A study of photomodulated reflectance on staircaselike, ndoped GaAs/Al_{ x }Ga_{1−x}As quantum well structures
 Omer Donmez^{1},
 Ferhat Nutku^{1}Email author,
 Ayse Erol^{1},
 Cetin M Arikan^{1} and
 Yuksel Ergun^{2}
DOI: 10.1186/1556276X7622
© Donmez et al.; licensee Springer. 2012
Received: 18 July 2012
Accepted: 23 August 2012
Published: 12 November 2012
Abstract
In this study, photomodulated reflectance (PR) technique was employed on two different quantum well infrared photodetector (QWIP) structures, which consist of ndoped GaAs quantum wells (QWs) between undoped Al_{ x }Ga_{1−x}As barriers with three different x compositions. Therefore, the barrier profile is in the form of a staircaselike barrier. The main difference between the two structures is the doping profile and the doping concentration of the QWs. PR spectra were taken at room temperature using a HeNe laser as a modulation source and a broadband tungsten halogen lamp as a probe light. The PR spectra were analyzed using Aspnes’ third derivative functional form.
Since the barriers are staircaselike, the structure has different ground state energies; therefore, several optical transitions take place in the spectrum which cannot be resolved in a conventional photoluminescence technique at room temperature. To analyze the experimental results, all energy levels in the conduction and in the valance band were calculated using transfer matrix technique, taking into account the effective mass and the parabolic band approximations. A comparison of the PR results with the calculated optical transition energies showed an excellent agreement. Several optical transition energies of the QWIP structures were resolved from PR measurements. It is concluded that PR spectroscopy is a very useful experimental tool to characterize complicated structures with a high accuracy at room temperature.
Keywords
Photomodulated reflectance Quantum well infrared photodetectors (QWIP) Aspnes’ third derivative form Excitonic levels. 85.30.De 85.60.q 71.55.Eq.Background
Quantum well infrared photodetector (QWIP) structures have been developed since 1990s [1]. There are many different types of QWIP structures. QWIPs can be categorized by their electrical properties: photovoltaic or photoconductive, or by their layer thicknesses: multiquantum wells (MQW) or superlattice structures. They can also be categorized by having optical responsivity at a single or multiple wavelengths. Multicolor QWIPs can be composed of double barriers [2], stepped quantum wells [3], and stepped barriers. The structures with stepped barriers are also called as staircaselike QWIPs in the literature [4].
In this work, photomodulated reflectance (PR) and photoluminescence (PL) experiments were carried out on two different staircaselike QWIP structures at room temperature. PR is a powerful characterization method to determine optical transitions in both bulk and lowdimensional multilayer semiconductor structures. Its absorptionlike character and high sensitivity makes it possible to observe optical transitions between ground and excited states, even at room temperature. PR spectroscopy utilizes the modulation of the builtin electric field at the semiconductor surface or at the interfaces through photoinjection of electron–hole pairs generated by a chopped incident laser beam. This technique produces sharp spectral features related to the critical points of the band structure. This provides a more explicit comparison of experimental results with theoretical models. However, PL only gives information about ground state transitions in QWs at room temperature. PR spectra were analyzed using the third derivative functional form (TDFF) in order to fit the optical transition energies, and the results were compared to the theoretical values calculated using transfer matrix method.
Theory
Transfer matrix technique is a common method for solving Schrödinger equation for MQW structures which consist of layers having different band gaps and effective masses. By virtue of this technique, energy levels, wave functions under zero or constant electric field can be calculated in complex structures [5–7]. In this work, we had employed this technique to calculate the energy levels in each QW at 300 K.
Similarly, the effective masses of holes in the Al_{ x }Ga_{1−x}As layers were also calculated using Equation 3, taking the density of states heavy hole effective masses as 0.81 and 0.55, and the averaged light hole effective masses were taken as 0.16 and 0.083 in AlAs and GaAs, respectively [9].
where n is the number of spectral features to be fitted; E is the photon energy; A_{ j }, φ_{ j }, E_{ gj }, and Г_{ j } are the amplitude, phase, band gap energy, and line broadening of the j_{ th } feature, respectively. m_{ j } represents the type of critical point depending on the dimensionality of the structure, and its value is 2.5 or 3 for 3D (bulk) or 2D cases, respectively. The background signal in the measurements was simulated and suppressed from Equation 4 by a linear f(E) function.
Methods
PR and PL measurements were carried out on two different MQW structures at room temperature. A tunable monochromatic probe light was provided by a 100W tungsten lamp, dispersed by a single grating monochromator, and the sample was pumped with a modulated 10mW HeNe laser at 632.8 nm that was mechanically chopped at 280 Hz. The reflected probe beam was measured by a Si photodiode. The AC and DC components of reflectance (R) and differential changes in R (ΔR) were acquired by a computer, simultaneously.
Results and discussion
Electron and hole energy levels and PR peaks of the QWIP structure obtained at T = 300 K
Structure name  QW number  Well width (nm)  e_{1} (meV)  hh_{1} (meV)  hh_{2} (meV)  lh_{1} (meV)  E_{g} (meV)  Effective E_{g} e_{1}hh_{1} (meV)  PR peak e_{1}hh_{1} (meV)  Effective E_{g} e_{1}hh_{2} (meV)  PR peak e_{1}hh_{2} (meV)  Effective E_{g} e_{1}lh_{1} (meV)  PR peak e_{1}lh_{1} (meV) 

ANA14  1  5.5  58.4  13.1  50.6  43.2  1.422  1.494  1.495  1.531  1.534  1.524   
IQE14  1.490    
ANA14  2  5  74.1  16.3  63.4  55.1  1.422  1.513    1.560    1.552  1.550 
  
IQE14  2  5  72.5  16.1  62.5  53.8  1.422  1.511    1.557    1.549   
1.545  
ANA14  3  5  70.5  15.9  61.4  52.2  1.422  1.509    1.554  1.550  1.545   
IQE14  1.505    1.545  
ANA14  4  5.5  60.2  13.4  51.6  44.6  1.422  1.496    1.534    1.527   
IQE14  1.534 
PL studies showed just a single broad peak for ANA14 structure at 1.525 eV and for IQE14 structure at 1.539 eV at room temperature. As seen from the calculated values of the excitonic transitions in different quantum wells, the energy differences between them are quite small; therefore, the observed PL peak cannot be attributed to just one transition. It can be concluded that observed PL peak represents additive information about some of the optical transitions. However, PR provides detailed information, resolving closely separated energy levels, even at room temperature.
Conclusion
The importance of the photomodulated reflectance spectroscopy in complicated semiconductor QW structures and hence in QWIPs has been verified by the experimental and the theoretical results obtained from this work. QWs with barriers having minor differences in the alloy composition can clearly be distinguished by PR measurements at room temperature. Indeed, e1hh1, e1hh2, and e1lh1 transitions were clearly observed and resolved. On the other hand, in PL measurements, only one single photoluminescence peak was observed.
Abbreviations
 MQW:

multiquantum well
 PL:

photoluminescence
 PR:

photomodulated reflectance
 QW:

quantum well
 QWIP:

quantum well infrared photodetector
 R:

reflectance
 TDFF:

third derivative functional form.
Declarations
Acknowledgments
We are grateful to Dr. Bulent Aslan and Dr. Ugur Serincan from Anadolu University for growing the ANA samples with MBE. This work was partially supported by The Scientific and Technological Research Council of Turkey (TUBITAK; project number 108T721), COST Action MP0805, Scientific Research Projects Coordination Unit of Istanbul University (project numbers 3587 and UDP 16607), and the Ministry of Development of Turkey (project number 2010K121050).
Authors’ Affiliations
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