Thermodynamics and Transport Model of Charge ... - IEEE Xplore

2728 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 55, NO. 10, OCTOBER 2008 

Thermodynamics and Transport Model of Charge 

Injection in Silicon Irradiated by a 

Pulsed Focused Laser 

Étienne Boulais, Vincent Binet, Jean-Yves Degorce, Guillaume Wild, 

Yvon Savaria, Fellow, IEEE, and Michel Meunier 

Abstract—Focused pulsed visible laser used in laser-trimming 

technologies such as the laser diffused-resistor process may inject 

charges in the semiconductor, leading to an interaction with highly 

sensitive circuits. In order to evaluate the process impact on those 

circuits, a study of the perturbation on the free-running frequency 

of a ring oscillator due to a nearby laser pulse has been made. The 

behavior of this modification as a function of the laser-pulse power 

exhibits complex features. A thermodynamics and electrical model 

of the charge injection by a focused pulsed laser on silicon has been 

developed. First, the laser-induced charge diffusion is calculated 

by a finite-element-model coupling Boltzmann semiclassical transport 

and thermodynamic equations; the last one being necessary, 

as relatively high laser power may increase significantly the local 

temperature. The result is then fed into an electrical model of 

the ring oscillator as a perturbation injected by a current source. 

This model coupled to parasitic-light effects due to geometrical 

changes during silicon melting is able to explain the oscillator’s 

operation-frequency modification. 

Index Terms—Charge injection, finite-element model, laser 

trimming, substrate effect, temperature effect. 

I. INTRODUCTION 

CLASSES of analog microelectronic circuits require highprecision 

resistors to function properly. Standard integrated 

fabrication processes’ intrinsic variability can introduce 

some uncontrolled changes in parametric values that can 

severely limit their accuracy, possibly resulting in a completely 

useless circuit. A solution to this problem consists in a postproduction 

trimming of resistor values to obtain the desired 

electrical characteristics. The possibility to configure circuits 

by creating or cutting metal links [1] allows designers to add re- 

Manuscript received October 5, 2007; revised June 27, 2008. Current version 

published September 24, 2008. This work was supported in part by the Natural 

Sciences and Engineering Council of Canada and in part by LTRIM. The review 

of this paper was arranged by Editor C.-Y. Lu. 

É. Boulais and M. Meunier are with the Laser Processing Laboratory, 

Engineering Physics Department, École Polytechnique de Montréal, 

Montreal, QC H3C 3A7, Canada (e-mail: etienne.boulais@polymtl.ca; michel. 

meunier@polymtl.ca). 

V. Binet, G. Wild, and Y. Savaria are with the Groupe de Recherche en 

Microélectronique, Electrical Engineering Department, École Polytechnique de 

Montréal, Montreal, QC H3C 3A7, Canada (e-mail: vincent.binet@polymtl.ca; 

guillaume.wild@polymtl.ca; yvon.savaria@polymtl.ca). 

J.-Y. Degorce was with the Laser Processing Laboratory, Engineering 

Physics Department, École Polytechnique de Montréal, Montreal, QC H3C 

3A7, Canada. He is now with the Université de Bordeaux, 33000 Bordeaux, 

France (e-mail: Degorce.JeanYes@celia.u-bordeaux1.fr). 

Digital Object Identifier 10.1109/TED.2008.2003027 

dundancy and correct malfunction in large VLSI circuits. Thinfilm 

resistors can also be trimmed by laser to improve accuracy 

of digital-to-analog converters [2], analog-to-digital converters 

[3], and read-only memories [4]. An alternative simple, costeffective, 

and rapid laser trimming process was recently proposed 

by Meunier et al. [5] and consists in the formation of 

diffused resistors that can be used directly in mixed signal and 

high-precision analog circuits [6]. This process uses a pulsed 

visible laser focused on a semiconductor structure consisting 

of two highly doped regions separated by a gap. The laser 

induces a local melting of the silicon surface, thus stimulating 

the diffusion of dopants and the formation of an analog resistive 

device, whose resistance can be accurately controlled by an 

iterative technique [7]. 

Electron–hole pairs that might be created by the laser during 

these processes and injected into the substrate must remain 

below an acceptable level for industrial applications, as they 

can possibly activate destructive phenomena such as latch up 

and corrupt accuracy in closed-loop trimming methods that 

rely on accurate analog measurements. There is thus a need 

to develop a tool that will enable us to accurately calculate 

the charge injection in an integrated circuit during a trimming 

process. Preceding works on laser interaction with electronic 

circuit has been made within the fields of fault-injection and 

single-event effects [8], [9]. However, as research in those fields 

involves very low power laser beam focused on transistors, laser 

trimming is usually processed at much higher power pulses (by 

three to four orders of magnitude), leading to a local temperature 

increase and to different charge-injection mechanisms and 

impacts on surrounding circuits. Therefore, models developed 

for fault-injection and single-event effects cannot be used, since 

thermodynamic effects on charge transport induced by laser 

heating are ignored. Previous work by Wild et al. [10] has 

shown that a ring oscillator can be used to detect very small 

laser-induced charge injection into the silicon by monitoring its 

frequency change during the tuning process. The purpose of this 

paper is to model both the charge injection in silicon due to a 

focused visible laser beam and the effect of charge injection 

on an operating ring oscillator. A finite-element model using 

coupled thermodynamic and semiclassical charge-transport 

equations is used for the charge-injection calculation, while an 

electrical model of the ring oscillator, including substrate and 

well extraction, is used to calculate the impact of the charge 

injection on the circuit. 

0018-9383/$25.00 © 2008 IEEE

BOULAIS et al.: THERMODYNAMICS AND TRANSPORT MODEL OF CHARGE INJECTION IN SILICON 2729 

Fig. 1. (a) Schematic of a ring oscillator composed of four inverters and an AND gate. All inverters are equidistant to the target. (b) Typical result of the FVC 

output after a 950-mW 100-ns pulsed laser irradiating the center of the ring oscillator situated at 30 μm. 

II. EXPERIMENTAL SETUP AND RESULTS 

As described in [10], the sensitive circuits used to detect 

injected charges in the experimental work are CMOS ring 

oscillators, manufactured by TSMC in a 0.18-μm technology 

that has a low-resistivity p-type substrate. Oscillating at a 

stable frequency, the ring oscillator, as previously presented by 

Wild [10], is composed of four inverters and a gating NAND acting 

as an inverter during the oscillation operation. A frequencyto-voltage 

converter (FVC) is used to drive the chip output at 

a voltage that represents the oscillator’s frequency, as shown 

in Fig. 1. The on-chip oscillation of about 380 MHz is first 

divided by eight using a frequency divider (FD), then each 

period is converted by the FVC to a dc voltage that drives the 

output of the chip through an analog buffer. The laser target 

is a laser diffused resistor (LDR) implanted in the center of 

the ring oscillator and located at various distance d to the 

ring oscillator, ranging from 20 to 40 μm. A test setup has 

been developed as described in [10] using a frequency-doubled 

continuous-wave Nd:YAG laser (532 nm) having an adjustable 

diameter and power. A pulse is selected from the continuous 

beam using an acoustooptic modulator and is focalized on 

the target. In all experiments, a single pulse is used with a 

pulse duration of 100 ns. The beam diameter is about 7 μm, 

and the emitted laser power P L is varying up to 1.5 W. Note 

that, throughout the text, the emitted laser power refers to 

the average laser power of the continuous-wave laser, taking 

into consideration losses due to the acoustooptic modulator. 

It is difficult to evaluate the optical losses due to the multiple 

reflections and the absorption in the interdielectric layers; 

the exact laser power arriving on the silicon is not known. 

A typical FVC variation for P L = 950 mW and d = 30 μm 

is given in Fig. 1(b). The measured maximum of the FVC 

output variation [FVCOV max defined in Fig. 1(b)] is shown in 

Fig. 2 as a function of the laser power P L . Estimations based 

on diffused-resistor creation experiments and in situ reflectivity 

measurements give a value for the melting power threshold of 

around P L,th−m =(1.1 ± 0.1) W. One can distinguish three 

main regions in these measured results: 1) In the first region, 

for P L < 0.375 W, the FVC output increases with P L ;2)in 

the second region (0.375 W 0.7 W), the FVC output increases slightly with scattered 

results. An increase in charge injection with increasing power 

was expected. The presence of region II was not expected. 

To explain these results, the effects of heating on the charge 

transport must considered. 

III. CONSTANT-TEMPERATURE ELECTRONIC 

TRANSPORT MODEL 

Many models describing the interaction between a laser pulse 

and a semiconductor developed over the past four decades focus 

on emulating the impact of single-event effects by ionizing 

radiation on static memories [9], [11], [12]. In these existing 

models, relatively low laser powers are assumed, as any heating 

phenomena are excluded from the calculation. However, the 

laser used for creating LDRs is different in terms of power 

level and pulse duration, since significant heating and melting 

of silicon is required. As a first approximation, the substrate’s 

temperature was assumed to remain constant throughout the 

process. It will be shown that this assumption is not accurate. 

It is important to note that the laser is not directly focused 

on the active area of a transistor under test, but rather on the 

LDR region, which introduces additional specificity into the


model. Electron–hole pairs are thus not directly generated on 

the transistor drain but can rather reach the circuit under test, 

which is a ring oscillator, through a drift and diffusion process 

that will be described by a finite-element model based on 

Boltzmann semiclassical transport equations. An electric model 

must also be used to characterize the effects of the injected 

charges on the circuit under test. 

A. Electrical Model 

In order to get an accurate model of the victim circuit, the 

complete circuit has to be extracted from a detailed layout. 

As the coupling between the laser-pulse impact and the victim 

circuit takes place through the substrate, the model must also 

include a thorough substrate extraction. As significant currents 

flow into the substrate, the potentials around active devices are 

significantly perturbed, which modulates the electrical parameters 

of the victim circuit through body effects. To include 

substrate coupling in the model, commercial softwares like 

SubstrateStorm, Substrate Coupling Analysis (SCA), or Assura 

RCX (Cadence Software) could be used to extract substrate 

parasitic components and, thus, build a resistive and capacitive 

substrate model. However, existing literature [13] on substrate 

modeling and parasitic extraction is mostly focused on noise 

coupling injected by a large number of switching gates. In [14], 

such models based only on capacitive coupling have shown 

inaccuracy when potentials vary over a wide range. These 

models become particularly inaccurate when the potentials shift 

by more than 400 mV and some normally inactive devices get 

activated. Mixed-mode simulations have shown that such large 

variations effectively occur in our case. In order to correctly 

model the charge-injection phenomena, a custom model of 

the substrate has been developed by enriching capacitive- and 

resistive-only substrate models given by the Cadence SCA 

tool. This custom substrate model includes vertical bipolar 

transistors and diodes to represent well–substrate junctions. 

They are added as discrete elements whose models are based on 

those provided by TSMC, and their size parameters are adjusted 

according to the physical layout of the circuit. 

Charge injection is then modeled by sources injecting currents 

through different junctions present in the ring-oscillator 

test circuit. As shown in Fig. 3, different perturbation sites have 

been identified to model the charge–circuit interaction in each 

of the inverters comprised in the circuit. Current source (A) 

simulates most of the charges collected by the n-well–substrate 

junction, whereas sources (B) and (C) connected between the 

source/drain nodes of the transistor and the bulk node represent 

charges collected by the NMOS. The last two sources (D) 

and (E) model injection into PMOSs’ drains and sources. 

All these sources correspond to possible physical-interaction 

mechanisms between charges present in the substrate and the 

circuit. Performing a series of circuit simulations, it was found 

that sources B, C, D, and E have relatively minor effects 

on the oscillator behavior and can be neglected. This can be 

understood because the surface of the well associated to source 

A is much larger (by a factor over ten) than the surface of the 

physical structures associated to the other sources. Using the 

detailed circuit models, including all available circuit, layout, 

substrate, and parasitic-device information, the complete ringoscillator 

model is then built and connected to the rest of the 

chip model, including the FVC, package, and bonding wires. In 

the first approximation, it was assumed that the FVC and other 

secondary circuits that are much further away from the laserpulse 

impact point remain unaffected by laser-induced charges. 

B. Constant-Temperature Semiconductor Transport Model 

In a first approximation, by neglecting temperature rise of the 

substrate, it is possible to model the charge-injection process in 

silicon by simply coupling a Beer–Lambert equation for light 

absorption with Poisson and Boltzmann equations describing 

the charge drift and diffusion processes. Dopants are assumed to 

be completely ionized within the considered temperature range. 

Continuity equation relating the electrons concentration n and 

the current density J n is thus given by 

∂n 

∂t = 1 −→ ∇·−→ 

Jn + G n − r n . (1) 

e 

A similar equation for holes has been used. Recombination 

term r n in (1) includes Shockley–Read–Hall (SRH) and 

Auger recombination. Appropriate coefficients for silicon can 

be found in [15]. A dynamic SRH recombination process can 

be used [16], but simulations showed that results were very 

close to those obtained by using a standard equilibrium SRH 

expression. Optical generation term G optical is calculated by 

assuming that every absorbed photon of energy hν causes an 

interband transition, thus creating a hole–electron pair 

α(T )I 

G optical = (2) 

hν 

where α is the temperature-dependent bulk-absorption coefficient 

and I in joules per square centimeter is the laser intensity 

arriving on the silicon. Intraband absorption is ignored, 

since simulations showed that, for laser powers used here, the 

maximum carrier density is not enough to stimulate such contribution. 

Current density is calculated through the Boltzmann 

kinetic equation [17] 

( ) 

−→ −→ F J n = neμ n E + nμn T ∇ 

T 

G n 5/2 

+ nμ n k B 

G n ∇T (3) 

3/2 

where μ n is the electron mobility, −→ E is the electric vector field, 

F is the quasi-Fermi level, and G m is defined as 

with 

G m = 

∫ ∞ 

0 

τx m e x−η dx 

(1 + e x−η ) 2 (4) 

η = F n − ε gap 

. (5) 

k B T 

Note that all these parameters are position ( −→ r )-dependent. 

Similar equations for p can be obtained where the laser term in 

(3) changes sign, and η p = −F p /k B T .


Fig. 3. 

Custom electrical model of an inverter of the ring oscillator. 

The exact position-dependent mobility parameters for both 

holes and electron are difficult to determine, since integrated 

circuits are not only composed of pure and crystalline silicon 

but also of polycrystalline silicon which has suffered many 

stresses in some regions, including high-power laser impacts 

and phase changes. Furthermore, the real doping-concentration 

profile remains unknown, since those parameters are not provided 

by the foundry. Position-dependent dislocations, defects, 

and dopants would all decrease the carrier mobility, resulting 

in a modified position and temperature-dependent mobility 

given by 

with 

μ M n,p(x, y, T )=φ(x, y, T )μ C n,p(x, y, T ) (6) 

φ(x, y, T ) ∈ [0, 1] (7) 

where the superscript M and C stands, respectively, for “modified” 

and “crystalline,” as the subscripts n and p, respectively, 

stands for electrons and holes. Carrier mobility in crystalline 

silicon can be found in standard texts [18]. Now, since the 

exact expression for ϕ(x, y, t) is very difficult to obtain, both 

theoretically and experimentally, we propose to use in a first 

approximation an equivalent mobility given by 

with 

μ eq 

n,p(x, y, T )=φμ C n,p(x, y, T ) (8) 

φ ∈ [0, 1] (9) 

where μ eq 

n,p is the equivalent mobility of electrons and holes and 

φ is an empirical parameter adjusted to fit experimental value. 

Similarly, the carrier recombination time is also expected to 

be different from the one for crystalline silicon, and a uniform 

equivalent recombination has been assumed 

τ eq 

n,p(x, y, t) =τ. (10) 

While the introduction of equivalent recombination times, 

absorption coefficient, and mobilities are required to fit experimental 

data, their influence over the general behavior of 

Fig. 4. FVC variation as a function of laser power, (circles) experiments, and 

(crosses) simulation. 

injected current as a function of incident laser power remains 

limited. Finite-element simulations were performed on a 

1.8-V reversed-biased p-n junction located at d = 30 μm from 

a pulsed focused laser. The calculated current was then inserted 

as a current source perturbing the electrical model to obtain the 

simulated variation of the FVC output voltage. Mobility factor 

and recombination time were then adjusted to fit experimental 

results. Simulations show that φ = 0.17 and τ = 200 ns reproduces 

the experimental results with the best accuracy. Fig. 4 

shows both the best-fit simulated and measured results of the 

FVC output variation as a function of P L . Results in Fig. 4 

show that, while the model predictions agree quite well with 

simulation results within the first region (P L < 0.375 W), it 

does not follow the behavior observed in the second region 

(0.375 W


IV. COUPLED THERMODYNAMICS AND 

TRANSPORT MODEL 

A. Coupled Thermodynamic and Transport Model 

Without Fusion 

In this improved model based on coupled thermodynamic 

and transport equations, the carrier spatial distribution is simulated 

in a two-step process. Temperature is first calculated 

using a model essentially based on the one introduced by 

Degorce et al. [19], involving the resolution of coupled 

Beer–Lambert and heat equations, where the phase transformation 

is accounted for by using an enthalpic model. Siliconoxide 

effect on temperature distribution is neglected to reduce 

the model’s complexity. The carrier distribution is then determined 

through the resolution of the coupled Boltzmann and 

Poisson equations. The temperature calculated in the first step 

is used into these equations without any explicit feedback. 

However, carrier-distribution effects on temperature are taken 

into account by using an empirical relation of the temperaturedependent 

absorption coefficient α(T ). This approximation reduces 

greatly the model’s complexity. The calculated maximum 

temperature gradient of 3.5 × 10 7 K/cm remains small enough 

to justify the use of Boltzmann equation for any laser power 

considered in this paper. As expected, temperature gradient has 

a considerable effect on the charge transport in the material 

which can be easily understood by looking at the Boltzmann 

equation. Developing (3), for the electrons, one can write 

Fig. 5. Schematic of the time evolution of the distribution of electronic current 

in the material. At the beginning of the pulse (A), electrons induced in the 

material diffuse from the laser impact point to the circuit. The laser heats 

the substrate, and when temperature gradient gets high enough over a certain 

area (B), this area experiences an inversion of its electronic current. After the 

end of the pulse (C), the temperature gradient gets lower, and the inverse current 

area disappear. 

( ) 

−→ G5/2 

J n = −enμ n ∇V + nμ n ∇F − k B nμ n − η ∗ ∇T 

G 3/2 

(11) 

where the first terms represent the drift and temperatureconstant 

diffusion current and the last one corresponds to 

a current generated when a temperature gradient is present 

within the material. A similar equation can be obtained for 

holes. Calculations show that the coefficient multiplying the 

temperature gradient (11) is always positive. In our application, 

in addition to injecting carriers, the laser acts as a heat source 

generating a thermal gradient having the same sign as the 

carrier concentration and the quasi-Fermi level. Therefore, the 

temperature gradient always opposes the effect of the carrierconcentration 

gradient, here represented by the quasi-Fermi 

level gradient, on the diffusion current. Strong temperature 

gradient could limit and even stop the diffusion of carriers from 

the laser impact point to the junction. Fig. 5 shows a schematic 

time profile of the electronic current present in the material. 

As shown in Fig. 5, when a strong temperature gradient is 

present in the material, an inversion of the electronic current is 

experienced over a small area of the substrate. Carriers are then 

confined in this small region limited by this diffusion barrier 

where they can recombine. Only carriers created at the very 

beginning of the laser pulse, which is before the formation of 

a strong temperature gradient, or created outside the diffusion 

barrier will eventually get to the junction. Fig. 6 shows a 

simulation result showing that this inversion of the electronic 

current indeed occurs for a 0.5-W laser pulse in a region located 

about 400 nm from the laser impact point. Fig. 7 now shows 

Fig. 6. Electronic current as a function of distance from laser impact point at 

the end of a 0.5-W pulse as calculated with (solid line) coupled thermodynamic 

and transport model and (dashed-dot line) constant-temperature semiconductor 

constant model. 

a comparison of the simulated FVC output voltage using this 

new model to the experimental results. Comparison of Fig. 7 

to Fig. 4 shows that introducing temperature effects into the 

semiconductor transport model permits one to almost reproduce 

the experimental behavior in the second region which could 

thus be attributed for a large part to the presence of strong 

temperature gradient within the substrate. It is of interest that 

the electrical model used to simulate FVC output is no longer 

valid beyond 0.7 W. At that point, the electric model predicts 

that current perturbation required to reproduce experimental 

values shortcuts the n-well junction. The linear-circuit model 

used here is then no longer a good approximation to the phenomena 

taking place. It is thus difficult to correlate simulated 

and experimental behaviors for incident powers beyond 0.7 W.


Fig. 7. FVC variations as a function of laser power, (circles) experiments, and 

(triangles) simulation. 

The physical model presented so far predicts a saturation of the 

current entering the junction as a function of the laser power in 

the third region. In fact, at those powers, the temperature rise 

in silicon is strong enough to induce melting of the substrate. 

Although melting of the surface is included in the model, 

its direct effect on electronic transport has been neglected. 

The next section introduces a model that considers those 

effects. 

B. Coupled Thermodynamic and Transport Model 

With Fusion 

Basically, the equations of coupled thermodynamic and 

transport model presented in the previous section remains 

essentially the same, except that one must include the effect 

of the melted silicon, which has become metallic. Inverse 

bremsstrahlung then becomes the main light-absorption 

mechanism, and direct electron–hole pair creation can be 

neglected. However, when fusion temperature is reached, 

semiconductor–metal phase transformation induces confined 

electrons in covalent bonds to reach conduction bands thus significantly 

increasing equilibrium electronic concentration [20]. 

The density of states of silicon is greatly modified when melted, 

and the Fermi level position decreases by approximately 0.6 eV 

according to experimental studies [21]. The solid–liquid interface 

is assumed to be at equilibrium so that thermionic 

charge injection can be neglected. Electron mobility is also 

modified [22]. Therefore, at relatively high laser power, the 

process will result in a metal–semiconductor heterostructure 

whose interface moves with the melted front. Because of the 

Fermi level drop in the melted silicon, carriers in liquid silicon 

are trapped inside a 0.6-eV well. Therefore, even if the carrier 

density within the melted silicon is very high, those carriers 

are probably not able to diffuse, and they probably stay trapped 

inside the melted region. Melting of the substrate is thus believed 

to have a negligible impact on the current perturbation 

affecting the sensitive circuit. From simulation results and using 

Fermi statistics, one can estimate the number of carriers in the 

melted region that is able to pass over the potential barrier to be 

approximately 10 19 times lower than the photoinduced charges 

injected in the solid semiconductor outside the melted region. 

As the laser power increases, reflected light from the impact 

point could be scattered to relatively large distances 

through multiple reflections in the interdielectrics and reach 

the p-n junction, thus creating additional electron–hole pair 

in the silicon. A simple calculation can be made to approximate 

the magnitude of this scattered light. Neglecting backscattering 

from dielectric/dielectric interface since their refraction 

indexes are expected to be very similar, the proportion of light 

backscattered from the irradiated surface, to the interface top 

layer/air, and back to the surface is about 10% of the incident 

light at the laser impact point. However, since the target is not 

experimentally located exactly at the laser waist, it is expected 

that the incoming lightwave will not be perfectly plane at the 

surface, yielding to a reflected light over a large area. Moreover, 

when melted, the silicon surface experiences different transformations 

that increase this light scattering. First, liquid silicon’s 

reflection coefficient is about 1.5 times larger than the one of 

solid silicon. In addition, besides reflection coefficient modification, 

silicon undergoes purely geometrical modification when 

melted. Fig. 8 shows an image from a transmission electron 

microscopy of a silicon area which has been melted by a laser 

irradiation whose parameters are analog to the one used for 

trimming processes. Silicon has experienced strong geometrical 

modification and has reshaped as a rounded pyramid, similar 

to a sombrero shape. Other shapes have been reported in 

the literature, including bowl, for silicon and other material 

surfaces [23], [24]. These studies showed that irradiating at 

low energy tends to create bowllike structures, while at higher 

energy, sombrero structures are mostly observed. As stated 

in [23], bowllike structure formation results from temperature 

gradient inducing thermocapillarity flow that drives material 

from the hot center to the cold periphery. However, at higher 

laser power, native oxide layer is removed (at least partially), 

thus creating a surfactant-concentration gradient driving material 

toward the center. The observed sombrerolike structure is 

expected to increase the quantity of scattered light reaching the 

transistor region. Wave front at the surface is indeed no longer 

plane, and reflections will occur at angles far from normal, thus 

increasing the proportion of light reaching regions distant from 

the laser impact point. Scattered light creates photo-induced 

carriers in regions far from impact point and outside the strong 

temperature gradient area. Those carriers then diffuse freely 

to the circuit area, thus contributing to the total current. Note 

that all samples contained those substrate deformation from 

the beginning, since measurements have been conducted on a 

previously irradiated circuit. Consequently, the laser power at 

the edge of region 3 in Fig. 2 does not stand for the point at 

which the deformation appears but rather for the point at which 

scattered-light induced carrier effect on the oscillator becomes 

dominant over the diffusion process. Within this model, lightscattered 

induced carrier generation is modeled as a uniform 

and constant light background proportional to the incident laser 

power. Light-scattered generation have thus to be added to the 

optical generation 

G = G optical + G scattering . (12)


Fig. 8. (a) TEM cross-sectional image showing geometrical changes in silicon surface induced by laser melting. (b) Schematic of the scattered-light induced 

carrier injection backscattered from the irradiated surface to the interface top layer—air—and back to the surface. 

Numerical simulations has shown that 0.5% scattered-light 

intensity reaching regions outside the strong temperature gradient 

area can generate a considerable current through the 

junction, thereby preventing the total perturbative current to 

saturate as the power is increased over 700 mW in region III. 

Such a scattering is reasonable considering the initial 10% light 

reflected from the reflection on dielectric layers. Considering 

the experimental evidence about the existence of sample surface 

deformations and the small intensity of parasitic light required 

to produce observable effects on current, parasitic-light photoinduced 

carriers are thought to play an important role on the 

FVC output behavior at higher power. 

V. CONCLUSION 

Laser-induced diffused-resistor fabrication processes involve 

pulsed visible laser interaction on chips containing highly 

sensitive circuitry. In order to evaluate the impact of the laser 

pulses on these circuits, a study of the perturbation induced 

on the free-running frequency of a ring oscillator has been 

made. The behavior of this modification as a function of the 

laser-pulse power exhibits a quasi-linear increase for low laser 

power, then a saturation and finally another increase for high 

laser power. An electric model of the ring oscillator and of 

the FVC circuit has been coupled to a semiconductor model 

of the charge injection to describe the impact of the laser 

pulse on the sensitive circuit. A simple model neglecting the 

temperature rise of the substrate is unable to describe properly 

the observed experimental behavior. A model based on thermodynamics 

and Boltzmann semiclassical transport equations 

of the charge injection by a focused pulsed laser in silicon has 

been developed to include the temperature rise of the substrate. 

Results show that below silicon melting, the charge injection 

increases linearly at low power and then saturates due to the 

presence of strong temperature gradient that confines photoinduced 

carriers in a small region around the laser impact point, 

thereby preventing them to diffuse to the oscillator. Above 

melting, silicon experiences a semiconductor-to-metal phase 

transition, injecting a lot of free carriers in the liquid silicon. 

However, based on experimental studies, those carriers are 

trapped in the liquid phase and are not able to diffuse to the 

oscillator and thus do not affect its oscillation frequency. In 

addition to this phase transition, melted liquid silicon when 

solidified experiences a geometrical transformation that creates 

light-scattered induced carriers that either affect directly the 

oscillator or is able to diffuse to it. This phenomenon appears to 

be responsible for the increase of the FVC response for higher 

laser power. 

ACKNOWLEDGMENT 

The authors would like to thank S. Laforte and R. Lachaîne 

for TEM imaging and valuable discussions. They would also 

like to thank A. Lacourse from LTRIM Technologies for stimulating 

discussions. Some of the tools and access to fabrication 

technologies were provided by CMC Microsystem. 

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Jean-Yves Degorce received the M.A.Sc. degree in 

solid state physics from the University of Paris VI, 

Paris, France, in 1989 and the Ph.D. degree in laser 

matter interaction from the École Polytechnique de 

Montréal, Montreal, QC, Canada, and the Université 

de Bordeaux, Bordeaux, France, in 2000. 

From 2000 to 2005, he was a Lecturer and 

Associate Researcher in laser processing with the 

Laser Processing Laboratory, Engineering Physics 

Department, École Polytechnique de Montréal. He 

is currently a Professor in classe préparatoire aux 

grandes écoles with the Université de Bordeaux. His current research interests 

include micro- and nanothermal modeling. 

Guillaume Wild received the Diploma degree in 

electrical engineering from the Ecole Superieure 

d’Electricite, Gif Sur Yvette, France, in 2002 and 

the M.A.Sc. degree from the École Polytechnique de 

Montréal, Montreal, QC, Canada, in 2005, under the 

supervision of Profs. Y. Savaria and M. Meunier. 

He is currently with Siemens, Amberg, Germany. 

Étienne Boulais received the B.Ing. degree in engineering 

physics from the École Polytechnique de 

Montréal, Montreal, QC, Canada, in 2007, where 

he has been working toward the Ph.D. degree 

in the Laser Processing Laboratory, Engineering 

Physics Department, under the supervision of 

Prof.M.Meunier. 

His research topic is in the field of the simulation 

of laser–matter interaction. 

Yvon Savaria (S’77–M’86–SM’97–F’08) received 

the B.Ing. and M.A.Sc. degrees in electrical engineering 

from the École Polytechnique de Montréal, 

Montreal, QC, Canada, in 1980 and 1982, respectively, 

and the Ph.D. degree in electrical engineering 

from McGill University, Montreal, in 1985. 

Since 1985, he has been with the École Polytechnique 

de Montréal, where he is currently a Professor 

and the Director of the microelectronics and 

microsystems research group in the Electrical Engineering 

Department. He has carried out work in 

several areas related to microelectronic circuits and microsystems. 

Vincent Binet received the Diploma degree in 

electrical engineering from the Ecole Superieure 

d’Electricite, Gif Sur Yvette, France, and the 

M.A.Sc. degree in microelectronics from the École 

Polytechnique de Montréal, Montreal, QC, Canada, 

in 2007, under the supervision of Profs. Y. Savaria 

and M. Meunier. 

He is currently with STMicroelectronics, 

Grenoble, France, in the IP advanced team in 

audio R&D. 

Michel Meunier received the B.Ing. and M.A.Sc. 

degrees in engineering physics from the École Polytechnique 

de Montréal, Montreal, QC, Canada, in 

1978 and 1980, respectively, and the Ph.D. degree 

from the Massachusetts Institute of Technology, 

Cambridge, in 1984. 

He is currently the Director of the Laser Processing 

Laboratory, Engineering Physics Department, 

École Polytechnique de Montréal. For close to 

30 years, he has been involved in laser processing 

of various materials and he has published over 

260 papers in this field. 

Dr. Meunier is a Canadian Research Chair in laser micro/nanoengineering of 

materials.

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