Quantum oscillations in the photocurrent of GaAs/AlAs p-i-n diodes

We report large amplitude quantum oscillations and negative differential conductance in the bias voltage-dependent photocurrent of p-i-n GaAs diodes with an AlAs barrier in the intrinsic ($i$) region. The oscillations appear only when the devices are illuminated with above-band gap radiation. They are strongly suppressed by a weak (∼2 T) in-plane magnetic field. Their period, amplitude, and magnetic field dependence are explained in terms of the quantized motion of confined photoexcited electrons and holes in the triangular potential wells formed by the AlAs barrier and the strong electric field in the intrinsic region. With increasing electric field, the energy levels of the electrons (holes) successively reach the top of their confining potentials, thus leading to a larger overlap of their wave functions with the free carriers in the $p$- (and $n$-) doped electrodes and to the observed oscillatory modulation of the recombination rate and photocurrent as a function of the applied voltage. The effect on the photocurrent oscillations amplitude of placing a layer of InAs quantum dots in the AlAs barrier layer is also examined.

Figure 1

Schematic band diagram of a p-i-n device with a tunnel barrier in the intrinsic ($i$) region at a forward applied bias $V$ = +0.5 V; it shows the motion of photoexcited carriers. A schematic diagram of the mesa structure is shown in the inset.

Figure 2

$I$($V$) characteristics for device A, showing the oscillatory photocurrent at low temperature (4 K) for different levels of laser illumination (λ = 633 nm).

Figure 3

Dependence of the peak-to-peak oscillation period Δ$V$ as a function of bias voltage $V$ and of laser intensity $P$ for device A.

Figure 4

(a) Temperature dependence of the oscillatory photocurrent of device A (bottom to top curves 1.7, 5, 10, 20, 50, 70, and 80 K). The inset shows the decrease of the oscillation amplitude as a function of temperature. (b) Dependence of the oscillatory photocurrent of device A on magnetic field $B$ = $B_x$, applied perpendicular to the current flow (i.e., parallel to the plane of the tunnel barrier). The inset shows the decrease of the oscillation amplitude as a function of $B_x$ for various bias voltages. The vertical arrows indicate the bias voltages selected for the plots of oscillatory amplitude shown in the insets.

Figure 5

Lower row of plots: Photocurrent oscillations at $T$ = 6 K for devices A, B, and C. Upper row of plots: Bias voltage positions and quantum numbers $j_m$ assigned to the photocurrent peaks associated with photoexcited electrons (blue symbols) and holes (red symbols) confined in the triangular quantum wells on $p$ and $n$ sides of the AlAs barrier. In (a) the values of electron and hole $j_m$ values for device A are obtained by fitting the “blue” and “red” parts of the oscillating $I$-$V$ curve, taken at a photoexcitation power $P$ = 0.8 mW. Here $j_m$ is the quantum number of the highest energy bound state of the triangular potential well at a particular bias voltage. In (b) blue and red numbers indicate calculated values of $j_m$ for the electrons and holes corresponding to the observed photocurrent resonances. The dashed blue (red) line indicates the bias voltage at which the conduction (valence) band edge in the doped $n$ (and $p$) regions becomes aligned with the top of the conduction (and valence) band AlAs barrier (see also Fig. 6).

Figure 6

(a) Schematic diagram illustrating the Airy function eigenstates and the mechanism proposed to explain the photocurrent oscillations. Photoexcited electrons occupy the quantized energy subbands $j$ of the triangular potential well (a similar diagram applies to the hole states on the other side of the barrier). With increasing electric field, the energy of the uppermost subband $j_m$ approaches the top of the potential well $E_C$, and eventually ionizes, joining the continuum states above the well; the increasingly strong overlap of the probability density of the electron eigenstate with the high density of free holes in the $p$-doped electrode leads to an increase in the rate of electron recombination with the holes (shown schematically by the downward solid arrow) and hence to a decrease in the photocurrent due to tunneling through the AlAs barrier. (b) A plot of the photocurrent oscillations at large reverse bias for device A at $P$ ∼ 100 μW. The blue arrow indicates the last observable photocurrent maximum, corresponding to the energy alignment of $E_C$ and $E_B$ in (a).