Inversion layers in abrupt p-n junctions

Wiele, F. Van de; Demoulin, E.

doi:10.1016/0038-1101(70)90059-6

Cited by 27 publications

(11 citation statements)

References 6 publications

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“…The depletion layer approximation had been first criticized by Gummel and Scharfetter from calculations on p þ n step homojunctions where these authors showed that the intercept voltage in highly dissymmetric junctions is not as expected from the simple depletion approximation [28]. However only very few papers in the literature dealt with this inversion layer related problem [29][30][31], and to our best knowledge, no indication on the temperature dependence had been published. It is amazing that the peculiar temperature dependence could be evidenced from measurements on solar cells combining a-Si:H and c-Si since one could think that a-Si:H, as a very defective material could greatly influence the capacitance behavior.…”

Section: Discussionmentioning

confidence: 89%

Revisiting the theory and usage of junction capacitance: Application to high efficiency amorphous/crystalline silicon heterojunction solar cells

Kleider

Alvarez

Brézard-Oudot

et al. 2015

Solar Energy Materials and Solar Cells

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International audienceWe briefly review the basic concepts of junction capacitance and the peculiarities related to amorphous semiconductors, paying tribute to Cohen and to his pioneering work. We extend the discussion to very high efficiency silicon heterojunction (SiHET) solar cells where both an amorphous semiconductor, namely hydrogenated amorphous silicon, and heterojunctions are present. By presenting both modeling and experimental results, we demonstrate that the conventional theory of junction capacitance based on the depletion approximation in the space charge region, cannot reproduce the capacitance data obtained on SiHET cells. The experimental temperature dependence is significantly stronger than that of the depletion-layer capacitance, while the bias dependence yields underestimated values of the diffusion potential, leading to strong errors if applied to the determination of band offsets using the procedure proposed precedingly in the literature. We demonstrate that this is not related to the amorphous nature of a-Si:H, but to the existence of a strongly inverted c-Si surface layer that requires minority carriers to be taken into account in the analysis of the junction capacitance

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Section: Discussionmentioning

confidence: 89%

Revisiting the theory and usage of junction capacitance: Application to high efficiency amorphous/crystalline silicon heterojunction solar cells

Kleider

Alvarez

Brézard-Oudot

et al. 2015

Solar Energy Materials and Solar Cells

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“…If one neglects the holes' contribution to the charge density in Eq. (17), the function f is then reduced to f* that is independent of V a f Ã ðu e ðxÞÞ ¼ exp u e ðxÞ À exp u e ð1Þ þ exp u e ð1Þðu e ð1Þ À u e ðxÞÞ; (30) and the capacitance is obtained from Eq. (29) by following the same procedure as given above and substituting f by f*.…”

Section: B Full Analytical Calculationmentioning

confidence: 99%

Explicit analytical modeling of the low frequency a-Si:H/c-Si heterojunction capacitance: Analysis and application to silicon heterojunction solar cells

Maslova

Brézard-Oudot

Gueunier‐Farret

et al. 2015

Journal of Applied Physics

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We develop a fully analytical model in order to describe the temperature dependence of the low frequency capacitance of heterojunctions between hydrogenated amorphous silicon (a-Si:H) and crystalline silicon (c-Si). We demonstrate that the slope of the capacitance-temperature (C-T) curve is strongly enhanced if the c-Si surface is under strong inversion conditions compared to the usually assumed depletion layer capacitance. We have extended our analytical model to integrate a very thin undoped (i) a-Si:H layer at the interface and the finite thickness of the doped a-Si:H layer that are used in high efficiency solar cells for the passivation of interface defects and to limit short circuit current losses. Finally, using our calculations, we analyze experimental data on high efficiency silicon heterojunction solar cells. The transition from the strong inversion limited behavior to the depletion layer behavior is discussed in terms of band offsets, density of states in a-Si:H, and work function of the indium tin oxide (ITO) front electrode. In particular, it is evidenced that strong inversion conditions prevail at the c-Si surface at high temperatures down to 250 K, which can only be reproduced if the ITO work function is larger than 4.7 eV. V

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“…Using (13a), ( l o b ) will be converted into an integral over energy qs, the rnagiiitude of which can be found by numerical integration. Considering also ( 7 ) . (8b), and (12b), (…”

Section: E ( X )mentioning

confidence: 99%

“…Kennedy [ 131 presents different expressions for U , in the ranges 1 5 N , / N , 5 10 and N A / N , > 10. He compares exact numerical solutions with three analytical approxirnation formulas, the first obtained by himself, the second found by Guniniel and Scharfetter [ 5 ] , and the third presented by Van de Wiele and Demoulin [7]. The calculated maximum errors in the junction capacitance C amount to 130,; in the solution of [5], to 77;> in that of [7], and to 3.5';" in U , can be determined by comparison with (1) in dependence on the impurity densities N , and N,.…”

Section: Introductionmentioning

confidence: 99%

Theoretical study of the depletion-layer capacitance in abrupt p–n semiconductor junctions

Weinhausen¹

1978

Phys. Stat. Sol. (a)

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For evaluation of capacitance‐voltage measurements on an abrupt pn semiconductor junction with reverse‐biased depletion layer an approximation equation for the quantity Ue is presented, where Ue is the value at the intercept of the extrapolated plot C−2 to the applied voltage axis. The approximation formula is compared with an exact calculation. The maximum error in the approximate relationship for Ue is less than 3% in a wide range of impurity density and applied reverse voltage, therefore the discrepancy in the space‐charge layer capacitance Cs is less than 1.5%. Cs is given by the relationship, which follows from Shockley's theory, if (U + UD) is replaced by (U + Ue).

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Inversion layers in abrupt p-n junctions

Cited by 27 publications

References 6 publications

Revisiting the theory and usage of junction capacitance: Application to high efficiency amorphous/crystalline silicon heterojunction solar cells

Revisiting the theory and usage of junction capacitance: Application to high efficiency amorphous/crystalline silicon heterojunction solar cells

Explicit analytical modeling of the low frequency a-Si:H/c-Si heterojunction capacitance: Analysis and application to silicon heterojunction solar cells

Theoretical study of the depletion-layer capacitance in abrupt p–n semiconductor junctions

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