Nonlinear dynamics of nonequilibrium holes in ptype modulationdoped GaInNAs/GaAs quantum wells
 Hagir Mohammed Khalil^{1}Email author,
 Yun Sun^{1},
 Naci Balkan^{1},
 Andreas Amann^{2} and
 Markku Sopanen^{3}
DOI: 10.1186/1556276X6191
© Khalil et al; licensee Springer. 2011
Received: 20 September 2010
Accepted: 2 March 2011
Published: 2 March 2011
Abstract
Nonlinear charge transport parallel to the layers of pmodulationdoped GaInNAs/GaAs quantum wells (QWs) is studied both theoretically and experimentally. Experimental results show that at low temperature, T = 13 K, the presence of an applied electric field of about 6 kV/cm leads to the heating of the high mobility holes in the GaInNAs QWs, and their realspace transfer (RST) into the lowmobility GaAs barriers. This results in a negative differential mobility and selfgenerated oscillatory instabilities in the RST regime. We developed an analytical model based upon the coupled nonlinear dynamics of the realspace hole transfer and of the interface potential barrier controlled by spacecharge in the doped GaAs layer. Our simulation results predict dc biasdependent selfgenerated current oscillations with frequencies in the high microwave range.
Introduction
During the past decade, dilute nitrides, particularly the quaternary material system of GaInNAs/GaAs, have attracted a great deal of attention, both because of unusual physical properties and potential applications for a variety of optoelectronic devices. The addition of a small amount of nitrogen induces a strong perturbation in the conduction band of matrix semiconductors, while having a negligible effect on the valence band. As a result, the electron mobility is greatly lowered and the hole mobility can become higher than the electron mobility, in materials with relatively high nitrogen content. High hole mobility coupled with the low hole confinement energy (110 meV in our calculation for the samples investigated in this study) [1] in the GaInNAs/GaAs quantum well (QW) structure makes it possible for holes in the well to gain enough energy to overcome the small band discontinuity under an electric field applied parallel to the layer interface, and to transfer into the lowmobility pdoped GaAs layer. This leads to a negative differential mobility (NDM) caused by realspace hot hole transfer, as we previously observed [1]. Therefore, under dc conditions, a selfgenerated current oscillation in the realspace regime, as proposed by Schöll and coauthors [2–5], is expected in pmodulationdoped GaInNAs/GaAs heterostructures.
Negative differential resistance instabilities in pmodulationdoped GaInNAs/GaAs QWs
Numerical parameters used in the simulation for the GaInNAs/GaAs sample [7]
Material  Thickness (Å)  Doping (m^{3})  

GaAs (cap)  500  Be: 1 × 10^{24}  ×3 
GaAs (barrier)  200  Be: 1 × 10^{24}  ×3 
GaAs (spacer)  50  UD  ×3 
Ga_{1x}In_{x}N_{y}As_{1y} QW  70  UD  ×3 
GaAs (spacer)  50  UD  ×3 
GaAs (barrier)  200  Be: 1x10^{24}  ×3 
GaAs (buffer)  500  UD  ×3 
The nonlinear transport processes depicted in Figure 1 are modeled by a set of dynamic equations relevant to current instabilities in semiconductors. We derive a set of nonlinear partial differential equations for the hole density in the wells (p _{ w } ), and in the barriers (p _{ b } ), the potential barrier in each of GaAs layers (Φ_{ B }), and the dielectric relaxation of the applied parallel field (ξ _{ II } ).
where J _{ II } is the external current density flowing through the external circuit at applied bias voltage U _{0}.
where p _{0} is the 3 D hole density in the well at low field.
Numerical results
Numerical parameters used in the simulation for the GaInNAs/GaAs sample [1]
Lw  7 mm 

Lb  25 mm 
ΔEv  0.12 eV 
${m}_{\text{w}}^{*}$  0.105 m0 
${m}_{\text{b}}^{*}$  0.62 m0 
d  50 μm 
h  28 μm 
${\tau}_{{E}_{\text{w}}}$  0.2 ps 
${\tau}_{{E}_{\text{b}}}$  0.1 ps 
TL  13 K 
μw  0.3 m2/Vs 
μb  0.021 m2/Vs 
Conclusion
In this work, we studied the transport processes parallel and perpendicular to the layers of ptype modulationdoped GaInNAs/GaAs multiQW structures far from the thermodynamic equilibrium. The simulation results of the steadystate predict an NDM induced by RST of hot holes in the QWs and the critical electric field of the onset of NDM to be the order of 6 kV/cm. This value agrees well with our previous experimental results. The numerically timedependent simulations indicate that the selfgenerated oscillation caused by RST with the frequency in the range 2050 GHz appears under the right applied electric field. The frequency of selfgenerated oscillation can be flexibly optimized to the range of considerable interest for applications as a simple way of generating highfrequency microwave power based on GaInNAs material system. According to our simulation, the predicted selfgenerated oscillation can be observed if the GaInNAs QW structure is optimized around 25 nm barrier and less than 2.4 × 10^{16} cm^{3} doping concentration. The current oscillation measurements will be performed using optimized structures fabricated into two terminal devices, and shunted with a 50 Ω resistor and highspeed circuit (highspeed oscilloscope and pulse generator). The experiment results are expected to be published in the near future.
Abbreviations
 NDM:

negative differential mobility
 QWs:

quantum wells
 RST:

realspace transfer.
Declarations
Acknowledgements
We acknowledge the collaboration within the COST Action MP0805 entitled "Novel Gain Materials and Devices Based on IIIVN Compounds".
Authors’ Affiliations
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