Modeling of minority-carrier transport in nonuniformly doped silicon regions with asymptotic expansions

Rinaldi, N.

doi:10.1109/16.249480

Cited by 16 publications

(4 citation statements)

References 40 publications

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“…It is clear that, for W = 0.2 µm, the QNQE model and the expression (20a) give accurate results provided that S is less than S C (∼10 5 cm s −1 ), while in the case of transparent model and (or) solution (20b) S must be greater than S C to ensure accuracy with respect to the exact numerical solution [10]. Therefore, if we rely on one of the three average value solutions, it requires the use of (29) to achieve a satisfactory accuracy over the same range of S.…”

Section: Resultsmentioning

confidence: 93%

“…In this study, we use the following hole lifetime, mobility, and apparent band-gap narrowing physical models of Del Alamo et al [14]: Figure 2 shows the variation of the emitter saturation current density J oe = J p (0)/u(0) against the emitter surface-recombination velocity S, calculated from transparent model [7], quasi-neutral quasiequilibrium model (QNQE) [8], expressions (20a), (20b), and (29), and exact numerical results [10].…”

Section: Physical Models Used In the Calculationmentioning

confidence: 99%

“…Selvakumar and Roulston [9] developed an analytical expression of the saturation current (C S ) by assuming that C S (= p 0 D p /L p ) is independent of the doping level. Rinaldi [10] completed and extended the works of Del Alamo and Swanson [7] and Park et al [8] by proposing a more general and more exact solution to the problem and derived some previous formulations as particular cases. Nevertheless, the solutions proposed by these authors have some disadvantages in that the expressions of the current density use two and three integrals that require a long computation time and must be evaluated numerically.…”

Section: Introductionmentioning

confidence: 97%

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A simple formulation of the saturation current density in heavily doped emitters

Zouari¹,

Arab²

2003

Can. J. Phys.

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In a non-uniformly and heavily doped emitter region of a bipolar transistor, the continuity equation and the minority-current equation cannot be solved exactly in closed form. This paper shows that the calculation of minority-carrier current density can be calculated by a simple approach. This approach is based on the average value of the equilibrium hole density p 0 , diffusion constant D p , and lifetime τ p of minority carriers and leads to two coupled differential equations of the first order. These equations can be solved easily and can give a simple expression for the current density. Three definitions of the average values of p 0 , D p , and τ p are used and lead to three expressions for the emitter current density. The latter is identical to the one established by Rinaldi using another mathematical analysis and gives very accurate results for a shallow emitter (W < 1 µm), irrespective of the range peak doping level N(W ) and surface-recombination velocity S. On the other hand, the other two expressions lead also to accurate results for the current density depending on the value of the surface-recombination velocity, but cannot be used when N(W ) is greater than 10 20 cm −3 and W is superior to 0.1 µm.Résumé : Dans la région d'émetteur du transistor bipolaire dopée fortement et non uniformément, la résoluation analytique des équations de courant et de continuité ne peut pas être faite de façon exacte. Dans ce papier, nous montrons que la densité de courant des porteurs minoritaires peut être calculée par une approche simple. Cette approche est basée sur les valeurs moyennes de la densité des trous à l'équilibre p 0 , la constante de diffusion D p et la duré de vie τ p des porteurs minoritaires ; elle aboutit à deux équations différentielles couplées de premier ordre. Ces équations peuvent être résolues facilement et donnent une expression simple de la densité courant. Trois définitions de la valeur moyenne de p 0 , D p et τ p sont utilisées et mènent à trois expressions de la densité de courant. La dernière est identique à celle établie par Rinaldi en utilisant une autre approche mathématique, et qui donne des résultats très satisfaisants pour des émetteurs peu profond (W < 1 µm) quel que soit le niveau du dopage N(W ) et la vitesse de recombinaison S à la surface de l'émetteur. D'autre part, les deux autres expressions aboutissent aussi à des résultats satisfaisants tout dépend de l'épaisseur et de l'état de surface de l'émetteur ; mais elles ne sont plus utilisées lorsque N(W ) est plus grand que 10 20 cm −3 et W supérieure à 0,1 µm.

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Section: Resultsmentioning

confidence: 93%

Section: Physical Models Used In the Calculationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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A simple formulation of the saturation current density in heavily doped emitters

Zouari¹,

Arab²

2003

Can. J. Phys.

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“…The difference between the two curves can be explained by the work of Rinaldi [28], who has demonstrated that the approximation of the transparent emitter model is valuable only for a thin emitter and for a high surface recombination velocity. In his second work [18], he has demonstrated that the effective recombination velocity, related to the polysilicon contacted emitter, decreases when the oxide thickness increases and consequently, the approximation of the transparent single-crystal emitter can not give accurate results.…”

Section: Effect Of the Polysilicon Thickness On The Normalised Currenmentioning

confidence: 99%

Minority carrier transport equation for bipolar transistors with polysilicon emitter contact

Zouari¹,

Arab²

2003

phys. stat. sol. (a)

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In order to improve the current gain via a reduction of the emitter base junction saturation current density, a perpendicular ordering of the grain boundaries (columnar grain boundaries) in the polysilicon emitterregion of a bipolar transistor is proposed. The complex polysilicon current component is obtained by a two-dimensional resolution of the current transport equation along the polysilicon region. The minority carrier current density component in the non-uniformly heavily doped single-crystal emitter is calculated by an average value approach. The influence of the two-dimensional structure of the polysilicon region on the current gain is analysed, and it is shown that the current gain decreases with increasing grain number. The evolution of the normalised current gain in terms of physical parameters is studied. The results show that the current gain improves with polysilicon thickness for a thin oxide layer, while it is insensitive for a thick oxide layer. In addition, the results show that the bulk recombination in a single-crystal emitter cannot be neglected in devices with a deliberately grown interfacial oxide. Base c c b p (0) J J G J J .

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Principles of Solar Cell Operation

Markvart

Castañer

2012

Practical Handbook of Photovoltaics

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Modeling of minority-carrier transport in nonuniformly doped silicon regions with asymptotic expansions

Cited by 16 publications

References 40 publications

A simple formulation of the saturation current density in heavily doped emitters

A simple formulation of the saturation current density in heavily doped emitters

Minority carrier transport equation for bipolar transistors with polysilicon emitter contact

Principles of Solar Cell Operation

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