Structure of GLIPs and Their Operation Principle

The GLIPunder consideration consists oftheGL-vdWheterostructure, which comprises N = 1,2,3,... GLs clad by the barrier layers and the two emitter and collector GLs (the top and bottom GLs, respectively). The latter GLs are doped by donors to provide their sufficiently high lateral conductivity. In contrast to our previously considered GLIPs [20, 21], we assume that the inter-GL barriers are selectively doped by acceptors and donors (as shown in Fig. 50.2) with equal densities E_B. The inner GLs can also be doped by acceptors with the density £gl.

To provide the localization of the photoexcited holes, the valence band offset, A_v, between the GLs and barrier layers is larger than the conduction band offset Д (i.e., A < A_v or Д v). A sufficiently strong dc bias voltage Vis applied between the contact GLs.

The GLIP operation is associated with the following processes [20, 21]: (1) the photoexcitation of the electron-hole pairs in the GLs due to the interband radiative transitions; (2) the tunneling injection of the thermalized electrons from the ground states in the GLs and the escape of the photoexcited electrons from their excited states followed by the propagation across the barrier layers; (3) the electron capture from the continuum states above the inter-GL barriers into the inner GLs.

Figure 50.2 A fragment of the GUP band diagram of a GUP with barrier layers doped by acceptors and donors ("dipole" doped) and GLs doped by acceptors. Wavy, solid, and dashed arrows indicate the processes of the electron photoexcitation, tunneling, and capture, respectively. The inset shows the barrier "tooth" and its parameters.

Equations of the Model

Generalizing the results of the recent calculations [20, 21], the density of the current across the GLIP caused by the incident infrared radiation with the intensity / (inside the device) and photon energy hcocan be presented as

with

Effect of Doping on the Characteristics of Infrared Photodetectors

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and

Here, the factor depending on hco in Eq. (50.2) reflects the Pauli exclusion principle, the quantity в_ы is the probability of the escape from the GL of the electrons photoexcited owing to the interband absorption of the photons with the energy hco, [5 = па/ , a = e²/ he is the fine structure constant, e and h are the electron charge and the Planck constant, is the barrier material refractive index, T is the temperature, £gl is Fermi energy in the inner GLs counted from the Dirac point, p is the capture efficiency [24-29] [which in the heterostructures under consideration can be very small: p N is the number of the inner GLs, and ^ = (Д - £_E)/A < 1, where £_e is the electron Fermi energy in the emitter GL. The parameter jfc plays the role of the emitter ideality parameter. It depends on the features of the electron injection from the emitter into the GLIP heterostructure bulk [26-31]. For the "ideal” emitter contact = 0, and the electric field in the near-emitter barrier is close to zero. This corresponds to the situation when the emitter provides the injection of such an amount of electrons which is dictated by the conditions in the device bulk.

The probability, 6_(tf of the photoexcited electrons escape from the GLs is determined by the ratio of the try-to-escape time r_esc and the electron energy relaxation time r_relax, and by the tunneling exponent. The latter depends on the energy (with respect to the barrier top) of the photoexcited electrons via the factor r₍₀ = (Д - hco/2)/A if (Д - A_gl) < hco < 2Д and rj₍₀ = 0 if hco> 2A, the characteristic "tunneling" field E_tunn =4-v/2mA^3/2/3e/i [32], (where m is the electron effective mass in the barrier layer), the height of the barrier "tooth” adjacent to the GL A_gl, which is determined by the real electric field in the barriers at the inner GLs £gl- Considering the doping of the barrier layers, we obtain the following formulas for the electric fields near the GLs £_gl and in the bulk of the barriers E_B:

with V_B = 4n eI._Bd/K_B and A_GL = E_CLd_CL, where d is the barrier layer thickness and d_GL is the spacing between the GLs and the donor sheets (see the inset in Fig. 50.2). The barrier doping effectively increases the rate of the photoexcited electron tunneling rate when the "tooth” height A_GL is sufficiently large, in particular, if A_GL ^ Д. For the definiteness, the latter relationship is assumed in the following. The Fermi energy of holes in the inner GLs at not too high temperatures can be expressed via the acceptor and hole density I_GL as e_GL = h t»w -у/яХ_CL , where щ — 10⁸ cm/s,