Modelling of wafer heating during rapid thermal processing

Kakoschke, R.; Bussmann, Ezra; Föll, H.

doi:10.1007/bf00343409

Cited by 41 publications

(13 citation statements)

References 7 publications

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“…2), spatial temperature variations across wafers at a certain time are expected to be small enough ( 200 K) so that spatial variations in thermal conductivity may be ignored [5]. Equation (1) is thus reduced to (3) The initial and boundary conditions for the system mentioned above are at (4) at (5) at (6) where is the emissivity for radiant heat loss emitted from the wafer edge. We may assume without loss of generality that the incident heat flux on both sides during processing is equal, i.e.,…”

Section: Thermal Modelmentioning

confidence: 99%

“…Hill and Jones [4] investigated thermal uniformity with a uniform intensity field and one in which the intensity was linearly enhanced to a maximum of 8% vertically over the last 15 mm of a 6-in wafer. Kakoschke et al [5] evaluated enhanced illumination intensities at wafer peripheries vertically and laterally for a compensation of edge heat losses during processing. Gyurcsik et al [6] introduced a two-step procedure for solving an inverse optimal-lamp-contour problem to achieve temperature uniformity in steady state.…”

Section: Introductionmentioning

confidence: 99%

“…The wafer is subjected to a steady uniformly distributed heat flux [2], [5] (uniform heat flux, i.e., intensity mode during processing). The temperature-dependent thermal properties of the silicon wafer are considered.…”

Section: Introductionmentioning

confidence: 99%

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Thermal uniformity of 12-in silicon wafer during rapid thermal processing by inverse heat transfer method

Lin

Chu

2000

IEEE Trans. Semicond. Manufact.

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Through an inverse heat transfer method, this paper presents a finite difference formulation for determination of incident heat fluxes to achieve thermal uniformity in a 12-in silicon wafer during rapid thermal processing. A one-dimensional thermal model and temperature-dependent thermal properties of a silicon wafer are adopted in this study. Our results show that the thermal nonuniformity can be reduced considerably if the incident heat fluxes on the wafer are dynamically controlled according to the inverse-method results. An effect of successive temperature measurement errors on thermal uniformity is discussed. The resulting maximum temperature differences are only 0.618, 0.776, 0.981, and 0.326 C for 4-, 6-, 8-and 12-in wafers, respectively. The required edge heating compensation ratio for thermal uniformity in 4-, 6-, 8-and 12-in silicon wafers is also evaluated.Index Terms-12-in silicon wafer, inverse heat-transfer method, rapid thermal processing, thermal uniformity.

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Section: Thermal Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermal uniformity of 12-in silicon wafer during rapid thermal processing by inverse heat transfer method

Lin

Chu

2000

IEEE Trans. Semicond. Manufact.

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“…This is due to the fact temperature differences as high as 300 'C across the wafer had been observed during processing in less sophisticated RTP environments. Excessive radiative and convective losses at the wafer edge compared to the center have been identified as the primary cause and studied in detail for the last couple of years [4][5][6][7]. The result is the improved design of the RTP equipments such as those with multiple heating zones, provision for slip-free ring, efficient system of reflectors etc.…”

Section: Introductionmentioning

confidence: 99%

“…The result is the improved design of the RTP equipments such as those with multiple heating zones, provision for slip-free ring, efficient system of reflectors etc. to compensate for the excessive heat loss at the wafer edge [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Critical Parameters Affecting the Temperature Uniformity During Rapid Thermal Processing

1994

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In this work we examine the effect of various system and wafer parameters such as the flowing ambient, the spatial distribution of incident energy flux, the slip-free ring and doping density on temperature non-uniformity occurring during rapid thermal processing (RTP). The effect of using two inert ambients, i.e. argon and nitrogen, on temperature non-uniformity occurring during RTP cycle is studied in detail. The importance of dynamic lamp power control in providing time dependent spatial variation of incident energy flux as a measure to improve the temperature uniformity is also examined. Finally the simulation studies are also done in the presence of a slip-free ring. The nature of photon capture by the silicon wafer and the correlation between doping density and the steady state temperature for any given open loop condition is discussed in detail. This analysis has been done using an analytical tool developed by us based on simple 3-dimensional physical models depicting a typical rapid thermal cycle[1].

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Transient Heating of Semiconductors by Radiation

Борисенко

Hesketh

1997

Rapid Thermal Processing of Semiconductors

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Modelling of wafer heating during rapid thermal processing

Cited by 41 publications

References 7 publications

Thermal uniformity of 12-in silicon wafer during rapid thermal processing by inverse heat transfer method

Thermal uniformity of 12-in silicon wafer during rapid thermal processing by inverse heat transfer method

Analysis of Critical Parameters Affecting the Temperature Uniformity During Rapid Thermal Processing

Transient Heating of Semiconductors by Radiation

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