The negative differential resistance of a resonant-tunneling diode (sometimes called double-barrier diode) was predicted by Tsu and Esaki in 1973,1 following their pioneering work on superlattices in the late 1960s and early 1970s. The structure and characteristics of this diode were first demonstrated by Chang et al. in 1974.2 Following the much improved results reported by Sollner et al. in 1983,3 research interest was escalated, partially due to maturing MBE and MOCVD techniques. In 1985, room temperature negative differential resistance in this structure was reported by Shewchuk et al.,4 and by Tsuchiya et al.5 Meanwhile, resonant tunneling of holes instead of electrons was observed by Mendez et al.6 For more detailed discussions on the device, the readers are referred to Refs. 7-9.


A resonant-tunneling diode requires band-edge discontinuity at the conduction band or valence band to form a quantum well and, thus, necessitates heteroepitaxy. The most popular material combination used is GaAs-AlGaAs (Fig. 10.1), followed by GalnAs-AlInAs. The middle quantum-well thickness is typically around 50 A, and the barrier layers range from 15 to 50 A. Symmetry of the barrier layers is not required so their thicknesses can be different. The well layer and the barrier layers are all undoped, and they are sandwiched between heavily doped, narrow energy-gap materials, which usually are the same as the well layer. Not shown in Fig. 10.1 are thin layers of undoped spacers (« 15 A GaAs) adjacent to the barrier layers to ensure that dopants do not diffuse to the


The structure of a resonant-tunneling diode using GaAs-AlGaAs hetero­structure as an example The energy-band diagram shows the formation of a quantum well













barrier layers. Because thin epitaxial layers and abrupt doping profiles are required, most reported studies used MBE for film deposition, but MOCVD has also been used occasionally. Device isolation is usually achieved by mesa etching, as shown in Fig. 10.1.


A resonant-tunneling diode utilizes the quantization of energy states in a quantum well, as shown in Fig. 10.2(a). Quantum mechanics prescribes that in a quantum well of width W, the conduction band (or valence band) is split into discrete subbands, and the bottom of each subband is given by



Подпись: (10.1)n = 1,2,3… .

Notice that this equation assumes infinite barrier height, and can only serve to give a qualitative picture. In practice, the barrier (AEc) lies in the range of

0. 2-0.5 eV, giving an (E] — Ec) of » 0.1 eV. Under bias condition, carriers can tunnel from one electrode to another via some energy states within the well. While tunneling of carriers out of the well is less constrained, tunneling of carriers into the well is the determining mechanism for the current, and this requires available empty states at the same energy level and also conservation of lateral momentum. Since the perpendicular momentum in a quantum well is zero (kx = 0), the energy of carriers in each subband is given by


E = E +



where kL is the lateral momentum. From Eq. (10.2), it should be noted that the energy of carriers are quantized only for the bottom of the subband, but the energy




ef Ec



Подпись: SF


Подпись: Ec





*n_l L_r











Подпись: Ec




Подпись: (e)


RESONANT-TUNNELING DIODEEnergy-band diagrams of a resonant-tunneling diode under different biases, (a) Equilibrium, (b) Resonant tunneling through Ex. (c) First region of negative resistance (d) Resonant tunneling through E 2- (e) Second region of negative resistance. Their corresponding electrical characteristics are shown in Fig. 10.3.


I-V characteristics of a resonant-tunneling diode with multiple current peaks Labels (a)-(e) correspond to the energy-band diagrams shown in Fig. 10.2

above En is continuous. The free-electron energy in the emitting electrode is, on the other hand, given by


Подпись: (10.3)*2,2 2.2 x 1

E = En + —I — + —T" c 2m 2m

Conservation of lateral momentum requires that the last terms of Eqs. (10.2) and

(10.3) are equal. This with the conservation of energy results in the relationship

E„+—Ј = E . (10.4)

C 2m

It can be further shown that the maximum number of carriers available for tunneling at a fixed energy occurs at kx = 0.8 This implies that for maximum tunneling current, the emitter Ec should line up with E„ (Ec = En) as shown in the bias conditions of Figs. 10.2(b) and 10.2(d). With higher bias, the emitter Ec is slightly above En and tunneling current is reduced, resulting in negative differential resistance. This phenomenon produces local current maxima shown in Fig. 10.3.

The ratio of local peak current (Jp) to valley current (,/v) is a critical measure of the negative differential resistance. The peak current is mainly due to tunneling which can be maximized by using material of lighter effective mass. In this respect, the material combination of GalnAs-AlInAs is advantageous over GaAs-AlGaAs. Maximum peak-current density of 3xl05 A/cm2 has been observed, and is quite temperature independent since it is a tunneling current. The nonzero valley current is mainly due to thermionic emission over the barriers, and it has a large temperature dependence (smaller Jv with lower temperature). Another small but conceivable contribution is due to tunneling of electrons to higher quantized levels. Even though the number of electrons available for tunneling at energy higher than Ep is very small, there is a thermal distribution tail and this number is not zero, especially when the quantized levels are close together. The maximum Jp/Jv ratio observed is about 50 at room temperature.

As discussed, each region of negative differential resistance is associated with tunneling through one particular quantized subband. The applied bias under which negative differential resistance is observed is roughly twice the value of (E„ — Ec)/q since only half of the bias is useful in aligning Ec to En (Fig. 10.2). Additional bias is also developed across the spacer layers, as well as the accumulation layer and depletion layer of the heavily doped materials next to the undoped spacers.

As an example, the characteristics shown in Fig. 10.3 have two regions of negative differential resistance for each voltage polarity. In practice, the second current peak is rarely observed, due to the small signal in a large background of thermionic-emission current. The illustration nevertheless brings out the potential advantage over a tunnel diode that is limited to only one region of negative differential resistance. This feature of multiple current peaks is especially important as a functional device, discussed further in the Applications section.

For structures with identical barriers, as in the case of Fig. 10.1, the I-V characteristics are symmetrical around the origin. However, the two barriers can be made different in both barrier height (material) and layer thickness, resulting in asymmetrical I-V characteristics.

Triple-barrier heterostructures with two successive quantum wells have also been studied, and multiple regions of negative differential resistance can be readily observed (Fig. 10.4). The first current peak is believed due to tunneling through the first quantized levels of both wells (Fig. 10.4(b)), while the second current peak can be attributed to tunneling though different quantized levels (Fig. 10.4(c)),11 or sequential tunneling with downward transition (Fig. 10 4(d)).12 In any case, due to an additional barrier, which acts as a filter, sharper current features (dl/dV) are possible as shown in Fig. 10.4(e). Resonant tunneling on structures with quadruple barriers (triple wells) have also been studied 13,14

The extreme case of multiple barriers is a compositional superlattice which consists of many alternating layers of barriers and quantum wells (see Appendix D9). Negative resistance from a compositional superlattice had been observed about the same time as from a resonant-tunneling diode.15 The 1-V Characteristics with multiple current peaks and the energy-band diagfams at various bias points are shown in Fig. 10.5. One major difference in the superlattice structure is that the quantized levels are broadened into narrow subbands. The first current peak can be observed with a bias comparable to the first subband width (Fig. 10.5(a)). Up to that point, the field is uniform across the superlattice. Additional bias causes a high-field domain to develop in one of the barriers (Fig. 10.5(b)), causing a misalignment of the subbands. In Fig. 10.5(c), current rises again when the first subband is aligned to the second subband. In Figs. 10.5(d) and 10.5(e), the number of barriers with high-field domain is increased to two.

An alternate approach to achieve multiple current peaks is to connect resonant-tunneling diodes in series.16-19 The structure can be realized with




Tunneling in a triple-barrier heterostructure Energy-band diagrams correspond to (a) equilibrium, (b) first peak current from tunneling through first quantized levels in both wells, (c) second current peak due to tunneling from first level to second level or (d) sequential tunneling with downward transition (e) Its I-V characteristics

vertically integrated double barriers, separated by heavily doped layers. This is in principle very different from the above structures of multiple quantum wells since here the resonant-tunneling diodes are only connected by relatively thick heavily doped layers, and there is no quantum mechanical communication between them. The resultant 1-V characteristics in Fig. 10.6 show multiple current peaks. Another useful characteristic is that the current peaks are at approximately the same level. This is advantageous for multi-value logic applications. When a voltage V is applied across n resonant-tunneling diodes, each one absorbs approximately Vln. In practice, a minute difference in the structures would favor one to switch into the negative resistance (off-resonance) first. Since current has to be continuous through all n devices, the overall current drops initially and



Tunneling in a compositional superiattice (a)-(e) Energy-band diagrams (conduction-band edge) with increasing bias (After Ref 15) (f) 1-V characteristics


Подпись: VOLTAGE (V) FIGURE 10.6

1-V characteristics of five resonant — tunneling diodes in series (After Ref 16)
follows the general shape of the individual diode. The current then rises with voltage again until another resonant-tunneling diode switches. The number of current peaks thus corresponds to the total number of resonant-tunneling diodes in series.


Because tunneling is inherently a very fast phenomenon that is not transit-time limited, the resonant-tunneling diode is considered among the fastest devices ever made. Furthermore, it does not suffer from minority charge storage. It has been demonstrated that as a mixer it can detect radiation up to 2.5 THz, and as an oscillator it can generate 700 GHz signals. Maximum operational oscillation frequency has been projected to be over I THz.20 Tunneling, on the other hand, is more difficult to supply high current and the output power of an oscillator is limited. The resonant-tunneling diode has also been used in fast pulse-forming circuits and trigger circuits.21 Other applications that have been mentioned include the frequency multiplier, harmonic generator and parity generator.7’10 The unique feature of multiple current peaks can result in efficient functional devices that can perform more complex functions with a single device where conventional design would take many more components. Examples are multi-value logic and memory.22 The resonant-tunneling diode also serves as the building block for other three-terminal devices such as the resonant-tunneling bipolar transistor (Chapter 38) and the resonant-tunneling hot-electron transistor (Chapter 39). It has been incorporated in structures to study hot-electron spectroscopy.23 For general applications of negative resistance, the readers can refer to Appendix C2.