Abstract
Reflectance anisotropy/difference spectroscopy (RAS/RDS) had been developed for monitoring epitaxial semiconductor growth, especially for the metal-organic chemical vapor deposition (MOCVD) of III/V semiconductors. But RAS is also well suited for the control of III/V growth with molecular beam epitaxy (MBE). Although the work on RAS has already started at least three decades ago, the potential of this in situ and real-time monitoring technique, especially for doping control, is not well known yet. Experimental results are given here on the identification of doping types and concentration during MBE growth, exemplarily for GaAs and AlGaAs. Especially, the dependence of the majority charge carrier concentration (i.e., the doping concentration) on the RAS signal difference between the nondoping and doping cases is addressed here.
1. Introduction
Monocrystalline layer growth is an essential competency in modern semiconductor technology. Any technique, such as reflection high-energy electron diffraction (RHEED) [1], which allows for in situ and real-time monitoring of the epitaxial growth, increases sample yield considerably. Another such technique is reflectance anisotropy/difference spectroscopy (RAS/RDS). The first 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. [4–7].
RAS has mainly been applied to metal-organic chemical vapor deposition (MOCVD) [8, 9], but it is useful for monitoring molecular beam epitaxy (MBE) as well [10, 11].
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]. This 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.
This 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 influence of the effusion cells’ temperatures, which is one of the main parameters to control in everyday epitaxy. Of course, there will be differences in the exact relation of the doping level to the effusion 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 difference between the nondoping and doping cases is addressed here.
2. RAS Principle and Measurement Details
This 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. The 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]. The major difference 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]. The optical setup is sketched in Figure 1. Moreover, a photograph of the RAS system, positioned fixed to the MBE machine, is shown in Figure 2. The RAS apparatus is of type EpiRAS®TT from Laytec, Berlin, Germany.
The wafer/sample to be overgrown is rotated during MBE growth [22, 23]. The 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. The usual wafer revolution speed is = 1 Hz down to 0.25 Hz in our case. The signal with a frequency of (see above) gives the desired data, and the signal with a frequency of just is erroneous and might stem from periodic reflections 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. The 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 different devices drawn on top of each other.
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 (field) 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 reflected with slightly different strengths, which makes the overall light beam slightly elliptically polarized.
The photoelastic modulator (PEM) acts as a switchable λ/2 plate. If it is in the off 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 reflected 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 reflected intensity passes through the analyzer. By turning the PEM periodically on and off (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 differences in the reflectivities for the two light components linearly polarized along one of the two main crystal axes.
The light is detected using a monochromator and a photodiode. Different photon energies can be used for the measurement. In case a complete spectrum is desired, a different 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. Thus, 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. The growth rate can be determined from the oscillation period [24, 25]. In the case of a layer material change from GaAs to Al0.5Ga0.5As, 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 definition 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. The genuine RAS signal is defined as the difference of the reflectivities R for the two crystal directions under consideration normalized to the mean reflectivity , for any specific photon energy:
The RAS signal is in the permille range.
The 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 reflectance 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 specific surface reconstructions or local roughness breaking the symmetry. In addition, nonlinear effects may play a role under certain circumstances [26]. The 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]. The RAS signal is very sensitive to the electronic structure of the surface. This 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 configurations characteristic of the material can be identified [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. There 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 different dimer concentrations on the surface [11, 22, 27]. They exist because different 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 Ga-rich surface occurs. This 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 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 AlxGa1−xAs in situ. Thus, 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 Al0.5Ga0.5As, respectively, is studied in detail. In Section 5, the doping of AlxGa1−xAs samples with other compositions is discussed.
3. GaAs Doping Monitoring Using RAS
3.1. p-GaAs (Be Doping)
In the case of p-GaAs, five 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 buffer layer of pure GaAs. Subsequently, p-doped GaAs with a thickness of 500 nm is deposited. For this purpose, the Be effusion 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. The undoped buffer layer also serves as a reference for the RAS spectrum.
The average is taken over the RAS spectra recorded during growth, with fluctuations 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 effusion cell temperature with the carrier concentration in p-doped GaAs layers. This relationship has to be rechecked after each maintenance of the chamber. The carrier concentration is determined ex situ by van der Pauw measurements [18].
The 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 effusion cell temperature. This is because less material remains in the effusion cell after the dopant is applied, and thus, the material flux decreases somewhat with time (here 18 samples later). It should be noted that the ordinate is logarithmic. Thus, to obtain the carrier concentration at a given Be effusion cell temperature from the fitted straight line, the following formula must be used:where p and n are the majority carrier concentrations for p-doping (acceptors) or n-doping (donors), respectively, T is the temperature in °C, and a1 and b1 are the determined fitting parameters. The 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 effusion cell temperature according to van’t Hoff’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 effusion cell temperature of 840°C (leading to heavy p-doping of 2⋅1019 cm−3) with the red curve. The averaged RAS spectrum of the undoped buffer 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 differences between the cases with and without doping are most pronounced. But the signal noise, given with the error bars, draws a different 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 identified. All prerequisites are fulfilled 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. The increase in the signal is clearly visible and occurs within about four measurement points (1 point per minute here), corresponding to a film thickness change of about 20 nm. Thereafter, the signal remains constant at the elevated value with some fluctuations.
This increase is explained in the literature with the linear electro-optical effect (Pockels effect) [31]. It describes a change in the refractive index by applying an electric field. During epitaxial growth, this field arises from a charge exchange between states in the bulk material and surface states. This exchange is attributed to the sample’s effort to reach thermal equilibrium.
To consider a relationship between the Be effusion cell temperature and the RAS signal, the RAS signal difference between the case of the doped sample/layer and the nondoping case (buffer) at a photon energy of 2.4 eV is examined.
The relationship given in Figure 6 between the RAS signal difference and the effusion cell temperature of Be for higher doping levels might be called linear, in first approximation (as we also do further on in similar situations). This is an approximation only because only three relevant sampling/data points with quite large error bars are considered.
Since the RAS signal difference is not directly dependent on the effusion cell temperature, the linear function might rather be called a “correlation” than a dependency.
The signal for the low effusion cell temperature deviates somewhat from this since the underlying effect leads to changes in the RAS signal only at sufficiently high doping levels. Therefore, this value was not taken into account when fitting the signal differences.
Having observed,(1)that the carrier concentration is exponentially dependent on effusion cell temperature,(2)that the RAS signal difference is (in first approximation) linearly dependent on effusion cell temperature,an exponential dependence of the carrier concentration on the RAS signal difference should be expected. Indeed, when the carrier concentration determined with van der Pauw measurements is plotted semilogarithmically against the RAS signal difference, as done in Figure 7, a relationship similar to that between carrier concentration and effusion cell temperature (equation (2)) is obtained, i.e.,with p being the carrier concentration (respectively, n) again, RASdiff being the RAS signal difference, and a2 and b2 being the fitting parameters.
An exponential dependence of the majority carrier (doping) concentration on the effusion cell temperature should be expected from van’t Hoff’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 difference (difference between the doping and nondoping cases) on the effusion cell temperature (see Figure 6), an exponential dependence of carrier concentration on the RAS signal difference should be expected also (as can be observed in Figure 7). There is no contradiction between the findings. 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 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 difference without additional ex situ measurements.
The fluctuations 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 difference is more reproducible than the error bars in Figures 6 and 7 suggest. The deviation for small doping levels is again attributed to the low sensitivity of the RAS signal to the underlying effect in this case.
3.2. 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 Ga2Te3) is used for n-doping. The correlation between the carrier concentration and the Te effusion 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 buffer of GaAs and a 500 nm thick n-doped layer. The observed RAS spectrum of the sample P1126 with a high effusion cell temperature of 205°C is shown in Figure 9 exemplarily.
The change in the RAS signal for a high doping level appears to be much more pronounced than for p-doping with Be. The biggest difference with p-doping, however, is that the signal drops off in the n-doping case and does not increase. Thus, p- and n-doping can be distinguished with RAS easily.
Again, the RAS signal value at 2.4 eV shows comparatively small fluctuations and a clear difference 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. This is because the spectra are not sign-corrected in the employed RAS instrument; i.e., the actual value gets negative and increasingly negative. Therefore, 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 difference is shown as a function of the effusion cell temperature in Figure 10 and the carrier concentration determined by van der Pauw measurements is shown in dependence on the RAS signal difference in Figure 11.
Comparing the results with those of p-GaAs, the same qualitative relationships can be observed. The linear relationship between the RAS signal difference and the effusion cell temperature (in Figure 10) is even more pronounced than that for p-GaAs. The error bars are also smaller than those in the p-doping case.
An increase with increasing effusion cell temperature can also be observed. As in Figure 8, the sample with the heaviest doping (P1126, 6⋅1018 cm−3) also shows a slightly stronger deviation from the expected behavior in Figure 11. This is again due to the upper limit for doping. A too high amount of Te also prevents good film growth, which is also evident in the larger error for the RAS signal.
Obviously, also for n-doped GaAs films, control of doping with RAS is possible, and samples can be analyzed with respect to their doping in situ.
Thus, 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. This 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 different responses of RAS to n- and p-doping, 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 different mobility of the two types of charge carriers.
4. Al0.5Ga0.5As Doping Monitoring Using RAS
The doping samples for Al0.5Ga0.5As have been prepared slightly differently than for GaAs. First, a 200 nm thick undoped buffer layer of GaAs has again been grown to ensure a good surface quality for subsequent growth. This has been followed by a 300 nm thick undoped Al0.5Ga0.5As layer that served as the RAS reference. A 500 nm thick doped Al0.5Ga0.5As 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-Al0.5Ga0.5As (Be Doping)
When determining the doping of Al0.5Ga0.5As, another aspect must be considered, namely, the selection of a suitable photon energy for both p- and 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 Al0.5Ga0.5As. They 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. The oscillations, of course, increase the errors in the averaged RAS spectra. Therefore, only the spectra, after the Fabry–Perot oscillations have decayed, are used for averaging. This 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 Al0.5Ga0.5As sample (P1184) due to the highest Be effusion cell temperature of 800°C (⋅1018 cm−3).
The RAS signal values show the same small (non-Fabry–Perot) fluctuations as the RAS signal for GaAs. It is observable again that the photon energies above 3.0 eV are more prone to RAS signal fluctuations than smaller energies. The photon energy of 2.7 eV is the best compromise between a clear difference between the RAS signals in the cases with and without doping, a small error, and a fast decay of the Fabry–Perot oscillations. Therefore, it is used for the analyses in the case of Al0.5Ga0.5As.
Figure 14 proves the exponential relationship between the determined charge carrier concentration and the Be effusion cell temperature using a semilogarithmic plot. It has to be redetermined after each chamber maintenance, as for GaAs.
The named p-doped Al0.5Ga0.5As samples are analyzed with RAS. The RAS signal differences in Figure 15 are of the same order as for p-GaAs, despite using the photon energy of 2.7 eV for p-Al0.5Ga0.5As instead of 2.4 eV for p- and n-GaAs. Again, this shows the expected relation. The RAS signal difference and the Be effusion cell temperature are linearly related (“correlated”) again.
An exponential relation between the carrier concentration and the RAS signal difference is also observed in a semilogarithmic plot in Figure 16. The errors in the RAS signal and, hence, in the signal difference 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 fit curve, it is clear that doping can also be inferred from the RAS signal for p-Al0.5Ga0.5As. As for GaAs, the errors are assumed to be somewhat too large due to the periodic (non-Fabry–Perot) fluctuations 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-Al0.5Ga0.5As (Te Doping)
The last detailed doping analysis given here is concerned with n-Al0.5Ga0.5As. Three samples are available for this purpose. These have been prepared according to the same scheme as the p-doped Al0.5Ga0.5As 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. This value is therefore weighed less in the determination of the fit curve. Actually, the used software program weighs the data points inversely proportional to their standard deviations. The 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-Al0.5Ga0.5As 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.
The photon energy of 2.7 eV is also suitable for the study of n-doping. Therefore, the same photon energy can be used for the analysis of Al0.5Ga0.5As in both doping cases.
The dependencies of the RAS signal difference with the Te effusion cell temperature (Figure 19) and the carrier concentration (Figure 20) are qualitatively the same as for GaAs and p-Al0.5Ga0.5As. Therefore, an in situ analysis of the doping can be performed here as well. The deviations of the mean values from the fitting curve are small. The errors are of the same order of magnitude as in the other cases studied.
5. AlxGa1−xAs 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 Al0.5Ga0.5As. Here, we will briefly 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. They have increasing amplitude with increasing Al contents and last longer before decaying to the point where averages with small fluctuations 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. This is possible as shown in Figure 21 for the p-doped Al0.9Ga0.1As sample P1136. That means, even for an Al fraction of x = 0.9, a photon energy can be found that has hardly any oscillations and has a sufficiently large signal difference for an average doping (1⋅1018 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 Al0.5Ga0.5As 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.
The 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 different Al fractions and constant Be or Te effusion 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. Therefore, at first 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. Thus, 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 difficult for Te atoms to find 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 AlxGa1−xAs, 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.
6. Conclusions
Taking GaAs, Al0.5Ga0.5As, and Al0.9Ga0.1As as material examples, we have shown that reflectance 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. The 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. This 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 different 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.
Data Availability
The data that support the findings of this study have been saved on optical data storage discs and are made available from the corresponding author upon reasonable request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
The authors are grateful for general technological assistance by the Nano Structuring Center (NSC) of the University of Kaiserslautern-Landau (RPTU). This research was funded by the German state of Rhineland Palatinate under contract 15202-386261/1108 from the Stiftung Rheinland-Pfalz fuer Innovation (Foundation Rhineland Palatinate for Innovation) and by the Deutsche Forschungsgemeinschaft (DFG–German Research Foundation) under contract FO157/63 and in the framework of the VIP project HOFUS of the German Federal Ministry of Education and Research (BMBF, Germany).