Bound-to-bound and bound-to-free transitions in surface photovoltage spectra: Determination of the band offsets for ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ and ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ quantum wells

We present an extensive study leading to a general understanding about the optical transitions involved in the surface photovoltage (SPV) spectra of type-I quantum well (QW) structures. SPV measurements were carried out on ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}∕\mathrm{GaAs}$ QW samples with varying QW width and on ${\mathrm{In}}_{0.15}{\mathrm{GaAs}}_{0.85}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ QW samples with varying aluminum content. The results are compared with experimental electroreflectance spectra, absorption spectra simulated with multiband $\mathbf{k}\bullet \mathbf{p}$ computations, and theoretical calculations of the electronic states in the QWs. Thus, the transitions which induce steps in the SPV spectra are unambiguously identified. Most remarkably, the bound electron-to-free hole transition is detected by SPV measurements. This distinguishes the SPV method from many other optical techniques like photoluminescence and photoreflectance spectroscopy that allow only the observation of bound-to-bound and free-to-free transitions. The analogous free electron-to-bound hole transition does not give rise to a feature in the SPV spectra. In addition, the bound-to-bound transitions $e_1\text{−}h{h}_1$, $e_1\text{−}l{h}_1$, and $e_2\text{−}h{h}_2$ are observed, if the respective states are confined. Also, the free-to-free transition $ce\text{−}ch$ is measured. We demonstrate how these transitions can typically be identified in the spectra without any further measurements or calculations. With this knowledge, the practical band offsets of the QW structure, i.e., the energy difference between the lowest confined states in the QW and the extended states in the barrier, can be extracted directly from the spectra. An advantage over conventional techniques for the determination of band offsets is that neither any additional knowledge of other QW parameters nor simulations are necessary. As an example for the application of the SPV technique, the electronic states and band offsets of a series of ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}{\mathrm{As}}_{0.98}{\mathrm{N}}_{0.02}∕\mathrm{GaAs}$ QWs with varying QW width are characterized. These experiments directly show that nitrogen affects only the conduction band states.

Figure 1

(a) SPV and $d\left(\mathrm{SPV}\right)∕dE$ spectra for a 9 nm-thick ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ SQW acquired at 300 K (line with data points and solid line, respectively). (b) The possible optical transitions as discussed in Ref. 7: (1) $e_1\text{−}h{h}_1$ (ground state), (2) $e_1\text{−}ch$, (3) $ce\text{−}h{h}_1∕e_2\text{−}h{h}_2$, and (4) $ce\text{−}ch$ (continuum).

Figure 2

Temperature dependence of the ground state (transition 1) and of the barrier (transition 4) of a 6.5 nm-thick ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}{\mathrm{As}}_{0.984}{\mathrm{N}}_{0.016}$ SQW as determined from SPV spectra (data points with error bars). Comparison of the same quantities measured with different techniques: PL for the ground state (crosses) and Varshni curve for the GaAs barrier (dashed line).

Figure 3

(a) SPV spectra for ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ SQWs with different well widths acquired at 300 K. The change of the position of transition 1 for different well widths is indicated by a solid line. The band gap of GaAs at 300 K is indicated by a dotted vertical line. The position of step 3 is also indicated. (b) Derivatives of the SPV spectra as a function of the detected energy. The peaks correspond to the steps in intensity of the SPV spectra. The first part of each spectrum (up to 1.38 eV) has been magnified for clarity; on the left-hand side of the curves the multiplication factors are shown. (c) Energy values of transition 1 (squares) and step 3 (spheres) in dependence of the well width. The solid and the dashed lines are the calculated values of $e_1\text{−}h{h}_1$ and $e_2\text{−}h{h}_2$, respectively. The dotted line is the calculated value of the transition $ce\text{−}h{h}_1$. The small crosses are the results from the electroreflectance measurements.

Figure 4

Contactless electroreflectance measurements (open circles) at 300 K of a 7 nm-thick ${\mathrm{In}}_{0.30}{\mathrm{Ga}}_{0.70}\mathrm{As}$ (a) and a 9 nm-thick ${\mathrm{In}}_{0.30}{\mathrm{Ga}}_{0.70}\mathrm{As}$ SQW (b). The solid lines are the multi-oscillator fits which were used to determine the energetic positions of the different transitions in the QWs (indicated by arrows in the figure).

Figure 5

SPV spectrum for a 9 nm-thick ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ SQW acquired at 300 K (line with data points) compared with calculated (using $\mathbf{k}\bullet \mathbf{p}$ method) InGaAs absorption spectra for light propagation perpendicular to (solid line) and in the QW plane with perpendicular E-field polarization (dashed line).

Figure 6

(a) SPV spectra for 9 nm-thick ${\mathrm{In}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ SQWs with different aluminum content in the barrier $(0<x<0.3)$ acquired at 275 K. The optical transitions visible in the spectra are indicated with different lines as guides for the eye: solid line $\left(e_1\text{−}h{h}_1\right)$, dotted-dashed line $\left(e_1\text{−}l{h}_1\right)$, dotted line $\left(e_1\text{−}ch\right)$, and dashed line $\left(e_2\text{−}h{h}_2\right)$. The band gap of the barrier GaAs and of the barrier ${\mathrm{Al}}_{0.075}{\mathrm{Ga}}_{0.0925}\mathrm{As}$ at 275 K are indicated by a dotted vertical line. (b) Derivatives of the SPV spectra as a function of the detected energy. The peaks correspond to the steps in intensity of the SPV spectra. The first part of each spectrum has been magnified for clarity; on the left-hand side of the curves the multiplication factors are shown. (c) Experimental points of the energy transitions extracted by the SPV spectra in the function of the aluminum content. The solid, the dotted-dashed, the dotted, and the dashed lines are the calculated values of the transitions $e_1\text{−}h{h}_1$,$e_1\text{−}l{h}_1$, $e_1\text{−}ch$, and $e_2\text{−}h{h}_2$, respectively.

Figure 7

(a) SPV and $d\left(\mathrm{SPV}\right)∕dE$ spectra for a 9 nm-thick ${\mathrm{In}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{As}∕{\mathrm{Al}}_{0.075}{\mathrm{Ga}}_{0.925}\mathrm{As}$ SQW acquired at 275 K. (b) Schematic drawing of the optical transitions visible in the spectrum: (1) $e_1\text{−}h{h}_1$, (2) $e_1\text{−}l{h}_1$, (3) $e_1\text{−}ch$, (4) $e_2\text{−}h{h}_2$, and (5) $ce\text{−}ch$ (continuum).

Figure 8

SPV spectra of a 7 nm-thick ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}∕\mathrm{GaAs}$ SQW sample and a 9 nm-thick ${\mathrm{In}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{As}∕{\mathrm{Al}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{As}$ SQW sample taken at 300 K. The transitions $e_1\text{−}h{h}_1$ and $e_1\text{−}l{h}_1$ show excitonic features. This helps to identify the position of the step $e_1\text{−}ch$. Note that the two spectra are shifted in energy by 100 meV from each other.

Figure 9

Experimental values of the practical band offsets $\Delta E_C^{*}$ and $\Delta E_V^{*}$ extracted from the SPV spectra of ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ SQWs as a function of the well width. The dashed lines are the theoretical simulations of the same quantities.

Figure 10

(a) SPV spectra for ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}{\mathrm{As}}_{0.098}{\mathrm{N}}_{0.02}$ SQWs with different well widths acquired at 300 K. The different positions of transition 1 for different well widths are indicated by a solid line. The fixed position of the barrier (GaAs) is indicated with a dotted vertical line. The presence of step 3 is also indicated. (b) Derivatives of the SPV spectra as a function of the detected energy. The peaks correspond to the steps in intensity of the SPV spectra. The first part of each spectrum (up to 1.30 eV) has been magnified for clarity; on the left-hand side of the curves the multiplication factors are shown. (c) Energy values of transitions 1 (squares) and 3 (spheres) in dependence of the well width. The solid and the dashed lines are the calculated values of $e_1\text{−}h{h}_1$ and $e_2\text{−}h{h}_2$, respectively.

Figure 11

Experimental values of the practical band offsets $\Delta E_C^{*}$ and $\Delta E_V^{*}$ extracted from the SPV spectra of ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}{\mathrm{As}}_{0.098}{\mathrm{N}}_{0.02}$ SQWs as a function of the well width. The dashed lines are the theoretical simulations of the same quantities. In the inset the influence of the well width on the structure of the electron states of ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ and ${\mathrm{In}}_{0.3}{\mathrm{Ga}}_{0.7}{\mathrm{As}}_{0.098}{\mathrm{N}}_{0.02}$ SQWs is shown. For illustrative purposes, the bottoms of the QWs are aligned. In reality, the energetic level of the GaAs barrier is the same for all the QWs.