Carrier diffusion in low-dimensional semiconductors: A comparison of quantum wells, disordered quantum wells, and quantum dots

We present a comparative study of carrier diffusion in semiconductor heterostructures with different dimensionality [$\mathrm{InGaAs}$ quantum wells (QWs), $\mathrm{InAs}$ quantum dots (QDs), and disordered $\mathrm{InGaNAs}$ QWs (DQWs)]. In order to evaluate the diffusion length in the active region of device structures, we introduce a method based on the measurement of the current-voltage and light-current characteristics in light-emitting diodes where current is injected in an area $<1\mu {\mathrm{m}}^2$. By analyzing the scaling behavior of devices with different sizes, we deduce the effective active area, and thus the diffusion length. A strong reduction in the diffusion length is observed going from QWs $\left(L_d\approx 2.7\mu \mathrm{m}\right)$ to QDs $\left(L_d<100\mathrm{nm}\right)$, DQWs being an intermediate case ($L_{\mathrm{diff}}\approx 0–200\mathrm{nm}$ depending on the carrier density). These results show that lateral composition fluctuations, either intended or unintended, produce strong carrier localization and significantly affect the carrier profile in a device even at room temperature.

Figure 1

(a) Schematics of the fabricated LED structures. (b) Cross-sectional SEM image of a $300\text{−}\mathrm{nm}$ aperture obtained by lateral oxidation from a $1\mu \mathrm{m}$-wide stripe.

Figure 2

Band diagram (CB: conduction band; VB: valence band) around the active region of the QD and QW LEDs under an applied bias of $1\mathrm{V}$, calculated by Simwindows (Ref. 17), assuming a $5\mathrm{nm}$-thick $\mathrm{InAs}$ QW as the active layer. The $32\mathrm{nm}$-thick $\mathrm{AlGaAs}$ with $\mathrm{Al}$ composition linearly graded from 0% to 85% acts as a hole injector by accelerating holes toward the active layer.

Figure 3

Measured J-V characteristics of (a) QD LEDs with a doped current spreading layer, and (b) QD LEDs with an optimized injection region. The current density is obtained by dividing the current by the oxide aperture area.

Figure 4

Measured I-V (left) and J-V (right) characteristics for QD (top), QW (middle), and DQW (bottom) LEDs with different current-aperture diameters. The current densities are calculated using the aperture diameter measured by SEM during the process.

Figure 5

(a) Estimated diffusion lengths in QW LEDs calculated from the ratio of current in each device to the current density in the $9\mu \mathrm{m}$-diameter device (see the text). (b) Current densities versus voltage, assuming $L_d=2.7\mu \mathrm{m}$.

Figure 6

(a) Estimated diffusion lengths in DQW LEDs calculated from the ratio of current in each device to the current density in the $8.8\mu \mathrm{m}$- diameter devices (see the text). (b) Current densities versus voltage, assuming $L_d=200\mathrm{nm}$.

Figure 7

Measured power-current (left) and efficiency-current density (right) characteristics for QD (top), QW (middle), and DQW (bottom) LEDs with different current-aperture diameters. The nominal current densities are calculated using the aperture diameter measured by SEM.

Figure 8

Radiative efficiency versus current density characteristics for QD (top), QW (middle), and DQW (bottom) LEDs with different current-aperture diameters. The current densities are calculated assuming no diffusion for the QDs, a diffusion length $L_d=2.7\mu \mathrm{m}$ for the QWs and $L_d=200\mathrm{nm}$ for the DQWs.