CVD REACTOR AND METHOD FOR CONTROLLING THE SURFACE TEMPERATURE OF THE SUBSTRATES

20230041558 · 2023-02-09

    Inventors

    Cpc classification

    International classification

    Abstract

    In a CVD reactor and a method for the open-loop/closed-loop control of the surface temperature of substrates arranged therein, the substrates lie on substrate-retaining elements, which are each supported by a gas cushion. Actual values of the surface temperatures associated with a respective substrate-retaining element are successively measured and the surface temperatures are controlled in a closed-loop manner to a common value by varying the gas cushion height. After measuring each actual value of the surface temperature associated with a substrate-retaining element and using only the respective last-measured actual value of the surface temperatures of each substrate-retaining element, a first average value is calculated, a difference value associated with the substrate-retaining element is calculated, and an approximate actual value is calculated for each of the other substrate-retaining elements by adding the associated difference value to the first average value, said approximate actual value being used for the open-loop/closed-loop control.

    Claims

    1. A method for controlling respective surface temperatures of substrates (4) that lie on substrate retaining elements (3) associated with a susceptor (2) disposed in a process chamber (14) of a chemical vapor deposition (CVD) reactor, the method comprising: successively measuring actual values (T1, T2, T3, T4, T5) of surface temperatures associated with the substrate retaining elements (3) including a first actual value (T3) associated with a first one of the substrate retaining elements (3) that was last measured in the successive measurements; controlling the surface temperatures to a common value in a closed-loop manner by varying a parameter; calculating a first average value (MT) based on the first actual value (T3) and the actual values (T1, T2, T4, and T5) associated with a first group of the substrate retaining elements (3) excluding the first substrate retaining element (3); calculating a difference value (dT3) associated with the first substrate retaining element (3) by forming a difference between the first average value (MT) and the first actual value (T3); and calculating, for one or more of the substrate retaining elements (3) in the first group, an approximated actual value (T′1, T′2, T′4, T′5) by adding a difference value (dT1, dT2, dT4, dT5) associated with the substrate retaining element (3) to the first average value (MT).

    2-5. (canceled)

    6. The method of claim 1, wherein the substrate retaining element is a substrate retainer (3) that is carried by a gas cushion (7), and wherein the parameter is a height of the gas cushion (7) or a composition of gas forming the gas cushion (7).

    7. The method of claim 1, wherein the parameter is a cooling or heating power supplied to one or more of the substrate retaining elements (3).

    8. The method of claim 1, further comprising: calculating a second average value (MT′) based on the first actual value (T3) and the one or more approximated actual values (T′1, T′2, T′4, T′5); and calculating, for each of the one or more approximated actual values (T′1, T′2, T′4, T′5), a difference between the approximated actual value (T′1, T′2, T′4, T′5) and the second average value (MT′), wherein the difference is used as an input variable for a first closed-loop controller (21), which controls the difference toward zero in a closed-loop manner.

    9. The method of claim 1, wherein the susceptor (2) is heated from a first temperature to a second temperature with steadily increasing temperature by a heating device (9) or cooled from the first temperature to a third temperature with steadily decreasing temperature.

    10. The method of claim 8, wherein one or more of a temperature of the susceptor (2), the first average value (MT), the second average value (MT′) or the one or more approximated actual values (T′1, T′2, T′4, T′5) is controlled toward a nominal value in a closed-loop manner with a second closed-loop controller (22).

    11. The method of claim 1, wherein the susceptor (2) comprises a circular disk shape and is arranged in the process chamber (14), wherein the substrate retaining elements (3) are arranged on said susceptor (2) on a circular arc line about a center of the susceptor (2), about which the susceptor (2) is rotated, and wherein the measured actual values (T1, T2, T3, T4, T5) are each determined at a position (18) within the process chamber (14) by means of a temperature measuring element (15).

    12. A chemical vapor deposition (CVD) reactor, comprising: a susceptor (2); a temperature measuring element (15); a plurality of substrate retaining elements (3) that are associated with the susceptor (2), wherein displacement of the susceptor (2) causes the substrate retaining elements (3) to successively move into a detection area of the temperature measuring element (15), by means of which a respective surface temperature associated with each of the substrate retaining elements (3) is successively measured, the successive measurements including actual values (T1, T2, T3, T4, T5) of the surface temperatures associated with the substrate retaining elements (3) including a first actual value (T3) associated with a first one of the substrate retaining elements (3) that was last measured in the successive measurements; a first closed-loop controller (21) configured to control the surface temperatures to a common value in a closed-loop manner by varying a parameter, wherein a first average value (MT) is calculated based on the first actual value (T3) and the actual values (T1, T2, T4, and T5) associated with a first group of the substrate retaining elements (3) excluding the first substrate retaining element (3), wherein a difference value (dT3) associated with the first substrate retaining element (3) is calculated by forming a difference between the first actual value (T3) and the first average value (MT), and wherein, for one or more of the substrate retaining elements (3) in the first group, an approximated actual value (T′1, T′2, T′4, T′5) is calculated by adding a difference value (dT1, dT2, dT4, dT5) associated with the substrate retaining element (3) to the first average value (MT).

    13. (canceled)

    14. The CVD reactor of claim 12, wherein a second average value (MT′) is calculated based on the first actual value (T3) and the one or more approximated actual values (T′1, T′2, T′4, T′5), and wherein, for each of the one or more approximated actual values (T′1, T′2, T′4, T′5), a difference between the approximated actual value (T′1, T′2, T′4, T′5) and the second average value (MT′) is used as an input variable for the first closed-loop controller (21), which controls the difference toward zero in a closed-loop manner.

    15. The CVD reactor of claim 12, further comprising a temperature controlling device (9) for heating susceptor (2) from a first temperature to a second temperature with steadily increasing temperature or cooling the susceptor (2) from the first temperature to a third temperature with steadily decreasing temperature.

    16. The CVD reactor of claim 14, further comprising a second closed-loop controller (22) for controlling one or more of a temperature of the susceptor (2), the first average value (MT), or the second average value (MT′) toward a nominal value in a closed-loop manner.

    17. (canceled)

    18. The method of claim 1, wherein the actual values (T1, T2, T4 and T5) associated with the substrate retaining elements (3) in the first group comprise last-measured values for each of the substrate retaining elements (3) in the first group.

    19. The CVD reactor of claim 12, wherein the actual values (T1, T2, T4 and T5) associated with the substrate retaining elements (3) in the first group comprise last-measured values for each of the substrate retaining elements (3) in the first group.

    Description

    BRIEF DESCRIPTION OF THE DRAWINGS

    [0011] An exemplary embodiment of the invention is described in greater detail below with reference to the attached drawings. In these drawings:

    [0012] FIG. 1 schematically shows a cross section of a CVD reactor according to the invention, wherein the CVD reactor has a plurality of substrate retaining elements that are designed in the form of substrate retainers 3,

    [0013] FIG. 2 schematically shows a top view of a susceptor 2 of the CVD reactor approximately along the line of section II-II in FIG. 1, wherein said susceptor has five storage spaces, in which a substrate retaining element 3 carrying a substrate 4 is respectively arranged,

    [0014] FIG. 3 schematically shows the mass flow controllers 20 for respectively making available a gas flow that is fed into supply lines 8 of the susceptor 2 in order to form a gas cushion 7, on which the substrate retaining element 3 lies and by means of which the substrate retaining element 3 is set in rotation,

    [0015] FIG. 4 schematically shows the progression of the surface temperatures T1, T2, T3, T4, T5 of the five substrate retaining elements 3 when the substrate temperature is essentially kept constant in a first phase A and when the substrate temperature is increased with a constant gradient over time in a second phase B,

    [0016] FIG. 5 shows an enlarged detail of FIG. 4 in order to elucidate the difference values dT1, dT2, dT3, dT4, dT5, and

    [0017] FIG. 6 shows a table of the surface temperatures (measured actual values) T1, T2, T3, T4, T5 measured in intervals n during an increase of the substrate temperature ST, the average values MT and MT′ formed thereof, as well as difference values dT1, dT2, dT3, dT4, dT5 calculated therefrom and approximated actual values T1′, T2′, T3′, T4′, T5′ calculated therefrom.

    DETAILED DESCRIPTION

    [0018] The CVD reactor illustrated in FIGS. 1 and 2 has an outwardly gas-tight housing 1. A susceptor 2 that has the shape of a circular disk and consists, for example, of graphite or coated graphite is located within the housing 1. A heating device 9 is located underneath the susceptor 2 and serves for heating the susceptor 2 to a susceptor temperature ST. The susceptor 2 is carried by a shaft 10 that can be rotated about an axis. Supply lines 8 extend within the shaft 10 and are fed by mass flow controllers 20. Each of the altogether five supply lines is fed by a mass flow controller 20, wherein the mass flow controller 20 is supplied with an inert gas such as hydrogen or nitrogen or a noble gas by a gas source 19. Five storage spaces, each for storing a substrate 4, are located in an upper side of the susceptor 2 that is directed toward the process chamber. The storage spaces are respectively formed by a substrate retaining element 3. It is possible to form these substrate retaining elements 3 using the same material as the susceptor 2, in which case the substrate retaining elements 3 may take the form of depressions within the susceptor 2, each for accommodating a substrate 4.

    [0019] In the exemplary embodiment, a total of five pockets are located in the upper side of the susceptor 2 that is directed toward the process chamber 14. A substrate retaining element 3 with the shape of a circular disc is located in each pocket. One of the supply lines 8 leads into the bottom 6 of each pocket 5 such that the gas exiting the mouth of the supply line 8 forms a gas cushion 7, which on the one hand rotationally drives the substrate retaining element 3 and on the other hand lifts the substrate retaining element 3. At least one substrate 4 lies on the substrate retaining element and can be coated with at least one layer, particularly a semiconductor layer, in a deposition process within the process chamber. The process gases required for this purpose are fed into the process chamber 14 by means of a gas inlet element 12, wherein the process gases are introduced into the process chamber 14 from gas outlet zones 13. The process chamber 14 is upwardly delimited by a process chamber ceiling 11 that has an opening 17, through which an optical path 16 extends. The optical path 16 connects a measuring point 18 located approximately in the center of the substrate retaining element 3 to an optical temperature measuring element 15 such as a pyrometer, by means of which the surface temperature of the substrate 4 or the substrate retaining element 3 can be determined. In addition, index elements are provided in order to determine the rotating position of the susceptor 2. These pieces of information are fed to a control device 23. Based on these pieces of information, the control device 23 can determine which of the five substrate retaining elements 3 passes through the detection area of the temperature measuring element 15 at a certain point in time in order to successively measure the current temperatures (measured actual values Tn) of the substrate retaining elements 3.

    [0020] The gas cushion, on which the substrate retaining elements 3 float, forms a heat transfer path in order to transfer heat from the susceptor 2 to the substrate retaining element 3. The heat transferred to the substrate retaining elements 3 depends on the height of the gas cushion such that the surface temperature of the substrate 4 can be varied by varying the height of the gas cushion.

    [0021] A first closed-loop controller 21 uses the actual temperature values T1, T2, T3, T4, T5 measured with the temperature measuring element 15 for specifying the gas flows of the mass flow controllers 20 in such a way that the actual values T1, T2, T3, T4, T5 approach their average value MT.

    [0022] In another embodiment, an arbitrary and universal nominal value can be used (e.g., a temperature difference from the susceptor bottom plate or from the process chamber ceiling).

    [0023] The method used for this purpose is described in greater detail below with reference to FIGS. 4 and 5, wherein the curves illustrated in FIGS. 4 and 5 show the resulting progression of the surface temperatures of the five substrate retaining elements when no closed-loop temperature control is carried out. The relative distances between the temperatures therefore remain unchanged over the entire length of the curves. In reality, the relative distances between the curves would be reduced due to the closed-loop control and ideally be zero. The susceptor temperature is not changed in a first phase A.

    [0024] The susceptor 2 rotates about its axis with a constant rotational speed that may lie between two and twenty revolutions per minute. The intervals, between which individual measurements on substrate retaining elements 3 that successively pass through the detection area of the temperature measuring element 15 are carried out, accordingly have lengths of a few seconds. The temperatures T1, T2, T3, T4, T5 of the individual substrate retaining element surfaces do not change in the first phase A, during which the susceptor temperature is kept constant at approximately 900° C. If the excluded closed-loop control would actually be carried out, the temperatures T1, T2, T3, T4, T5 would approach an average value.

    [0025] The susceptor temperature steadily increases in the second phase B, for example due to an increase of the heating power.

    [0026] An average value MT is determined in each of the two phases A, B as follows:


    MT(k)=⅕.Math.(T.sub.1(k)+T.sub.5(k−1)+T.sub.4(k−2)+T.sub.3(k−3)+T.sub.2(k−4))

    k={6, 11, 16, 21, . . . } for S=1, N=5


    MT(k)=⅕.Math.(T.sub.2(k)+T.sub.1(k−1)+T.sub.5(k−2)+T.sub.4(k−3)+T.sub.3(k−4))

    k={7, 12, 17, 22, . . . } for S=1, N=5


    MT(k)=⅕.Math.(T.sub.3(k)+T.sub.2(k−1)+T.sub.1(k−2)+T.sub.5(k−3)+T.sub.4(k−4))

    k={8, 13, 18, 23, . . . } for S=1, N=5


    MT(k)=⅕.Math.(T.sub.4(k)+T.sub.3(k−1)+T.sub.2(k−2)+T.sub.1(k−3)+T.sub.5(k−4))

    k={9, 14, 19, 24, . . . } for S=1, N=5


    MT(k)=⅕.Math.(T.sub.5(k)+T.sub.4(k−1)+T.sub.3(k−2)+T.sub.2(k−3)+T.sub.1(k−4))

    k={10, 15, 20, 25, . . . } for S=1, N=5
    N: number of substrate carriers
    S: position of the susceptor (wafer number) for k=1|S={1, 2, 3 . . . N}
    Point in time of the measurement:

    [00001] t ( k ) = 6 0 [ s ] N .Math. ω .Math. rpm .Math. .Math. k .Math. k

    ω: rotational frequency of the susceptor.
    In the most general sense, the average value formation takes place as follows:

    [00002] MT ( k ) = 1 N .Math. .Math. N n = 1 T ( N - ( ( n - k + N - S ) mod N ) ) ( k - n + 1 ) k , k > N , n { 1 , 2 , 3 , 4 , .Math. , N }

    Modulo: n mod m results in the residual quantity b of the division n divided by m, the sign of b corresponds to the sign of m,
    wherein N is the total number of substrate retaining elements 3, which in the exemplary embodiment is equal to five.

    [0027] The average value formation is carried out during each measurement, wherein the temperature value of the substrate retaining element 3 currently located in the detection area of the temperature measuring element 15 and otherwise the previously measured temperature values of all other substrate retaining elements are used, but wherein only one respective measured value and always only the most recent measured value is used. In the region of phase B, this leads to the average value being characterized by measured temperature values that were recorded in the past, i.e. at different substrate temperatures ST. FIG. 4 shows that the curve of the average value MT extends underneath the measured curve of the measured temperature values of the individual substrate retaining elements 3. A sharp bend in the measured curves in the illustration leads to a delayed gradient rise of the curve of the average value.

    [0028] Not only a current actual value, but also a difference value is calculated during each measurement as follows:


    dT1(k)=T1(k)−MT(k)|k={6,11,16,21, . . . } for S=1,N=5


    dT2(k)=T2(k)−MT(k)|k={7,12,17,22, . . . } for S=1,N=5


    dT3(k)=T3(k)−MT(k)|k={8,13,18,23, . . . } for S=1,N=5


    dT4(k)=T4(k)−MT(k)|k={9,14,19,24, . . . } for S=1,N=5


    dT5(k)=T5(k)−MT(k)|k={10,15,20,25, . . . } for S=1,N=5.

    In the most general sense, the difference value can be calculated as follows:


    dT.sub.(N−((n−k+N−S)modN))(k)=T.sub.(N−((n−k+N−S)modN))(k)−MT(k)|n=1.

    [0029] The difference value at the points in time t.sub.4, t.sub.5, t.sub.1, t.sub.2 and t.sub.3 are illustrated in FIG. 4. FIG. 5 shows how approximated temperatures T5′, T1′, T4′ and T2′ are calculated at the time t.sub.3 based on the average value MT determined at the time t.sub.3 by using the previously determined difference values dT.sub.1, dT.sub.2, dT.sub.4, dT.sub.5. The temperature T3 of the third substrate retaining element is measured at the point in time t3. The average value MT is initially calculated by using the actual temperature values T4, T5, T1, T2 measured previously at the points in time t4, t5, t1, t2, respectively. Approximated temperatures T5′, T1′, T4′, T2′ are calculated by using the difference values dT4, dT5, dT1, dT2 calculated at the points in time t4, t5, t1, t2 as follows.


    T′1(k)=T1(k)|k={6,11,16,21, . . . } for S=1,N=5


    T′2(k)=MT(k)+dT2(k−4)


    T′3(k)=MT(k)+dT3(k−3)


    T′4(k)=MT(k)+dT4(k−2)


    T′5(k)=MT(k)+dT5(k−1)

    In the most general sense, the approximated temperatures are calculated as follows:


    T′.sub.(N−((n−k+N−S)modN))=MT(k)+dT.sub.(N−((n−k+N−S)modN))(k−n+1) k∈custom-character,k>N,n∈{1,2,3,4, . . . ,N}.

    [0030] A second average value can then be calculated from the approximated temperatures Tn′ as follows


    MT′(k)=⅕(T′.sub.1(k)+T′.sub.2(k)+T′.sub.3(k)+T′.sub.4(k)+T′.sub.5(k))

    or, in the most general sense, in accordance with

    [00003] MT ( k ) = 1 N .Math. n = 1 N T n ( k ) .

    [0031] The respective closed-loop control or open-loop control of the mass flow controllers 20 is carried out with the aid of this second average value MT′, which may correspond to the current susceptor temperature if this susceptor temperature rises with a constant gradient, wherein the closed-loop/open-loop control takes place in such a way that a difference between the approximated actual temperature T1′ and the second average value MT′ is controlled toward zero in a closed-loop manner.

    [0032] FIG. 6 shows how the temperatures change on a temperature ramp in the form of a table.

    [0033] The preceding explanations serve for elucidating all inventions that are included in this application and respectively enhance the prior art independently with at least the following combinations of characteristics, wherein two, multiple or all of these combinations of characteristics may also be combined with one another, namely:

    [0034] A method, which is characterized in that an approximated actual value Tn′, which is used for the open-loop/closed-loop control, is determined after each measurement of a measured actual value Tn of the surface temperature associated with a substrate retaining element 3 by using the last-measured actual value Tn of the surface temperature of at least one other substrate retaining element 3.

    [0035] A method, which is characterized in that a first value MT is calculated with the actual values Tn of the surface temperature of a plurality of other substrate retaining elements 3 or each substrate retaining element 3 and/or in that the first value MT is an average value MT of the last-measured actual values Tn of the surface temperatures and/or in that a difference value dTn associated with the substrate retaining element 3 is calculated by forming a difference between the actual value Tn measured during the measurement and the first value or average value MT and/or in that the approximated actual value Tn′ is calculated for each of the other substrate retaining elements 3 by respectively adding the associated difference value dTn to the value MT.

    [0036] A method, which is characterized in that the substrate retaining element is a substrate retainer 3, which is supported by a dynamic gas cushion, and in that the parameter is the height of the gas cushion 7 or a composition of the gas forming the gas cushion 7 and/or in that the parameter is a cooling or heating power supplied to a substrate retaining element 3.

    [0037] A method, which is characterized in that a second average value MT′ is calculated after a or each measurement by using the actual value Tn determined during the measurement and the last-calculated approximated actual values Tn′ associated with one, a few or all of the other substrate retaining elements 3, and in that the difference between the approximated actual value Tn′ and the second average value MT′ is used as input variable for a first closed-loop controller 21, which controls the difference toward zero in a closed-loop manner.

    [0038] A method, which is characterized in that the susceptor 2 is heated from a first temperature to a second temperature with steadily increasing temperature by means of a heating device 9 or cooled to a second temperature with steadily decreasing temperature, and in that actual values are in the process cyclically measured in successive intervals on a number of substrates 4 that are associated with the susceptor 2 and respectively lie on one of the substrate retaining elements 3.

    [0039] A method, which is characterized in that a susceptor temperature, the first or second average value or one of the approximated actual values Tn′ is controlled toward a nominal value in a closed-loop manner with a second closed-loop controller 22.

    [0040] A method, which is characterized in that the susceptor 2 used has the shape of a circular disk and is arranged in a process chamber 14 of a CVD reactor, wherein the substrate retaining elements 3 are arranged on said susceptor on a circular arc line about a center of the susceptor 2, about which the susceptor 2 is rotated, and wherein the measured actual value of the surface temperature is determined at a position 18 within the process chamber 14 by means of a temperature measuring element 15.

    [0041] A CVD reactor, which is characterized in that the control device 23 is designed in such a way that a value MT is determined after each measurement of a measured actual value of the surface temperature associated with a substrate retaining element 3 by using the last-measured actual value Tn of the surface temperature of one or each substrate retaining element 3, in that a difference value dTn associated with the substrate retaining element 3 is calculated by forming a difference between the actual value Tn measured during the measurement and the value MT, and in that an approximated actual value Tn′, which is used for the open-loop/closed-loop control, is calculated for at least one other substrate retaining element 3 by adding the associated difference value dTn to the value MT.

    [0042] A CVD reactor, which is characterized in that a first value MT is calculated with the actual values Tn of the surface temperature of a plurality of other substrate retaining elements 3 or each substrate retaining element 3 and/or in that the first value MT is an average value MT of the last-measured actual values Tn of the surface temperatures and/or in that a difference value dTn associated with the substrate retaining element 3 is calculated by forming a difference between the actual value Tn measured during the measurement and the first value or average value MT and/or in that the approximated actual value Tn′ is calculated for each of the other substrate retaining elements 3 by respectively adding the associated difference value dTn to the value MT.

    [0043] A CVD reactor, which is characterized in that a second average value MT′ is calculated after a or each measurement by using the actual value Tn determined during the measurement and the last-calculated approximated actual values Tn′ associated with one, a few or all of the other substrate retaining elements 3, and in that the difference between the approximated actual value Tn′ and the second average value MT′ is used as input variable for a first closed-loop controller 21, which controls the difference toward zero in a closed-loop manner.

    [0044] A CVD reactor, which is characterized in that the susceptor 2 is heated from a first temperature to a second temperature with steadily increasing temperature by means of a heating device 9 or cooled to a second temperature with steadily decreasing temperature, and in that actual values are in the process cyclically measured in successive intervals on a number of substrates 4 that are carried by the susceptor 2 and respectively lie on one of the substrate retaining elements 3.

    [0045] A CVD reactor, which is characterized in that a susceptor temperature or the first or second average value is controlled toward a nominal value in a closed-loop manner with a second closed-loop controller 22.

    [0046] All disclosed characteristics are essential to the invention (individually, but also in combination with one another). The disclosure of the associated/attached priority documents (copy of the priority application) is hereby fully incorporated into the disclosure content of this application, namely also for the purpose of integrating characteristics of these documents into claims of the present application. The characteristics of the dependent claims also characterize independent inventive enhancements of the prior art without the characteristics of a claim to which they refer, particularly for submitting divisional applications on the basis of these claims. The invention specified in each claim may additionally comprise one or more of the characteristics that were disclosed in the preceding description and, in particular, are identified by reference symbols and/or included in the list of reference symbols. The invention also concerns design variations, in which individual characteristics cited in the preceding description are not realized, particularly as far as they are obviously dispensable for the respective intended use or can be replaced with other, identically acting technical means.

    LIST OF REFERENCE SYMBOLS

    [0047] 1 Housing [0048] 2 Susceptor [0049] 3 Substrate retaining element [0050] 4 Substrate [0051] 5 Pocket [0052] 6 Bottom [0053] 7 Gap, gas cushion [0054] 8 Supply line [0055] 9 Heating device [0056] 10 Shaft [0057] 11 Process chamber ceiling [0058] 12 Gas inlet element [0059] 13 Gas outlet zones [0060] 14 Process chamber [0061] 15 Temperature measuring element [0062] 16 Optical path [0063] 17 Opening [0064] 18 Measuring point [0065] 19 Gas source [0066] 20 Mass flow controller [0067] 21 First closed-loop controller [0068] 22 Second closed-loop controller [0069] 23 Control device [0070] A First phase [0071] B Second phase [0072] dTn Difference value [0073] dT1 Difference value [0074] dT2 Difference value [0075] dT3 Difference value [0076] dT4 Difference value [0077] dT5 Difference value [0078] MT First average value [0079] MT′ Second average value [0080] n Number [0081] ST Susceptor temperature [0082] Tn Actual value of surface temperature [0083] Tn′ Approximated actual value [0084] T1 Surface temperature [0085] T2 Surface temperature [0086] T3 Surface temperature [0087] T4 Surface temperature [0088] T5 Surface temperature [0089] T1′ Approximated actual value [0090] T2′ Approximated actual value [0091] T3′ Approximated actual value [0092] T4′ Approximated actual value [0093] T5′ Approximated actual value [0094] t1 Point in time [0095] t2 Point in time [0096] t3 Point in time [0097] t4 Point in time [0098] t5 Point in time