Transport in two-dimensional modulation-doped semiconductor structures

Abstract

We develop a theory for the maximum achievable mobility in modulation-doped 2D GaAs-AlGaAs semiconductor structures by considering the momentum scattering of the 2D carriers by the remote ionized dopants which must invariably be present in order to create the 2D electron gas at the GaAsAlGaAs interface. The minimal model, assuming first order Born scattering by random quenched remote dopant ions as the only scattering mechanism, gives a mobility much lower (by a factor of 3 or more) than that observed experimentally in many ultra high-mobility modulation-doped 2D systems, establishing convincingly that the model of uncorrelated scattering by independent random remote quenched dopant ions is often unable to describe the physical system quantitively. We theoretically establish that the consideration of spatial correlations in the remote dopant distribution can enhance the mobility by (up to) several orders of magnitudes in experimental samples. The precise calculation of the carrier mobility in ultra-pure modulation-doped 2D semiconductor structures thus depends crucially on the unknown spatial correlations among the dopant ions in the doping layer which may manifest sample to sample variations even for nominally identical sample parameters (i.e., density, well width, etc.), depending on the details of the modulation-doping growth conditions.

Scattering mechanisms in shallow undoped Si/SiGe quantum wells

“…The selective placement of charges introduces spacial correlations in the disorder potential, which was shown to be at the origin of the extremely high mobilities observed in modulation-doped GaAs/AlGaAs 2DEGs. 41 The mobility as a function of 2DEG density is computed for depth d = 50nm, and the results from 20 random realizations are shown as a solid green line in Fig. 2.…”

Cyclotron decay time of a two-dimensional electron gas from 0.4 to 100 K

“…In our sample, this carrier concentration variation is fundamentally inconsistent with the sample mobility of µ dc = 3.6 × 10 6 cm 2 V −1 s −1 , which has previously been found to occur in samples with low defect density, atomically smooth interfaces, and otherwise homogenous properties 6 . The difference between τ s and τ q has been previously predicted and results from the importance of small an-gle scattering in this high mobility sample.…”

“…From the relevant Boltzmann equation, τ DC is weighted by f θ = 1 − cos θ , which suppresses small angle scattering contributions. In contrast, τ q in homogeneous samples has f θ = 1 and is a determined by the full W k, k , as has been discussed previously 6,24,51,52 . In homogeneous samples, τ q is closely related to the dissipative component cyclotron decay time, τ s .…”

“…The gallium arsenide two-dimensional electron gas (2DEG) in a quantum well has long been used as a model system to study the fundamental limits of electronic transport [1][2][3][4][5][6] . New device geometries that exploit quantum interference in these samples provide an additional degree of freedom that is increasingly important as devices with ever smaller feature sizes are developed 7,8 .…”

Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions

“…A natural interesting question is whether this is a mere coincidence or is an indicator for the predicted emergent Dirac fermion nature of the half-filled Landau level. While answering this question definitively is well beyond the scope of the current work, which is entirely on the many-body renormalization of bare anisotropy in zero-field interacting 2D Dirac and Schrödinger systems, we mention one more tantalizing experimental finding in this context by Pan et al (7) who established that the half-filled Landau level conductivity in high-mobility modulation-doped 2D structures manifests a linear-in-carrier density dependence (similar to that observed in graphene (27)) in contrast to the expected quadratic density dependence observed and predicted in the corresponding zero-field 2D conductivity of the usual Schrödinger system (28). If our speculations about a possible connection between our result and the emergent Dirac nature of the composite fermion liquid at half-filling are correct, then it also follows that the long-range nature of Coulomb interaction is an essential part of the physics here since we only find the square-root suppression of the bare anisotropy for long-range Coulomb interaction and not for the short-range contact interaction.…”