Figure 2.2: Schematic view of the μ-Czochralski process.

Figure 2.3: (a) Microscope picture of a crystallized silicon layer with incomplete grains (b) an SEM image of single grains.

In order to achieve high device performance, the active area of the devices should be inside the grains avoiding the grain boundaries. Grain size is mainly defined by the pitch of the holes in the grain filter mask. However, the grains reach their full size only if the laser energy density is sufficiently high. Thus, during the crystallization, first the required energy density is tested for the expected grain size. Figure 2.3(a) shows a crystallized layer after excimer laser exposure. In this experiment, the grain filter mask is designed for 6 μm grains.

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However, lateral growth of the grains is not complete and grains did not reach their full size. The SEM image in Figure 2.3(b) shows an example of single grains which reach the maximum grain size. The crystallization energy of a silicon layer with a certain thickness also depends on laser pulse duration as outlined below.

2.3 Thick Silicon Layer Crystallization

Here, the crystallization of the thick silicon layer is discussed according to the variations of three process parameters; pulse wavelength, pulse duration and substrate temperature. The silicon substrate thickness is 525 ±15 µm.

Pulse Wavelength

Absorption coefficient (α) of silicon varies inversely with the pulse wavelength (λ). The excimer laser operates at 308 nm resulting in a small absorption length (δ) in silicon. Therefore, for thick films, different sources have to be considered. In [2], absorption coefficient values of silicon is given as a function of the source wavelength at room temperature. Longer wavelengths help increasing the absorption depth (δ) as given in Eq.2.1. Thus, the green laser with a 515 nm wavelength has an advantage in the thick silicon crystallization process compared to the excimer laser. The effect of the crystallization wavelength is analyzed only numerically using the COMSOL Multiphysics simulation tool and the results are reported in Chapter 2.5.

1 ( )

δ =

α λ

2.1

Pulse Duration

The crystallization of thick silicon layers is significantly more difficult than that of thin layers. Thick layers require higher laser energy density and this brings an ablation risk. Therefore, the ablation threshold energy density must be enhanced to prevent extreme surface heating before complete melting and crystallization. In case of long pulse duration, heat is deposited into the layer slower than in the case of short pulses and prevents ablation. There are different methods for recrystallization with long pulses, such as Xenon flash lamp annealing or solid phase crystallization with rapid thermal annealing (RTA) [3][4]. However, these methods have pulse durations from tens of microseconds to seconds, and so they may introduce severe thermal damage to the underlying substrate due to long heat diffusion length (Figure 2.4). A green laser with the maximum pulse

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duration of 1200 ns is a more convenient source for crystallization of thick silicon.

The heat diffusion length [m] in the material is calculated by [5]

L T

L

=

2 κτ

2.2

κ [m2_{/s] is the thermal diffusivity which is the ratio of the heat conducted}

through the material to the heat stored per unit volume. τL[s] is the duration of

the laser pulse.

nm μm mm

Heat diffusion

10 ns 100 ns 10 μs 100 μs 10 ms 100 ms

Excimer Laser

Green Laser Xenon flash lamp RTA

Pulse duration

Figure 2.4: Annealing methods with different heat diffusion lengths.

The effect of the laser pulse duration is analyzed both numerically and experimentally. The green laser pulse duration can be varied from 300 ns to 1200 ns. It is used as the source in the simulations and the results are used as a reference to the experiments. In the simulations, the short and the long pulse duration comparison is made using 25 ns and 250 ns pulses. Although the simulated pulse durations are shorter than the values used in the experiments (due to computational reasons), the variation from 25 ns to 250 ns is already adequate to analyze the pulse duration effect, as it is seen in the results reported in Chapter 2.6.

Substrate Temperature

Another challenge in thick silicon crystallization is the thermal stress. Tensile stress mainly originates from the difference between the deposition temperatures of the film and the substrate, but it must be noted that in this case the crystallization temperature has a considerable additional effect in causing thermal stress. Experiments are done with different film thicknesses using only the excimer laser that has a sample holder heating system. Thermal stress is discussed in Chapter 2.7.

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2.4 Simulations

2.4.1 Heat Diffusion Method

Transient temperature profiles of the thick silicon annealing are by the heat diffusion method. In the model, only transient conduction is analyzed. Annealing is done under vacuum; therefore, convectional heat transfer is neglected. Another form of the heat loss during the annealing process is radiation. When the surface is heated up by the laser, thermal radiation is emitted from the silicon to the chamber. This loss is negligible compared to downward diffusion and the surface cooling is over 15 orders smaller than the heating of the laser pulse [6]. Thus, the radiation component can be omitted from the model, as well.

The Fourier’s conduction equation [7] is given in Eq.2.3. T is the transient temperature of the material, k is the thermal conductivity, ρ is the material density, cp is the specific heat capacity and Q [W/m3] is the heat source.

p p

c

Q

c

T

k

dt

dT

ρ

+

∇

=

(

)

2.3 In these simulations, the heat source is the laser pulse and calculated by [8]:

Q (x,t)= (1-Rsurface)ElaserPulse(t)αexp(-αx) 2.4

Rsurface is the reflectivity, Pulse(t) [s-1] is the laser pulse profile, α [m-1] is the

material absorption coefficient, E [J/m2_{] is the energy density of the source}

laser.

2.4.2 Material Properties and Expressions

The 2D simulation model is illustrated in Figure 2.5. The thickness of the a-Si layer is varied and SiO2 thickness is kept constant. As seen in the figure, the

grain filter (GF) is defined as a 100 nm wide trench buried in the oxide layer. Material properties of the silicon substrate and the SiO2 are chosen from the

COMSOL library. Material and thermodynamic constants of the a-Si, c-Si and liquid-Si layers are shown in Table 2.1 and Table 2.2. Thermal conductivity and specific heat capacity are taken from [9]–[12]. The absorption coefficient and reflectivity of the surface are wavelength and phase dependent constants. Therefore, excimer laser (308 nm) and green laser (515 nm) have a different absorption depth in the silicon layer [2]. In the simulations presented in this

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chapter, the initial layer is a-Si. When the laser pulse is applied as the source, silicon melts at 1420ºK and depending on the absorption length of the laser radiation a certain depth of the surface is melted. At this depth, the simulation model takes the phase change into account for the respective wavelength and applies the constants of the liquid phase.

During the melting and solidification of the layer, heat is absorbed and released but the temperature does not change. Thus, latent heat is also taken into account. Without this component, the model would increase the layer temperature regardless of the phase change and drastically deviate from the result.

a-Si SiO₂ Substrate GF GF a-Si SiO₂ Substrate a-Si SiO₂ Substrate GF GF

Figure 2.5: The geometry of the structure used in the COMSOL finite element simulation.

During the crystallization process, the wafer is placed on a specific holder that could be kept at room temperature or heated up to 450ºC. The holder temperature is defined as the boundary condition in the simulation. The bottom of the modeled structure is set to a constant temperature.

Table 2.1 Absorption coefficient and reflectivity values of silicon for excimer and green laser. Material 308 nm 515 nm α [cm-1_] a-Si _c-Si liquid-Si 1.5x106 1.5x106 1.63x106 2x105 8x103 1x106 R a-Si c-Si liquid-Si 0.52 0.6 0.7 0.35 0.4 0.7 21

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Table 2.2 Main thermodynamic properties of silicon.

Mass density ρ [kg/m3_] a-Si _c-Si liquid-Si

2250 2330 2520

Melting point (°K) a-Si _c-Si 1420 ₁₆₈₇

Latent heat (J/kg) a-Si _c-Si 1.32x10_1.79x1066

2.5 Wavelength Dependence of Pulsed Laser Crystallization

The effect of the source wavelength is analyzed using the COMSOL simulation tool for a 1.5 μm thick a-Si layer. In the first simulation, the excimer laser and in the second, the green laser source is used. A pulse duration of 25 ns and an energy density of 2000 mJ/cm2_{are applied to the a-Si film. The substrate}

temperature is set to 300 ºK.

Simulation results are shown in Figure 2.6 with the top hat laser beam. The transient temperature change of the silicon layer is plotted at varying depths with intervals of 100 nm from the surface on.

Surf 800 nm 900 nm 1 µm 1.1 µm 1.2 µm 1.4 µm 1.4 µm 1.5 µm Melting point Pulse=25 ns (a) 22

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Surf 800 nm 900 nm 1 µm 1.1 µm 1.2 µm 1.4 µm 1.4 µm 1.5 µm Melting point Pulse=25 ns (b)

Figure 2.6: Heat transfer simulation results of 1.5 μm thick silicon layer annealed using (a) the excimer laser and (b) the green laser. Energy density of 2000 mJ/cm2_{is applied} at room temperature. The pulse duration is 25 ns. The temperature is evaluated at the surface (Surf) and at the varying depths.

With the excimer laser, the model shows that 1.1 μm depth could be melted. However, the temperature at deeper layers could not reach the melting temperature of a-Si. At 1.2 μm depth only a temperature of 480 ºK could be reached. In the second simulation, under the same conditions, the green laser is used as the heat source. As seen in the figure, the green laser could heat up the layer to 1050 ºK at 1.2 μm depth. Transient analysis also shows that the green laser reaches a deeper layer than the excimer laser in the same time scale.

2.6 Effects of the Laser Pulse Duration

Thicker layers require higher energy density to melt, but at such high values the surface temperature increases drastically and results in ablation before full layer melting. Ablation threshold energy density (Ev) increases with a longer pulse

duration [13]; therefore, in general, longer pulse duration also helps in increasing the maximum melt depth. With the long pulse, despite the same amount of heat is deposited to the layer as in short pulse crystallization, the grain size increases with the pulse duration since the heat transfer is longer [14].

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As is proven in [13] with Raman spectroscopy, crystallinity within the grain improves with the pulse duration, as well.

To compare the effect of short and long pulse durations in pulsed laser crystallization, first heat transfer simulations are done using COMSOL Multiphysics tool and then crystallization is analyzed experimentally using the green laser source.

2.6.1 Simulations

In the simulations, the thickness of the sample a-Si layer is 850 nm and the material constants are selected from Table 2.1 and Table 2.2. 25 ns and 250 ns laser pulses with energy density of 2000 mJ/cm2_{are compared in the}

simulations and results are shown in Figure 2.7 for various depths. The top hat laser beam is shown on the plots. As seen in Figure 2.7(a), with 25 ns pulse duration, the whole layer completely melts. However, the surface temperature reaches the ablation threshold before the full layer melts. On the other hand, with the 250 ns pulse (Figure 2.7(b)), again the 850 nm-thick layer melts completely yet the surface temperature is in a safe range where ablation (ablation temperature is ~3000 °K) is prevented.

Surf 100 nm 200 nm 300 nm 400 nm 500 nm 600 nm 700 nm 800 nm Pulse= 25 ns Melting point (a) 24

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Surf 100 nm 200 nm 300 nm 400 nm 500 nm 600 nm 700 nm 800 nm Melting point Pulse=250 ns (b)

Figure 2.7: Heat transfer simulation results of 850 nm thick silicon layer with the green laser source for pulse duration of (a) 25 ns and (b) 250 ns. Energy density of 2000 mJ/cm2_{is applied at room temperature. The temperature is evaluated at the surface} (Surf) and at the varying depths.

2.6.2 Experiments

In the experiments, in order to crystallize a 1 μm thick a-Si layer for large grain formation, a green laser (Yb:YAG Laser Jenlas®_{Asama) is used (Innovavent}

GmbH) [15]. The green laser system specifications are shown in Table 2.3.

Table 2.3 Yb:YAG green laser specifications.

Wavelength 515 nm

Pulse duration 250 ns-1200 ns

Max energy density 6 J/cm2

Beam width (FWHM) 30 μm

Beam length 2 mm

Process temperature 25°C

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The pulsed green laser has an adjustable pulse duration and in the crystallization experiments of the 1 μm thick silicon layer, 300 ns and 1200 ns pulse durations are used. x-y profile of the green laser beam is shown in Figure 2.8. The system optics create a laser line on the wafer with a length of 2 mm with top-hat intensity profile and a Gaussian profile of width of 30 μm full-width-half-maximum (FWHM). FWHM=30 µm y= 2 m m Grain filter

Figure 2.8: x-y axis profile of the green laser beam

Required crystallization energy density and ablation threshold are investigated for these two pulse durations. Two masks are prepared with 4 μm-8 μm and 9 μm-14 μm grain filter pitch. In the experimental results, reported grain size is equal to the corresponding grain filter pitch.

For the first experiment, pulse duration of 300 ns is used. Experiments start with 2000 mJ/cm2 _{and the energy density is increased up to 5800 mJ/cm}2_{. It is found}

that crystallization started at 3500 mJ/cm2 _{and 14 μm grains are formed at 3800}

mJ/cm2_{. The microscope pictures of the 300 ns crystallization experiments are}

shown in Figure 2.9. The ablation started to occur at 5000 mJ/cm2_.

As seen in the figure, 4 μm-10 μm size grains are in a square shape. However, when the grain filter pitch is larger than 10 μm, the laser beam line (Figure 2.8) can cover the grain filters only in the y-direction while the width of the beam (FWHM=30 μm) is not sufficient to cover the adjacent grain filters in the x-direction. Therefore, while the grain size reached to 10 μm in the y-direction; it could only reach to its half size in the x-direction. In the figure, the dark sports are the hillocks created by adjacent grains. The grain filter (GF) and hillocks locations are shown in Figure 2.9(g).

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Hillock

Figure 2.9: Green laser crystallization results with pulse duration of 300 ns at room temperature. The grain size is (a) 4 μm (b) 6 μm (c) 8 μm (d) 10 μm (e) 12 μm (f) 14 μm and (g) zoom image of 4 μm size grains showing the GF and the hillocks.

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Figure 2.10: Green laser crystallization results with pulse duration of 1200 ns at room temperature. The grain size is (a) 4 μm (b) 6 μm (c) 8 μm (d) 10 μm (e) 12 μm (f) 14 μm.

Figure 2.11: The ablation in 1 μm thick layer after exposed to pulsed green laser beam with pulse duration of 1200 ns and energy density of 6400 mJ/cm2_{at room temperature.}

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For the second experiment, a pulse duration of 1200 ns is used. Experiments again started with 2000 mJ/cm2 _{and the energy density is increased in steps of}

200 mJ/cm2_{up to 6800 mJ/cm}2_{. It is found that crystallization started at 4300}

mJ/cm2 _{and 14 μm grains are formed at 4500 mJ/cm}2_{. Crystallized layers with}

different grain sizes are shown in Figure 2.10. The ablation threshold is found to be at 6400 mJ/cm2_{. The ablated layer is presented in Figure 2.11. The results of}

the long pulse experiments are summarized Figure 2.12 and Table 2.4.

In Figure 2.12, the grain sizes are marked with respect to the corresponding laser energy density (ED). Maximum grain size is 14 μm for both 300 ns and 1200 ns green laser experiments. The layer still had capacity to store higher amount of heat before the ablation. Thus, by increasing the laser fluence to a value below the ablation threshold, larger grains can be obtained with a new grain filter mask with a grain pitch >14 μm. It must be noted that, the grain size cannot be larger than the pre-defined grain filter pitch no matter how much the applied laser fluence is. As explained herein, the spot size of the green laser source must be enlarged as well to achieve larger grains.

4 6 8 10 12 14 16 18 20 3400 3900 4400 4900 5400 5900 6400 6900 Gr ain S iz e [u m ] ED [mJ/cm^2] 300 ns 1200 ns Ablation

for 300 ns Ablation for 1200 ns

Figure 2.12: Grain size vs. energy density of 1 μm thick layer.

Table 2.4 Grain size and ablation ED values for 300 ns and 1200 ns green laser crystallization experiments.

300 ns 1200 ns

Max. Grain Size [μm] 14 14

Ablation ED [mJ/cm2_] ₅₀₀₀ ₆₄₀₀

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An SEM image is shown in Figure 2.13 which confirms that with 30 μm FWHM green laser beam, single grain is formed from pre-determined position of the grain-filter and the size of the grain both in the x and y directions reaches 8 μm. Electron back-scattering diffraction (EBSD) images are shown in Figure 2.14. Inverse pole figures and image quality maps show that inside the grains there are no random grain boundaries. The boundaries are predominantly Σ3 and slightly Σ27 and Σ9 CSL-GBs, which are marked in yellow, red and pink colors on the EBSD image, respectively.

Figure 2.13: SEM picture of 1 μm-thick 8 μm single grains crystallized by the green laser at room temperature using 300 ns pulse duration with energy density of 3700 mJ/cm2_.

Figure 2.14: EBSD mapping of 1 μm-thick 8 μm single grains crystallized by the green laser at room temperature using 300 ns pulse duration with energy density of 3700 mJ/cm2_{. Σ3 (yellow), Σ27 (red) and Σ9 (pink) CSL-GBs inside the 8um single grain.}

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2.7 Thermal Stress Evaluation and Crack Prevention

Thermal stress results from the difference between the thermal expansion coefficients of the film and the substrate. The thermal stress can be calculated by [16] f th f s p

E

(

) T

1 y

s = s − s ∆

−

2.5 where σf and σs are the average thermal expansion coefficient of the film and

the substrate, respectively. ΔT is the difference between the deposition temperature and the measurement temperature which is room temperature in this case. Ef is the elastic (Young’s) modulus of the film and yp is the Poisson’s

ratio [16].

It is known that, for the crystallized thin films, the observed thermal stress originates not only from the deposition, but also from the laser crystallization. Excimer laser crystallization introduces a tensile stress due to the difference between the thermal expansion coefficient of silicon and the underlying barrier layer and the difference between the film crystallization temperature and the substrate temperature [17]. Substrate temperature (backside) is defined by the temperature of the wafer holder.

480 500 520 540 560 0 0.2 0.4 0.6 0.8 1 1.2 Raman shift [cm-1] N or m al iz ed r am an i nt ens ity 1000 nm 850 nm 3.4 cm-1

Figure 2.15: Raman spectroscopy of 1000 nm and 850 nm thick silicon substrates after pulsed excimer laser crystallization.

For the stress evaluation, two samples are prepared for Raman spectroscopy measurements. 1000 nm and 850 nm-thick samples are fully crystallized and the Raman spectrum is shown Figure 2.15. After excimer laser, single grains are

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formed in a 1000 nm thick layer. Raman peak of this layer is at 520 cm-1 _which

agrees with the Raman band of the crystalline silicon [18]. The layer had cracks and as it is also understood from the Raman spectrum; tensile stress of the crystallized film is released by these cracks; therefore, Raman shift matches with the peak of the crystalline silicon (520 cm-1_{). On the other hand, the}

difference between the Raman shift of the c-Si and Raman shift of a single grain in a 850 nm-thick crack free layer is 3.4 cm-1_.

60 µm 60 µm

Figure 2.16: Results of the excimer laser thick silicon crystallization experiments. Microscope picture of (a) 1.4 μm thick silicon layer at 25 °C with pulse duration of 25 ns, (b) 1.15 μm thick silicon layer at 25°C with pulse duration of 25 ns. SEM image of (c) 1 μm thick silicon layer at 450°C with pulse duration of 250 ns, (d) 850 nm thick silicon layer at 450°C with pulse duration of 250 ns.

To investigate the effects of the crystallization temperature on stress, further experiments are conducted with the excimer laser at the substrate temperatures of 25ºC and at 450ºC. Experiments started with 1.4 μm thick a-Si layer at 25ºC with 25 ns pulse. As seen in Figure 2.16(a), already before grain formation, the layer peels off with energy density less than 3000 mJ/cm2_{and the exposed parts}

of the substrate became unusable. Again with pulse duration of 25 ns, at the 32

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same wafer holder temperature, the same energy densities are applied to a 1.15 μm thick layer. As shown in Figure 2.16(b), the layer does not peel off but still has cracks due to the high thermal stress before crystallization starts. 1.4 μm and 1.15 μm thick layer crystallization is not successful. In another experiment, 1 μm thick LPCVD a-Si is deposited. For this layer, the wafer holder temperature is increased to 450°C and pulse duration is increased to 250 ns by the pulse expender. The pulse extender extends the pulse up to 8 pulses without distortion or loss of coherence in order to extend the pulse duration. The layer is exposed to laser energy densities from 1500 mJ/cm2 _{up to 4700 mJ/cm}2_{. The}

layer is fully crystallized at 3600 mJ/cm2_{and 6 μm grains are formed (Figure}

2.16(c)) However, the layer still has cracks when investigated under SEM. For larger grains, higher energy density has to be applied to the layer. Yet, the ablation threshold of the layer is found to be 4000 mJ/cm2_{. The process window}

is very narrow due to agglomeration. The substrate is already heated to 450 °C to prevent cracks and peel off by means of stress reduction. Thus, in order to enhance the grain size, the layer thickness is decreased to 850 nm under the same conditions used in the 1 μm thick layer crystallization experiment, 8 μm grains are obtained in crack-free crystallized layer (Figure 2.16(d)). This crystallized layer later is used for the lateral PIN photodiodes which are explained in Chapter 3.

2.8 Conclusions

In order to increase the depletion depth of the lateral PIN photodiodes, the thickness of the intrinsic region should be increased. In this chapter, thick silicon film crystallization is analyzed using pulsed excimer and green laser sources.

First the effect of the pulse wavelength is investigated using COMSOL simulation tool. Green laser with 515 nm emission wavelength has longer absorption depth than excimer laser (308 nm). In the simulations, it is proven that the green laser melts a deeper layer than the excimer laser when the same laser energy density is used as the source.

Thick layers need a higher amount of heat for complete melt. If the crystallization energy is higher than the ablation threshold, the layer cannot be crystallized due to rapid surface ablation. It has been proven numerically and experimentally that, the green laser enhances the ablation threshold with its long pulse duration. 1 μm thick a-Si layer is crystallized with 300 ns and 1200 ns pulsed green laser and 14 μm grains are obtained at energy density of 3800 mJ/cm2_{and 4500 mJ/cm}2_{. The ablation thresholds are found to be at 5000}

mJ/cm2_{and 6400 mJ/cm}2_{, respectively. Therefore, a 1 μm thick layer still has}

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room for more heat deposition. Thus, even larger grains can be obtained in future work with a grain filter mask that has a pitch larger than 14 μm.

The green laser is more advantageous in thick silicon layer crystallization and large grain formation with its longer emission wavelength and longer pulse duration in comparison to the excimer laser. However, the spot size of the green laser is 30 μm x 2 mm. Thus, the system is not ready to be used in the crystallization of device layers but with modifications in the optical system, such as integration of lenses or micro-lens arrays and beam homogenizer, this limitation can be resolved.

Another difficulty in thick silicon crystallization is stress formation from two different origins. Firstly, from the difference between the deposition temperatures of the layers and secondly the tensile stress which is introduced during the laser crystallization. With substrate heating (450ºC) and pulse extender (250 ns), the crystallization stress of 850 nm-thick silicon is reduced considerably and 8 μm size crack-free grains are obtained with the excimer laser.

References

[1] J. Derakhshandeh, N. Golshani, R. Ishihara, M. R. Tajari Mofrad, M. Robertson, T. Morrison, and C. I. M. Beenakker, “Monolithic 3-D Integration of SRAM and Image Sensor Using Two Layers of Single-Grain Silicon,” IEEE Trans. Electron Devices, vol. 58, no. 11, pp. 3954– 3961, Nov. 2011.

[2] R. A. Street, Technology and applications of amorphous silicon, vol. 37. Springer, 2000.

[3] Q. Li, “Investigation on solid-phase crystallization techniques for low temperature polysilicon thin- film transistors,” M.Sc. Thesis, Rochester Institute of Technology, 2013.

[4] W. Skorupa and H. Schmidt, Subsecond Annealing of Advanced

Materials: Annealing by Lasers, Flash Lamps and Swift Heavy Ions.

Springer, 2014.

[5] J. Feng, J. Yan, and S. Zhou, “Dynamic Behaviors of PbS Irradiated by Laser Pulse,” PIERS Online, vol. 3, no. 6, pp. 847–850, 2007.

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[6] P. P. Donohue, “ANNEALING STUDIES OF DETECTOR MATERIALS FOR UNCOOLED THERMAL IMAGING,” Ph.D. Dissertation, University of Southampton, 2001.

[7] Y. Cengel, “Introduction to Thermodynamics and Heat Transfer,” The McGraw−Hill, 2008.

[8] B. S. Yilbas and S. Z. Shuja, “Laser Surface Processing and Model Studies,” in Laser Surface Processing and Model Studies, Springer Berlin Heidelberg, 2013.

[9] S. De Unamuno and E. Fogarassy, “A thermal description of the melting of c-and a-silicon under pulsed excimer lasers,” Appl. Surf. Sci., vol. 36, no. 1, pp. 1–11, 1989.

[10] H. C. Webber, “Computer simulation of high speed melting of amorphous silicon,” Appl. Phys. Lett., vol. 43, no. 7, p. 669, 1983. [11] Z. Zhou, S. Mukherjee, and W.-K. Rhim, “Measurement of

thermophysical properties of molten silicon using an upgraded electrostatic levitator,” J. Cryst. Growth, vol. 257, no. 3–4, pp. 350–358, Oct. 2003.

[12] G. E. Jellison and D. H. Lowndes, “Measurements of the optical properties of liquid silicon and germanium using nanosecond time-resolved ellipsometry,” Appl. Phys. Lett., vol. 51, no. 5, p. 352, 1987. [13] R. Ishihara, W. C. Yeh, T. Hattori, and M. Matsumura, “Effects of Light

Pulse Duration on Excimer-Laser Crystallization Characteristics of Silicon Thin Films,” vol. 1759.

[14] M. R. T. Mofrad, “Monolithic 3D Integration of Single-grain Silicon TFTs,” Ph.D. Dissertation, Delft University of Technology, 2012. [15] Y. et all. Arai, “Backside-activation Technique of Power Device IGBTs

by a Microsecond-pulsed Green Laser,” in 17th Int. Conf. on Advanced

Thermal Processing of Semiconductors, 2009.

[16] S. Wolf and others, Silicon Processing for the VLSI Era, vol. 2: Process

Integration. Lattice Press, 1990.

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[17] N. H. Nickel, “Laser Crystallization of Silicon - Fundamentals to Devices,” Elsevier B.V., 2003.

[18] G. Yue, J. D. Lorentzen, J. Lin, D. Han, and Q. Wang, “Photoluminescence and Raman studies in thin-film materials: Transition from amorphous to microcrystalline silicon,” Appl. Phys.

Lett., vol. 75, no. 4, p. 492, 1999.

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Chapter 3 SG-Lateral PIN Photodiodes for Large Area

X-ray Image Sensors

In this chapter, thick SG-PDs are introduced for indirect X-ray image sensors. Thick lateral PIN photodiode designs are fabricated in order to increase the light on/off ratio of the photodiodes at 550 nm by increasing the depletion region depth. 1 μm and 850 nm-thick a-Si layers are crystallized with 6 μm x 6 μm and 8 μm x 8 μm grains, respectively. Details of the crystallization were explained in Chapter 2. PIN photodiodes are explained in Chapter 3.2 and the design specifications are given in Chapter 3.3. I-V characteristics of the SG photodiodes are compared with SOI and a-Si photodiodes. The effect of the annealing energy density for the doping activation on SG-PDs is investigated by comparing I-V and spectral characterization of two samples. SNR (signal to noise ratio) values are calculated for these devices and the results are given in Chapter 3.4. The ideality factor of the fabricated devices are also calculated and compared with respect to the substrate material type and the intrinsic region position.

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3.1 Introduction

SG technology has advantages for image sensor applications with lateral PIN photodiodes and high mobility TFTs. The mobility of SG-TFTs can reach up to 600 cm2_{/Vs and 200 cm}2_{/Vs for SG-NMOS and PMOS transistors, respectively.}

SG-photodiodes can be monolithically stacked upon CMOS FETs or TFTs [1]. They are attractive for their use in large-area image sensors, especially for human size medical devices such as X-ray image sensors [2].

In this chapter, thick (>800 nm) single grain photodiodes are introduced for indirect X-ray image sensors. The single grain photodiodes are developed to read the emission spectrum of CsI(TI) scintillator that has an emission maximum at 550 nm.

3.2 PIN Photodiodes

The PIN photodiode was invented by Jun-ichi Nishizawa and his colleagues in 1950 [3]. Low dark current and high sensitivity are the main advantages of the PIN photodiodes in comparison to PN photodiodes. Silicon PIN photodiodes are sensitive to wavelengths from UV to the infrared region. Some of the applications of PIN photodiodes are RF switches, attenuators and photo detectors [4]–[6] . P+ N+ I P+ I N+ Vp Vn Vp Vn (a) (b)

Figure 3.1: Schematics of (a) vertical and (b) lateral PIN photodiode.

Different from PN photodiodes, P and N regions of the PIN photodiode are separated by an intrinsic region. PIN photodiodes have vertical and lateral orientations and their schematics are shown in Figure 3.1. In vertical orientation, first the N+_{region is deposited, doped and annealed. After}

passivation, the intrinsic region is deposited. P+_{region deposition and}

Single-grain Silicon Technology for Large Area X-ray Imaging

Single-grain Silicon Technology

for Large Area X-ray Imaging

Single-grain Silicon Technology for

Large Area X-ray Imaging

Aslıhan ARSLAN

Contents

Chapter 1

Introduction

Detector

Scintillator

X-Ray

Chapter 2

Laser Crystallization of Thick Si Film

with the μ-Czochralski Process

GF

1

( )

δ =

α λ

L

=

2

κτ

c

Q

c

T

k

dt

dT

ρ

ρ

+

∇

∇

=

(

)

Hillock

E

(

) T

1 y

s = s − s ∆

−

Chapter 3

SG-Lateral PIN Photodiodes for Large Area

X-ray Image Sensors