Full Band Atomistic Modeling of Homo-junction InGaAs Band-to-Band Tunneling Diodes Including Band Gap Narrowing

A homo-junction In0.53Ga0.47As tunneling diode is investigated using full-band, atomistic quantum transport approach based on a tight-binding model (TB) and the Non-equilibrium Green’s Function formalism. Band gap narrowing (BGN) is included in TB by altering its parameters using the Jain-Roulston model. BGN is found to be critical in the determination of the current peak and the second turn-on in the forward bias region. An empirical excess current that mimics additional recombination paths must be added to the calculation to model the diode behavior in the valley current region. Overall the presented model reproduces experimental data well. The downscaling of MOSFETs has lead to a drastic increase of power consumption, an unmanageable heat generation due to leakage currents, and a non-scalable supply voltage. Since energy efficiency is one of the biggest issues today, transistors that can help reduce the power consumption of integrated circuits and yet increase performance are highly desirable. Band-toband tunneling field-effect transistors (TFETs) represent an attractive alternative to MOSFETs towards low voltage operations and small power consumption. In effect, they can exhibit sub-threshold swing (SS) below the kT/q limit of MOSFETs due to the injection of cold electrons. However, a sharp source to channel interface and an excellent channel electrostatic control through the gate contact are two key issues in TFETs to obtain a high ON-current and a low SS. These two properties are rather difficult to obtain experimentally. On the contrary, band-to-band tunneling (BTBT) diodes can be relatively easily fabricated and offer a very good opportunity to test the tunneling properties of a given material and its potential as a TFET. Also, a thorough investigation of the underlying physics of BTBT diodes will help understanding the TFET operation, and assist the analysis of TFET design. In BTBT diodes, current mainly flows through the junction either by tunneling or by thermionic emission. The tunneling currents depend exponentially on the energetic height and spatial width of the tunneling barrier. The desired large current densities demand rapid band bending at the tunnel junction and therefore very large doping densities. The large doping densities in turn can cause band gap narrowing (BGN), which further modulates the tunneling barrier heights. We are not aware of a study on such intricate interplay of doping densities, electrostatic potentials, and material band gaps using an atomistic full band approach. Here BGN is treated in the framework of the tight-binding (TB) approach by using the Jain-Roulston model, which considers the shift of the conduction and valence bands separately. BGN effects are analyzed through quantum transport simulation, and an analytically calculated excess current is added to reduce the remaining discrepancy between the experimental and simulation results around the current valley region. A homogeneous InGaAs BTBT diode lattice matched to InP and fabricated by D. Pawlik et al. is simulated using the general-purpose quantum transport device simulator, OMEN to illustrate the effectiveness of the approach presented here. Based on the fabricated In0.53Ga0.47As BTBT diodes in Fig. 1(a), the one-dimensional structure in Fig. 1(b) is considered as simulation domain. An abrupt step-junction with constant doping profiles on both sides is used to model the p-n interface. An industrial standard classical drift-diffusion model, augmented by a simple tunneling model such as the Wentzel-KramersBrillouin (WKB) approximation requires considerable user customization to reproduce experimental data and the usage of sometimes non-physical parameter values. Furthermore, it is not predictive enough to treat tunneling devices whose behaviors are dominated by quantum mechanical effects. Therefore, to investigate the I-V characteristics of the considered devices, a fullband, atomistic quantum transport simulator based on the TB model and the Non-equilibrium Green’s Function (NEGF) formalism is used. The sp3d5s* TB model with spin-orbit coupling is chosen for the simulation at 300K. Within the TB model the proper coupling of the conduction to the valence bands through imaginary bands is automatically included, spatial variations of the band gap and the electrostatic fields can be naturally included in the Hamiltonian construction for the quantum transport, therefore incorporating a complete non-local band-to-band tunneling model. The abrupt and dramatic changes in the doping profile effectively create a hetero-structure at the p-n junction and a full quantum approach can properly account for the spatial modulation of the electronic charge, which cannot be modeled accurately with semi-classical models. FIGURE 1. (a) The fabricated device structure (b) The simulated structure of a InGaAs BTBT diode without (solid line) and with (dashed line) BGN. In heavily-doped semiconductors, high impurity concentrations and small carrier-to-carrier distances increase carrier-carrier and carrier-impurity interactions. Such interactions lower the conduction band edge or raise the valence band edge of heavily-doped semiconductors and result in a net band gap reduction called band gap narrowing. In BTBT diodes where both layers are heavily-doped, BGN should be taken into account since it modulates the band edges and strongly influences the magnitude of the tunneling current through the junction. Here, the BGN at each band edge of the pand nsides of the diode as a function of doping concentration (N) is calculated with the Jain-Roulston model. The shift of major and minority band edges (ΔEmaj and ΔEmino, respectively) can be written as ΔEmaj = A N 10 " #$ % &' 1 3 + B N 10 " #$ % &' 1 2 (1) ΔEmin = C N 10 " #$ % &' 1 4 + D N 10 " #$ % &' 1 2 (2) The parameters A, B, C, and D are derived from the material properties of p-type In0.53Ga0.47As according to Ref. 8. For n-type, the parameters are obtained by linearly interpolating the published values for n-GaAs and the parameters extracted from experimental data for n-InAs. Table I shows the parameters used for the calculation of BGN in pand n-type In0.53Ga0.47As. The calculated band shifts as well as the total BGN are summarized in Table II. TABLE I. BGN parameters of In0.53Ga0.47As.