Method and device for the in-situ determination of the temperature of a sample

Abstract

The invention relates to a method and to a device for the in-situ determination of the temperature ϑ of a sample, in particular to a method and to a device for the surface-corrected determination of the temperature ϑ of a sample by means of the band-edge method.

It is provided that, for the in-situ determination of the temperature ϑ of a sample (10) when growing a layer stack (12) in a deposition system, a surface-corrected transmission spectrum T′(λ) is calculated by determining the quotient of the transmission spectrum T(λ) and a correction function K(λ), the correction function K(λ) being calculated from a determined reflection spectrum R(λ). Subsequently, the spectral position of the band-edge λ.sub.BE is determined from the transmission spectrum T′(λ), and the temperature ϑ is determined from the spectral position of the band-edge λ.sub.BE by means of a known dependency ϑ(λ.sub.BE).

Claims

1. A method for the in-situ determination of the temperature ϑ of a sample when growing a layer stack in a deposition system, comprising the following steps: a) transmitting a first optical radiation through the sample, wherein the first optical radiation has a first intensity spectrum I.sub.1(λ) which extends spectrally on either side of a band-edge of the sample, and measuring the radiation obtained after transmission through the sample in order to determine a transmission spectrum T(λ); b) irradiating a second optical radiation onto a surface of the sample to be coated, wherein the second optical radiation has a second intensity spectrum I.sub.2(λ) and the spectral range of the second optical radiation includes the spectral range of the first optical radiation, and measuring the radiation obtained after reflection from the surface in order to determine a reflection spectrum R(λ); c) calculating a surface-corrected transmission spectrum T′(λ) by determining the quotient of the transmission spectrum T(λ) and a correction function K(λ) according to formula (1)
T′(λ)=T(λ)/K(λ),  (1) wherein the correction function K(λ) is calculated from the reflection spectrum R(λ); d) determining the spectral position of the band-edge λ.sub.BE from the transmission spectrum T′(λ); and e) determining the temperature ϑ from the spectral position of the band-edge λ.sub.BE by means of a known dependency ϑ(GIBE).

2. The method of claim 1, wherein the transmission spectrum T(λ) is a normalized transmission spectrum T.sub.norm(λ) and the reflection spectrum R(λ) is a normalized reflection spectrum R.sub.norm(λ).

3. The method of claim 1, wherein, when growing a layer stack made up of transparent layers, the correction function K(λ) is calculated according to formula (2) $\begin{array}{cc}K\left(\lambda \right)=\frac{1-R\left(\lambda \right)}{1-R_0\left(\lambda \right)}& \left(2\right)\end{array}$ from the reflection spectrum R(λ), wherein the divisor contains the reflection spectrum R.sub.0(λ) of the sample before the deposition.

4. The method of claim 1, wherein, when growing a layer stack made up of partially absorbing layers, the temperature ϑ is determined by means of a correction function K(λ), which is calculated by iteratively repeating steps c) to e), from the reflection spectrum R(λ) and a starting value ϑ.sub.0 for the temperature ϑ as parameters of a model for the layer stack that has already been applied, wherein a temperature determined during the iteration in step e) is used as the new temperature parameter for the model until the difference between the current value for the temperature ϑ.sub.i and the temperature ϑ.sub.i+1 determined thereby in step e) is below a specified threshold value.

5. The method of claim 4, wherein the starting value ϑ.sub.0 for the temperature ϑ is the process temperature ϑ.sub.P of the deposition system, associated with the reflection spectrum R(λ).

6. The method of claim 1, wherein the dependency ϑ(λ.sub.BE) is at least approximately derived from a reference database in accordance with the material of the sample and the sample thickness d.

7. The method of claim 1, wherein the dependency ϑ.sub.d1(λ.sub.BE) known for a predetermined sample thickness d.sub.1 is used for determining the dependency ϑ.sub.d2 (λ.sub.BE) for a sample thickness d.sub.2 that differs therefrom, by the dependency λ.sub.BE(ϑ) being ascertained using an emissivity-corrected pyrometer in a temperature range Δϑ which is covered both by the pyrometer and the method, and by the dependency ϑ.sub.d2(λ.sub.BE) being accordingly adapted in the temperature range outside Δϑ, which is only covered by the method according to the invention, from the progression of the known dependency ϑ.sub.d1(λ.sub.BE).

8. The method of claim 7, wherein, proceeding from a known dependency ϑ(λ.sub.BE) for known sample doping level, a corresponding dependency is ascertained for a sample having differing or unknown doping level.

9. A device for carrying out the method of claim 1, comprising: a) a second radiation source, configured to irradiate the second optical radiation onto the surface of the sample to be coated; b) a spectrometer, configured to determine the transmission spectrum T(λ) and a reflection spectrum R(λ); and c) an electronic data-processing apparatus, configured to carry out method steps c) to e) from claim 1 using the transmission spectrum T(λ) and the reflection spectrum R(λ) to determine the temperature ϑ.

10. The device according to claim 9, further comprising a first radiation source, configured to transmit the first optical radiation through the sample.

Description

DRAWINGS

[0057] Exemplary embodiments of the invention are explained in greater detail with reference to the drawings and the following description. In the drawings:

[0058] FIG. 1 shows schematic views of a method for determining the temperature of a sample by means of the band-edge method according to the prior art,

[0059] FIG. 2 shows a schematic view of a first embodiment (sample heater as light source) of a method according to the invention for determining the temperature of a sample by means of the band-edge method,

[0060] FIG. 3 shows a schematic view of a second embodiment (having an additional light source) of a method according to the invention for determining the temperature of a sample by means of the band-edge method,

[0061] FIG. 4 shows a simulated modification of the band-edge signature depending on the thickness of a layer stack,

[0062] FIG. 5 shows a simulated dependency of the correction function K(λ) depending on the thickness of a layer stack,

[0063] FIG. 6 shows a schematic view of a method according to the invention for determining the correction function K(λ) when growing a layer stack made up of partially absorbing layers, and

[0064] FIG. 7 shows a calibration specification for deriving the calibration curve of a sample of unknown sample thickness d by means of emissivity-corrected pyrometry.

EMBODIMENTS OF THE INVENTION

[0065] FIG. 1 shows schematic views of a method for determining the temperature ϑ of a sample 10 by means of the band-edge method according to the prior art. In particular, FIG. 1 a) shows a method in which the sample heater of the deposition system is used as an external first radiation source 20 for a first optical radiation A. The first optical radiation A is transmitted through the sample 10, wherein the first optical radiation A has a first intensity spectrum I.sub.1(λ) which extends spectrally on either side of a band-edge (BE) of the sample 10, and the radiation A′ obtained after transmission through the sample 10 is measured in order to determine a transmission spectrum T(λ). The sample 10 may in particular be a semiconductor substrate. A layer stack 12 is applied to the front side 14 of the sample 10. This embodiment is also referred to as a transmitted-light configuration.

[0066] The transmission spectrum T(λ) measured by the spectrometer 30 is composed of several components. These are a component A′.sub.1 having wavelengths λ<λ.sub.BE, a component A′.sub.2 having wavelengths λ>λ.sub.BE, and an additional interference component C′, which originates from a thermal MBE source, for example. The radiation A.sub.1 having wavelengths λ<λ.sub.BE is absorbed during transmission through the sample 10. However, the sample 10 likewise emits corresponding thermal radiation, such that this wavelength range appears in the measured transmission spectrum T(λ) as an interference signal in the background. The radiation A.sub.2 having wavelengths λ>λ.sub.BE is largely transmitted during transmission through the sample 10. In the transmission spectrum T(λ), the band-edge characteristic used for the temperature determination is thus essentially apparent as a transition region between the spectral components A′.sub.1 and A′.sub.2, the background radiation C′ being superimposed on the spectrum.

[0067] FIG. 1 b) shows an alternative method in which an additional first radiation source 20 is used for generating a first optical radiation A. The method corresponds to that described with regard to FIG. 1 a), but the first radiation A is first reflected or scattered by the backside 16 of the sample 10. Preferably, scattering takes place at locations of surface roughness, such that the measurement of the radiation A′ obtained after transmission through the sample 10 is using a scattered component which has been transmitted perpendicularly through the surface 14 of the sample 10 to be coated. This embodiment is also referred to as a scattered-light configuration.

[0068] For both embodiments, in the band-edge method, the spectral position of the band-edge λ.sub.BE is first determined from the transmission spectrum T(λ). The temperature ϑ of the sample 10 is subsequently determined therefrom by means of a known dependency ϑ(λ.sub.BE). A significant drawback of the prior art is, however, that, due to the layer stack 12, surface effects are superimposed on the transmission spectrum T(λ), which make it difficult to accurately determine the spectral position of the band-edge λ.sub.BE. These contributions from the growing layers are usually ignored in the prior art and result in temperature errors.

[0069] FIG. 2 shows a schematic view of a first embodiment (sample heater as light source) of a method according to the invention for determining the temperature ϑ of a sample 10 by means of the band-edge method. This embodiment is based on the relationships described in FIG. 1 a). Therefore, the reference signs and their allocation apply accordingly. However, in addition, a second optical radiation B is irradiated onto a surface 14 of the sample 10 to be coated, wherein the second optical radiation B has a second intensity spectrum I.sub.2(λ) and the spectral range of the second optical radiation B includes the spectral range of the first optical radiation A, and the radiation B′ obtained after reflection from the surface is measured in order to determine S2 a reflection spectrum R(λ). Here, the second optical radiation B is emitted by a second radiation source 22, the radiation preferably being incident onto the sample 10 perpendicularly to the surface on the front side 14 of the sample 10. A determination S4 of the temperature ϑ from the spectral position of the band-edge λ.sub.BE by means of a known dependency ϑ(λ.sub.BE) thus takes place according to the invention by means of the determination S1 of a transmission spectrum T(λ) and the determination S2 of a reflection spectrum R(λ).

[0070] FIG. 3 shows a schematic view of a second embodiment (having an additional light source) of a method according to the invention for determining the temperature 7, of a sample 10 by means of the band-edge method. This embodiment is based on the relationships described in FIG. 1 b). Therefore, the reference signs and their allocation apply accordingly. Similarly to the embodiment according to FIG. 2, here too, a second optical radiation B is additionally irradiated onto a surface 14 of the sample 10 to be coated, wherein the second optical radiation B has a second intensity spectrum I.sub.2(λ) and the spectral range of the second optical radiation B includes the spectral range of the first optical radiation A, and the radiation B′ obtained after reflection from the surface is measured in order to determine S2 a reflection spectrum R(λ). Reference is made to the description of FIG. 2 in this regard.

[0071] FIG. 4 shows a simulated modification of the band-edge signature depending on the thickness of a layer stack 12. In the simulation, layers of Al.sub.0.5GaAs of different thicknesses, which would visibly deform the band-edge signature of the sample (solid line) and would result in a distorted temperature measurement, were applied to a 100 μm thick GaAs sample (where ϑ=300 K) which was polished on both sides. The graph also indicates in what direction the band-edge signature would shift as the temperature increases ϑ.

[0072] FIG. 5 shows a simulated dependency of the correction function K(λ) depending on the thickness of a layer stack 12. In the simulation, a layer system composed of Al.sub.0.5GaAs on GaAs (where ϑ=300K) was compared for two different thicknesses of the Al.sub.0.5GaAs layer. The correction function K(λ) was calculated according to formula (2)

[00003]$\begin{array}{cc}K\left(\lambda \right)=\frac{1-R\left(\lambda \right)}{1-R_0\left(\lambda \right)}& \left(2\right)\end{array}$

[0073] from the reflection spectrum R(λ), wherein the divisor contains the reflection spectrum R.sub.0(λ) of the sample before the deposition.

[0074] FIG. 6 shows a schematic view of a method according to the invention for determining the correction function K(λ) when growing a layer stack 12 made up of partially absorbing layers. This is a method in which, by iteratively repeating steps c) to e) according to claim 1, the temperature ϑ is calculated by means of a correction function K(λ) from the reflection spectrum R(λ) and a starting value ϑ.sub.0 for the temperature ϑ as parameters of a model for the layer stack 12 that has already been applied, wherein a temperature determined during the iteration in step e) is used as the new temperature parameter for the model until the difference between the current value for the temperature ϑ.sub.i and the temperature ϑ.sub.i+1 determined thereby in step e) is below a specified threshold value. Specifically, a determination S2 of a reflection spectrum R(λ) according to the invention and a determination S30 of a starting value ϑ.sub.0 are first carried out. Using these parameters, an adaptation S31 of the model for the already applied layer stack 12 is carried out. By means of the model, a calculation S32 of a correction function K(λ) is subsequently carried out. A calculation S3 of a surface-corrected transmission spectrum T′(λ) requires the determination S1 of a transmission spectrum T(λ). A determination S4 of the temperature ϑ.sub.i is then carried out by means of the conventional band-edge method.

[0075] A comparison S41 of the difference |ϑ.sub.i+1−ϑ.sub.i| with a specified threshold value is also carried out for the iteration. If the difference is greater than the threshold value, another adaptation S31 of the model is carried out for the already applied layer stack 12, the current value for the temperature ϑ.sub.i+1 being used as a new temperature parameter for the model. In another iteration step, the corresponding steps are then cycled through again, but another determination S1 of the transmission spectrum T(λ) does not take place within the iteration loop. This determination is transferred from the preceding cycle unchanged for the calculation S3 of an iteratively improved, surface-corrected transmission spectrum T′(λ). If, during the comparison S41 of the difference |ε.sub.i+1−ϑ.sub.i|, the difference is ultimately less than the threshold value, an output S42 of the temperature ϑ.sub.i+1 is made as the final result of the temperature measurement.

[0076] FIG. 7 shows a calibration specification for deriving the calibration curve of a sample 10 of unknown thickness d by means of emissivity-corrected pyrometry. The dependency ϑ.sub.d1(λ.sub.BE) known for a predetermined sample thickness d.sub.1 is used here for determining the dependency ϑ.sub.d2 (λ.sub.BE) for a sample thickness d.sub.2 that differs therefrom, by the dependency λ.sub.BE(S) being ascertained using an emissivity-corrected pyrometer in a temperature range Δϑ which is covered both by the pyrometer and the method, and by the dependency ϑ.sub.d2(λ.sub.BE) being accordingly adapted in the temperature range outside Δϑ, which is only covered by the method according to the invention, from the progression of the known dependency ϑ.sub.d1(λ.sub.BE). From a known calibration curve for a certain sample thickness ϑ.sub.d1=750 μm), an analogous calibration curve can be derived thereby for a sample 10 that is made of the same material but does not have a precisely known thickness d.sub.2. To do this, an emissivity-corrected pyrometric measurement is carried out for a set of different temperatures in a temperature range M (known as the common temperature range) in which both a band-edge measurement and a pyrometric measurement (i.e. a sufficient quantity of thermal photons is emitted) are possible. The calibration curve can then be modified or extrapolated (e.g. by offset shift or other suitable methods) such that it matches the pyrometric measurement in the common temperature range.

LIST OF REFERENCE SIGNS

[0077] 10 Sample [0078] 12 Layer stack [0079] 14 Front side [0080] 16 Backside [0081] 20 First radiation source [0082] 22 Second radiation source [0083] 30 Spectrometer [0084] S1 Determination of a transmission spectrum T(λ) [0085] S2 Determination of a reflection spectrum R(λ) [0086] S30 Determination of a starting value ϑ.sub.0 [0087] S31 Adaptation of the model for the already applied layer stack [0088] S32 Calculation of a correction function K(λ) [0089] S3 Calculation of a surface-corrected transmission spectrum T′(λ) [0090] S4 Determination of the temperature ϑ and ϑ.sub.i (with iterative calculation) [0091] S41 Comparison of the difference |ϑ.sub.i+1−ϑ.sub.i| with a specified threshold value [0092] S42 Output of the temperature ϑ [0093] A, A′ First optical radiation [0094] B, B′ Second optical radiation [0095] d Sample thickness [0096] BE Band-edge [0097] ϑ Temperature of the sample [0098] ϑ.sub.P Process temperature