In Situ and Real-Time Monitoring of Doping Levels by Reflectance Anisotropy Spectroscopy (RAS) during Molecular Beam Epitaxial (MBE) Growth of III/V Semiconductors

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Introduction
Monocrystalline layer growth is an essential competency in modern semiconductor technology.Any technique, such as refection high-energy electron difraction (RHEED) [1], which allows for in situ and real-time monitoring of the epitaxial growth, increases sample yield considerably.Another such technique is refectance anisotropy/diference spectroscopy (RAS/RDS).Te frst proof of the principle concerning this technique is dated back as early as 1966 and has been done by Cardona et al. [2].Yet, the development of RAS into an everyday tool started in 1985 and has been driven by Berkovits et al. [3] and Aspnes et al. [4][5][6][7].
Recent publications reporting on the use of RAS for monitoring of epitaxial growth of new materials, i.e., GaAsBi alloys, interesting for technological applications are [12,13].
In [14], Lastras-Martinez et al. have already discussed the use of RAS for the in situ determination of doping levels in both n-and p-type GaAs.In [15,16], our group has pointed out that doping levels can be retrieved via RAS even during reactive ion etching (RIE) instead of growth.
RAS is an optical tool allowing for precise determination of the state of the epitaxial growth front.Usually, only surface-related information is used, and the bulk-related one, in principle, is intentionally disregarded by normal incidence of the broadband RAS light onto the sample (typically semiconductor wafers or wafer pieces).
Yet, there are situations, where the ever-increasing (bulk) thickness of the uppermost currently grown layer results in Fabry-Perot oscillations of the RAS signal.Even then, this information can be used, that is, for the determination of the current thickness of the uppermost layer with precision in the low nm range.Although such a precise thickness change determination might be considered an exotic application of RAS, the latter is well suited for everyday epitaxial work, e.g., to monitor the doping type and doping level [17].Tis in situ technique helps to make doping of monocrystalline III/V semiconductor layers much more controlled than any later ex situ tool like a van der Pauw measurement [18] can do.
Tis contribution is intended to highlight the opportunities RAS gives to epitaxy personnel in monitoring doping.Just as an example, but also as an important example, the material system (Al)GaAs is used throughout.Although this line of thought follows the already mentioned work reported by another group in [14], we want to stress the infuence of the efusion cells' temperatures, which is one of the main parameters to control in everyday epitaxy.Of course, there will be diferences in the exact relation of the doping level to the efusion cell temperature from machine to machine and even from growth run cycle to growth run cycle, but the retrieved functions are of interest themselves.Especially, the dependence of the majority charge carrier concentration (i.e., the doping concentration) on the RAS signal diference between the nondoping and doping cases is addressed here.

RAS Principle and Measurement Details
Tis contribution deals with RAS as a monitoring technique for MBE processes.All results refer to samples prepared in an MBE machine from DCA Instruments Oy, Turku, Finland, of type DCA MBE R450.Wafers with a maximum diameter of 2″ can be installed.With a special holder, a quarter of a 2″ wafer might be used as well.In the case of GaAs substrates, they usually have a (100) surface.Te wafers are purchased as "epi-ready"; i.e., apart from thermal oxide removal before growth, no further precleaning of the wafers is necessary.
RAS is structurally reminiscent of ellipsometry [19,20].Te major diference is the (nearly) normal incidence of light onto the wafer or sample surface, by which the ellipsometric information of an atomically smooth structure is willfully suppressed [21].Te optical setup is sketched in Figure 1.Moreover, a photograph of the RAS system, positioned fxed to the MBE machine, is shown in Figure 2. Te RAS apparatus is of type EpiRAS ® TT from Laytec, Berlin, Germany.
Te wafer/sample to be overgrown is rotated during MBE growth [22,23].Te highest RAS signal values occur for angles of the rotating wafer, which correspond to the sketch in Figure 1, i.e., when the direction of linear light polarization is under ±45 °to the main crystal axes.A situation like that occurs twice during each full revolution of the sample.
Actually, the instrument picks up the light signals with its two maxima and two minima over the complete revolution and calculates the genuine RAS signal from that.Te usual wafer revolution speed is ] � 1 Hz down to 0.25 Hz in our case.Te signal with a frequency of 2] (see above) gives the desired data, and the signal with a frequency of just ] is erroneous and might stem from periodic refections at the RAS light entrance window/ viewport of the vacuum chamber in case of a slight wobbling of the wafer holder.It is used to correct the desired data by the RAS system.
In practice, the angle of incidence might not exactly vanish, which can lead to spurious signals.To account for this problem, the azimuthal polarization angle has to be aligned carefully.Te light incidence is at least nearly normal to the wafer/sample surface, but it is drawn with a relatively large nonzero angle of incidence in Figure 1, just to make the sketch better understandable and not to have diferent devices drawn on top of each other.Figure 1: Sketch of the light path of the RAS system and, hence, for the explanation of the RAS principle.Te light incidence is at least nearly normal to the wafer/sample surface, but it is drawn with a relatively large nonzero angle of incidence, just to make the sketch better understandable and not to have diferent devices drawn on top of each other.Te shown angle of the wafer with respect to the direction of linear polarization of the incident light corresponds to those situations when the RAS signal is largest.

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Advances in Materials Science and Engineering Light is emitted from a xenon lamp, with emission photon energies approximately between 1.5 and 5.5 eV.A polarizer is used to linearly polarize the light before it impinges onto the substrate surface through the viewport/ window integrated into the MBE growth chamber.For the maximum signal, both main crystal axes on the surface of the sample have to be at an angle of ±45 °to the polarization axis of the polarizer (as already mentioned above).In these moments, the light has two linearly polarized in-phase components of equal (feld) strength, polarized along one or the other main crystal axis.
On the sample surface, the symmetry is broken by local anisotropies, e.g., by nonsaturated bonds on the sample surface (dangling bonds) [22].Due to symmetry breaking, the two components of the light are refected with slightly diferent strengths, which makes the overall light beam slightly elliptically polarized.
Te photoelastic modulator (PEM) acts as a switchable λ/2 plate.If it is in the of state, the polarization state ellipse has its long main axis perpendicular to the direction to be transmitted by the analyzer, and thus, only a small part of the refected intensity will be transmitted through the analyzer.If the PEM is in its on state, the ellipse is rotated by 90 °to be aligned with the direction to be transmitted by the analyzer, and thus, most of the refected intensity passes through the analyzer.By turning the PEM periodically on and of (with 50 kHz, due to PEM crystal resonance, not related to the needs of the RAS measurements), the ellipticity of the polarization ellipse can be deduced.As explained above, it represents the diferences in the refectivities for the two light components linearly polarized along one of the two main crystal axes.
Te light is detected using a monochromator and a photodiode.Diferent photon energies can be used for the measurement.In case a complete spectrum is desired, a diferent photon energy is used by the instrument from revolution to revolution of the wafer.If the revolution frequency is ] = 1 Hz, it will last N s to take a full spectrum with N data points (photon energies).For this reason, we go for a relatively small number of photon energies (N = 9 here with photon energies between 1.8 eV and 4.2 eV with a step size of 0.3 eV) in order to have a complete spectrum within a relatively small amount of time.Tus, we trade the number of data points per spectrum against data collection speed.
In general, the larger the photon energy (the smaller the wavelength), the smaller the depth of penetration into the material.At small photon energies (<1.8 eV), Fabry-Perot oscillations of the RAS signal versus layer thickness or time might occur during the growth of a layer.Te growth rate can be determined from the oscillation period [24,25].In the case of a layer material change from GaAs to Al 0.5 Ga 0.5 As, these oscillations can even be observed up to photon energies of 2.7 eV over half an hour at typical epitaxial growth rates.
For giving the defnition of the genuine RAS signal, the (1-10) and the (110) crystal axes are assumed here, which also represent the relevant crystal directions for the samples investigated here.Te genuine RAS signal is defned as the diference of the refectivities R for the two crystal directions under consideration normalized to the mean refectivity 〈R〉, for any specifc photon energy: Te RAS signal is in the permille range.
Te extinction ratio of the polarizer and the analyzer for the polarization direction to be blocked with respect to the polarization direction to be transmitted is between 10 −5 and 10 −6 according to the RAS supplier.But due to its small value and as it applies to any refectance value, it is of no concern.
In principle, for (nearly) normal light incidence and a hypothetically perfectly plane surface, the RAS signal should vanish.If the signal is nonzero, surface anisotropies must be responsible, e.g., due to specifc surface reconstructions or local roughness breaking the symmetry.In addition, nonlinear efects may play a role under certain circumstances [26].Te surface energies are also very sensitive to changes in the atomic positions on the surface [7].Even smooth surfaces can exhibit RAS signals due to dangling bonds on the surface [22].Te RAS signal is very sensitive to the electronic structure of the surface.Tis includes the dielectric function [22,26].
In addition, RAS responds to the change between growth and a situation on hold with surface stabilization [11,27]; i.e., dimer confgurations characteristic of the material can be identifed [28].To give an example, the RAS signal at photon energies around 2.6 eV is very sensitive to As dimer accumulation.During As stabilization, there are relatively many As dimers on the surface.When growth starts, the signal becomes smaller because the Ga atoms now added break up the dimers and growth occurs.Tere are fewer As dimers on the surface, and As monomers cannot be detected at this energy [11,22,27,29].Non-Fabry-Perot oscillations occurring at this photon energy can be explained by diferent dimer concentrations on the surface [11,22,27].Tey exist because diferent surface reconstructions occur at corners and edges of each new monolayer (atomic double layer in binary III-V semiconductors), and thus, the As dimer concentration varies at these locations.Furthermore, during the growth of each monolayer, a change from an As-to a Garich surface occurs.Tis is also a cause of non-Fabry-Perot oscillations of the RAS signal.Ga dimers can be detected at photon energies around 2.0 eV [22].
For a long time, it was not certain what causes the RAS signal peaks.In some publications, for example, the strong RAS signal at 2.6 eV is attributed to an energetic transition in the bulk material of GaAs (e.g., [23]).However, the theory that the As dimers contribute to the strong signal has gained acceptance meanwhile [22,26,29].Other studies show that photon energies with strong RAS signals can be qualitatively assigned to transitions in the bulk material at the Γ-and Λ-points in k-space [23,24].Two very informative reviews of the theory on RAS measurements and advances in the calculation of spectra are given in [22,26].
In practice, often it is not important which physical reasons (electric dipoles, . ..) the peaks in the RAS spectrum have, but that the spectra are typical and reproducible for Advances in Materials Science and Engineering certain growth fronts.Epitaxial personnel can rely on these peaks without knowing their physical reason.
In Sections 3-5, we show how RAS can be used to monitor the doping of GaAs and Al x Ga 1−x As in situ.Tus, an estimate for the successful fabrication of a sample can be made before further investigations.In Sections 3 and 4, the n-and p-doping of GaAs and Al 0.5 Ga 0.5 As, respectively, is studied in detail.In Section 5, the doping of Al x Ga 1−x As samples with other compositions is discussed.

p-GaAs (Be Doping).
In the case of p-GaAs, fve samples are considered.All samples are prepared according to the same scheme.After the wafer has been loaded and the oxide has been removed thermally, each sample is grown with a 200 nm thick bufer layer of pure GaAs.Subsequently, pdoped GaAs with a thickness of 500 nm is deposited.For this purpose, the Be efusion cell is additionally opened.If the latter is heated to a certain temperature, the growing GaAs layer will be doped accordingly.Be atoms have two valence electrons and replace Ga atoms, which have three valence electrons, during doping.Since the crystal lattice then lacks electrons to saturate all bonds, p-doping occurs.Te undoped bufer layer also serves as a reference for the RAS spectrum.
Te average is taken over the RAS spectra recorded during growth, with fuctuations accounted for as statistical errors.Whenever the term "averaged spectrum" is used throughout this contribution, averaging is carried out for any of the nine data points (i.e., nine photon energies) and over a complete period of growth without changing growth parameters (i.e., usually over the complete growth duration for the given layer).Each single measured spectrum strongly resembles the corresponding averaged spectrum given in this contribution, but in the latter, the arithmetic mean, i.e., the mean value, is used for any data point (i.e., photon energy).Each error bar represents the standard deviation at the corresponding RAS photon energy.
Figure 3 shows the connection of the set Be efusion cell temperature with the carrier concentration in p-doped GaAs layers.Tis relationship has to be rechecked after each maintenance of the chamber.Te carrier concentration is determined ex situ by van der Pauw measurements [18].
Te prepared test samples are numbered in the order of their preparation.In Figure 3, it can be seen that P1140 is slightly less heavily doped than P1122, regardless of the same efusion cell temperature.Tis is because less material remains in the efusion cell after the dopant is applied, and thus, the material fux decreases somewhat with time (here 18 samples later).It should be noted that the ordinate is logarithmic.Tus, to obtain the carrier concentration at a given Be efusion cell temperature from the ftted straight line, the following formula must be used: where p and n are the majority carrier concentrations for pdoping (acceptors) or n-doping (donors), respectively, T is the temperature in °C, and a 1 and b 1 are the determined ftting parameters.Te amount of doping material vaporized (and incorporated into the sample) is exponentially related to temperature [30], as should be expected from the exponential dependence of the partial pressure of the doping material on the efusion cell temperature according to van't Hof's law. Figure 4 reveals the RAS spectrum, averaged over all measurements taken during the growth of the doped layer, of a p-doped GaAs sample (P1140) for a high Be efusion cell temperature of 840 °C (leading to heavy p-doping of 2•10 19 cm −3 ) with the red curve.Te averaged RAS spectrum of the undoped bufer is shown in black as a reference; with p-doping, the RAS signal increases for any photon energy.
Looking at the graph in Figure 4 with its measured functions averaged over the growth duration of the relevant layers, the photon energy of 3.3 eV seems to be best suited for p-GaAs doping monitoring purposes because the signal diferences between the cases with and without doping are most pronounced.But the signal noise, given with the error bars, draws a diferent picture.Photon energies that are candidates for doping calibration must also have as small uncertainties (noise) as possible in the RAS signal so that doping can be clearly identifed.All prerequisites are fulflled for the photon energy of 2.4 eV.
For 2.4 eV, the RAS transient for the p-doped sample P1140 is given in Figure 5. Te increase in the signal is clearly visible and occurs within about four measurement points (1 point per minute here), corresponding to a flm thickness change of about 20 nm.Tereafter, the signal remains constant at the elevated value with some fuctuations.
Tis increase is explained in the literature with the linear electro-optical efect (Pockels efect) [31].It describes a change in the refractive index by applying an electric feld.During epitaxial growth, this feld arises from a charge exchange between states in the bulk material and surface  states.Tis exchange is attributed to the sample's efort to reach thermal equilibrium.
To consider a relationship between the Be efusion cell temperature and the RAS signal, the RAS signal diference between the case of the doped sample/layer and the nondoping case (bufer) at a photon energy of 2.4 eV is examined.
Te relationship given in Figure 6 between the RAS signal diference and the efusion cell temperature of Be for higher doping levels might be called linear, in frst approximation (as we also do further on in similar situations).Tis is an approximation only because only three relevant sampling/data points with quite large error bars are considered.
Since the RAS signal diference is not directly dependent on the efusion cell temperature, the linear function might rather be called a "correlation" than a dependency.
Te signal for the low efusion cell temperature deviates somewhat from this since the underlying efect leads to changes in the RAS signal only at sufciently high doping levels.Terefore, this value was not taken into account when ftting the signal diferences.

Having observed,
(1) that the carrier concentration is exponentially dependent on efusion cell temperature, (2) that the RAS signal diference is (in frst approximation) linearly dependent on efusion cell temperature, an exponential dependence of the carrier concentration on the RAS signal diference should be expected.Indeed, when the carrier concentration determined with van der Pauw measurements is plotted semilogarithmically against the RAS signal diference, as done in Figure 7, a relationship similar to that between carrier concentration and efusion cell temperature (equation ( 2)) is obtained, i.e., with p being the carrier concentration (respectively, n) again, RAS dif being the RAS signal diference, and a 2 and b 2 being the ftting parameters.An exponential dependence of the majority carrier (doping) concentration on the efusion cell temperature should be expected from van't Hof's law on the temperature dependence of the doping material's partial pressure (see above, text related to Figure 3).Since there is a linear dependence ("correlation") of the RAS signal diference (difference between the doping and nondoping cases) on the efusion cell temperature (see Figure 6), an exponential dependence of carrier concentration on the RAS signal diference should be expected also (as can be observed in Figure 7).Tere is no contradiction between the fndings.But it is not well understood yet, why the RAS signal difference only increases linearly with temperature, while the carrier concentration increases exponentially.A super-linear Advances in Materials Science and Engineering dependence might be expected with temperature due to the exponentially increasing surface density of doping atoms.By relating the RAS signal to the carrier concentration, it is clear that the magnitude of the doping can be determined in situ (after test growth processes for calibration) from this RAS signal diference without additional ex situ measurements.
Te fuctuations in the RAS signal seen in Figure 5 are subject to some non-Fabry-Perot periodicity, so the statistical errors were probably assumed to be too large, and the average value of the diference is more reproducible than the error bars in Figures 6 and 7 suggest.Te deviation for small doping levels is again attributed to the low sensitivity of the RAS signal to the underlying efect in this case.

n-GaAs (Te Doping).
In this section, the suitability of the RAS signal for n-doping control of GaAs is investigated.In the research group, Te (actually Ga 2 Te 3 ) is used for ndoping.Te correlation between the carrier concentration and the Te efusion cell temperature (retrieved from van der Pauw measurements for comparison) is illustrated in Figure 8.All measured data show the expected correlation.Only sample P1126, which has been doped at 205 °C, deviates slightly probably because an upper limit for the doping has been reached.
Analogously to the p-GaAs case, the samples have been grown with a 200 nm thick bufer of GaAs and a 500 nm thick n-doped layer.Te observed RAS spectrum of the sample P1126 with a high efusion cell temperature of 205 °C is shown in Figure 9 exemplarily.
Te change in the RAS signal for a high doping level appears to be much more pronounced than for p-doping with Be.Te biggest diference with p-doping, however, is that the signal drops of in the n-doping case and does not increase.Tus, p-and n-doping can be distinguished with RAS easily.
Again, the RAS signal value at 2.4 eV shows comparatively small fuctuations and a clear diference between the observed cases.Other photon energies could be used as well.But it is convenient for everyday epitaxial work to stick to the same value as used in the case with p-doping.
At lower photon energies, the RAS signal increases again.Tis is because the spectra are not sign-corrected in the employed RAS instrument; i.e., the actual value gets negative and increasingly negative.Terefore, a photon energy should be used where this is not the case.
Analogously to the p-GaAs case and Figures 6 and 7, the RAS signal diference is shown as a function of the efusion cell temperature in Figure 10 and the carrier concentration determined by van der Pauw measurements is shown in dependence on the RAS signal diference in Figure 11.
Comparing the results with those of p-GaAs, the same qualitative relationships can be observed.Te linear relationship between the RAS signal diference and the efusion cell temperature (in Figure 10) is even more  An increase with increasing efusion cell temperature can also be observed.As in Figure 8, the sample with the heaviest doping (P1126, 6•10 18 cm −3 ) also shows a slightly stronger deviation from the expected behavior in Figure 11.Tis is again due to the upper limit for doping.A too high amount of Te also prevents good flm growth, which is also evident in the larger error for the RAS signal.
Obviously, also for n-doped GaAs flms, control of doping with RAS is possible, and samples can be analyzed with respect to their doping in situ.
Tus, especially for more sophisticated samples, such as grown laser samples, it is relatively easy to check whether the doping of the layers is proceeding as desired.Tis is where the biggest advantage of RAS becomes apparent.An analysis with the ex situ van der Pauw method would not be possible for such laser samples, since only near-surface layers can be examined for their charge carrier concentration and the laser samples have complex layer sequences.
Due to the diferent responses of RAS to n-and pdoping, RAS can even be used to determine the type of doping beyond doubt.For van der Pauw measurements, this requires making assumptions or inferring the type of doping via the diferent mobility of the two types of charge carriers.
. Al 0.5 Ga 0.5 As Doping Monitoring Using RAS Te doping samples for Al 0.5 Ga 0.5 As have been prepared slightly diferently than for GaAs.First, a 200 nm thick undoped bufer layer of GaAs has again been grown to ensure a good surface quality for subsequent growth.Tis has been followed by a 300 nm thick undoped Al 0.5 Ga 0.5 As layer that served as the RAS reference.A 500 nm thick doped Al 0.5 Ga 0.5 As layer has been grown on top of this.At a very high Al content, an additional 10 to 50 nm thick GaAs layer has been grown to prevent the sample from oxidizing too quickly.At Al contents of x � 0.5, however, this measure is not necessary yet.
4.1.p-Al 0.5 Ga 0.5 As (Be Doping).When determining the doping of Al 0.5 Ga 0.5 As, another aspect must be considered, namely, the selection of a suitable photon energy for both pand n-doping.As shown in Figure 12 using 2.7 eV as an example (sample P1142), Fabry-Perot oscillations of the RAS signal occur when switching from GaAs to Al 0.5 Ga 0.5 As.Tey occur at higher photon energies, the larger the Al fraction is.For an Al fraction of x � 0.5, they can be observed up to a photon energy of about 3.0 eV.At 2.7 eV, the oscillations can be observed for up to half an hour.Te oscillations, of course, increase the errors in the averaged RAS spectra.Terefore, only the spectra, after the Fabry-Perot oscillations have decayed, are used for averaging.Tis again leads to acceptable error ranges in Figure 13, which shows the RAS spectra in the p-doped and undoped cases for the most heavily doped Al 0.5 Ga 0.5 As sample (P1184) due to the highest Be efusion cell temperature of 800 °C (p � 6.5•10 18 cm −3 ).
Te RAS signal values show the same small (non-Fabry-Perot) fuctuations as the RAS signal for GaAs.It is observable again that the photon energies above 3.0 eV are more prone to RAS signal fuctuations than smaller energies.Te photon energy of 2.7 eV is the best compromise between a clear diference between the RAS signals in the cases with and without doping, a small error, and a fast decay of the Fabry-Perot oscillations.Terefore, it is used for the analyses in the case of Al 0.5 Ga 0.5 As.
Figure 14 proves the exponential relationship between the determined charge carrier concentration and the Be efusion cell temperature using a semilogarithmic plot.It has to be redetermined after each chamber maintenance, as for GaAs.
Te named p-doped Al 0.5 Ga 0.5 As samples are analyzed with RAS.Te RAS signal diferences in Figure 15 are of the same order as for p-GaAs, despite using the photon energy of 2.7 eV for p-Al 0.5 Ga 0.5 As instead of 2.4 eV for p-and  Advances in Materials Science and Engineering n-GaAs.Again, this shows the expected relation.Te RAS signal diference and the Be efusion cell temperature are linearly related ("correlated") again.
An exponential relation between the carrier concentration and the RAS signal diference is also observed in a semilogarithmic plot in Figure 16.Te errors in the RAS signal and, hence, in the signal diference are larger than in the case of p-GaAs due to non-Fabry-Perot oscillations that occur.
From the plots and the relatively small deviations from the ft curve, it is clear that doping can also be inferred from the RAS signal for p-Al 0.5 Ga 0.5 As.As for GaAs, the errors are assumed to be somewhat too large due to the periodic (non-Fabry-Perot) fuctuations of the RAS signal during growth, so that the values should actually be more accurate in reality than the error bars suggest.4.2.n-Al 0.5 Ga 0.5 As (Te Doping).Te last detailed doping analysis given here is concerned with n-Al 0.5 Ga 0.5 As.Tree samples are available for this purpose.Tese have been prepared according to the same scheme as the p-doped Al 0.5 Ga 0.5 As samples.However, it is noticeable in Figure 17 that sample P1145 has a relatively large statistical (as well as systematic) error in the determination of the carrier concentration.Tis value is therefore weighed less in the determination of the ft curve.Actually, the used software program weighs the data points inversely proportional to their standard deviations.Te data point with the largest standard deviation has the least weight.
As with n-GaAs, it can be seen in Figure 18 that the changes in the spectrum for n-Al 0.5 Ga 0.5 As are more pronounced than in the p-doped case.As for GaAs, the RAS signals of the doped layers are lower than those of the undoped layers in the n-doping case.
Te photon energy of 2.7 eV is also suitable for the study of n-doping.Terefore, the same photon energy can be used for the analysis of Al 0.5 Ga 0.5 As in both doping cases.Advances in Materials Science and Engineering Te dependencies of the RAS signal diference with the Te efusion cell temperature (Figure 19) and the carrier concentration (Figure 20) are qualitatively the same as for GaAs and p-Al 0.5 Ga 0.5 As.Terefore, an in situ analysis of the doping can be performed here as well.Te deviations of the mean values from the ftting curve are small.Te errors are of the same order of magnitude as in the other cases studied.

Al x Ga 1−x As Doping Monitoring Using RAS
In the previous sections, it has been shown that the analysis of doping by RAS is possible for both GaAs and Al 0.5 Ga 0.5 As.Here, we will briefy point out what needs to be considered for Al contents x ≠ 0 and x ≠ 0.5.
First of all, the larger the Al contents are, the stronger the Fabry-Perot oscillations are due to the larger refractive index step relative to the GaAs background.Tey have increasing amplitude with increasing Al contents and last longer before decaying to the point where averages with small fuctuations can be obtained.Moreover, they can be observed at increasingly larger photon energies.For test samples, the layers can always be chosen thick enough to be able to wait for the decay of the oscillations.For real samples with relatively thin layers, however, a photon energy with weak or no oscillations should be chosen.Tis is possible as shown in Figure 21 for the p-doped Al 0.9 Ga 0.1 As sample P1136.Tat means, even for an Al fraction of x � 0.9, a photon energy can be found that has hardly any oscillations and has a sufciently large signal difference for an average doping (1•10 18 cm −3 ).In this case, it is the RAS signal at the photon energy of 3.6 eV.
For Al fractions x < 0.5, one can use the spectra of GaAs and Al 0.5 Ga 0.5 As as a guide to obtain/interpolate an estimate for possible photon energies.Presumably, photon energies of 2.4 or 2.7 eV are also suitable then.
Te fact that a separate calibration of the doping analysis has to be performed for all Al fractions becomes clear in Table 1, where the determined carrier concentrations for diferent Al fractions and constant Be or Te efusion cell temperatures are given.Care has been taken to keep the growth rate constant at about 0.3 ML/s in all cases.
As the Al contents increase, the charge carrier concentration decreases.In the case of p-doping, Be atoms must displace group III atoms for doping to occur.Presumably, Be atoms replace Ga atoms more readily than they replace Al atoms, so that less doping occurs at higher Al contents in the layer.
In the case of n-doping, Te atoms replace the group V atoms and thus As atoms.Terefore, at frst glance, with a constant Te supply, the doping should remain the same even as the Al contents increase.However, even here, the doping tends to decrease.Tus, it might be that Al atoms also bind the surrounding As atoms more strongly than is the case of Ga atoms.With more Al atoms, correspondingly, it would be more difcult for Te atoms to fnd weakly bound As atoms, and thus, the doping level would be lower.
Overall, thus, it can be concluded that for all Al fractions x in Al x Ga 1−x As, a photon energy can be found that ensures monitoring of doping with RAS.However, the calibration has to be performed separately for each Al fraction since the doping decreases with increasing Al fractions.

Conclusions
Taking GaAs, Al 0.5 Ga 0.5 As, and Al 0.9 Ga 0.1 As as material examples, we have shown that refectance anisotropy/difference spectroscopy (RAS/RDS) can be a valuable tool to monitor doping of III/V semiconductors during epitaxial growth in situ and in real time.Te RAS system has to be mounted perpendicularly above the substrate to be overgrown.After calibration, any ex situ time-consuming van der Pauw measurements will not be necessary anymore.Especially for sophisticated samples, such as laser layer sequences to be grown epitaxially (just to give an example), it is relatively easy to check whether the doping of the layers is proceeding as desired.Tis is where the greatest advantage of RAS becomes apparent.An analysis with the van der Pauw method would not be possible for such laser samples, since it is performed ex situ after growth, only near-surface layers can be examined for their charge carrier concentration, and the laser samples have complex layer sequences.Due to the diferent responses of RAS to n-and p-doping, RAS can even be used to determine the type of doping beyond doubt.
Using RAS during MBE, doping problems or success will be known instantly during the epitaxial process, which increases epitaxial yield considerably.It can be clearly seen that the charge carrier concentration decreases with increasing Al contents.
Advances in Materials Science and Engineering photoeleastic modulator (as switchable λ/2 wave-plate)

Figure 2 :
Figure 2: Photograph of the MBE machine with the RAS apparatus adjusted for normal RAS light incidence onto the wafer/sample surface.

3 )Figure 4 :Figure 5 :Figure 6 :
Figure 4: Averaged RAS spectrum of a GaAs sample (P1140, 840 °C Be efusion cell temperature) with p-doping, shown in red.Te RAS spectrum for the undoped sample/bufer is shown in black.Te connecting lines are merely guides to the eye.

Figure 12 : 5 Figure 13 : 3 )Figure 14 :Figure 15 :
Figure 12: RAS transient during preparation of p-doping sample P1142 with Al 0.5 Ga 0.5 As for RAS photon energy 2.7 eV. Te connecting lines are only visual aids.
Figure 7: Relationship between carrier concentration and RAS signal diference for p-GaAs at 2.4 eV.Te smallest doping has not been considered in the ft.Te ordinate is logarithmic (a 2 � 16.8 ± 0.04, b 2 � 34.1 ± 0.6, leaving the data point for sample P1129 out for ft calculation).

Table 1 :
Comparison of charge carrier concentrations at constant doping levels.