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

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