new analytical expressions for dark current calculations of highly doped regions in semiconductor...

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 1, JANUARY 1997 171

New Analytical Expressions for DarkCurrent Calculations of Highly Doped

Regions in Semiconductor DevicesA. R. Burgers, Cor Leguijt, Peter Lolgen, and Wim C. Sinke

Abstract—We studied highly doped quasi-neutral regions ofsemiconductor devices with position dependent doping concentra-tion in the absence of illumination. An important parameter of ahighly doped region is its dark current. To clarify how the dopingprofile influences the dark current, simple analytical expressionsare useful.

To this end, we first transformed the transport equations toa simple dimensionless form. This enables one to write alreadyexisting analytical expressions in an elegant way. It is demon-strated how, from any analytical dark current expression, a directcounterpart can be derived.

Next, we derived a dimensionless form for a nonlinear first-order differential equation for the effective recombination ve-locity. Starting from the analytical solution of this differentialequation for uniformly doped regions and using linearizationtechniques, we obtained two new simple and accurate expressionsfor the dark current. The expressions are valid for general dopingprofiles with different minority carrier transparencies. The exactsolution is included between both new approximate solutions.The new expressions are compared with previous approximatesolutions.

I. INTRODUCTION

M ANY attempts were made to arrive at simple closed-form formulas for the dark current and minority carrier

concentrations in highly doped regions. These are usefulfor optimizing doping profiles and gaining physical insightinto electrical behavior. In solving the transport equationsfor arbitrary doping profiles, there is always a compromisebetween accuracy and simplicity. There are various ways tocombine these as well as possible.

After a literature discussion we introduce our new coordi-nate transformation. The transformation simplifies the trans-port equations considerably. It turns out that one materialparameter, the newly introduced “characteristic dark current,”plays a central role. The physical interpretation of the char-acteristic dark current will be clarified. The transformationyields simpler forms of previous expressions. The transformed

Manuscript received September 19, 1995; revised June 26, 1996. The reviewof this paper was arranged by Editor P. N. Panayotatos. This work has beencarried out within the framework of the program “Solar Cells for the 21stCentury” from the Netherlands Organization for Scientific Research NWOwith support from The Netherlands Energy Research Foundation ECN.

A. R. Burgers and W. C. Sinke are with ECN Renewable Energy, 1755 ZGPetten, The Netherlands.

C. Leguijt was with ECN Renewable Energy, 1755 ZG Petten, The Nether-lands. He is now with Energy North West (ENW), 1009 DC Amsterdam, TheNetherlands.

P. L Lolgen was with ECN Renewable Energy, 1755 ZG Petten, TheNetherlands. He is now with Siemens AG, Munich, Germany.

Publisher Item Identifier S 0018-9383(97)00320-1.

equations have a symmetry which is exploited to obtain di-rectly from any analytic dark current expression a counterpart.Examples on usage of the symmetry will be given.

Next, two first-order nonlinear differential equations for thedimensionless recombination velocityand its reciprocalare derived and analyzed. Starting from an approximate initialsolution, which coincides with the exact solution for uniformlydoped regions, and linearizing the differential equations aroundthis initial solution yields two new expressions. The exact so-lution is shown to be included between both new expressions.

The limiting behavior of the new expressions is comparedwith previous analytical expressions. The new expressionsare compared with the exact numerical solution and previousanalytical expressions for several profiles.

II. L ITERATURE

In 1989, Cuevas and Balbuena [1] a review of literaturein this field, which we will update here for dark currentcomputations. Models are grouped by the method they use.

A. Assumption of Special Relations Betweenthe Material Properties

When special relations between material properties areassumed, closed form analytical solutions possible of thesecond-order equation for the current density are possible.The accuracy of the assumption limits the usefulness of theexpressions obtained. Abenante [2] assumes with

and some constants, the diffusion coefficient andthe doping concentration.

Lindholm [3] assumes and exponentialdependence of the doping concentrationon depth and thatthe electric field is position independent. Verhoef and Sinke[4] extend the model of Lindholm with adjustable apparentbandgap narrowing. Instead of working with an average valueof the mobility as Lindholm does, they use a power-lawdependence of on

Selvakumar [5] and Rinaldi [6] solve the transport equationsassuming constant The problem is to find agood estimate for in case of nonuniform doping. Rinaldi[6] obtained a much improved estimate for this average value.

B. Transparency is Assumed

Del Alamo et al. [7] uses the differential equation for therecombination velocity Assuming transparency, analytic

0018–9383/97$10.00 1997 IEEE

172 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 1, JANUARY 1997

solutions are obtained. The applicability of the expressionsis limited by the simplifying physical assumptions.

C. Breakdown of the Region Under Analysisin Several Subregions

The highly doped region is divided into several subregions.Simple analytical solutions for individual regions are coupledtogether, making the final solution less simple. Amantea[8] distinguishes regions where transport is either field—ordiffusion dominated. Fossum and Shibib [9] distinguish highlydoped regions where bandgap narrowing and majority carrierdegeneracy are important and a lowly doped region wherethat is not the case. A third region near the surface isdistinguished with short lifetimes. This region is characterizedby an effective recombination velocity.

Jankovic and Karamarkovic [10] combine this regionalapproach with the differential equation for

Iterative solutionsare attempted to the system of differentialequations or a reformulation of it. Applying one iterationgives simple analytical expressions which can be sufficientlyaccurate. Parket al. [11], Cuevas [12] and Rinaldi [13] makedirect use of the transport equations for current density andcarrier concentration. Rinaldi [13] shows that for thin emittersand the right choice of the model of Selvakumar [5]is equivalent to his new first-order approximation. For thickemitters this method requires many iterations.

De Castro and Rudan [14] transform the transport equationsto an integral equation for the excess carrier concentration.Iterative solution of this equation converges fast, but does notgive simple expressions.

Our work falls into this last category. It uses iterativemethods for the differential equation of

III. T RANSPORT EQUATIONS AND

COORDINATE TRANSFORMATION

In this section, we will present a coordinate transform,which simplifies the transport equations, making them moresuitable to subsequent analysis.

We focus on p-type material. For n-type material the deriva-tion is completely analogous. Let and be the equilibriumconcentrations of electrons in the doped material and intrinsicmaterial, respectively, and be theexcess electron concentration. The minority carrier currentconsists of a drift and a diffusion component. The electric field

for the drift component is given by

(1)

The two low injection minority carrier transport equationsare written as follows:

(2)

(3)

We assume the silicon surface is at and that it has arecombination velocity This corresponds to the boundary

condition

(4)

We define the normalized excess carrier concentrationWith these definitions we obtain (see e.g., Cuevas [1])

(5)

(6)

Two material constants are needed, and Thecrucial step is to define a new coordinate as follows:

(7)

In the sequel, differentiation with respect towill be indi-cated by the symbol Effectuating transformation (7) whichis different from the coordinate transformation of Rinaldi [6]on (5) and (6) leads to

(8)

(9)

where we used Now we define a characteristicdark current This is equivalent to the

of Rinaldi [6]. This leads to

(10)

(11)

We see a formally simple set of equations with only onematerial constant explicit. However the diffusion length isstill required to do the coordinate transform. If both sides aredivided by we obtain

(12)

(13)

This exposes a nice symmetry betweenand which willturn out to be useful later on.

IV. DIFFERENTIAL EQUATIONS FOR , AND

In this section, we will introduce the normalized effectiverecombination velocity and its reciprocal We will derivesecond-order linear differential equations for and andnonlinear first-order differential equations forand

Without loss of generality, it is assumed in this work thatthe recombination velocity is known at with thedevice present at For every -coordinate, we definea recombination velocity as used by del Alamoet al.[7]. describes the effective recombination velocity of theregion to the left of

(14)

BURGERSet al.: NEW ANALYTICAL EXPRESSIONS FOR DARK CURRENT CALCULATIONS 173

We define a dimensionless recombination velocityand its reciprocal can be expressed in

terms of and as follows:

(15)

If we know we can decouple (10) and (11) using (15)and reduce them to first-order equations

(16)

(17)

From the system of (10) and (11), it is straightforward toobtain two linear second-order differential equations forand

(18)

(19)

On differentiation of (16) and (17) and subsequent substi-tution of (18) and (19) we obtain two equivalent first-ordernonlinear differential equations for and

(20)

(21)

We have as boundary conditionNote that (21) can be rewritten as follows:

(22)

By comparing (20) and (22) we can conclude that anyanalytical expression obtained forthe differential equation for can be immediately transferredto one for by replacing by its reciprocal and by

V. THE CHARACTERISTIC DARK

CURRENT AND PASSIVATION

This section will discuss the physical meaning of thecharacteristic dark current and show how to work withthe differential equations for by looking at the case of auniformly doped region with a p-n junction at In theuniform doping case, (20) reduces to

(23)

The solution to this equation with dimensionless recombina-tion velocity at can be written in several equivalentforms

(24)

In order to calculate the dark current, the junction is assumedto be in reverse bias. We therefore haveor equivalently Suppose we want to compute the

contribution to the dark current of the region Weproceed as follows:

(25)

For a high–low junction this is the familiar result encoun-tered in many textbooks, for instance Sze [15]. For thickregions or large this equation reduces to

We see that in the case of a uniformly doped infinitely thickregion, the characteristic dark current corresponds to itsdark current.

From (24) it is possible to define passivation. An infinitelythick region has a This corresponds with a recom-bination velocity If the surface recombinationvelocity at (with the device present at happensto be we could replace the air at in athought experiment with uniformly doped material with thesame doping level as at the surface

This half space of uniformly doped material could becharacterized at by a recombination velocity ofWe therefore call a surface passivated ifOtherwise it is unpassivated.

VI. USAGE OF SYMMETRY

The symmetry found between- and -equation can beexploited as noted at the end of Section IV. Suppose we havean analytical expression for the dark-current of the followinggeneral form:

(26)

A new analytical dark current expression is then

(27)

Park et al. [11] presented a model of dark current calcu-lations of highly doped regions make direct use of the (2)and (3). This work has been generalized by Cuevas [12] andRinaldi [13], [6]. We will demonstrate the usage of symmetryby applying it to this work. First it is shown how theseexpressions look using our coordinate transform. We define


with recursively definedas follows:

The functions and were assignedtheir names in analogy with the work of Park, Rinaldi, andCuevas for easy reference and have the following properties:

Since the pairs and satisfy(10) and (11), and represent two independentsolutions for the excess carrier concentration while and

represent two independent solutions for Parkputs the junction at thus and therecombining surface at We introduceThe solution to transport equations with boundary condition

is

(28)

(29)

(30)

Approximate expressions can be obtained by truncating theseries expansions. Table I shows the number of terms retainedin successive approximations as proposed originally by Parkand in Rinaldi [13]. The comparison demonstrates that thenotion of order of the approximation is not well-defined inthis context as noted by Cuevas [12] and Rinaldi [13].

Cuevas [12] and Rinaldi [13] independently presented im-proved approximate solutions based on retaining the samenumber of terms in both the nominator and denominator. Theseapproximations are also given in Table I. We will refer tothese approximations as homogeneousth-order truncationsto distinguish them from the th-order approximations fromPark.

Consider the 0th-order approximation from Park. In ournotation it reads

(31)

The symmetry mapping changes into and viceversa and into and vice versa. Applying the symmetry

TABLE ITHE NUMBER OF TERMS RETAINED IN THE EXPANSION OF THE FUNCTIONS

A(y); B(y); A(y), AND B(y) AS A FUNCTION OF THEORDER OFAPPROXIMATION

mapping from to equation we obtain

(32)

This is the 0th-order approximation from Rinaldi [13]. Inthe same way it can be demonstrated that the homogeneousapproximations of Cuevas [12] and Rinaldi [13] are invariantunder this symmetry mapping. As it should be, the exact seriessolution (30) is also invariant under the symmetry mapping.

The symmetry mapping can be applied to the analyticalsolution obtained in Rinaldi [6], which reads in our notation

(33)

(34)

(35)

(36)

Applying the symmetry mapping we find

(37)

(38)

(39)

(40)

This is a first new analytical expression for the dark current.


VII. FIRST-ORDER NEWTON APPROXIMATION

In this section, we will show how an initial solution canbe improved through linearization of either the differentialequation for or the

Let the operator be defined as follows:

(41)

Let be an initial solution which satisfies the boundarycondition Let The operator canbe linearized as follows by discarding the term:

(42)

An improved solution is found by demanding

(43)

An important thing to note is that the discarded isalways positive. This means that and are overestimatedin the linearization. This implies that for all iterates (exceptthe initial solution) one has the useful inclusion

On expansion of we obtain

(44)

In analogy to (16) we can define for every iterate acorresponding normalized excess carrier concentration

(45)

The solution of the differential (44) is elementary. An inte-grating factor is With the help of this integratingfactor we get

(46)

On expressing in we obtain an alternative formulation

(47)

Note that by imposing and andone looks for a fixed point of the Newton iteration

process and in this way one obtains an integral equation foreither or Also note that although the differentialequations for and are equivalent, the linearizations are notequivalent.

VIII. C HOICE OF STARTING SOLUTION

The idea is to take as a first approximation the solutionof the general (20) by discarding the term leadingto (23). We obtain the following start solution for the-equation

(48)

In this case we havewith some arbitrary constant. We introduce the function

which can be written as

We obtain for and by analogy for the-equation forthis initial approximate solution

(49)

(50)

From the expressions (49) and (50), we can directly deriveexpressions for the total dark current of a nonuniformly dopedregion analogous to the derivation in Section V for uniformlydoped regions

(51)

(52)

Our analytical expressions (51) and (52), are formallydifferent from those in Rinaldi [6] and from the truncated seriesexpansions from Section VI and therefore new.

One can easily check that formula’s (51) and (52) reproducethe exact result for the case of uniform doping independentof the thickness of the profile. This is in contrast with thetruncated Park-like expressions from Section VI, which aretruncated Taylor series expansions of the relevant hyperbolicfunctions around a point, whereas we linearize a differentialoperator.

In order to get a feeling for the expressions is it useful tolook at some extreme cases. For both our linearizationsand the truncated Park-like solutions yield the correct value

Table II gives limiting values for andfor various cases. These will be compared with limiting casesfor other expressions. First we compare with the homogeneousfirst-order expression from Cuevas [12] and Rinaldi [13] whichreads in our notation

(53)


TABLE IILIMITING VALUES OF (51) AND (52)

Fig. 1. The three simulated BSF implanted doping profiles used. See TableI for transparency and dose of the profiles.

Equation (53) is correct in the limit of thin regions for allvalues of By comparing (53) with the limiting expressionsfrom Table II one can see that the linearization based on (51)coincides with (53) for low as does the 0th-order Park (31)while the linearization based on (52) coincides with (53) forhigh values as does the 0th-order Rinaldi (32).

Equation (51) does not give the correct limiting value forsmall for a high value and (52) does not give the correctvalue for a low value, although the deviations are not as bigas in the case of the 0th-order Park and Rinaldi approximationsas will be demonstrated in the results section.

For opaque regions, the following relation can be easilyestablished between our approximate solutions andand that of Rinaldi [6]:

- (54)

IX. RESULTS

We performed simulations for six doping profiles. Threedoping profiles (shown in Fig. 1), as used in a solar cell BackSurface Fields (BSF), resulting from an implantation simula-tion program were used: one transparent, one opaque and anintermediate profile. Also three Gaussian doping profiles were

TABLE IIISOME CHARACTERISTICS OF THETHREE SIMULATED DOPING PROFILES

USED. THE DEFINITIONS OF �1 AND �2 ARE GIVEN IN (56) and (57).

Fig. 2. Comparison for simulated BSF implantation profile 1 and threevalues of the dimensionless recombination velocity at the surface of the exactsolution of the differential equation fors and the two linearized solutions(49) and (?50.

Fig. 3. Comparison for simulated BSF implantation profile 1 of the nor-malized dark currents(W ) = Jn0(W )=J0c(W ) for different values of thedimensionless recombination velocity at the surface according to the exactsolution and the two linearized solutions (49) and (50).

used

(55)

A peak doping level of cm and a basedoping level cm were used. For the width


TABLE IVTHE NORMALIZED DARK CURRENT Jn0(w)=J0c(w) FOR GAUSSIAN DOPING PROFILES OF DIFFERNT WIDTHS AND

THREE DIFFERENT VALUES OF THE DIMENSIONLESS SURFACE RECOMBINATION VELOCITY s0 = S0Ln(0)=Dn(0)


of the profiles we used 0.01m 1 m, and 100 m TableIII lists the doses, transparencies and at the surfacefor the profiles used. Two measures were used for the opacityof the profiles

(56)

(57)

The definition for (56) is from Rinaldi [6]. The definitionfor (57) follows directly from our coordinate transform.In these cases both definitions lead to rather similar opacityvalues. The definition for seems to be somewhat simpler.

The differential equation for (20) can be solved numer-ically. Fig. 2 shows for profile 1 how the exact solution isenclosed between the results based on linearization for both

and equation. Even though this is an almost transparentprofile, the profile based on (49) is less accurate for highvalues and the profile based on (50) is less accurate for low

values. Fig. 2 also shows the start solution according to(48). The start solution departs little from a constant sinceprofile 1 is almost transparent. The start solution is muchimproved upon.


Figs. 3–5 show the normalized dark currentfor the three simulated implantation profiles.

For the thickest profiles there is little influence of therecombination velocity at the surface, indicating the usefulnessof both and

Table IV shows the normalized dark currentfor the three Gaussian profiles. A tabular

representation has been chosen since in a graph some ofthe differences are indiscernable. Different solutions are com-pared. Both the solution from Rinaldi, (33)–(36), and ourvariant, (37)–(40), are very accurate. Unfortunately, they donot include the exact solution. Our approximate solutions (51)and (52) do provide an inclusion and are not more than 15%off for the whole range of transparencies. The average valueof our linearizations is not more than 10% off. The truncatedseries expansions from Section VI are inaccurate for thickregions as expected.

X. CONCLUSIONS

The coordinate transformation with the diffusion lengthresults in a simple formulation of the transport equations. Afterthe coordinate transform only one position dependent materialproperty, describes the problem. The diffusion length is


still needed, but hidden in the coordinate transform. isthe dark current of an infinitely thick uniformly doped layer.Because of its central role in the analysis and its physicalmeaning we coin the term “characteristic dark current” for

The symmetry between the equations for the normalizedcarrier concentration and the current density has been exploitedto obtain directly a counterpart for any analytic dark currentexpression. This led to a variant of the analytical expressionin Rinaldi [6].

A simple dimensionless form has been derived of the differ-ential equation for the effective dimensionless recombinationvelocity A similar equation can be written down for itsreciprocal Starting from a solution, which coincideswith the exact solution for uniform doping, and applying alinearization technique to both the differential equations forand two new approximate expressions were obtained for thedark current of a highly doped region.

A useful result is that linearizations of the differentialequations for and provide an inclusion of the exact solution.The computation time of the linearizations is dominated by cal-culation and weighted averages ofand its reciprocal. Also the coordinate transform has to becomputed. From the calculations and limiting expressions wesee that for transparent regions and low recombining surfaceswe can best use approximations based on linearization ofthe equation for and for highly recombinative surfaces thelinearization of

The new expressions were compared with previous solutionsfor six doping profiles. Our new expressions give a goodestimate of the dark current. The estimates are much better thanthose obtained from truncated series solutions for electricallyopaque profiles. The estimates are simpler but less accuratethan those obtained in Rinaldi [6] and our variant of that.For the latter estimates, also the integrals of and itsreciprocal have to be computed in addition to the computationsrequired for the linearizations.

ACKNOWLEDGMENT

The authors would like to thank two of the reviewers for athorough review and some valuable suggestions.

REFERENCES

[1] A. Cuevas and M. A. Balbuena, “Review of analytical models for thestudy of highly doped regions of silicon devices,”IEEE Trans. ElectronDevices, vol. 36, pp. 553–560, Mar. 1989.

[2] L. Abenante, “Equivalent solution for the minority carrier transport indoped silicon,”Solid-State Electron., vol. 36, no. 12, pp. 1797–1800,1993.

[3] F. A. Lindholm and Y. H. Chen, “Current–voltage characteristic forbipolar p-n junction devices with drift fields, including correlationbetween carrier lifetimes and shallow-impurity concentration,”J. Appl.Phys., vol. 53, no. 12, pp. 8863–8866, 1982.

[4] L. A. Verhoef and W. C. Sinke, “Minority-carrier transport in nonuni-formly doped silicon—An analytical approach,”IEEE Trans. ElectronDevices, vol. 37, pp. 210–221, Jan. 1990.

[5] C. R. Selvakumar, “Simple general analytical solution to the minoritycarrier transport in heavily doped semiconductors,”J. Appl. Phys., vol.56, no. 12, pp. 3476–3478, 1984.

[6] N. Rinaldi, “Modeling and optimization of shallow and opaque heavilydoped emitters for bipolar devices,”IEEE Trans. Electron Devices, vol.42, pp. 1126–33, June 1995.

[7] J. A. del Alamo, J. van Meerbergen, F. D’Hoore, and J. Nijs, “High–lowjunctions for solar cell applications,”Solid-State Electron., vol. 24, pp.533–538, 1981.

[8] R. A. Amantea, “A new solution for minority-carrier injection intothe emitter of a bipolar transistor,”IEEE Trans. Electron Devices, vol.ED-27, pp. 1231–1238, 1980.

[9] I. G. Fossum and M. A. Shibib, “An analytical model for minoritycarrier-transport in heavily doped regions of silicon devices,”IEEETrans. Electron Devices, vol. ED-28, pp. 1018–1025, Sept. 1981.

[10] N. D. Jankovic and J. P. Karamarkovic, “Analytical model for the effec-tive recombination velocity at an arbitrarily doped high–low junction,”IEE Proc., vol. 135, Part I, no. 5, pp. 136–138, 1991.

[11] J. S. Park, A. Neugroschel, and F. A. Lindholm, “Systematic analyticalsolutions for minority-carier transport in semiconductors with position-dependent composition, with application to heavily doped silicon,”IEEETrans. Electron Devices, vol. ED-33, pp. 240–249, Feb. 1986.

[12] A. Cuevas, R. Merchan, and J. C. Ramos, “On the systematical analyticalsolutions for minority-carrier transport in nonuniform doped semicon-ductors: Application to solar cells,”IEEE Trans. Electron Devices, vol.40, pp. 1181–1183, June 1993.

[13] N. Rinaldi, “Modeling of minority-carrier transport in nonuniformlydoped silicon regions with asymptotic expansions,”IEEE Trans. Elec-tron Devices, vol. 40, pp. 2307–2317, Dec. 1993.

[14] E. de Castro and M. Rudan, “Integral-equation solution of minority-carrier transport problems in heavily doped semiconductors,”IEEETrans. Electron Devices, vol. ED-31, pp. 785–792, June 1984.

[15] S. M. Sze,Physics of Semiconductor Devices, 2nd ed. New York:Wiley, 1981.

[16] C. Leguijt, “Surface passivation for silicon solar cells,” Ph.D. disserta-tion, Utrecht University, The Netherlands, 1995.

[17] P. Lolgen, “Surface and volume recombination in silicon solar cells,”Ph.D. dissertation, Utrecht University, The Netherlands, 1995.

A. R. Burgers was born in Breezand, The Nether-lands, in 1961. He received the M.S. degree inmathematics from the University of Leiden, TheNetherlands, in 1984. He is currently pursuing thePh.D. degree.

In 1984, he joined The Netherlands Energy Re-search Foundation (ECN), Petten, The Netherlands,where he worked on mathematical modeling. Since1991, he has been doing research in solar cells,focusing on modeling and light-trapping.

Cor Leguijt was born in Krommeniedijk, TheNetherlands in 1966. He received the M.S. degreein experimental physics from the University ofAmsterdam, (UvA), The Netherlands, in 1990, andthe Ph.D. degree from the University of Utrecht,The Netherlands, in 1995. He performed his Ph.D.research on surface passivation of crystalline siliconsolar cells at The Netherlands Energy ResearchFoundation (ECN), and the Delft Institute for MicroElectronics and Submicron-Technology (DIMES).

He is currently with Energy North West (ENW),Amsterdam, working on the implementation of renewable energy.


Peter Lolgen was born in Munich, Germany, in1964. He received the M.S. degree in solid-statephysics from the Rheinisch-Westfalische Technis-che Hochschule, Aachen, Germany in 1989, andthe Ph.D. degree from the University of Utrecht,The Netherlands, in 1995. Supported by the FOMAMOLF Institute, he performed his Ph.D. researchon aluminum back surface fields and bulk pas-sivation of crystalline silicon solar cells at TheNetherlands Energy Research Foundation (ECN).

He is currently with Siemens AG, Munich, Ger-many.

Wim C. Sinke was born in Flushing, The Nether-lands, in 1955. He received the M.S. degree inexperimental physics in 1981, and the Ph.D. de-gree in 1985, both from the University of Utrecht,The Netherlands. He performed his Ph.D. researchon ion implantation and laser annealing of siliconwhile working at the FOM Institute for Atomic andMolecular Physics from 1982 to 1985.

In 1986, he joined the Hitachi Research Labora-tory, Tokyo, Japan, to study structural properties ofamorphous silicon. He returned to the FOM Institute

in 1987 to lead a group involved in research on silicon solar cells, ionimplantation, and laser processing of semiconductors. In 1990, he joined TheNetherlands Energy Research Foundation (ECN), Petten, The Netherlands,where he founded and heads the solar cell research group. Since 1994, he hasheld the position of Professor at the University of Utrecht.

Dr. Sinke received the Dutch Jacob Kistemaker prize for his work on siliconand silicon solar cells in 1992.

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