Category Archives: COMPLETE GUIDE TO SEMICONDUCTOR DEVICES

RESISTIVITY AND MOBILITY

RESISTIVITY AND MOBILITY

IMPURITY CONCENTRATION (/cm3)

RESISTIVITY AND MOBILITY

RESISTIVITY (n-cm)

IMPURITY CONCENTRATION (/cm3)

FIGURE D4 1

Resistivity of (a) Si and (b) Ge and GaAs as a function of doping concentration (After Refs I and 2)

RESISTIVITY AND MOBILITY

03

O

S

Подпись: 03 O S

10“

Подпись: 10“

Ј

Подпись: Ј(a)

RESISTIVITY AND MOBILITY

101:

Подпись: 101:

1017

Подпись: 1017

10”

Подпись: 10”

(b)

Подпись: (b)Ј

fc

8

s

RESISTIVITY AND MOBILITY

ОO’“1

Подпись: ОO'“1

I015 10’6 1017 1015

IMPURITY CONCENTRATION (/cm3)

Подпись:Ј

(c)

Подпись: (c)Ta

8

10′-

Подпись: 10'-s

FIGURE D4.2

Carrier mobility as a function of impurity concentration for (a) Si, (b) Ge, and (c) GaAs at room temperature (After Ref 2)

REFERENCES

1 J C Irvin, ‘ Resistivity of bulk, silicon and of diffused layers m silicon,” Bell Syst Tech J, 41, 387 (1962)

2 S M SzeandJ C Irvin, “Resistivity, mobility and impurity levels in GaAs, Ge, and Si at 300°K,” Solid-State Electron „ 11, 599 (1968)

RESISTOR

REAL-SPACE-TRANSFER DIODE

HISTORY

The concept of the real-space-transfer (RST) diode to obtain negative differential resistance was conceived by Gribnikov in 1972,’ and independently by Hess et al. in 1979.2 Analytical modeling was presented by Shichijo et al. in 1980.3 Computer simulations using the Monte Carlo method were performed by Glisson in the same year.4 The first experimental evidence of the negative resistance from a RST diode was shown by Keever et al. in 1981.5 Demonstration of an RST oscillator was made by Coleman et al. in 1982.6 This device is still under investigation and has not been produced commercially.

STRUCTURE

The requirement of a real-space-transfer diode is a heterojunction whose two materials have different mobilities. In addition, for an «-channel device, the material having lower mobility must also have a high conduction-band edge Ec. A good choice is the GaAs-AlGaAs heterostructure. Although modulation doping is not a requirement, the heavy doping in the AlGaAs further decreases its mobility and at the same time, the absence of doping in the GaAs layer increases its mobility. Modulation doping results in high mobility ratio and, thus, has been used commonly for the RST diode. An example of the structure is shown in Fig. 11.1. The thickness of the intrinsic GaAs is not important as the main channel is confined to the AlGaAs-GaAs heterointerface. Typically a GaAs thickness of ~ 1 (im is used. The AlGaAs layer has to be much thicker than the main channel for efficient real-space transfer. In this case, since the main channel is thin

FIGURE II. I

REAL-SPACE-TRANSFER DIODEAn example for the RST diode in which GaAs-AIGaAs heterostructure and modulation doping are employed

(= 100 A), the AlGaAs can be about 1000 A. The doping in this AlGaAs layer ranges between 1017 to 1018 cm-3. A thin layer of intrinsic AlGaAs (~ 50 A) is typical for modulation doping to ensure that the heterointerface is separated from the heavily doped region to avoid impurity scattering. The /7+-regions can be formed by diffusion of the impurity from the alloyed contacts which commonly is made of AuGe.

Fine control of the layer thickness and doping profile necessitates MBE or MOCVD growth. The example shown here has only one layer of channel, but a multichannel structure can be built with repeated heterojunctions on top of one another.

CHARACTERISTICS

The real-space-transfer effect is similar to the transferred-electron effect (see Chapter 7), and it is sometimes difficult to separate them experimentally in a heterostructure. The transferred-electron effect is due to the properties of a single, homogenous material. When carriers are excited by a high applied field to a satellite band in the momentum-energy space, the mobility is decreased and the current is lowered, resulting in negative differential resistance. In the real-space-transfer effect, transfer of carriers is between two materials (in real space), rather than two energy bands (in momentum space). In low fields, electrons (in an /7-channel device) are confined to the material (GaAs) with low Ec and higher mobility. The high-field energy-band diagram is shown in Fig. 11.2. Carriers near the anode acquire enough energy from the field to overcome the conduction-band discontinuity and flow to the adjacent material (AlGaAs) of lower mobility. This current can be considered as thermionic — emission current with the electron temperature replacing the room temperature. Thus, a higher field results in a smaller current, the definition of negative differential resistance. Typical I-V characteristics are shown in Fig. 11.3. The critical field for this real-space transfer has been shown to be between

1. 5-3 kV/cm, while that for the transferred-electron effect is typically 3.5 kV/cm for GaAs. One has to bear in mind that these critical fields are obtained from two different types of channels (heterointerface vs. bulk), and cannot be used alone to separate the effects. Another property of the real-space transfer is that there is

better control over factors such as conduction-band discontinuity, mobility ratio, and film thicknesses so that device characteristics can be varied and optimized.

The modeling of the RST diode is complicated, and there are no equations derived explicitly for the exact I-V characteristics. Qualitatively, the following expressions can be used to get an insight of the origin of the negative resistance. Assume that the total carrier density per unit area is Ns, distributed between the GaAs modulation-doped channel layer L | (m^) and AlGaAs layer Z2 (ns2),

AlGaAs

Подпись: AlGaAs The fraction of carriers excited to the AlGaAs layer is defined as

FIGURE 11.2

Energy-band diagram showing the conduction-band edge Ec of the RST diode under bias Electrons in the mam channel acquire energy from the field to overcome the barrier to spill over to the AlGaAs layer

FIGURE 11.3

Typical current-voltage (field) characteristics of a RST diode

REAL-SPACE-TRANSFER DIODE

(11.2)

and is a function of the applied field. It starts at zero at low field and approaches the ratio of Z2/(Zi + Lj) at high field. The total current is given by

I = AqnsXn^ + Aqns2n2^

(11.3)

Подпись: (11.3)= AqZN^^-iM^-ЯJR]

where A is the cross-section area of the channel. The differential resistance is given by

(11.4)

Подпись: (11.4)= AqNsЯl-

and it can be shown to be negative for a proper choice of n |, n 2 and dRiel’S. In the GaAs-AlGaAs modulation-doped system, n ~ 8000 cm[2]/V-s and p. 2 is less than 500 cm2/V-s at room temperature. Experimental data show that the current peak-to-valley ratio is not very high, with a maximum value around 1.5. Computer simulations show that a ratio of more than 2 can be achieved.

APPLICATIONS

One of the advantages of the RST diode is high-speed operation. The response time is limited by the movement of carriers across the heterointerface between the two materials, and is much faster than in a traditional diode where the transit time of carriers between the cathode and anode is the dominating factor. So far the application is demonstrated only by oscillators. The real-space-transfer effect is also applied in a three-terminal device (see Chapter 32-RST Transistor).

The general applications of negative differential resistance are listed in Appendix C2.

RESONANT-TUNNELING DIODE

HISTORY

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.

STRUCTURE

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

FIGURE 10.1

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

rc+-GaAs

 

»-AIGaAs

 

f-GaAs

 

r-AIGaAs

 

RESONANT-TUNNELING DIODE

n+-GaAs SUBSTRATE

 

RESONANT-TUNNELING DIODE

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.

CHARACTERISTICS

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

RESONANT-TUNNELING DIODE

(10.1)

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

RESONANT-TUNNELING DIODE

E = E +

n

(10.2)

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

BARRIER wEll BARRIER

RESONANT-TUNNELING DIODE

If—

ef Ec

Подпись: If— EF EC RESONANT-TUNNELING DIODE

Sf

Подпись: SF

Ec

Подпись: Ec

Ey

 

Ey

 

*n_l L_r

(a)

 

(b)

 

(C)

 

RESONANT-TUNNELING DIODE

Ef

RESONANT-TUNNELING DIODE

Ec

Подпись: Ec

Ey

Подпись: Ey RESONANT-TUNNELING DIODE

(e)

Подпись: (e)

FIGURE 10.2

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.

FIGURE 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

(10.3)

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

RESONANT-TUNNELING DIODE

RESONANT-TUNNELING DIODE

FIGURE 10.4

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

RESONANT-TUNNELING DIODE

FIGURE 10.5

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

VOLTAGE (V)

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.

APPLICATIONS

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.

ISOTYPE HETEROJUNCTION

HISTORY

An isotype heterojunction is different from an anisotype heterojunction in that the dopants of the two sides are of the same type. It can be an n-n heterojunction or a p-p heterojunction. (Discussions of the anisotype heterojunction can be found in Section 1.5.3.) The first heterojunction was the anisotype, which was suggested by Shockley in 1951, to be incorporated into the emitter-base junction to increase the current gain of a bipolar transistor.1 This application was analyzed in more detail by Kroemer in 1957.2 The isotype heterojunction had been studied in different material systems. These include Ge-GaAs by Anderson in 1962,3 InP-GaAs by Oldham and Milnes in 1963,4 Ge-GaAsP by Chang in 1965,5 and GaAs-AlGaAs by Womac and Rediker in 1972,6 by Chandra and Eastman7,8 and Lechner et al.9 in 1979. Theoretical analysis of the device has been presented by some of these authors, namely Anderson,3 Chang,5 and Chandra and Eastman.10

STRUCTURE

An n-n isotype heterojunction is shown in the schematic cross-section of Fig. 5.1, using the GaAs-AlGaAs system as an example. The layers are grown epitaxially. For good-quality heterostructure epitaxy, the lattice constants of the two materials have to be matched within « 5%. The heterointerface must be extremely abrupt to achieve rectification rather than have ohmic characteristics. This transition region has to be less than « 100 A thick.10-12 Also, for best rectification behavior, the doping level in the wide-energy-gap material should be non-degenerate and

ISOTYPE HETEROJUNCTION

FIGURE 5.1

Schematic cross-section of an isotype heterojunction, using an n-n AlGaAs-GaAs system

ISOTYPE HETEROJUNCTION

FIGURE 5.2

Energy-band diagrams of an isotype heterojunction (a) Isolated layers (b) Joined layers, at equilibrium (c) Under forward bias (d) Under reverse bias

lighter than that in the narrow-energy-gap counterpart. Isolation between diodes can be achieved by mesa etching down to the substrate layer.

CHARACTERISTICS

(5.1)

Подпись: (5.1)For a heterojunction of two materials of different electron affinities, work functions and energy gaps, the band-edge discontinuities in Fig. 5.2(b) are related by

(5.2)

Подпись: (5.2)A Er = q(x.-X7)

A Ey =

For the GaAs-AlGaAs system, GaAs is referred to as material 1. The potential barrier for the majority carriers is usually formed on the wide-energy-gap material, in this case AlGaAs. This system is similar in nature to a Schottky barrier with the narrow-energy-gap layer replacing the metal contact.

(5.3)

Подпись: (5.3)As shown in Fig. 5.2(a), the Fermi level in isolated AlGaAs is higher than that in GaAs. Conceptually, upon contact of these two materials, electrons transfer from AlGaAs to GaAs, causing a depletion layer in AlGaAs and an accumulation layer in GaAs. Such an accumulation layer does not exist in the anisotype heterojunction. In order to calculate the barrier height and band bending, the boundary condition for electric field is used,

K.% . = KJg ,

I ml 2 m2

g[1].

ml

Подпись: mlthe maximum field in the accumulation layer, which occurs at the

heterointerface, given by

2c1nd J kT q

fC^-r,) —

exp—————— 1

. kT

ISOTYPE HETEROJUNCTION

(5.4)

 

ml

 

<?m2’s the maximum field in the depletion layer, given by

(5.5)

Подпись: (5.5)

m2

Подпись: m22qND2(‘f’2-V2)

(5.6)

Подпись: (5.6)f,1 and Wi are band bendings at equilibrium. V; and V2 are the portions of applied forward voltage developed across GaAs and AlGaAs, respectively {Vf— V + V2). With another known relationship

(‘rl-vx) + (‘r2-v1)

ISOTYPE HETEROJUNCTION

FIGURE 5.3

Typical I — V characteristics of an isotype heterojunction, (a) Linear plot, (b) Semilog plot.

ISOTYPE HETEROJUNCTION

ISOTYPE HETEROJUNCTIONFIGURE 5.4

Energy-band diagram showing the effect of a graded layer / on the resultant barrier height.

these net potentials QҐ — Vj and lF2 — V2), as a function of applied bias, can be obtained by iterating Eqs. (5.3)-(5.6). Of particular interest is the barrier height at equilibrium, solved with Vj= = V2 = 0, giving

2 n

Подпись: 2 n(5.7)

I

exp

exp

exp

kT

kT

kT

The thermionic-emission current under bias can be obtained from f-q-fO (-qV,) T (qV’t

kT

2nm

ISOTYPE HETEROJUNCTION

(5.8)

 

Qualitatively, the square-root term represents the average carrier velocity, A^expU-fV’tT’) is the number of electrons above the barrier an^ the next two terms are due to opposite effects on the barrier exerted by V, and Vy. For better comparison to a Schottky barrier, this equation can be rearranged to give

r2

J = A

exp

exp

kT

kT

‘~q$b (~qV

kT J

exp

ISOTYPE HETEROJUNCTION

(5.9)

 

It can be seen that if V = 0, the current is identical to a Schottky diode where A* is the effective Richardson constant for the wide-energy-gap material.

To eliminate the variable V in the above equation, an approximation is made from Eqs. (5.3)-(5.5)5

qVT,-Vx)

exp

kT

ISOTYPE HETEROJUNCTION

— (‘Ґ — Vf) kT f

 

(5.10)

 

where ‘Ґ= Ґ,1 + ~$s — $s2’ Substituting V into Eq. (5.9) gives

7

irJ

i.

exp

exp

~kT

kT

qXi

kT.

— 1

exp

ISOTYPE HETEROJUNCTION
ISOTYPE HETEROJUNCTION

(5.11)

 

In comparison to a standard therm ionic-emission current of a Schottky-barrier diode, a few points are worthy of mentioning. The temperature dependence of the coefficient is now T instead of T2. The term (1 — Vf/’V) affects both the forward current and the reverse current. It causes the forward current to have a more gradual exponential rise with voltage. The reverse current also becomes non-saturating. A typical set of I-Vcharacteristics of an isotype heterojunction is shown in Fig. 5.3.

Another important deviation from a Schottky diode is that the barrier height becomes temperature dependent. This is implied in the derivation of the barrier height from Eqs. (5.3)—(5.7). Since the temperature dependence on current is a useful technique to measure parameters for thermionic-emission current, the barrier height in Eq. (5.11) can be eliminated to give

(zsT)

V kT *

qv,

-1

exp

Ur

q2’FNt

D2

J =

I

2nm 2kT

ISOTYPE HETEROJUNCTION
ISOTYPE HETEROJUNCTION

exp

 

(5.12)

 

As mentioned in Section 5.2, the transition between the two materials at the heterointerface has to be abrupt. This transition region, indicated as / in Fig. 5.4, has been shown to decrease the barrier height. A transition region of only w 150 A can reduce the barrier to the extent that rectification vanishes and ohmic behavior results.10-12

A structure with two isotype heterojunctions has been reported.13 As shown by the energy-band diagram in Fig. 5.5, the barrier is formed by a thin wide-energy-gap material (« 500 A), sandwiched between two narrow — energy-gap materials. The I-V characteristics in Fig. 5.6 show that the current is symmetrical, and, at low temperature, nonlinear. The nonlinearity is due to the decrease of the effective barrier height with bias, as shown in Fig. 5.5(b).

APPLICATIONS

The isotype heterojunction is not a practical device for rectification. The fabrication requirement is quite stringent. The barrier height obtained is usually lower than that from the metal-semiconductor junction. Also, the reverse current

AlGaAs GaAs I | GaAs

FIGURE 5.6

I-V characteristics of the rectangular barrier at different temperatures. (After Ref. 13)

Подпись:

J qv

Подпись: J qvJ L

00

Подпись: 00(b)

FIGURE 5.5

A rectangular barrier formed by two isotype heterojunctions, (a) Under equilibrium (b) Under bias.

AljGa^jAs

GaAs

Ec

GaAs

ISOTYPE HETEROJUNCTION

• En

 

JfWf TF

 

(a)

 

(b)

 

ISOTYPE HETEROJUNCTION

FIGURE 5.7

Energy-band diagrams of a sawtooth graded-composition barrier, (a) Equilibrium, (b) Under forward bias, (c) Under reverse bias.

does not saturate with voltage. This device, currently, has no commercial value. It is only used as a research tool to study the fundamental properties of heterojunctions.

RELATED DEVICE

Graded-Composition Barrier

The first graded-composition barrier was reported by Allyn et al. in 1980, with a saw-tooth barrier as shown in Fig. 5.7.14 In this example, the energy gap is varied by the Al and Ga concentrations in the AlxGa|_xAs layer. This barrier layer is typically « 500 A. The outer layers are GaAs. The I-V characteristics are shown
in Fig. 5.8 where the forward current is a thermionic-emission current and the reverse current is a tunneling current through the thin barrier.

A barrier of triangular shape, shown in Fig. 5.9, is also possible.13 The electrical characteristics in Fig. 5.10 are asymmetrical, reflecting the different control of barrier height by the two polarities. This asymmetry is similar to that in a planar-doped-barrier diode. Both directions of currents are due to thermionic emission of majority carriers.

ISOTYPE HETEROJUNCTION

FIGURE 5.8

I-V characteristics of a saw-tooth graded — composition barrier (After Ref 14)

Подпись: ISOTYPE HETEROJUNCTION ISOTYPE HETEROJUNCTIONEc

(a) (b) (c)

FIGURE 5.9

Energy-band diagrams of a triangular graded-composition barrier (a) Equilibrium (b) Under forward bias (c) Under reverse bias Currents in both directions are due to thermionic emission

ISOTYPE HETEROJUNCTION/

FIGURE 5.10

I-V characteristics of a triangular graded-composition bamer