1. Theory

Definition: Wafer temperature sensors measure substrate temperature during thermal processing, either by radiation thermometry (pyrometry) of emitted infrared light or by contact thermocouples, including thin-film thermocouples on instrumented wafers (TI patent; NIST abstract).
Planck emission: Radiance depends on temperature and on spectral emissivity, so emissivity uncertainty is the main pyrometry error (background knowledge, DeWitt and Nutter; TI patent).
Emissivity correction: Reflectance measurement, modulated-lamp ripple analysis and reflector cavities reduce emissivity sensitivity (TI patent; Bell Labs abstract; background knowledge).
Traceability: Pyrometers are calibrated against ITS-90 blackbodies and thermocouple wafers (NIST abstract).

2. Working Principle

Pyrometer: A light pipe or optics collects radiation in a narrow band and a detector converts it to temperature (NIST abstract; TI patent).
Emissivity sensing: A chopped infrared laser or modulated lamp gives reflectance at each point (TI patent; Bell Labs abstract).
Thermocouples: Wire and thin-film thermocouples give contact references (NIST abstract).
Control: Multi-point readings drive lamp zones every 20 to 200 ms (TI patent).

3. Applications

Rapid thermal processing: Implant anneal, oxidation and silicidation (TI patent; Bell Labs abstract).
Epitaxy: Substrate temperature in CVD and MBE (RHEED page; background knowledge).
Calibration: Thermocouple wafers for chamber matching (NIST abstract).
Yield: Reduced wafer-to-wafer variation from backside emissivity correction (Bell Labs abstract).

Radiation Thermometry

Name	Formula	Related Formulae	Variables/Constants
Planck radiance and Wien limit	$L_{λ} = ε \frac{2 h c ^{2}}{λ ^{5}} \frac{1}{e ^{c_{2} / λ T} - 1} \approx ε \frac{c _{1}}{λ ^{5}} e^{- c_{2} / λ T}$	$c_{2} = \frac{h c}{k _{B}} = 14388 μ m K$	$L_{λ} : s p ec t r a l r a d ian ce$ $ε : s p ec t r a l e mi ss i v i t y$ $c_{1}, c_{2} : r a d ia t i o n co n s t an t s; P l an c k an d W i e n f or m s (ba c k g r o u n d k n o w l e d g e, D e W i tt an d N u tt er); T I p a t e n t : w a f er b l a c k - b o d y r a d ia t i o n a u ni q u e f u n c t i o n o f t e m p er a t u r e o n ce e mi ss i v i t y i s k n o w n; N I S T ab s t r a c t : s p ec t r a l r a d ian ce t e m p er a t u r e f r o m a l i g h t - p i p e r a d ia t i o n t h er m o m e t er co n v er t e d t o w a f er t e m p er a t u r e$ $(co m p u t e d : t h e b l a c k b o d y p e ak a t 1273 K i s a t 2.28 μ m)$
Temperature error from emissivity error	$\frac{Δ T}{T} = - \frac{λ T}{c _{2}} \frac{Δ ε}{ε}$	$shorter λ \Rightarrow smaller error$	$Δ ε / ε : r e l a t i v e e mi ss i v i t y er r or; W i e n se n s i t i v i t y (ba c k g r o u n d k n o w l e d g e, D e W i tt an d N u tt er); T I p a t e n t : co n v e n t i o na l p y r o m e t r y er r or s u p t o t e n s or h u n d r e d s o f d e g r ees, 5.4 μ m l a ser f or e mi ss i v i t y m e a s u r e m e n t; N I S T ab s t r a c t : e mi ss i v i t y co n t r ib u t es ab o u t 2.0^{\circ} C o f a 3.5^{\circ} C (k = 1) L P R T u n cer t ain t y a t 700 t o 900^{\circ} C$ $(a ss u m e d : 0.95 μ m u n l ess s t a t e d; co m p u t e d : a 10 p er ce n t e mi ss i v i t y er r or g i v es 10.7 K a t 1273 K an d 0.95 μ m, 30 K a t 2.7 μ m an d 61 K a t 5.4 μ m; N I S T^{'} s 2.0^{\circ} C a t 1173 K im pl i es 2.2 p er ce n t e mi ss i v i t y u n cer t ain t y)$
Kirchhoff emissivity	$ε = 1 - R - T_{r}$	$T_{r} \to 0 \Rightarrow ε = 1 - R$	$R : r e f l ec t an ce$ $T_{r} : t r an s mi tt an ce; K i r c hh o f f r e l a t i o n (ba c k g r o u n d k n o w l e d g e, D e W i tt an d N u tt er); T I p a t e n t : c h o pp e d 5.4 μ m l a ser m e a s u r es r e f l ec t an ce an d t r an s mi tt an ce, o n l y r e f l ec t an ce in t h e p r e f er r e d e mb o d im e n t s in ce t r an s mi ss i o n i s u s u a l l y z er o a t p r ocess t e m p er a t u r e, r o ug hn ess sc a tt er in g p a r am e t er f r o m 1.3 t o 5.4 μ m d a t a, s i l i co n p a r tl y t r an s p a r e n t b ey o n d 1.5 μ m b e l o w 600^{\circ} C an d o p a q u e ab o v e ab o u t 600^{\circ} C, s i l i co n e mi ss i v i t y d a t a 543 t o 1070 K o v er 0.4 t o 15.0 μ m$ $(m y r e a d in g : b e l o w ab o u t 600^{\circ} C l am p l i g h t t r an s mi tt e d t h r o ug h t h e w a f er r e a c h es t h e p y r o m e t er, so l o w - t e m p er a t u r e r e a d in g s n ee d a d i f f er e n t m e t h o d)$

Emissivity Correction and Calibration

Name	Formula	Related Formulae	Variables/Constants
Effective emissivity with a reflector	$ε_{e f f} = \frac{ε}{1 - ( 1 - ε ) ρ _{r} F}$	$ρ_{r} F \to 1 \Rightarrow ε_{e f f} \to 1$	$ρ_{r} : r e f l ec t or r e f l ec t an ce$ $F : v i e w f a c t or b e tw ee n w a f er an d r e f l ec t or; c a v i t y r e l a t i o n (ba c k g r o u n d k n o w l e d g e, R ooz e b oo m); N I S T ab s t r a c t : e f f ec t i v e e mi ss i v i t y m o d e l s f r o m w a f er o pt i c a l p r o p er t i es an d w a f er an d c hamb er g eo m e t r y, m o d e l - cor r ec t e d r e a d in g s a g r ee in g w i t h t h er m oco u pl es$ $(a ss u m e d : ρ_{r} = 0.9, F = 0.95; co m p u t e d : ε = 0.68 g i v es 0.936 an d 0.60 g i v es 0.912, so an 11.8 p er ce n t e mi ss i v i t y c han g e b eco m es 2.6 p er ce n t)$
Ripple (modulated-lamp) correction	$S (t) = S_{e m} + R_{w} Φ_{l am p} (t)$	$R_{w} = \frac{S ~}{Φ ~ _{l am p}}, ε = 1 - R_{w}$	$S : d e t ec t e d s i g na l$ $S_{e m} : t h er ma l e mi ss i o n$ $R_{w} : w a f er r e f l ec t an ce$ $Φ_{l am p} : l am p r a d ia t i o n r e a c hin g t h e d e t ec t or b y r e f l ec t i o n, t i l d e : A C co m p o n e n t s; B e l l L ab s ab s t r a c t : l am p p o w er m o d u l a t e d a t t h e p o w er - l in e f r e q u e n cy or b y so f tw a r e, f l u c t u a t in g an d q u a s i - s t e a d y co m p o n e n t s se p a r a t e d t o s u pp r ess l am p r e f l ec t i o n s an d cor r ec t e mi ss i v i t y, an o u t g r o w t h o f t h e r i ppl e t ec hni q u e, t es t e d o n w a f er s w i t h ba c k s i d e o x i d e, ni t r i d e an d p o l y s i l i co n; d eco m p os i t i o n (ba c k g r o u n d k n o w l e d g e, R ooz e b oo m)$ $(m y r e a d in g : t h e w a f er t e m p er a t u r e c ann o t f o l l o w f a s t l am p r i ppl e, so t h e A C p a r t o f t h e s i g na l i s p u r e r e f l ec t e d l am p l i g h t)$
Calibration budget	$u_{T} = \sum_{i} u_{i}^{2}$	$u_{T C} < 0.4^{\circ} C$	$u : s t an d a r d u n cer t ain t y co m p o n e n t s; N I S T ab s t r a c t : L P R T c a l ib r a t e d a g ain s t an I T S - 90 b l a c k b o d y, t o t a l 3.5^{\circ} C (k = 1), e f f ec t i v e e mi ss i v i t y ab o u t 2.0^{\circ} C, w i r e an d t hin - f i l m t h er m oco u pl es b e l o w 0.4^{\circ} C, 700 t o 900^{\circ} C; r oo t - s u m - s q u a r e (ba c k g r o u n d k n o w l e d g e)$ $(co m p u t e d : t h e r e mainin g co m p o n e n t s t o t a l 2.9^{\circ} C)$

Contact Sensors and Control

Name	Formula	Related Formulae	Variables/Constants
Thermocouple voltage	$V = \int_{T_{r e f}}^{T} (S_{A} - S_{B}) d T$	$S_{K} \approx 41 μ V/K, S_{S} \approx 10 to 12 μ V/K$	$S_{A}, S_{B} : S ee b ec k coe f f i c i e n t s o f t h e tw o w i r es$ $T_{r e f} : r e f er e n ce j u n c t i o n; r e l a t i o n an d t y p i c a l t y p e K an d t y p e S v a l u es (ba c k g r o u n d k n o w l e d g e, D e W i tt an d N u tt er); N I S T ab s t r a c t : co mbina t i o n w i r e an d t hin - f i l m t h er m oco u pl es o n t h e w a f er$ $(co m p u t e d : a 1^{\circ} C er r or i s 41 μ V f or t y p e K an d ab o u t 11 μ V f or t y p e S)$
Multi-point control	$T_{j} (t) \to lamp zone powers P_{k}$	$Δ t_{u p d a t e} = 20 to 200 ms$	$T_{j} : t e m p er a t u r e a t se n s in g p o in t j$ $P_{k} : z o n e p o w er; T I p a t e n t : f o u r se n s in g p o in t s e x t e n d ab l e t o man y, u p d a t es e v er y 20 t o 200 m s, c h o pp in g a t 100 Hz t o 10 kHz, 5 kHz r e f l ec t e d - b e am m o d u l a t i o n, P b S e or H g C d T e d e t ec t or s a t 77 t o 200 K, f i l t er ban d w i d t h 0.1 t o 0.5 μ m, 800^{\circ} C e x am pl e p r ocess$ $(m y r e a d in g : p er - p o in t e mi ss i v i t y cor r ec t i o n l e t s t h e co n t r o l l er f l a tt e n r a d ia l t e m p er a t u r e r a t h er t han o n l y t h e a v er a g e)$
Surface fix points	$T_{f i x} : oxide desorption, reconstruction changes$	$GaAs about 560^{\circ} C; Si(111) 7x7 to 1x1 at 830^{\circ} C$	$R H E E D p a g e : r eco n s t r u c t i o n t r an s i t i o n s a s in - s i t u t e m p er a t u r e r e f er e n ces in M B E; u se f or p y r o m e t er o f f se t c a l ib r a t i o n (ba c k g r o u n d k n o w l e d g e)$ $(m y r e a d in g : f i x p o in t s cor r ec t t h e o f f se t b u t n o t t h e s l o p e, so tw o a r e n ee d e d f or a f u l l c a l ib r a t i o n)$

Important Questions

Ques: Why does emissivity limit pyrometer accuracy?

Because the pyrometer sees $ε$ times blackbody radiance, and an emissivity error looks like a temperature error. In the Wien limit, $Δ T / T = - (λ T / c_{2}) (Δ ε / ε)$ (background knowledge, DeWitt and Nutter). For a 10 per cent emissivity error at 1273 K, the temperature error is 10.7 K at an assumed 0.95 $μ m$ but 61 K at 5.4 $μ m$ (computed), so short wavelengths are preferred. The TI patent states that uncorrected pyrometry can err by tens or even hundreds of degrees, because film stacks on the wafer change emissivity by interference. NIST’s calibrated light-pipe thermometer has 3.5 $^{\circ} C$ total uncertainty, of which effective emissivity contributes about 2.0 $^{\circ} C$ , implying about 2.2 per cent emissivity uncertainty at 900 $^{\circ} C$ (computed). Reference: D. P. DeWitt and G. D. Nutter (eds.), Theory and Practice of Radiation Thermometry, Wiley 1988, and F. Roozeboom (ed.), Advances in Rapid Thermal and Integrated Processing, Kluwer 1996 (background knowledge; not opened); M. M. Moslehi and H. N. Najm, ‘Multi-point pyrometry with real-time surface emissivity compensation’, US patent 5,156,461, Texas Instruments (filed May 1991) (fetch-tool summary); B. K. Tsai and D. P. DeWitt, ‘ITS-90 Calibration of Radiometers Using Wire/Thin-Film Thermocouples in the NIST RTP Tool: Effective Emissivity Modeling’, RTP ‘99 conference (1999), NIST abstract page (fetch-tool summary).

Ques: Which wavelength is better for wafer pyrometry: near 1 or 5.4 micrometres?

The TI patent measures emissivity with a 5.4 $μ m$ laser, with PbSe or HgCdTe detectors, while light-pipe pyrometers in RTP commonly work near 1 $μ m$ (background knowledge, Roozeboom). For emissivity error the shorter wavelength is far better: a 10 per cent error gives 10.7 K at 0.95 $μ m$ against 61 K at 5.4 $μ m$ at 1273 K (computed). The long wavelength has advantages the patent uses: silicon is opaque there above about 600 $^{\circ} C$ , and active reflectance measurement removes most of the emissivity error at any wavelength. Without active correction, a band near 1 $μ m$ is more likely the better choice; with real-time reflectance compensation, the 5.4 $μ m$ band becomes usable and less affected by lamp light near the lamp peak (my reading). Reference: M. M. Moslehi and H. N. Najm, ‘Multi-point pyrometry with real-time surface emissivity compensation’, US patent 5,156,461, Texas Instruments (filed May 1991) (fetch-tool summary); D. P. DeWitt and G. D. Nutter (eds.), Theory and Practice of Radiation Thermometry, Wiley 1988, and F. Roozeboom (ed.), Advances in Rapid Thermal and Integrated Processing, Kluwer 1996 (background knowledge; not opened).

Ques: How does a reflector plate reduce emissivity sensitivity?

By forming a cavity that returns the wafer’s own radiation. With a highly reflective plate under the wafer, emitted light that the wafer fails to emit because of low emissivity is partly made up by multiple reflections, giving $ε_{e f f} = ε / [1 - (1 - ε) ρ_{r} F]$ (background knowledge, Roozeboom). With an assumed plate reflectance of 0.9 and view factor of 0.95, an emissivity of 0.68 becomes 0.936 effective and 0.60 becomes 0.912, so an 11.8 per cent change in true emissivity shrinks to 2.6 per cent (computed), about a fourfold reduction in temperature error. NIST’s effective emissivity models account for wafer optical properties and chamber geometry in this way, and their corrected light-pipe readings agreed with thermocouples (NIST abstract). Reference: D. P. DeWitt and G. D. Nutter (eds.), Theory and Practice of Radiation Thermometry, Wiley 1988, and F. Roozeboom (ed.), Advances in Rapid Thermal and Integrated Processing, Kluwer 1996 (background knowledge; not opened); B. K. Tsai and D. P. DeWitt, ‘ITS-90 Calibration of Radiometers Using Wire/Thin-Film Thermocouples in the NIST RTP Tool: Effective Emissivity Modeling’, RTP ‘99 conference (1999), NIST abstract page (fetch-tool summary).

Ques: What is ripple pyrometry?

A way of measuring wafer reflectance using the lamps themselves. Lamp power fluctuates at the power-line frequency or under software modulation, and the wafer temperature cannot follow fast ripple, so the AC part of the detected signal is lamp light reflected by the wafer, while the quasi-steady part includes thermal emission (Bell Labs abstract; my reading). Dividing the AC signal by the lamp ripple gives reflectance and hence emissivity, $ε = 1 - R$ for an opaque wafer (background knowledge). The Bell Labs work, an outgrowth of the ripple technique, tested wafers with backside oxide, nitride and polysilicon and reported reduced wafer-to-wafer and lot-to-lot variation in electrical results and higher yield. The TI patent achieves the same with a chopped laser at each sensing point. Reference: Nokia Bell Labs, ‘Wafer Temperature Measurement in Rapid Thermal Processors with Modulated Lamp Power’ (December 1999; Springer DOI 10.1007/s11664-999-0125-8), abstract page (fetch-tool summary); D. P. DeWitt and G. D. Nutter (eds.), Theory and Practice of Radiation Thermometry, Wiley 1988, and F. Roozeboom (ed.), Advances in Rapid Thermal and Integrated Processing, Kluwer 1996 (background knowledge; not opened); M. M. Moslehi and H. N. Najm, ‘Multi-point pyrometry with real-time surface emissivity compensation’, US patent 5,156,461, Texas Instruments (filed May 1991) (fetch-tool summary).

Ques: How are pyrometers calibrated to true wafer temperature?

Against blackbodies and instrumented wafers. NIST calibrated its light-pipe radiation thermometer against an ITS-90 blackbody and compared emissivity-corrected readings with wire and thin-film thermocouples bonded to a silicon wafer, whose uncertainty is below 0.4 $^{\circ} C$ , between 700 and 900 $^{\circ} C$ (NIST abstract). Thermocouple voltage integrates the difference of Seebeck coefficients; type K gives about 41 $μ V$ per kelvin and type S about 10 to 12 (background knowledge), so a 1 $^{\circ} C$ error is only 11 $μ V$ for type S (computed). Of NIST’s 3.5 $^{\circ} C$ pyrometer uncertainty, removing the 2.0 $^{\circ} C$ emissivity term leaves 2.9 $^{\circ} C$ from other sources (computed). In MBE, reconstruction transitions such as GaAs oxide desorption near 560 $^{\circ} C$ give additional fix points (RHEED page). Reference: B. K. Tsai and D. P. DeWitt, ‘ITS-90 Calibration of Radiometers Using Wire/Thin-Film Thermocouples in the NIST RTP Tool: Effective Emissivity Modeling’, RTP ‘99 conference (1999), NIST abstract page (fetch-tool summary); D. P. DeWitt and G. D. Nutter (eds.), Theory and Practice of Radiation Thermometry, Wiley 1988, and F. Roozeboom (ed.), Advances in Rapid Thermal and Integrated Processing, Kluwer 1996 (background knowledge; not opened); Reflection High-Energy Electron Diffraction (RHEED) page of this vault.

Ques: Why can’t a pyrometer read a cold silicon wafer?

Because silicon is partly transparent in the infrared at low temperature. The TI patent notes that wafers can remain at least partly transparent to lamp radiation beyond 1.5 $μ m$ below about 600 $^{\circ} C$ , while appearing opaque to its 5.4 $μ m$ probe beam at typically 600 $^{\circ} C$ or higher. Below this, lamp light transmitted through the wafer reaches the pyrometer and adds a large error, and emission itself is weak, since the Planck peak at 1273 K is already at 2.28 $μ m$ and moves to longer wavelengths as temperature falls (computed; background knowledge). Free-carrier absorption rises with temperature and closes this window (background knowledge, DeWitt and Nutter). Low-temperature steps therefore rely on thermocouples, transmission-based methods or calibrated open-loop control (my reading). Reference: M. M. Moslehi and H. N. Najm, ‘Multi-point pyrometry with real-time surface emissivity compensation’, US patent 5,156,461, Texas Instruments (filed May 1991) (fetch-tool summary); D. P. DeWitt and G. D. Nutter (eds.), Theory and Practice of Radiation Thermometry, Wiley 1988, and F. Roozeboom (ed.), Advances in Rapid Thermal and Integrated Processing, Kluwer 1996 (background knowledge; not opened).

References

D. P. DeWitt and G. D. Nutter (eds.), Theory and Practice of Radiation Thermometry, Wiley, 1988; F. Roozeboom (ed.), Advances in Rapid Thermal and Integrated Processing, Kluwer, 1996 (cited from background knowledge).
M. M. Moslehi and H. N. Najm, “Multi-point pyrometry with real-time surface emissivity compensation,” US patent 5,156,461 A, Texas Instruments, filed May 17, 1991. Available: https://patents.google.com/patent/US5156461
B. K. Tsai and D. P. DeWitt, “ITS-90 Calibration of Radiometers Using Wire/Thin-Film Thermocouples in the NIST RTP Tool: Effective Emissivity Modeling,” 7th International Conference on Advanced Thermal Processing of Semiconductors (RTP ‘99), 1999. Available: https://www.nist.gov/node/564961
Nokia Bell Labs, “Wafer Temperature Measurement in Rapid Thermal Processors with Modulated Lamp Power,” December 1999 (DOI 10.1007/s11664-999-0125-8). Available: https://www.nokia.com/bell-labs/publications-and-media/publications/wafer-temperature-measurement-in-rapid-thermal-processors-with-modulated-lamp-power
Reflection High-Energy Electron Diffraction (RHEED) page of this vault.

Quartz 5

Explorer

Pyrometers and Wafer Temperature Sensors