# Temperature Estimation during Pulsed Laser Sintering of Silver Nanoparticles
## 1 Introduction  
With the increasing need for developing innovative electronics devices, new methods for patterning integrated circuits are devised to replace or compliment the conventional microcircuit patterning techniques. Conventional photolithography has been in practice since the fabrication of the first transistor in 1948 [1]. This patterning technique is costly, wasteful, and complex for large-scale fabrication [2]. Moreover, the following subtractive processes such as reactive ion etching and wet etching produce hazardous chemicals (i.e., film materials and chemical etchants) [3, 4]. Since the current advances in flexible electronics demand the use of polymer and paper substrates that are sensitive to high temperatures and chemical etchants, the conventional subtractive microfabrication processes are not applicable [5]. As a potential alternative, the demonstration of a roll-to-roll printing and sintering system on polymer substrates establishes a gateway to the future of the electronic industry [6, 7]. Printed electronics has facilitated the printing techniques of metal nanoparticles (NPs) for the fabrication of electronic devices such as near-field communication (NFC) tags [8], thin-film transistors [9], organic field-effect transistors (OFETs) [10], biosensors [11], and stretchable sensors [12]. Different metal NPs such as silver (Ag) [13], copper (Cu) [14], and gold (Au) [15] of different sizes ranging from 2 to 50 nm are used due to their high electrical conductivity. These metal NPs are included in sinks with organic additives (binders, dispersants, and organic solvents) to prevent their agglomeration among NPs. NPs'sinks are printed onto various substrates to form the desired circuit patterns, followed by a sintering step to render the printed tracks conductive. The thermal sintering is conventionally performed in an oven, which is called oven sintering. However, the oven sintering method requires high-temperature heat treatment at a minimum of around 200 \({}^{\circ}\)C and a long heating time of up to about 1 h or more, which limits the use of heat-vulnerable substrates such as glass, polymer, and paper. [16]. To minimize the damage, rapid sintering methods such as electrical [17], microwave [18], infrared [6], intense pulsed light [19], and laser [20] sintering methods have been extensively investigated. Among them the laser sintering method is further divided into continuous wave (CW) laser and pulsed laser sintering methods based on the mode of the laser operation. Both have their shortcomings and advantages. CW laser sintering is known to produce lower resistivities [21]; however, it induces large thermal diffusion length and is not compatible with the sintering of sub-micrometer sized patterns due to large heat affected zones [10]. On the other hand, one of the major advantages of pulsed laser sintering method is the reduced thermal diffusion length and smaller heat-affected zone at shorter pulse durations [10; 22], which is crucial for the minimization of thermal damage of the substrate. In order to use a pulsed laser for NPs sintering, it is essential to select optimum laser parameters for obtaining low electrical resistivities as well as avoiding thermal damage to the substrate in use. Laser parameters such as intensity, pulse duration and repetition rates decide the maximum sintering process temperature. Therefore, among others, accurate thermal analysis during the pulsed laser sintering is indispensable since the maximum sintering temperature is known to be highly responsible for the electrical properties and surface morphology of the Ag NPs [23]. As such, several thermal analysis studies during pulsed laser sintering of metal NPs have been reported [20; 24]. A millisecond pulse laser was used by [PERSON] et al. for the investigation of heating effects during pulsed laser sintering of Ag NPs. They estimated the Ag NPs melting temperature via theoretical calculations based on a heat diffusion model.