Unraveling of free-carrier absorption for terahertz radiation in heterostructures

The relation between free-carrier absorption and intersubband transitions in semiconductor heterostructures is resolved by comparing a sequence of structures. Our numerical and analytical results show how free-carrier absorption evolves from the intersubband transitions in the limit of infinite number of wells with vanishing barrier width. It is explicitly shown that the integral of the absorption over frequency matches the value obtained by the $f$-sum rule. This shows that a proper treatment of intersubband transitions is fully sufficient to simulate the entire electronic absorption in heterostructure THz devices.

Figure 1

(a) Lowest three minibands for the SLs together with the dispersion of bulk GaAs (dotted line) neglecting nonparabolicity. (b) Absorption at 300 K for the SLs, calculated by the NEGF model together with the Drude expression (3) for bulk absorption (dotted line) using $m_c=m_{\mathrm{SL}}=0.071m_e$ and $\tau =46$ fs. The inset shows the NEGF calculations (symbols) at 77 K together with the corresponding result of Eq. (5) using ${\sigma }_0$ from Table and ${\tau }_m=70$, 100, 110, 100 fs for the sample with the barrier width of 0.5, 1.5, 2.5, 3.5 nm, respectively (lines).

Figure 2

(a) A double quantum well (well widths 8.5 nm, barrier width 1.5 nm) with its lowest eigenstates. Dashed and dot-dashed lines refer to symmetric and antisymmetric states, respectively. The arrows depict the transitions associated with the peaks in the absorption spectrum. (b) Absorption spectrum calculated by the NEGF model for the double quantum well and the corresponding SL. (c) Evolution of the absorption for 2, 3, and 4 wells with the same parameters as the double well from (a). In order to obtain absorption in the entire waveguide, it is assumed that the multi-quantum-well structure is periodically repeated with a separation by a 7.5 nm barrier. All calculations are done at $T=300$ K.