Ultrafast Photocurrent Measurement of the Escape Time of Electrons and Holes from Carbon Nanotube $p\mathrm{\text{−}}i\mathrm{\text{−}}n$ Photodiodes

Ultrafast photocurrent measurements are performed on individual carbon nanotube $p\mathrm{\text{−}}i\mathrm{\text{−}}n$ photodiodes. The photocurrent response to subpicosecond pulses separated by a variable time delay $\Delta t$ shows strong photocurrent suppression when two pulses overlap ($\Delta t=0$). The picosecond-scale decay time of photocurrent suppression scales inversely with the applied bias $V_{SD}$, and is twice as long for photon energy above the second subband $E_{22}$ as compared to lower energy. The observed photocurrent behavior is well described by an escape time model that accounts for carrier effective mass.

Figure 1

Experimental apparatus and photocurrent characteristics of the NT $p\mathrm{\text{−}}i\mathrm{\text{−}}n$ photodiode. (a) Experimental apparatus: M1 translating mirror, M2 fixed mirror, BS beamsplitter. (b) $I\mathrm{\text{−}}{V}_{SD}$ characteristics at $T=40\mathrm{K}$ and $E_{\mathrm{ph}}=1.51\mathrm{eV}$, for device 1 with open-circuit voltage $V_{\mathrm{OC}}=E_{11}/e=0.48\mathrm{V}$, $V_1=-8\mathrm{V}$, $V_2=8\mathrm{V}$, $V_G=1\mathrm{V}$. (c) Photocurrent vs photon energy at $V_{SD}=0.25\mathrm{V}$. All other parameters same as in (a). The top axis has been divided by $V_{\mathrm{OC}}$ to assign the $E_{22}$ peak.

Figure 2

Single pulse photocurrent of the NT $p\mathrm{\text{−}}i\mathrm{\text{−}}n$ photodiode. (a) Single pulse photocurrent vs optical intensity at $T=40\mathrm{K}$, $E_{\mathrm{ph}}=1.51\mathrm{eV}$ and $V_{SD}=0\mathrm{V}$ for device 1. Inset, single pulse photocurrent divided by the elementary charge $e$ and the repetition rate of the laser $f$ vs optical intensity. (b) Same data as (a) in log-log scale.

Figure 3

Double-pulse photocurrent of the NT $p\mathrm{\text{−}}i\mathrm{\text{−}}n$ photodiode. (a) Photocurrent vs time delay between two pulses at $V_{SD}=0\mathrm{V}$ at increasing intensities ($n=5$, 11, and $26\times {10}^{12}$ photons per $\mathrm{pulse}/{\mathrm{cm}}^2$ from top to bottom) for the same device and conditions as Fig. 2. (b) Normalized photocurrent vs time delay at $V_{SD}=0\mathrm{V}$ (solid circles) and $V_{SD}=-0.3\mathrm{V}$ (open circles). (c) Extracted decay constant vs $V_{SD}$. The red dashed line corresponds to the experimental resolution limit and the blue solid line labels ${\tau }_0=0.5\mathrm{ps}$. Inset, same data plotted as inverse decay constant $1/\tau$ vs $V_{SD}$. The high reverse bias decay constant data is not shown in the inset. (d) Schematic of the escape time model for electrons and holes in the $p\mathrm{\text{−}}i\mathrm{\text{−}}n$ junction. Electrons (and holes, not shown) photoexcited at the center of the device travel a distance $L$ to escape the junction.

Figure 4

Double-pulse photocurrent of the NT $p\mathrm{\text{−}}i\mathrm{\text{−}}n$ photodiode as a function of photon energy. Inset, normalized photocurrent at $T=40\mathrm{K}$ vs time delay at $E_{\mathrm{ph}}=1.51\mathrm{eV}$ (blue) and $E_{\mathrm{ph}}=0.85\mathrm{eV}$ (red) for device 2 with $V_{SD}=0.25\mathrm{V}$. Device 2 has the same device geometry as device 1 with $V_1=-10\mathrm{V}$, $V_2=10\mathrm{V}$, $V_G=0.5\mathrm{V}$ and $V_{\mathrm{OC}}=0.5\mathrm{V}$. Main panel: extracted inverse decay constants as a function of $V_{SD}$ for $E_{\mathrm{ph}}=1.51\mathrm{eV}$ (blue) and $E_{\mathrm{ph}}=0.85\mathrm{eV}$ (red) with linear fits to the data.