Roughness-induced piezoelectric scattering in lattice-mismatched semiconductor quantum wells

It is well known¹ that transport properties of a two-dimensional electron gas (2DEG) in a semiconductor quantum well (QW) can be strongly affected by the quality of interfaces between the well and barrier layers. The QW can be in an unstrained or strained status in dependence on lattice match or mismatch of the well layer to the barriers. For any (unstrained or strained) QW, interface roughness was shown² to produce random fluctuations in the well awidth, which modulate the confinement energy and result in a scattering potential for the 2D motion of confined charge carriers.

Hereafter, this conventional treatment of interface roughness is, for short, referred to as surface roughness scattering and has been considered by a number of authors.^{2 - 5}

It was pointed out that in combination with other scatter-ing sources, viz. impurity doping and alloy disorder, surface roughness scattering is able to quantitatively describe experi-mental findings about the low-temperature mobility of elec-trons in lattice-matched QW’s, e.g., made from GaAs/AlAs (Ref. 4). Nevertheless, it has been shown that the well-known scattering mechanisms turn out to fail in the interpretation of the electron mobility measured in some latticemismatched QW’s, e.g., from In_0.2Ga_0.8As/GaAs (Ref. 6) and In_0.15Ga_0.85As/Al_0.23Ga_0.77As (Ref. 7). Therefore, Lyo and Fritz⁶ had to assume another source of scattering which stems from strain fluctuations due to a random distribution of In atoms. However, their theory was found to be unable to explain a large difference in the mobility of the samples studied in Refs. 6 and 7, in which the difference in the structure and the In content is small. So far, this has remained as a challenging problem in the theory of electron mobility for lattice-mismatched InGaAs-based QW’s. On the other hand, a full understanding of scattering mechanisms in these sys-tems is clearly of great interest since they have been exten-sively applied in electronic and optoelectronic devices.

It was indicated^{8 - 11} that interface roughness gives rise to drastic fluctuations in a strain field. As a result, Feenstra and Lutz⁹ found that for Si/SiGe heterostructures, the roughness-induced strain variations cause a random shift of the conduction band edge. This, in turn, generates a perturbing defor-mation potential as a new scattering source, which yields much better agreement with experimental data¹² than surface roughness scattering does.

Recently, Quang and co-workers^10,11 have proved that due to interface roughness the strain field in a well layer of cubic symmetry has nonvanishing shear components even if it has been grown on a @001#-oriented substrate. Therefore, in an actual strained zinc-blende structure QW there exists a large fluctuating density of bound piezoelectric charges and a high relevant electric field. The random piezoelectric field must also act as a scattering mechanism. In what follows, this is simply referred to as piezoelectric scattering (not confused with that due to acoustic phonons) and, to date, has not been considered within the area of transport theory.

Thus, the goal of our paper is to develop a theory of the low-temperature mobility of charge carriers in real lattice-mismatched QW’s, taking explicitly into the roughness-induced piezoelectric field. We will be concerned mainly with QW’s made of zinc-blende structure material, e.g., In-GaAs, especially grown on a (001) substrate. However, we will give a brief discussion on the possibility of applying our theory to describe transport in other lattice-mismatched sys-tems such as Si/SiGe heterostructures and nitride-based QW’s.

The paper is organized as follows. In Sec. II below, we formulate our model and the basic equations used to calculate the low-temperature disorder-limited 2DEG mobility in terms of an autocorrelation function. This function is derived in Sec. III for surface roughness scattering in a square QW,taking adequate account of the finiteness of its potential bar-riers. In Sec. IV, this function is derived for piezoelectric scattering which appears as an effect due to both lattice mismatch and interface roughness, taking plausible account of elastic anisotropy of cubic crystals. Section V is devoted to numerical results, conclusions, and application of the theory to explain some experimental findings. Finally, a summary is presented in Sec. VI.

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