Numerical simulation of optical devices

zyxwvu zyxwvutsrqponm zyxwvuts zyxwvu zy zyxwvutsrqponmlkjihgf IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 12, NO. IO, OCTOBER 1993 1557 Numerical Simulation of Optical Devices Maria Cristina Vecchi, Massimo Rudan, Senior Member, IEEE, and Giovanni Soncini Abstract-The description of the optical-generation phenomena has been incorporated in the semiconductor-deviceanalysis program H F I E L D S, keeping the structural and geometrical flexibility of the original code. To this purpose a substantial effort has been devoted to the software implementation. The latter required the introduction of a number of optical windows and interleaved material layers through which a radiation with arbitrary spectrum, incidence angle, and polarization state enters the crystal. The corresponding generation rate at each node of the discretization grid is then evaluated by adding up the contribution of each monochromatic component of the impinging radiation. A preliminary report has been given in [l].The code equipped with this new capability makes the description of realistic semiconductor optical sensors feasible, as demonstrated by several examples given in the paper. As an additional feature, the black-body radiation has been incorporated into the code to allow for the simulation of solar cells. After a brief review of the underlying physics, given in Section I, the software implementation is described in Section I1 and a number of examples are illustrated in Section 111. with p = q(p -n + NA - NA), P = 4Nom (1.6) (1.7) + qD, grad n , (1.4) respectively. The remaining equations hold in the semiconductor domains only. The symbols in (1 .1)-( 1.7) have the customary meaning of the semiconductor-device theory. Hence, only the form of the optical terms G,OP',Gip' will be discussed here in some detail. It is worth noting that, for the sake of completeness, different symbols for the electron- and hole-generation/recombination terms have been used in the continuity equations. In fact, if the concentration of traps in the band gap is large and a transient condition holds, it would turn out G:P' # Gip' and U,, f U,. As a consequence, it would be necessary to add to (1.2), (1.3) a continuity equation for the traps, and modify the RHS (1.6) of Poisson's equation accordingly. However, in the practical cases the concentration of traps is low enough to avoid these complicacies (see also the discussion in Section 1.3). The numerical solution of system (1. l ) , (1.2), (1.3) is carried out in H F I E L D S by discretizing the equations on a two-dimensional, triangular grid [2]. This transforms the system of PDE's in a (non-linear) algebraic system whose unknowns are the values of cp, n , and p at the grid nodes. To incorporate the optical-generation effects it is then necessary to evaluate GZpt, Gip' at each grid node belonging to the semiconductor. This is done in two steps: in the first one, the intensity and the direction of the electromagnetic wave which actually enters the semiconductor crystal are evaluated. This calculation accounts for the characteristics of the impinging radiation and for the geometrical structure and physical nature of the material layers interleaved between the radiation source and the crystal. In the second step, the carrier generation produced by radiation at each grid node is evaluated. Jp = - q p pP grad P - 4Dp grad P , (1.5) 1.2. Treatment of the Electro-Magnetic Radiation zyxwvuts zyxwvutsrq zyxwvu I. PHYSICAL ASPECTS 1.I. Basic Equations HE SYSTEM of (non-linear) PDE's constituting the semiconductor-device model and incorporating the optical-generation effects is made of Poisson's equation T -div (E grad p) = p (1.1) and of the electron- and hole-continuity equations an -- at 1 - div J , = GZP' - U,,, 4 supplemented by the drift-diffusion expression for the electron and hole current densities J , = -qp,,n grad p and by the expression for the charge density. Eq. (1.1) holds in the semiconductor and in the insulator domains Manuscript received August 11, 1992; revised March 15, 1993. This paper was recommended by Associate Editor J . White. M. C. Vecchi and M. Rudan are with the Dipartimento di Elettronica, Informatica e Sistemistica, Universita di Bologna, 40136 Bologna, Italy. G. Soncini is with the Dipartimento di Ingegneria dei Materiali, Universita di Trento, Mesiano (Trento), Italy and IRST-Divisione Microelettronica, 38050 Povo (Trento), Italy. IEEE Log Number 92 12217. The material layers mentioned above are modeled using the following simplifying assumptions. A stack of m - 2 layers of different materials is considered, separated by plane and parallel interfaces. The stack is placed between medium 1 (initial medium), in which the radiation'source is located, and medium m (final medium), coinciding with a semiconductor zone (Fig. 1). Further, it is assumed that all the m media are optically linear, isotropic, and homogeneous, 0278-0070/93$03.00 0 1993 IEEE zyxwvutsrqponm 1 (initialmedium) case) is taken into account by the complex refraction index ncm. The calculation of the transmission coefficient 3 is carried out by introducing the transmission coefficients ~ T and 3 T M associated with the transverse electric (TE) and transverse magnetic (TM) waves, and expressing 3 as a linear combination of the above [3]: 2 3 3 = + a 2 3 ~ b2&E. ~ E (1.13) The coefficients in (1.13) turn out to be m-2 a 2 = b2 = cos2 P 1 ++BB ~~ / / sin2 A ~P A ~ (1.14) 9 zyxwvutsrqp m-1 sin2 P + B ~ / cos2 A ~P 1+B ~ / A ~ (1.15) zyxwvutsrqp zyxwvut zyxwvut zyxwvutsrqpon zyxwvutsrq m (finalmedium) Fig. 1 . Stack of rn material layers separated by plane and parallel interfaces. the initial and final media have an infinite extension in the direction z normal to the interfaces, and the electromagnetic wave is described by a superposition of plane and monochromatic waves. Thanks to the above hypotheses, the refraction angle 0; in the final medium and the transmission coefficient 3 of the whole structure (i.e., the fraction of the electromagnetic intensity transmitted to the final medium) are easily calculated for each monochromatic component of the impinging radiation. Quantities 0 ; and 3 turn out to depend on the frequency v of the monochromatic component, on the initial angle of incidence O1 and polarization state of the impinging radiation, on the layers' thicknesses di, i = 2, , m - 1 and on the (typically complex) refraction indices of all the media involved, nck = nk(1 + j l k ) , k = 1, * * * , m. Their expressions are easily derived following e.g., [3]. The derivation is summarized in the following, starting with the final refraction angle 0; whose expression is 9 for a specific polarization state of the incident wave, or a 2 = b2 = 1/2 foranon-polarized wave. In (1.14), (1.15), 0 5 B / A 5 1 is the ratio between the axes of the polarization ellipsis of the incident wave, and 0 5 P I7r/2 is the angle between one of the axes and the incidence plane. The transmission coefficients &,, 3 T M , in turn, are given by 3TE = vl Re { 1/vcm(sin e, . ItTE12, 1 ~ T M= - Re TI {q,(sin sin 8, sin 0 ; e; + cos e, = qn, (cos 6 - 3;, sin 6)/Q, sin 0; = nl sin e,/Q. (1.8) (1.9) In (1.8) and (1.9), nl is the real part of the refraction index of the initial medium, while nm, S;, are the real part and the imaginary term of the refraction index of the final medium. Quantities q, 6, and Q in (1.8) are, in turn, expressed by means of the relationships q exp ( j 6) = cos e, = J1 - sin2 e,, (1.10) el, (1.11) = e;)} + COS 8, COS e;)} (1.18) The real quantity q l and the complex one vcmin (1.17), (1.18) are the intrinsic impedances of the initial and final medium, respectively; in turn, tTE is the (complex) ratio between the amplitude of the electric field transmitted to the final medium and that of the incident one for a TE wave, and tTM is the corresponding quantity for a TM wave. Finally, using the speed of light in vacuum and the magnetic permeabilities of the media to define the quantities n1 PI = -cos el, (1.19) CP 1 (1.20) zyxwvutsrq sin 0, = n l / n c , sin and COS (1.17) - - cos 0 ; (1.16) n: sin2 el + q2ni(cos 6 - rrnsin s ) ~ . (1.21) qi (1.12) It is seen that angle 0 ; depends only on the electromagnetic properties of the initial and final medium, and that the absorption in the final medium (silicon in this CPi = - cos ei, (1.22) nci ei = Ji'TZ&, sin ei = n l / n c i sin el, cos (1.23) (1.24) zyxwvutsrqponmlk zyxwvutsrqponmlkj zyxwvutsrqponm zyxwvutsrqpo zyxwvutsrqp 1559 VECCHI er al.: NUMERICAL SIMULATION OF OPTICAL DEVICES i = 2, , m, the expressions for q l , qcm,tTE, found to be Ill = tTM CP1 are (1.25) -3 nl (1.26) 2Pl ~ T E= (mil + m 1 2 ~ r n ) ~+l + m22~m)' (m21 24 1 ~ T M= (mil + mi2qrn)ql + + (mil (1.27) (1.28) mhqm)' zyxwvuts zyxwvut The quantities that are now left to define in (1.27) are the elements mil, mI2,m21,m22of the 2 X 2 characteristic matrix % associated to a stack of homogeneous layers for a TE wave [3]. Similarly, in (1.28), for the elements m i l , mi2, m i l , miz of the corresponding TM-wave characteristic matrix %'. By remembering that d;, i = 2, * * , m - 1 are the thicknesses of the intermediate layers, the expressions of %, 3X'are obtained as the product of the TE and TM characteristic matrices of the individual layers - - 311. = %,(d,) zyxwvutsrqponmlkjihgfed %3(d3) - * * * Xm-l(dm-,) (1.29) %' = %$(d,) * Fig. 2. Transmission coefficient for an Air-Si02-Si structure. The curves correspond to four different oxide thicknesses. %$(d3) * * %;-l(dm-l), (1.30) where cos (yidj) -j/pj sin (yidi) where 3Z'" are the intensities of the incident and transmitted wave, respectively, and hv is the photon energy. Different attenuation mechanisms are possible for an electro-magnetic wave crossing a doped semiconductor, namely 1) excitation of lattice vibrations, 2) excitation of free electrons (holes) between states belonging to the same band, 3) excitation of free electrons (holes) between different conduction (valence) bands, 4) excitation of electrons from the valence band to states belonging to the band-gap, or from the latters to the conduction band, and 5) excitation of electrons from the valence to the conduction band. Of the above mechanism, only the last two directly contribute to the generation terms in (1.2), (1.3), hence to the photocurrent. The other mechanisms contribute to cos (yidi) - j / q i sin (yidi) reduce the intensity of the electromagnetic wave, hence 3 2 ; (d;) = to decrease the number of photons available for generat- j q j sin (yidj) cos (yidj) ing free carriers in the semiconductor. Due to this, they and have an indirect influence on the generation terms as well. However, theoretical calculations and experimental evi2av y; = -nci cos Oi. (1.33) dence indicate that, for non-degenerate semiconductors in C the visible range the last mechanism, i.e., the excitation An example of application of (1.13) is given in Fig. 2, of electrons from the valence to the conduction band, where the transmission coefficient 3 of an air-Si02-Si largely dominates [4]. For degenerate semiconductors, on structure is plotted as a function of the wavelength at four the contrary, the excitation of free electrons or holes (see different oxide thicknesses, for a non-polarized wave. It point 3 above) may become significant. This mechanism, is seen that the behavior of 3 is such that the distance in turn, makes the absorption to depend also on the carrier between the peaks decreases as the oxide thickness in- spatial distribution, hence on the doping distribution itcreases. self. From the viewpoint of the semiconductor-device model, the equations can still be solved at the additional 1.3. Optical-Generation Rate cost of taking into account the dependence of the opticalThe expression for 3 determined in the previous section generation term on the carrier concentration. For the sake allows one to express the photon flux at the semiconductor of simplicity, heavy degeneracy has not been considered in this paper. From this discussion it follows that one may surface and for each monochromatic component as adopt the simplifying assumption of keeping only the last (1.34) mechanism (i.e., item no. 5 in the above list) in the computation, and neglecting the others. Hence, each photon %;(dJ = -jpi sin (yidi) cos (yidi) zyxwvuts 1560 zyxwvutsrqpo zyxwvutsrq zyxwvutsrqp zyxwvuts zyxwvutsrq zyx IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 12, NO. 10, OCTOBER 1993 absorption produces one electron-hole pair, and the expression of GZP' = GpOPt = GoPt let07 SiliconalT=300K - (1.35) holds for each monochromatic component and for the total radiation as well. Furthermore, assuming that the excitation of an electron by a photon in an elementary layer of thickness d t takes place independently of what happens to all the other electrons, it follows that the decrease d+ in the photon flux across the elementary layer is proportional to the flux entering the layer and to d t . Hence + -d+(O = a+(t)d t , (1.36) where a is the absorption coefficient for the band-to-band transitions. Thanks to the simplifying assumption introduced above, the effects of the non-uniform doping and free carriers can be neglected, and the absorption coefficient becomes independent of position and equals the intrinsic one. Then, for a given semiconductor, a turns out to be a function of the radiation frequency v and lattice temperature TL only [5]. The dependency of a on the frequency, in silicon at room temperature, is shown in Fig. 3 by way of example. Due to (1.36), the photon absorption is expressed by means of a Poisson statistical distribution in which the mean penetration length is A = l / a . For each monochromatic component the photon flux at a given depth 4 in the semiconductor along the propagation direction turns out to be W 0 I= ($)2 27rh2 exp (hc/k,Th) - 1 dh (1.42) zyxwvutsrqp zyxwvut +"(E) = exp (--at),a = a ( v , TL). (1.37) Since each photon absorption produces one electron-hole pair, it follows CP'(t) d t = -d+,(t), whence Fig. 3. Silicon absorption coefficient as a function of wavelength at T = 300 K. G:P' (4) = a+ovexp (-at). (1.38) (1.39) The total optical generation rate Gop'(t) is then found by adding up the monochromatic contributions (1.39), viz Gop'(t) = GZp'(4). (1.40) As a final remark, we quote the relevant expressions describing a black-body radiation, which will be used in the next paragraphs. The energy density per unit wavelength of the black body is given by u ( h ) = 87rhc exp (hc/k,Th) - 1 ' (1.41) where Tis the black-body temperature and the other symbols have the usual meaning. The solar spectrum can be approximated by that of a black body at T = 5800 K. It follows that the solar constant, i.e., the power impinging on the unit area outside the earth's atmosphere, is given where Rs = 7 X lo* m is the radius of the sun, RSE= 1.5 x 10" m is the sun-earth distance, and U = 5.652 X W m-2 * K - 4 is the Stefan-Boltzmann constant. Letting T = 5800 K in (1.42), it is found I = 135.3 m * W cmP2. As mentioned above, this value pertains to the solar spectrum outside the atmosphere, and is referred to as the "air mass zero" (AMO) condition [9]. 11. SOFTWARE IMPLEMENTATION 2. I . Illumination Windows Optical generation has been implemented in such a way as to allow the maximum geometrical and structural flexibility. To this purpose, it is worth mentioning that H F I E L D S has the capability of managing a number of different semiconductor zones for a given device, supplemented with the necessary interfaces toward insulating zones, and different types of contacts, gates, and floating gates. In this context, a "zone" is a two-dimensional closed region whose physical properties are fully specified. For instance, in the simple case of an insulating zone one must provide the insulator's permittivity and the fixed charge stored in it. A semiconductor zone is specified in a similar manner, but the physical properties to be provided are of course much more numerous. The maximum number of semiconductor zones that can be dealt with in each simulation is ten. The illumination conditions can be prescribed independently for each of them, since the code has been the capability of managing up to ten illumination windows per semiconductor. The illumination window is defined as the portion of the semiconductor boundary on which a radiation impinges. Consistently with the hypoteses outlined in the previous section, each window is a segment laying along the boundary. For its definition it zyxwvu VECCHI er al.: NUMERICAL SIMULATION OF OPTICAL DEVICES zyxwvutsrq 1561 then suffices to provide the coordinates of the two edges, which need not coincide with any of the grid nodes. Apart from the coordinates, the parameters to be defined for each window are the following. (1.8) and (1.9); the possible occurrence of total refraction is checked at this stage, evaluating the photon flux (Pop transmitted to the final medium, using (1.13) and (1.34). A flag indicating the material of which the final medium is made. This information will be used by H F I E L D S to fetch the real and imaginary part of the refraction index, and the absorption coefficient, at each frequency. It is worth reminding here that the final medium is assumed semi-infinite. A similar flag indicating the material of which the initial medium is made. The initial medium is assumed to be a semi-infinite perfect dielectric. More flags indicating the existence and nature of possible intermediate layers (up to six), which may be absorbent or not. The thickness of each existing layer must be specified as well (see (1.31) and (1.32). The incidence angle, i.e., the angle between the direction of the impinging radiation and the normal to the window. A flag indicating the verse of propagation along the prescribed direction. A flag indicating if a black-body spectral distribution is present. If this is the case, the black-body temperature must be provided as well. More flags indicating the existence (besides that of the black-body radiation) of up to twelve independent spectral components. The properties of the existing spectral components must than be specified as follows: The wavelength in vacuum and the intensity. A flag indicating if the component is polarized or not. If this is the case, the angle and polarization ratio must be specified as well (see (1.14) and (1.15)). Then, a two-dimensional strip (Fig. 4) is constructed by drawing two lines starting from the window’s edges and entering the semiconductor in the O h direction. If node i falls within the strip, and is placed in the correct half plane with respect to the verse of the wave propagation then the contribution of the monochromatic wave to the opticalgeneration rate at node i is evaluated by: zyxwvutsrqpo zyxwv zyx zyxw zy fetching the absorption coefficient of the final medium a ( ~TL) , at the current frequency v, determining the distance t j of node i from the window along the direction defined by the final refraction angle Oh, evaluating the optical-generation rate due to the monochromatic wave, using (1.39) with 4 = t i . The procedure depicted above is nested in a double loop scanning the monochromatic components defined for each of the existing windows, and results in accumulating the individual contributions into the total generation rate G O p t (ti). Finally, in order to scan all the nodes belonging to semiconductors, the calculation is repeated for each semiconductor zone present in the device structure. 2.3. Treatment of the Black-Body Radiation If a black-body radiation is to be considered, its effects are taken into account by H F I E L D S using (1.34), (1.39), and (1.40). The differences between this case and that related to the individually-defined spectral components, as far as the software implementation is concerned, are the following: 1) all the relevant quantities are expressed in terms of wavelength instead of frequency, and 2) the intensity I ( ’ ) in (1.34) is not given as an input datum but is evaluated by the code consistently with (1.42). To this purpose, a finite wavelength-interval B = [Amin, A,], is selected and then subdivided into N A smaller intervals of equal amplitude AA. The band B includes the visible part of the spectrum. In this way, the physical models and the simplifying assumptions listed in the previous paragraph hold and, at the same time, most of the intensity radiating from the sun is taken into account. The value of NA,in turn, is taken large enough to attain a sufficient accuracy in the calculation of the integral in (1.42). The continuous spectrum in B is then replaced by a finite num, ber of wavelengths A, = Amin (s - l)AA, s = 1, N A , whose intensity is defined as zyxwvutsrqpo 2.2 Evaluation of the Optical Generation The effect of the user-defined wavelength, mentioned in the previous section, on the total optical-generation rate is found by adding up the monochromatic contributions. In addition to that, a further contribution comes from the definition of a black-body radiation, whose temperature is imposed by the user. For each window, the black-body radiation is then automatically partitioned into a number of monochromatic components whose effects are then added to those of the individually-defined wavelengths. Let us now focus on the evaluation of the generation rate at a specific node, say node i , in a given semiconductor zone. For each window defined over the zone, and for each monochromatic wave associated to the window, the number of photons entering the zone and the final refraction angle are determined. This is done by: 0 zyxwvuts fetching from the database the refraction index of all the media crossed by the wave. assembling the characteristic matrices (1.3 1) and (1.32) associated to the intermediate layers, and evaluating the final refraction angle Oh, given by + A y5 AA. exp (hc/k,TA,) - 1 - (2.1) Using the above expression to replace in (1.34), and introducing (1.39) recast in terms of wavelength, yields the black-body optical generation 1562 zyxwvut zyx zyxwvutsrqponmlkjihg IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 12, NO. 10, OCTOBER 1993 \ > : * Y * # * * Optical Window (200 urn) i * * : silicn dioxide 9 i zyxw It zyxwvutsrq zyxwvutsrq zyxwvutsrqpon pdimlsi0Il~ junction depth well depth n-well \ \ X paubstrate Fig. 4 , The optical generation effect, for each monochromatic component of the impinging radiation, occurs in the two-dimensional strip defined by the optical window and by the verse of wave propagation. where as = a (As), gs = 3 (As). Here 3$ is calculated using the coefficients for non-polarized light in (1.13). Remembering (1.40), the total optical generation is finally found to be Gop'(E) = Fig. 5. Structure of the two diodes described in Sections (3.1) and (3.2). lected in order to have x j p = 0.56 pm, so that xi,, - x j p = 7 pm. The applied biases are selected as follows: both junctions are reversely biased and, for a given bias V, of the lower junction, that of the upper one ( V u ) is tuned in such a way as to deplete the n-well region completely. In this way, for each pair (Vu, V,) the inversion point of the electric field occurs at a different position in the n-well region. By way of example, the electric potential calculated by H F I E L D S along a cross section of the device at Vu = 8 V is shown in Fig. 6. The position of the inversion point of the electric field is about xinv= 4.35 pm in this case. At a given value of xinv,the upper contact will collect only the holes generated in the region x I xinv.In particular, for a monochromatic radiation at frequency v , the amount of collected holes will depend on the relative magnitude of A = 1/ a (Y) and xinv,thus providing a correlation between current and frequency. The results of the simulations carried out on the device described above are shown in Figs. 7 and 8. In the first one, the current due to the optically-generated holes collected at the upper contact is drawn as function of Vu at different wavelengths. The current is normalized to its value at Vu = 15 V which, for the frequency range under investigation, corresponds to a position of the inversion point deep enough in the n-well region to have the majority of holes collected by the upper contact. In Fig. 8 the simulated and experimental relative spectral response r] , at a constant reverse bias Vu = 1 V , are shown as a function of the wavelength. Indicating with A , Zuv the junction area and the current collected at the upper contact at frequency Y , respectively, the relative spectral response is defined as in [9], namely zyxwvutsrqp Gig([) + E' G;pt(E), V I (2.3) where symbol Cl refers to the individually-defined components only. 111. RESULTS 3.1. Colour-Sensing Photodiode The physical soundness and software implementation of the model depicted in the previous paragraphs have been tested on a number of devices. The results are illustrated in the following. The first set of simulations has been carried out on a photodiode presented in [6]. This device is a part of a more complex circuit which works as a colour sensor. The colour discrimination is obtained through the frequency dependence of the silicon absorption coefficient. In fact, short-wavelength radiation generates most of the electron-hole pairs within a semiconductor zone close to the surface, while long-wavelength radiation generates them in a wider region. By varying the extension of the depleted region it is possible to pinpoint the wavelength of the impinging radiation. The photodiode has been realized with a pf region diffused in an n-well which, in turn, was epitaxially grown on a p substrate. More specifically (referring to the structure of Fig. 5 ) , the oxide thickness is 0.2 pm, the p substrate has a constant acceptor concentration N~~~ = 5 x loi5 cm-j, the n-well region is made of an epitaxial layer with Nepi (3.1) = 7 x 1014(3m-j and xi,, = 7.56 pm, and the pf region is made of a diffusion whose peak concentration is 5 x In both Figs. 7 and 8, the dots refer to the experiments 10" ~ m - The ~ . standard deviation of the diffusion is se- taken from [ 6 ] ,and the continuous lines refer to the sim- zyxwvu zyx zyxwvutsrqponml zyxwv 1563 VECCHI er al.: NUMERICAL SIMULATION OF OPTICAL DEVICES ment between simulation and experimental data resulted in the whole frequency range. 0 zyxwvutsrqponmlkj zyxwvutsrqp L2E-03 60E-04 I BE-03 Device depth ( c m ) Fig. 6. Behaviour of the electric potentials along a cross section of the colour-sensing photodiode described in Section (3.1). I . zyxwvutsrqpo Simulation result . . . . . . Experimental data (Wolfenbuttel) 04t zyxwvutsrqponmlkjihg zyxwvutsrqponmlkjihgfedcbaZYXWV X = 400,550,630 nm 01 02, 0 ; 0 I i I 2 I 3 I 4 / 5 - 7 6 A 8 , ! 1 , 1 I I _1 1 0 1 1 1 2 1 3 1 4 1 5 9 Reverse Voltage ( V ) Fig. 7. Colour-sensing photodiode (Section 3.1): simulation and experimental Illmax curves as a function of the reverse voltage of the upper junction for three different values of wavelengths. The upper, intermediate, and lower curves correspond to X = 480, X = 550, and X = 630 nm, respectively. zyxwvutsrqponmlkjihgfe IO, e, C 0 3.2. CMOS-Compatible Sensor The second set of simulations has been carried out on a specially-designed, CMOS-compatible photodiode fabricated at IRST. The structure under test is structurally similar to that shown in Fig. 5 , and consists of a 200 X 200 pm2 square photodiode made of a p + region diffised in and n-well region. The latter, in turn, was diffused in a p substrate. Two guard rings provide the device isolation with respect to the carriers generated outside the photodiode area. The relatively large dimensions of the photodiode allow for an easier characterization of both the physical and electro-optical parameters. The peak values of the doping concentrations are 5 x l O I 9 and 10l6cmP3 in the p + and n-well region, respectively. In the p substrate, the dopant concentration ranges from 4 X l O I 4 to 4 x 10l6 cmP3. The oxide thickness is tOx = 3 pm, whereas the junction depths are x j p = 0.7 pm and xi,, = 4.7 pm for the p + and the n-well regions, respectively. Both the above regions are accessed through lateral contacts. The electro-optical measurement setup consists of a monocromator-illuminator system with a halogen lamp source and a reference calibrated detector. Orthogonallyimpinging radiation at a wavelength ranging from 400 to 1000 nm has been selected. An HP 4145B parameter analyzer has been used for the measurement of the electrical parameters. Figs. 9 and 10 show the results of the numerical simulation and experiments, respectively. In these figures, the normalized current versus reverse bias is drawn at different wavelengths. Two different terms contribute to the photocurrent: the first one (essentially diffusive) refers to the optical generation in the quasi-neutral regions of the diode, while the second (essentially ohmic) is due to the optical generation in the depleted region. The obtained results show that at short wavelengths the photocurrent is dominated by the diffusive term, and depends weakly on the bias because the optical generation occurs just beneath the semiconductor surface, i.e., far from the depleted region of the p + n junction. Conversely, the ohmic term becomes more important at -long wavelength since the latter reach the depleted layer, and the photocurrent exhibits a stronger dependence on the applied bias. The comparison between the experimental and simulation data shows a good agreement, especially at short wavelengths. As in the previous example, at wavelengths shorter that 550 nm the effect of surface states becomes significant: in this case the estimated density of state ranges from 5 x 10" to 5 x 10" cm-' eV-', with a capture cross-section still set at cm2. The lower limit 5 x 10" of the density of states refers to the midgap region, and has independently been determined by preliminary measurements carried out at IRST. The poorer agreement at long wavelengths is to be ascribed to the insufficient knowledge of the finer details of the doping , , , , I Simulation result ~ 0 400 150 500 550 600 (I50 700 750 800 Wavelength ( n m ) Fig. 8. Colour-sensing photodiode (Section 3.1): simulated and experimental spectral response at constant reverse bias of the upper junction. ulations . The electron-hole pairs optically generated near the interface undergo a heavy recombination effect which has been taken into account in the simulations by introducing a surface-state distribution at the semiconductorinsulator interface. This has been accomplished in H F I E L D S by means of a distribution of states along the gap of the form given in [9], in which the capture crosssection was set at cm2. The other parameters describing the surface states were selected in order to fit the short-wavelength response, resulting in a distribution ranging from 5 x 10" cm-2 eV-' to 5 x 1 0 ' ~cm-2 ev-'. The long-wavelength response was found to be practically unaffected by the surface states, and a satisfactory agree- 1564 zyxwvut zyxwvutsrqponmlkjihgf zyxwvutsrqponmlkjihgfedcbaZYX zyxwvu zyxwvutsrqponmlkjihg IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 12, NO. 10, OCTOBER 1993 eo, S l r n l ~ l a l ~ oresult n ( w i t h s s.) __ . I c owt 0. . . 1- . . . - . :::I zyxwvutsrqponmlkj zyxwvuts zyxwvutsrqpo . . . -30 L A 300 20 50 o n o L . - - - 30 IO 0 . I . , 500 400 Slmulalion result , 600 800 700 ' , 900 , I000 4 0 Wavelength (nrn) Ikverse Voltage ( V ) Fig. 9. CMOS-compatible sensor (Section 3.2): simulated I / I m a x curves as a function of the reverse voltage of the upper junction at different values of wavelengths. The upper and lower curves correspond to X = 400 and X = 800 nm, respectively. The wavelength of the intermediate ones is 500, 600, and 700 nm. Fig. 1 1 . CMOS-compatible sensor (Section 3.2): simulated and experimental spectral response at constant reverse bias of the upper junction. , * , I L + , Experimental dala junction depth X O i n l O L L I O ~- = 400.. ..800nm ' LA 20 30 . 1 40 50 Reverse Voltage ( V ) Fig. 10. CMOS-compatible sensor (Section 3.2): experimental l / I m a x curves as a function of the reverse voltage of the upperjunction at different values of wavelengths. The wavelengths are the same as in Fig. 9. Fig. 12. CCD-oriented structures described in Section 3.3. distribution with the device. This reflects somehow onto the path of the carriers, especially of those generated at a larger distance from the interface. In Fig. 1 1 the simulated and experimental current of the photodiode vs . wavelength, at constant impinging power density (90 pW/cm2) and constant reverse bias (1 V), are shown. The experimental spectrum has been normalized to the lamp spectral emission. The figure shows several peaks due to the multiple reflection and interference phenomena resulting from the presence of a stack of Si02 layers above the semiconductor surface. Preliminary simulations showed that the number and position of the peaks depends more critically on the stack's total thickness than on the thickness and composition of the individual layers, since the latter present similar values of the refraction index. Therefore, in the final simulation a uniform 3.0 pm Si02 has been used. area. The latter is made of an n+ region diffused in a p substrate with a doping concentration of Nsub= 1 X lOI4 ~ m - The ~ . first diode (buried-channel diode) has a n region with a peak concentration No = 10l6 cmP3, a junction depth xjn = 0.9 pm, and an oxide thickness tox = 2.39 pm. The second one (diffused diode) has a n+ region with a peak concentration No = lo2' cmP3, a junction depth x j n = 1.6 pm, and an oxide thickness tox = 2.32 pm. Both photodiodes are reversely biased at 5 V. The incident radiation has a constant power density of 90 pW/cm2 and a wavelength ranging from 400 to lo00 nm. The measurement set-up is the same as the one described above. It is worth noting that, in order to make the comparisons with the experiments easier, the spectral response 3.3 CCD-Oriented Structures The third set of simulations has been carried out on two different photodiodes fabricated at IRST with a CCD-oriented process, characterized by three polysilicon levels, two metallizations and one buried channel. Both structures under test (see Fig. 12) consist of 100 X 100 pm2 square photodiodes with a 90 x 90 pm2 photosensible has been used in the examples illustrated here. Its relationship with the relative spectral response (3.1) is RS = q 3 q / ( h v ) . Opposite to the previous example, where the photocurrent was due to the generation occurring in the vicinity of the upper junction only, here the contribution comes from the whole structure. Hence, a much larger portion of the device in the direction of the light propa- (3.2) zyxwvutsrqponm 1565 VECCHI er al.: NUMERICAL SIMULATION OF OPTICAL DEVICES gation (i.e., vertical in Fig. 12), had to be considered in the simulation in order to take into account the carriers photogenerated by long-wavelength radiation. Fig. 13 shows the spectral response of the buried-channel diode. The high responsivity of the diode at short wavelengths is due to the small concentration of traps at the semiconductor-insulator interface. In the figure, each curve refers to a different interface-state concentration, showing the effect of the latter on the spectral response. The comparison between experimental and simulated data reflects the high quality of the oxide-silicon interface; the latter, in fact, is obtained by the same step of the CCD-oriented process during which the gate oxide is grown, and yields a global surface-state concentration lower than 10" cm-2. Fig. 14 shows the spectral response of the diffised diode. In this case the spectral response at short wavelengths is weakly dependent on the trap density at the interface, since for this diode the junction is deeper than for the buried-channel one. At long wavelengths the agreement between experimental and simulated data becomes poorer due to a lower than expected minority-carrier lifetime in the p substrate. The simulated spectral responses show an inversion in the middle of the considered spectrum with respect to the corresponding experiments. This is to be ascribed again to some uncertainty in the junction depth and doping distribution of the two diodes. 06 - eipcrimcnlal data simulateddata i ---simulatedd i l l 2 ..-.- os - x) Fig. 13. Simulated and experimental spectral response of the buried-channe1 diode of Section 3.3. The simulations refer to three different concentrations of trap states. zyxwvutsrq zyxwvutsrqpo zyxwvut zyxwvut zyxwvutsrq zyxwvu zyxwvutsrqpon 0.6 - crpcmenlaldata mulalion data ---- 0.5 0.4 0.3 0.2 3.4 CMOS Capacitor The fourth set of simulations has been carried out on a CMOS capacitor. Also this device, whose structure is shown in Fig. 15, has been realized at IRST. Its size is 100 x 100 pm2 with a photosensible area of 90 x 90 pm2. The polysilicon gate illuminated by the impinging radiation (photogate) is 106 X 106 pm2 and has a thickness tpoly= 0.35 pm. The thickness of the gate oxide is tpat, = 0.1 pm, while that of the oxide covering the polysilicon is tOx= 2.39 pm. The capacitor is built on a n+ region diffised on a p substrate. The doping concentration of the substrate is Nsub= l O I 4 cmP3, while the peak concentration and the junction depth of the n+ region are No = 2 X 10l6 cm-3 and xi. = 0.9 pm, respectively. On this region, another gate is present (output gate) at 0.15 pm from the photogate. Its function is to collect the charge generated under the photogate and transfer it to a reversely-biased contact realized on a heavily-doped re~ , = 1.6 pm). In this device the gion (No = lo2' ~ m - xjn illuminated region is covered with a layer made of three materials: two oxide layers and one polysilicon layer. The presence of a polysilicon layer makes the behavior of the spectral response quite different from those obtained from the photodiodes, where only oxide layers were present. This is due to the absorbent nature of polysilicon. In contrast with the air-oxide-silicon structure, in this case the transmission coefficient 3 (1.13) is not characterized by uniform oscillations but shows some evident peaks. As suggested in [7], the optical behaviour of polysilicon can be assimilated to that of silicon, obtaining a qualitatively 0.1 400 MO WO 700 800 WO x) Wavelength (nm) Fig. 14. Simulated and experimental spectral response of the diffused diode of Section 3.3. similar transmission coefficient. The description of the latter can be improved by considering a complex refraction index of polysilicon which depends not only on the frequency but also on the grain size and doping concentration. In fact, this dependency has been accounted for in the simulations using the data taken from [8]. The transmission coefficient for the Si02-polysilicon-Si structure is shown in Fig. 16. The capacitor spectral response has been obtained applying 1 V to the photogate, 5 V to the output gate, and 10 V to the output contact, while keeping the substrate at 0 V. Fig. 17 shows the comparison between the simulated and experimental spectral response: although the peaks in the simulated curve are steeper and slightly shifted with respect to the experimental ones, the agreement is qualitatively satisfactory. Apart from the error arising from the incomplete knowledge of the electromagnetic behavior of polysilicon, the discrepancies in the horizontal position of the peaks, as well as the differences in their relative amplitudes, are to be ascribed to the inaccuracy in the measurements of the thickness of the three layers. 1566 zyx zyxwvutsrqponmlkjihgfe IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 12, NO. IO, OCTOBER 1993 silicon dioxide (2.99 urn) + , output contact Optical Window Fig. 15. Structure of the CMOS capacitor described in Section 3.4. 0.8 I Fig. 16. Transmission 0.35 0.4 coefficient for structure. zyxwvu zyxwvut zyxw The device is built on a p-type substrate uniformly doped with NA = 4.5 x 10I6 ~ m - The ~ . S I M S profile reported in [lo] has been reproduced in H F I E L D S by means of a double Gaussian diffusion with Nol = 3 X lo2', No2 = 1019 cm-3 peak concentrations, rol = 0, r02 = 50 nm average penetrations, and u1 = 12, u2 = 55 nm standard deviations, respectively, resulting in an xi,, = 230 nm junction depth. The dielectric layers deposited on the silicon substrate have been reproduced as well, namely a 5-nm Si02 layer, a 150-nm MgF2 layer, and a 150-nm ZnS layer. For the Si02 layer a refraction index n = 1.45 has been used. Those reported in [lo] for the other two materials are in the range 1.35-1.40 and 2.25-2.35, respectively, and the minimum value for both has eventually been used in H F I E L D S since their fluctuations have shown little effect on the results. The three layers are designed in order to form an antireflection coating. The effect of the latter has been simulated as well and is shown in Fig. 18, where the transmission coefficient 3 is drawn as a function of the wavelength. The continuous line represents the transmission coefficient of a pure air-silicon structure, i.e., before depositing the layers, hence it essentially describes the reflection at the silicon interface. The dashed line represents a situation, not appreciably different from the previous one, where only the Si02 layer is present and, finally, the dotted curve shows the combined effect of the three layers. The simulations have been carried out imposing a blackbody radiation, at different values of the temperature and impinging power, brought to the cell through an illumination window coinciding with the device's effective area A, = 2 X 2 cm2. The wavelength-band B introduced in section 2.3 has been set to [300, 10001 nm. For convenience we shall indicate with Z(B)the value obtained from (1.42) when the integral is camed out on B . Of course the value of Z(B) is smaller than that associated with the full spectrum. For instance, at T = 5800 K it is Z(B) = 96 instead of Z = 135.3 mW * cm2. This figure is close to zyxwvutsrqp an Air-SiO,-PolySi-SiO,-Si i Fig. 17. Simulated and experimental spectral response of the CMOS capacitor of Section 3.4. 3.5 Solar Cell The last example of application consists of a solar cell, whose structure has been taken from published data [ 101. zyxw VECCHI zyxw zyxwvutsrqponml zyxwvutsrqponmlk zyxwvutsrqponmlkji 1567 al.: NUMERICAL SIMULATION OF OPTICAL DEVICES et I . . 0 - Air& Air-SiO2-SI ---Air-ARC-SI -.... -0 02 -0.04 -0.06 -0.OR -0.1 zyxwvutsrqponmlkjih zyxwvutsrqponml -0.12 04 300 400 500 sm 700 My) WO lam Wavelength (nm) Fig. 18. Solar cell (Section 3.5): transmission coefficient of the antireflection coating compared with those of simpler structures, namely Air-Si and Air-Si02-Si. 0 , I ' ."Id 0 01 0.2 03 04 v (V) OS 06 07 OR Fig. 20. Simulated I-V curve of the solar cell at T = 5800 K black-body temperature. The load characteristic, the maximum-power current, and the maximum-power voltage are also shown. I zyxwvutsrqponmlkjih I i TABLE I -004 -0 12 OIR I. r ' 0 ~ ........................................ ~~~ ......... .......-- __I' ~~ Simul. Exper. r101 120 636 114 560 63.7 4.9 384 83.5 16.6 142 64 1 145 525 76.1 3.6 400 82.2 18.7 I 01 02 03 04 v (VI 05 06 07 OR TABLE I1 Fig. 19. Simulated I-Vcurves of the solar cell in the fourth quadrant. The curves refer to three different values of the black-body temperature. - that of [lo], namely I = 100 mW cm2. It should be remarked, however, that the latter value is to be ascribed to the "air mass 1.5 condition'' in which the experiments reported in the above reference have been carried out. The AM1.5 condition (sun at 45" above the horizon), which represents a satisfactory energy-weighted average for terrestrial applications, introduces a non-uniform attenuation in the spectral energy density with respect to the AM0 condition. It follows that the spectrum used in our simulations is somewhat different from the experimental one, despite the near identity of the impinging power densities. Because of this, the comparisons which will be shown below are of qualitative nature only. The portion of the simulated I-V curves belonging to the fourth quadrant are shown in Fig. 19 at three different black-body temperatures, namely T = 5300, 5800, and 6300 K. It is seen that the effect of a temperature change is large on the short-circuit current Z,, and less important on the open-circuit voltage Vac. The intermediate curve, which corresponds to T = 5800 K, is repeated in Fig. 20, where it is used for the evaluation of the maximum-power output P,. The two dashed lines show the maximumpower current (I,) and voltage ( V,), respectively, while Black-body Temperature (K) 5300 5800 6300 82 626 78 550 42.9 7.0 252 83.6 17.0 120 636 114 560 63.7 4.9 3 84 83.5 16.6 167 644 160 560 89.8 3.5 552 83.5 16.3 zyxwvutsrqp the thicker line represents the corresponding load characteristic I = - V I R , , R, = V m / I m Letting . P , = I, V,, Pin = A,Z(B), the fill factor and the efficiency of the cell are derived from the above quantities as [9] (3.3) The results of the simulations have been grouped in tabular form: Table I shows the relevant parameters calculated at T= 5800 K and compares them with those taken from [lo], Table I1 shows a comparison between the simulated parameters calculated at the three different temperatures, and Table I11 shows a comparison between the zyxwvutsrq 1568 zyxwvutsrqponmlkjih IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS, VOL. 12, NO. 10, OCTOBER 1993 TABLE 111 Concentration Factor 10 1 20 30 40 50 60 ~ 120 636 114 560 63.7 4.9 384 X 1 83.5 16.6 1203 695 I158 610 707 0.53 384 x 10 84.5 18.4 2410 713 2311 630 1456 0.27 384 x 20 84.7 18.9 3618 723 3470 640 222 1 0.18 384 x 30 84.9 19.3 4829 731 4608 650 2995 0.14 384 X 40 84.9 19.5 6043 736 5817 650 378 1 0.11 384 X 50 85.0 19.7 ~ 1259 740 7028 650 4568 0.09 384 X 60 84.9 19.8 zyxwvutsrq zyxwvutsrqpo zyxwvutsrqpon zyxwvu those refemng to r] and V,, as functions of the concentration factor, are also drawn in Figs. 21 and 22. A comparison with published data is possible, in this case, using those of [ 111 where a device similar to that of [ 101 is presented. Again a fair agreement with the experiments is found. IV. CONCLUSIONS The introduction of the optical-generation effect in a general-purpose semiconductor-device analysis program has been described in this paper. The following aspects have been developed. 165 I IO Conccnrnlron Factor 100 A sound physical description of the optical part, which takes into account the presence of both perfectly dielectric and absorbent media together with multiple refraction phenomena. The introduction of the optical-generation effect into H F I E L D S with the maximum structural and geometrical flexibility, maintaining the generality of the original simulator. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO zyxwvutsrqponmlkjihgfe Fig. 21. Simulated efficiency of the solar cell as a function of the concentration factor. 0 76 I 1 0 14 0 72 07 U 0“ Coupling these items, the simulation of realistic optical devices became possible, profiting by the more detailed characterization and greater accuracy provided by a numerical-analysis program with respect to the standard analytical approaches. The capabilities of the code have been illustrated in several examples. The results show that the effects of absorption, multiple-reflection and interference phenomena exhibited by the spectral response of the sensors definitely justify the implementation effort required by the description of the e.m. wave propagation through the material layers. This becomes particularly relevant for the many applications where the dependence of the solidstate sensor response on the wavelength of the impinging radiation is critical. zyxwvutsrqponmlk zyxwvutsrqponmlkjihgfedcba 0 68 0 h6 11 (12 Coiicciilrriiuii Factor 100 Fig. 22. Simulated open-circuit voltage of the solar cell as a function of the concentration factor. same parameters calculated at different values of the impinging power. It is seen from Table I that all the simulated parameters are in the correct range (it is worth adding that no parameter fitting has been attempted here). The purpose of Table I1 is more academic, that is, showing what the trend of the relevant quantities would be if the temperature of the illuminating body changed. Finally, Table I11 shows the effect of a factor C inserted in (1.42) to emulate the presence of a concentrator. Some data of Table 111, namely REFERENCES zyxwvutsrqpo [l] G. Verzellesi, M. C. Vecchi, M. Zen, and M. Rudan, “Optical Generation in Semiconductor Device Analysis, a General-purpose Implementation,” in Proc. of the Fourrh SISDEP Conf., Zurich, W. Fichtner, D. Aemmer, eds., pp. 57-64, 1991. [2] G. Baccarani, R. Guerrieri, P. Ciampolini, and M. Rudan, ‘“FIELDS” : A Highly Flexible 2-D Semiconductor-Device Analysis Program, in Proc. of the NASECODE IV Conf., Dublin, J . J. H. Miller, ed., pp. 3-12, 1985. zyxwvutsrq zyxwvutsrqponm zyxwvutsrqpon zyxwvutsrqponml zyxwvutsrqp zyxwvut VECCHI et al.: NUMERICAL SIMULATION OF OPTICAL DEVICES [31 M. Born and E. Wolf, Principle of Optics. New York: Pergamon, 1980. 141 R. H. Bube, Photoconductivity of Solids. New York: Wiley, 1960. 151 H. R. Philipp and E. A. Taft, “Optical Constants of Silicon in the Region 1 to 10 eV,” Phys. Rev., vol. 120, no. 1, 1960. R. Wolfenbuttel, Integrated Silicon Colour Sensors. Delft University of Technology, 1988. 171 C. Anagnastopoulos and G. Sadasiv, “Transmittance of Air/SiO,/ Polysilicon/SiO,/Si structures,” IEEE J. Solid-State Circuits, vol. 10, pp. 177-179, June 1975. G. Lubberts, B. C. Burkey, F. Moser, and E. A. Trabka, “Optical Properties of Phosphorus-Doped Polycristalline Silicon Layers,” J. Appl. Phys., vol. 52, no. 11, 1981. [9] S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981. [lo] M. A. Green, A. W. Blakers, J. Shi, E. M. Keller, and S . R. Wenham “High-Efficiency Silicon Solar Cells,’’ IEEE Trans. Electron Devices, vol. ED-31, May 1984. [ l l ] M. Finetti, P. Ostoja, S. Solmi and G. Soncini, A New Technology to Fabricate High-Frequency Silicon Concentrator Solar Cells, IEEE Trans. Electron Devices, vol. ED-27, Apr. 1980. Maria Cristina Vecchi received the degree in electrical engineering from the University of Bologna in 1990 and, since then, has been working at the Dipartimento di Elettronica, Informatica e Sistemistica (DEIS) of the same University. At DEIS, she has been engaged in an activity on the numerical simulation of semiconductor devices, with emphasis on the optimization techniques for process design and on the simulation of optical sensors. She is presently visiting the IBM T.J. Watson Research Center of Yorktown Heights, NY, working on higher-order transport models in semiconductors. 1569 Massimo Rudan (M’80-SM’92) received a degree in electrical engineering in 1973 and a degree in physics in 1976, both from the University of Bologna, Bologna, Italy. After serving as a Naval officer, he joined the Dipartimento di Elettronica, Informatica e Sistemistica (DEIS) of the University of Bologna in 1975, where he investigated the physical properties of the MOS structures and the problems of analytical modelling of semiconductor devices. From 1978 he has been teaching an annual course of Quantum Electronics in the Faculty of Engineering of the same University, firstly as Lecturer and then as Associate Professor. Since 1983 he has been working in a group involved in numerical analysis of semiconductor devices, acting as Task leader in a number of EEC-supported Projects in the area of CAD for VLSI. In 1986 he was a visiting scientist, on a oneyear assignment, at the IBM Thomas J. Watson Research Center at Yorktown Heights, NY, studying the discretization techniques for the higherorder moments of the Boltzmann Transport Equation. He was again with IBM later, investigating and implementing impact-ionization models based on the average energy of the carriers. In 1990, he was appointed Full Professor of Microelectronics at the University of Bologna. Giovanni Soncini graduated in electronics in 1965 at the School of Engineering of the University of Bologna, and received the Ph.D. (Libera Docenza) in quantum electronics carrying on research mainly at the Politecnico of Milan and Stanford University. Since 1970 he has been responsible for the research activity on MOS physics and technology at the LAMEL Institute, established in Bologna by the Italian National Council for Research. In 1984 he became Assistant Professor of Microelectronics at the University of Bologna, and in 1987 became Full Professor of Aerospace Electronics at the School of Aerospace Engineering of the University of Rome. In 1990 he moved to the chair of Microelectronics Materials and Technologies at the Materials Engineering School of the University of Trento, and acts as Scientist in Charge of the Microelectronics Division of IRST. He is the author of more than 70 publications in international journals and books on Microelectronics Technology, and Chairman of International Conferences. Workshoo. and Schools. His main interest is now in VLSI CCE/CMOS technolog’ies and development of smart sensors.