Annealing, an important step ¡n semiconductor materials processing, can be accomplished by rapidly healingthe silicon wafer to a high temperature for a short period of time. The schematic shows a method involving the use of a hot plate operating at an elevated temperature T h . The wafer, initially at a temperature of T w , i , is suddenly positioned at a gap separation distanceL from the hot plate. The purpose of the analysis is tocompare the heat fluxes by conduction through the gaswithin the gap and by radiation exchange between thehot plate and the cool wafer. The initial time rate ofchange in the temperature of the wafer, ( d t w / d t ) t , is alsoof interest. Approximating the surfaces of the hot plateand the wafer as blackbodies and assuming their diameter D to be much larger than the spacing L . the radiativeheat flux may be expressed as q ″ r a d = σ ( T h 4 − T w 4 ) .The silicon wafer has a thickness of d = 0.78 mm , adensity of 2700 kg/ni’. and a specific heat of 875 J/kg ⋅ K . The thermal conductivity of the gas in the gapis 0 .0436 W/m ⋅ K . (a) For T h = 600 ° C and T w , i = 20 ° C , calculate the radiative heat (lux and the heat flux by conductionacross a gap distance of L = 0.2 mm . Also determine the value of ( d t w / d t ) t , resulting from each ofthe heating modes. (b) For gap distances of 0.2, 0.5, and 1 .0 mm, determinethe heat fluxes and temperature-time change as afunction of the hot plate temperature 300 ≤ T h ≤ 1300 ° C . Display results graphically. Comment on the relative importance of the two heat transfer modes and the effect of the gap distance onthe heating process. Under what conditions could awater he heated to 900°C in less than 10 s?
Annealing, an important step ¡n semiconductor materials processing, can be accomplished by rapidly healingthe silicon wafer to a high temperature for a short period of time. The schematic shows a method involving the use of a hot plate operating at an elevated temperature T h . The wafer, initially at a temperature of T w , i , is suddenly positioned at a gap separation distanceL from the hot plate. The purpose of the analysis is tocompare the heat fluxes by conduction through the gaswithin the gap and by radiation exchange between thehot plate and the cool wafer. The initial time rate ofchange in the temperature of the wafer, ( d t w / d t ) t , is alsoof interest. Approximating the surfaces of the hot plateand the wafer as blackbodies and assuming their diameter D to be much larger than the spacing L . the radiativeheat flux may be expressed as q ″ r a d = σ ( T h 4 − T w 4 ) .The silicon wafer has a thickness of d = 0.78 mm , adensity of 2700 kg/ni’. and a specific heat of 875 J/kg ⋅ K . The thermal conductivity of the gas in the gapis 0 .0436 W/m ⋅ K . (a) For T h = 600 ° C and T w , i = 20 ° C , calculate the radiative heat (lux and the heat flux by conductionacross a gap distance of L = 0.2 mm . Also determine the value of ( d t w / d t ) t , resulting from each ofthe heating modes. (b) For gap distances of 0.2, 0.5, and 1 .0 mm, determinethe heat fluxes and temperature-time change as afunction of the hot plate temperature 300 ≤ T h ≤ 1300 ° C . Display results graphically. Comment on the relative importance of the two heat transfer modes and the effect of the gap distance onthe heating process. Under what conditions could awater he heated to 900°C in less than 10 s?
Solution Summary: The author calculates the heat flux due to radiation and conduction across the gap and the temperature of the wafer.
Annealing, an important step ¡n semiconductor materials processing, can be accomplished by rapidly healingthe silicon wafer to a high temperature for a short period of time. The schematic shows a method involving the use of a hot plate operating at an elevated temperature
T
h
. The wafer, initially at a temperature of
T
w
,
i
, is suddenly positioned at a gap separation distanceL from the hot plate. The purpose of the analysis is tocompare the heat fluxes by conduction through the gaswithin the gap and by radiation exchange between thehot plate and the cool wafer. The initial time rate ofchange in the temperature of the wafer,
(
d
t
w
/
d
t
)
t
, is alsoof interest. Approximating the surfaces of the hot plateand the wafer as blackbodies and assuming their diameter D to be much larger than the spacing L. the radiativeheat flux may be expressed as
q
″
r
a
d
=
σ
(
T
h
4
−
T
w
4
)
.The silicon wafer has a thickness of
d
=
0.78
mm
, adensity of 2700 kg/ni’. and a specific heat of
875
J/kg
⋅
K
. The thermal conductivity of the gas in the gapis
0
.0436
W/m
⋅
K
.
(a) For
T
h
=
600
°
C
and
T
w
,
i
=
20
°
C
, calculate the radiative heat (lux and the heat flux by conductionacross a gap distance of
L
=
0.2
mm
. Also determine the value of
(
d
t
w
/
d
t
)
t
, resulting from each ofthe heating modes. (b) For gap distances of 0.2, 0.5, and 1 .0 mm, determinethe heat fluxes and temperature-time change as afunction of the hot plate temperature
300
≤
T
h
≤
1300
°
C
. Display results graphically. Comment on the relative importance of the two heat transfer modes and the effect of the gap distance onthe heating process. Under what conditions could awater he heated to 900°C in less than 10 s?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.