Category Archives: COMPLETE GUIDE TO SEMICONDUCTOR DEVICES

PLANAR-DOPED-BARRIER DIODE

HISTORY

The planar-doped-barrier (PDB) diode is often called the cS-doped-barrier diode or triangular-barrier diode, due to the shape of the potential barrier. It belongs to a class of bulk-barrier diodes which are different from the most common majority-carrier device, the Schottky-barrier diode whose barrier is formed at the semiconductor surface. The development that led to this device started from the idea of enhancing the Schottky-barrier height by a thin, depleted region of high concentration of the opposite type at the surface, proposed by Shannon in 1974.1 Shannon, later in 1979, developed a new majority-carrier device called a camel diode in which the metal-semiconductor barrier was eliminated and the barrier was created by an n++-p+-n structure (see Section 4.5.1).2 The planar-doped barrier was first reported by Malik et al. in 1980.3 The structure differs from the camel diode by having layers of intrinsic regions inserted between the oppositely doped layers, i. e., n+-i-p+-i-n+ structure. More detailed discussions of the device can be found in Refs. 4-7.

STRUCTURE

A typical planar-doped-barrier diode in GaAs is shown in Fig. 4.1. Because the middle p+-layer has to be fully depleted, it is very thin and it lies in the range of 2-10 nm. Such a thin, heavily doped layer can only be controlled by MBE or MOCVD growth. Besides, thermal cycles during subsequent processing have to be constrained to avoid excessive diffusion. The doping level is typically in the 1018 cm-3 range. The intrinsic regions range from tens of nm to several hundred

FIGURE 4.1

PLANAR-DOPED-BARRIER DIODECross-section of a planar-doped-barrier diode in GaAs 3

nm, and have concentrations in the 1014 cm 3 range. The mesa structure can be obtained by etch-back of the planar epitaxial layers.

CHARACTERISTICS

The charge density per-unit-area in the middle p+-layer, when fully depleted, has a value equal to

(4.1)

Подпись: (4.1)qN.8

where S is the planar-doped layer thickness. This charge sheet induces space-charge regions in the two w+-layers (Fig. 4.2), giving rise to electric fields

(4.2)

(4.3)

Подпись: (4.2) (4.3) ?rh = №2

The barrier height (from Fermi level) at zero bias can be given by

x2Qa

(4.4)

Подпись: (4.4)

’’bo

Подпись: ’'bo+ V

Equation (4.4) ignores fields set up at the junctions between the w+-layer and the intrinsic layer. It underestimates <j>bo by an amount which becomes non-negligible for small Qyj.5,6 These equations show that the barrier height can be tailored by parameters NA, S, X] and x2, and is much more flexible than the Schottky-barrier diode whose barrier is determined mainly by the metal work function. The capacitance of the PDB diode is given by

PLANAR-DOPED-BARRIER DIODE(a)

(b)

 

(c)

 

PLANAR-DOPED-BARRIER DIODE

PLANAR-DOPED-BARRIER DIODE(d)

(e)

 

FIGURE 4.2

Properties of a planar-doped-barner diode (a) Doping profile (b) Space-charge density and (c) electric-field profile in equilibrium Energy-band diagram (d) in equilibrium and (e) under forward bias, with positive voltage applied to the top (left) layer

 

PLANAR-DOPED-BARRIER DIODE

and is independent of bias.

It is known that, in the injecting side of the barrier where carriers are going against the potential, if the potential variation exceeds kTlq within one mean free path, the current conduction is limited by thermionic emission. A PDB diode typically falls into this category. Under bias, the barriers faced by the two H+-layers are no longer symmetrical, as shown in Fig. 4.2(e). With a positive voltage V applied to the surface (left) layer, the barriers are modified to

x, F

Подпись: x,F

bo

Подпись: bo(4.6)

(4.8)

where A* is the effective Richardson constant (see Chapter 3 and Appendix B5). The applied voltage V can be either positive or negative, and both polarities are valid in Eq. (4.8). Typical characteristics are shown in Fig. 4.3. The factors, also known as barrier leverage factors, xi/(xi+x2) and x2/(x]+x2) determine the portion of voltage applied to 0and 0b2, respectively. These factors control the effective

J= A* I2 = /T2

(jC j + X^)

bo

The thermionic-emission current under this condition is given by

 

exp

I kT )

— exp

I kT ;

 

exp

-q(j>

bo

exp

(Xj +x2)kT,

■ exp

FIGURE 4.3

Typical I-V characteristics of a planar-doped-barrier diode in (a) semi-log scale and (b) linear scale Asymmetry is due to x, < jc2.

(a) (b)

x qV

-x. qV

kT

(.x + x-) kT

x2V

 

(4.7)

 

PLANAR-DOPED-BARRIER DIODE
PLANAR-DOPED-BARRIER DIODE

PLANAR-DOPED-BARRIER DIODE PLANAR-DOPED-BARRIER DIODE

ideality factor (n value) of the I-V characteristics. Also, in an asymmetrical structure (x, * x2), the voltage polarity that forces higher current is considered the forward bias. In the above example, x2 > *i, and positive V is the forward direction.

APPLICATIONS

The PDB diode is a majority-carrier device. It has no minority-carrier storage and is capable of high-frequency operations. It has certain advantages over the Schottky-barrier diode. First, the barrier can be varied between zero to approximately the energy-gap value. The degree of symmetry between the forward and reverse directions can also be adjusted. Second, the barrier is not at the metal-semiconductor interface so that it is more stable in response to electrical stress. Third, since all the layers are semiconductors, the PDB structure is more flexible as a device building block. Applications of the PDB diode are listed below.

1. Referring to the energy-band diagram of Fig. 4.2(e), if extra minority carriers (holes) are supplied by external means, they would accumulate at the peak of the valence band. These positive charges set up a field that reduces the barrier heights <j>bi and <j>b2, resulting in a larger thermionic-emission (majority-carrier) current. This property of current gain is used in a photodetector (see Section 54.5.4) and switch (see Chapter 17).

2. Two PDB diodes back-to-back are used to form a hot-electron transistor (see Chapter 35). The planar-doped barrier has also been incorporated as the channel or the gate of various FETs.

3. As a microwave mixer and detector, it has performance similar to that of a Schottky-barrier diode.8 It can also be used as a special subharmonic mixer that requires symmetrical I-V characteristics.9 In this case it replaces two Schottky-barrier diodes in anti-parallel.

4. It can replace the Schottky barrier as the injecting junction in a BARITT diode10 or a TED.

RELATED DEVICE

Camel Diode

A camel diode can be viewed as the extreme case of asymmetry in a PDB diode with x = 0. It has a three-layer structure shown in Fig. 4.4. The center layer is again fully depleted. The doping concentrations of the three layers increase toward the surface. Since the heavily doped layers are very near the surface, and the sharpness of the doping profiles is less critical, ion implantation and standard

n++

p*

n

(a)

T~

qfao

* *

Подпись: n++ p* n (a) T~ qfao * *

&

Подпись: &FIGURE 4.4

(a) Doping profile and (b) energy-band diagram of a camel diode.

chemical vapor deposition, instead of MBE, can be used for fabrication. The barrier height, in this case, is given by2,4

<t>

+ V

bo

qNf

2 E

PLANAR-DOPED-BARRIER DIODE

(4.9)

 

(Vn is negative for degenerate semiconductor.) Under bias, it behaves like a Schottky-barrier diode except with a small dependence of barrier height on bias, giving an ideality factor slightly larger than unity (typically « 1.2). Both the camel diode and the PDB diode belong to what is called bulk unipolar diode.7,11

1.

RELATED DEVICES

Mott Barrier

A Mott barrier has a metal contact on a lightly doped surface layer on a more heavily doped substrate (Fig. 3.8). The lightly doped layer is fully depleted, and the space charge is negligible so that the electric field is constant. The capacitance of the device is small and independent of bias. The current, in this case, is diffusion limited rather than thermionic emission limited."

Metal-Insulator-Semiconductor Tunnel Diode

In the metal-insulator-semiconductor (MIS) structure, a thin interfacial layer such as an oxide is intentionally introduced before metal deposition (Fig. 3.9).20,21 The interfacial layer thickness lies in the range of 1-5 nm. The current is reduced from Eq. (3.5) to

RELATED DEVICES

(3.12)

where C, is the mean barrier height in eV, and S is the oxide thickness in nm (product is normalized to be dimensionless). The interfacial layer reduces the

majority-carrier current without affecting the minority-carrier current, and this

raises the minority injection efficiency. This structure is used in other devices

such as the solar cell, MISS switch, and surface oxide transistor.

S CHOTTKY-B ARRIER DIODE

HISTORY

The metal-semiconductor (MS) junction is more commonly known as the Schottky-barrier diode. It is sometimes called the surface-barrier diode. Due to the energy-band discontinuity at the interface, injected carriers possess excess energy and the structure is also referred to as a hot-carrier diode or a hot-electron diode. An MS junction is also a useful building block for many other devices. A special type of MS junction is the ohmic contact where the semiconductor is heavily doped. Obviously ohmic contacts are required for every semiconductor device because the final conductor at the chip level is always a metal.

The metal-semiconductor system is among the oldest semiconductor devices. Application of the device can be traced to before 1900. The realization of a potential barrier resulting from space charge in the semiconductor surface was initiated in 1938 by Schottky,1 and by Mott2 independently. The formulation of the thermionic-emission theory was established by Bethe in 1942.3 This theory was later refined by Crowell and Sze in 1966.4 The theory of surface states developed by Bardeen in 1947 was instrumental for better understanding of experimental results.5 The use of silicide in place of metal on silicon substrates was pioneered by Lepselter and coworkers in 1968.6,7 The epitaxial silicide process developed by Tung in 1984 provides new insight into intrinsic metal-semiconductor properties.8 In-depth treatment of the Schottky-barrier structure can be found in Refs. 9-14.

S CHOTTKY-B ARRIER DIODE

METAL

OXIDE

S CHOTTKY-B ARRIER DIODEMETAL

(b)

FIGURE 3.1

Schottky-barrier diode in the form of (a) point contact, (b) deposited metal, and (c) deposited metal with oxide isolation and diffusion guard ring.

STRUCTURE

The early version of the Schottky diode was in the form of a point contact (Fig. 3.1) where a metal wire, called a cat’s whisker, is pressed against a clean semiconductor surface. (A point contact has the characteristics of either a Schottky barrier or a p-n junction, depending on the forming process.) Such a structure was unreliable and not reproducible, and was subsequently replaced by vacuum-deposited metal. A diffused guard ring shown in Fig. 3.1(c) is often used to avoid leakage and breakdown effects caused by the high electric field at the perimeter of the diode. For silicon substrates, metallic silicides can also be used in place of the metals.

A critical step in fabricating a Schottky-barrier diode is to prepare a clean surface for an intimate contact of the metal. In manufacturing, the surface is cleaned chemically. Experimentalists have also explored cleaved surfaces, as well as cleaning by back-sputtering in vacuum. The metal is usually deposited in vacuum, either by evaporation or sputtering. Chemical deposition is gaining popularity, especially for refractory metals. Plating can also be used but contamination from the solution is not controllable. Silicides on silicon substrates are usually made by metal deposition, followed by heat treatment to form the silicides. Such a system can be potentially more ideal because the reaction consumes silicon and the silicide-semiconductor interface propagates below the original surface. One advantage of a Schottky structure is the low temperature processing. The need for high temperature steps in impurity diffusion or impurity activation after ion implantation can be avoided.

CHARACTERISTICS

The formation of a Schottky-barrier junction is shown by the energy-band diagrams in Fig. 3.2. Assuming an ideal interface, the barrier height should be given by

S CHOTTKY-B ARRIER DIODE

(a) (b)

dVb, + K)

Ec

ef

n

Ey

 

(C) (d)

 

FIGURE 3.2

Energy-band diagram for metal-semiconductor structure (a) Isolated metal and «-semiconductor (b) Connected and under equilibrium (c) Under forward bias (positive voltage applied to the metal for n-type substrate) (d) Under reverse bias Also shown are rounded, reduced barrier heights due to image-force lowering

 

S CHOTTKY-B ARRIER DIODE

h = K~Zs ‘ (3-J)

Experimentally, such a relationship is seldom realized exactly. The discrepancy is not yet fully understood. Presently, a few proposals exist, considering (1) an insulating layer at the interface (similar to that of Fig. 3.9), (2) surface traps, (3) metal-induced gap states, and (4) structure-dependent interface dipoles. As a result, the barrier formation has a weaker dependence than Eq. (3.1) on the metal work function. Typical barrier heights of metals and silicides on w-type semiconductors are listed in Table 3.1. Their corresponding barrier heights on p-type substrates, even with the above imperfections, are given by

4&bn + hi) = Eg ‘ (3.2)

This relationship is experimentally observed. The depletion width is given by

qN

and the corresponding capacitance is

SCHOTTKY-BARRDER DIODE

Подпись: SCHOTTKY-BARRDER DIODEBarrier heights for metals and silicides on n-type semiconductors (q<fi/,„ in eV) at 300 K (* at 77 K).u (*)15 Barrier heights on p-type materials « Eg — qtj>i, n.

Si

Ge

SiC

GaP

GaAs

GaSb

InP InAs

InSb

ZnS

ZnSe

CdS

CdSe

CdTe

AI

Ag

Au

Au/Ti

B)

0 68-0 74 0 56-0 79 0 81-0 83

048 0 45

20 1 95

I 05 1 2 1 18

0 73-0 80 0 88 0 90

0 89-0 92

0 61

Ohmic 0 54 Ohmic 0 40-0 49 Ohmic 0 53

0 18* 0 17*

08 1 65 20

0 74

1 22

1 35-151

1 14

Ohm )c 0 35-0 56 0 68-0 78 0 84

0 43 0 70

0 76 0 66-0 78 0 86

078

Ca

Co «

CoSi2#

Cr

Cu

0 40 0 64 0 64 0 57-0 59 0 66-0 79

05 0 48

1 18 1 20

0 56 0 82

1 75

1 10

0 36-0 50

0 33

0 82

Fe

In

lr

Mg

Mo

0 65

0 77 04 0 56-0 68

042 0 42

1 04

0 83 0 65

0 82

1 11 0 86

049

0 78 0 69

MoSо2*

Na

Mi M

NiSii

Os

0 63-0 69 0 43 0 66-0 70 0 66 07

04

078-0 83

045 0 53

0 83

Pb Pd « Pd2Si * * PtSi*

06 0 71 0 71-0 75 0 90 0 81-0 86

145

0 86

1 87 1 84

1 14 1 4

0 62 0 85-1 1

0 37

0 68 0 86

0 89

Rh 0 72 RhSi 0 70 Ru 0 76 (SN)xPolymer Sb

0 40 038

1 0-1 2 0 86

0 8-0 9

2 7-3 0

1 7 1 34

1 1

0 6-0 7

076

Sn Tl «

TiSi2#

w

WSi2

0 50 0 58-0 60 0 66 86

048

0 75 0 75-0 84

0 66-0 71

Zn

ZrSi2

0 75 0 55

FIGURE 3.3

S CHOTTKY-B ARRIER DIODECapacitance characteristics vs. reverse bias.

Ј

Подпись: Ј

(3.4)

Подпись: (3.4)1 2^bi+vr) ^2

qe N

Capacitance measurement plotted in this format (Fig. 3.3) can yield the barrier height as well as the doping concentration (or area). This technique can be extended to profile non-uniform doping concentration (see Eq. (1.18)).

The current transport in a Schottky barrier is thermionic emission of majority carriers over the barrier (see derivation in Appendix B5), given by

r2

J = A

— 1

exp

exp

~kT )

qIi

nkT)

S CHOTTKY-B ARRIER DIODE

(3.5)

 

with

(3.6)

Подпись: (3.6)* 4nqm k2

A = —————

Common effective Richardson constants A used for Ge, Si and GaAs are shown in Table. 3.2. The n value (> 1) in Eq. (3.5) is called the ideality factor. The

TABLE 3.2

Commonly used values of Richardson constants (A ) for Si, GaAs and Ge. (A/cm2-K2)

Si

GaAs

Ge

«-type

110

4.4

143

p-type

30

74

41

r

Подпись: r

/

Подпись: //(log)’

S CHOTTKY-B ARRIER DIODE

"V

(b)

FIGURE 3.4

Typical 1-V characteristics of a Schottky barrier in (a) linear current plot and (b) logarithmic current plot.

underlying cause for n > 1 can be an interfacial layer, barrier height inhomogeneity, or image-force lowering which is voltage dependent.

The minority-carrier hole current, on the other hand, is limited by diffusion as in the case of a p-n junction and is therefore given by

S CHOTTKY-B ARRIER DIODE(3.7)

This diffusion current is usually 4-6 orders of magnitude smaller than the thermionic-emission current. It is the dominance of the majority-carrier current with minimum minority-carrier storage that enables the Schottky barrier to operate at much higher frequencies (« 100 GHz) compared to a p-n junction (« 1 GHz).

Another current component in addition is the depletion-region generation/recombination current (see Appendix B2), given in the form

I — f rr

(3.8)

Подпись: (3.8)r qVf

J = J exp ———- — 1

The magnitude of Jre depends on the quality of the semiconductor material. If Jre is larger than the corresponding component in Eq. (3.5), the current for small forward bias, as well as the reverse current, will be increased.

Typical 1-V characteristics are shown in Fig. 3.4. The «value can be measured from the exponential rise of current with voltage. At high forward bias, current is leveled off by series resistance or high current injection. At high reverse bias, breakdown occurs whose mechanism is similar to the impact ionization breakdown in p-n junction.

After fabrication of a Schottky-barrier diode, it is often required to measure its barrier height. There are altogether five methods to do so and they are listed below:

1. 1-V characteristics: A current level is measured when Vj is extrapolated to zero. With a known effective Richardson constant, Eq. (3.5) is used to deduce the barrier height. Due to the exponential dependence of current on

the accuracy of A is not critical.

2. Temperature dependence: The dependence of forward current on temperature can yield the barrier height (Eq. (3.5)). For a fixed Vj, a plot of log(J/T2) vs. 1 IT gives the activation energy of q(<pi, — Vj).

3. C-Vcharacteristics: Equation (3.4) andFig. 3.3 are used to obtain the built-in potential and doping concentration. Barrier height is then the sum of qy//,, and qV„ (or qVp).

4. Photoresponse: The quantum efficiency for carriers excited from the metal over the barrier is known to be a function of photon energy hv. If the square root of the photoresponse is plotted against the photon energy, the barrier height can be obtained as shown in Fig. 3.5.

5. Photovoltaic effect: When a Schottky barrier is exposed to light, a short-circuit current Jsc or an open-circuit voltage can be obtained. The relationship is given by16

*c + l

J

0

S CHOTTKY-B ARRIER DIODE

v

oc q

 

(3.9)

 

S CHOTTKY-B ARRIER DIODEPlotting Voc vs. Jsc at different illumination levels provides J0 and n. The dark current J0 obtained can be used to calculate the barrier height.

FIGURE 3.5

Photoresponse vs photon energy to determine Schottky-barner height

In the presence of image-force lowering (see Appendix B6), the tip of the barrier is rounded off as shown in Fig. 3.2. The amount of barrier lowering is given by

S CHOTTKY-B ARRIER DIODE(3.10)

S CHOTTKY-B ARRIER DIODEwhere is the maximum field near the interface and is given by

(3.11)

Among the above measurement methods, all yield the final effective barrier height with the exception of the C-V method where the built-in potential y/bt obtained would be overestimated by A<f>i, and must be corrected to obtain the exact barrier height.

S CHOTTKY-B ARRIER DIODEThe barrier height for a metal on a semiconductor is known to be independent of the semiconductor doping level, if the doping is uniform. However, it can be modified by a thin sheet of heavily doped layer at the surface, as first suggested by Shannon.1718 As shown in Fig. 3.6, a layer of n+-region reduces the effective barrier height (on n-type substrate) due to increased image-force lowering and increased tunneling. A layer of //-region increases the barrier due to band bending in the bulk of the semiconductor.

S CHOTTKY-B ARRIER DIODE

FIGURE 3.6

Modification of barrier height from (a) original value, (b) with n+-layer to reduce <j>b, (c) with //’-layer to increase <j>b.

APPLICATIONS

The main features of a Schottky-barrier diode are high-frequency capability and low forward-voltage drop. These features plus the ease of fabrication make the device useful in a wide range of applications.19

1. As a general purpose rectifier, it can be used in many circuit applications outlined in Appendix C 1-Applications of Rectifiers.

2. Due to its high-frequency capability, among all rectifiers the Schottky barrier is the most widely used diode as microwave mixer and detector.

3. Due to its low loss (low voltage drop) in forward bias, it is used quite extensively in power electronics. In particular, it is used in low-voltage, high-current power supplies.

4. Due to the non-linear I-V characteristics, it can be used as a varistor (see Section 12.5.1).

5. It can be used as a varactor based on the variation of depletion-layer capacitance under reverse bias (see Section 1.5.4).

6. It is a fundamental building block for many other devices such as the solar cell, photodetector, metal-base transistor, MESFET, etc.

7. A special form of Schottky junction is the ohmic contact which is required to connect every semiconductor device to other devices or to the external environment.

8. In a clamped bipolar transistor, a Schottky diode is connected between the base and the collector as shown in Fig. 3.7. In the saturation regime of the transistor operation, the base-collector junction is under forward bias. When a Schottky diode is connected in parallel, most of the current passes through the Schottky device, and minority-carrier storage is eliminated in the base-collector p-n junction. As a result the turn-off time of the bipolar transistor is greatly reduced.

FIGURE 3.8

Energy-band diagram for Mott diode

Подпись:COLLECTOR?

-X-

BASE

EMITTER

FIGURE 3.7

An n-p-n bipolar transistor with Schottky-diode clamp

b

•i h

S CHOTTKY-B ARRIER DIODEN

S CHOTTKY-B ARRIER DIODE

n

S CHOTTKY-B ARRIER DIODE

FIGURE 3.9

Подпись: Energy-band diagram for MIS tunnel diode

9. It is also used as a clamping diode in integrated injection logic circuits and transistor-transistor logic circuits.

10. Due to the low temperature processing, a Schottky barrier is used as a tool for characterization of the semiconductor material, especially on surface properties.

P-i-n DIODE

HISTORY

The p-i-n diode is a refinement of the p-n junction for special applications. After the p-n junction was developed in the late 1940s, the p-i-n diode was first used as a low-frequency, high-power rectifier in 1952 by Hall,1 and in 1956 by Prince.2 The presence of an intrinsic layer can substantially increase the breakdown voltage for high-voltage application. This intrinsic layer also provides interesting properties when the device is operated at high frequencies in the microwave and radio-wave range. It was not until 1958 that the device started to be used in microwave applications by Uhlir.3 More details on this device can be found in Refs. 4-9.

STRUCTURE

A p-i-n diode consists of an intrinsic layer sandwiched between the opposite types of a p-n junction. The intrinsic layer has a very low concentration of either «-type or p-type in the order of 1013 cm-3, and a resistivity in the order of kfi-cm. The intrinsic-layer thickness (xj) ranges between 10 |_im to 200 |im. The outsidep — and «-layers are usually heavily doped. As shown in Fig. 2.1, the p-i-n diode can be realized as a planar structure or a mesa structure, both fabricated on degenerate substrate material. In the planar structure, an intrinsic epitaxial film is grown and the p+-region is introduced by either diffusion or ion implantation. A mesa structure has epitaxially grown layers with dopants incorporated, and is capable of higher-frequency operation because the intrinsic layer can be made thinner with better control. Isolation of the device is achieved by mesa etching and

+

n

+

p

P-i-n DIODE

(b)

 

I

 

P-i-n DIODE
P-i-n DIODE

FIGURE 2.1

A p-i-n diode with (a) planar structure and (b) mesa structure.

surface passivation such as oxidation. The advantages of a mesa structure are reduced fringing capacitance and inductance, and improved surface breakdown voltage. The substrate material for the p-i-n diode has been almost exclusively silicon until the early 1980s when GaAs was also studied.

CHARACTERISTICS

The special feature of a p-i-n diode is a wide intrinsic layer that provides unique properties such as low capacitance, high breakdown voltage with reverse bias, and most interestingly, carrier storage for microwave applications with forward bias. Near zero or at low reverse bias, the lightly doped intrinsic layer starts to be fully depleted (Fig. 2.2(c)), and the capacitance is given by

Once fully depleted, its capacitance is independent of reverse bias. Since there is little net charge within the intrinsic layer, the electric field is constant (Fig. 2.2(d)) and the reverse breakdown voltage is given by

(2.2)

For silicon, the breakdown field %bd >s approximately 2xl05 V/cm. These two equations show that the parameter xj controls the trade-off between frequency response (from capacitance) and power (from maximum voltage).

When the p-i-n diode is under forward bias, both types of carriers are injected into the intrinsic layer, and the carrier profiles are shown in Fig. 2.2(f). It is usually assumed that within the intrinsic layer, the electron and hole concentrations are the same (Pj~ns), and that they are uniform within the intrinsic layer. The current conduction is through recombination,

P-i-n DIODE

P-i-n DIODE

P-i-n DIODE

(0

 

FIGURE 2.2

p-i-n diode shown in (a) structure cross-section, (b) impurity profile, (c) space charge distribution, (d) electric field, (e) energy-band diagram at equilibrium, and (f) carrier concentrations under forward bias.

 

P-i-n DIODE

P-i-n DIODE

FIGURE 2.4

Typical RF resistance as a function of DC forward current (After Ref 5)

FIGURE 2.3

DC J-Vcharacteristics of ap—n diode

Подпись:

-r

Jo

Подпись: -r Jo

jr

Подпись: jrqUdx

0

qnjX,

T (2.3)

The carrier lifetime r is a critical parameter in designing a p-i-n diode. The relationship of n/ to applied voltage is complicated, and the final I-Vrelationship is given here without proof 9-11

Jf

2 kTJ

*qnPaFL

exp

P-i-n DIODE

(2.4)

 

The parameter FL is a further function of xj and r, and it has a value between 0.01 and 0.3. Da is called the ambipolar diffusion coefficient and is given by

D =

Подпись: D =n! + Pj

D + D

P «

2D D ~ p ”

~ D +D

P " (2.5)

The forward current is shown in Fig. 2.3. The ideality factor of 2 is a characteristic of recombination current.

A similar equation can be obtained from standard recombination/generation consideration which can provide some physical insight. The recombination current within a depletion region is given by

qh

2kT.

qxIni

J = ———- exp

re 2r

P-i-n DIODE

(2.6)

 

(see Appendix B2). Assuming that x} is comparable to the ambipolar diffusion length,

D

Подпись: D(2.7)

‘*V’

j

.2 kTj

Substitution of r into Eq. (2.6) gives

qn D

^ i a

-exp

2x,

P-i-n DIODE

(2.8)

 

This result is similar to Eq. (2.4).

It should be noted that since the p-i-n diode is similar to a p-n junction diode, the diffusion current component should also be considered. In practice, this component is small since both regions surrounding the intrinsic layers are heavily doped. High Na and ND result in small diffusion current, due to the relationship

f Tt 1 7

 

exp

— 1

 

J

_

^ kT,

_

 

 

D

 

D

 

J = qn

 

(2.9)

 

L N

 

The most interesting phenomenon for a p-i-n diode, however, is for small signals at high frequencies (> l/(2wr)) at which the stored carriers within the intrinsic layer are not completely swept by the RF signal or by recombination. At these frequencies there is no rectification or distortion and the p-i-n diode behaves like a pure resistor whose value is solely determined by the superimposed DC bias or current. This dynamic RF resistance is simply given by

Rrf Pa

^ni^n + Hp)A

(2.10)

Подпись: (2.10)Jfr^„ + Hp)A

Here Eq. (2.3) has been assumed for Jj. The RF resistance is controlled by the DC current. Typical characteristics are shown in Fig. 2.4.

For modulation and switching applications, even the mean bias point can vary with time. The upper limit of this modulation frequency is determined by the reverse recovery characteristics. When a p-i-n diode is switched from forward bias to reverse bias abruptly, the stored charges continue to contribute to a large reverse current until they are fully drained away (Fig. 2.5). The reverse current is determined by the series resistance Rs (Ir = I,/r/Rs), and the delay time td is given by

( JA

(2.11)

Подпись: (2.11)t. = r In 1 + — d I

The transition time tlr is a complicated function of the doping profile and diode geometry. This reverse recovery time is the sum of td and tlr and it puts an upper limit on the rate at which the quiescent bias point can be switched.

APPLICATIONS

1. RF switching: The RF resistance of a p-i-n diode is controlled by the quiescent bias. This feature makes it practical as a circuit, shown in Fig. 2.6, called a series switch. When the diode is forward biased it is considered a short. At zero or reverse bias, it is considered a capacitor or an open circuit.

2. Attenuation and modulation: Because the RF resistance is a continuous function of quiescent bias, it can be varied to attenuate and modulate the RF signal. The modulation frequency is limited by the reverse recovery given in Eq. (2.11). RF switching is an extreme case of attenuation and modulation.

3. Phase shifting: Phase shifting of an RF signal can be achieved by using transmission lines of different lengths. The p-i-n diodes can be used as switches for selecting these transmission lines.

4. Limiter: As mentioned before, at RF frequencies, a p-i-n diode behaves like a pure resistor. However, this is valid only when the RF signal is below a critical level. Above this level, the RF resistance drops, similar to that of the DC resistance. This property enables it to be used for protection of radar receivers, when it is connected in parallel, against excessive transmitter power.

5. Power rectifier: Due to the thick intrinsic layer, a p-i-n diode has a high breakdown voltage and can be used as high power rectifier.

6. Photodetector: For a photodetector, a wide region with a built-in field is advantageous such that light can be completely absorbed within this region. A p-i-n structure is used as a nuclear-radiation detector and is one of the most common photodetectors (see Chapter 50).

RELATED DEVICES

Zener Diode

A Zener diode has a well-controlled breakdown voltage, called Zener voltage, and sharp breakdown characteristics in the reverse bias regime. In spite of the name, the breakdown can be due to either impact ionization or Zener tunneling. Zener breakdown is caused by quantum-mechanical tunneling of carriers between the conduction band and the valence band (see Appendix B7-Tunneling). It occurs in junctions with higher doping concentrations and the critical field required is approximately 1 MV/cm. A Zener diode is usually used to establish a fixed reference voltage.

Step-Recovery Diode

The step-recovery diode is sometimes called a fast-recovery diode, a snap-off diode, or snap-back diode. The response of a standard p-n junction is limited by the minority-carrier storage, with the reverse recovery represented by Fig. 1.5. A step-recovery diode has a special doping profile such that the field confines the injected carriers much closer to the vicinity of the junction. This results in a much shorter transition time tlr (but with the same delay time tj). The sharp turn-off of current approaches a square waveform which contains rich harmonics, and is often used in applications of harmonic generation and pulse shaping.

Anisotype Heterojunction

An anisotype heterojunction is a junction not only of opposite types, but also of different semiconductor materials. The structure requires good lattice match between the two materials, and Ge-GaAs can be used as an example.8 The distinct features are the discontinuity in the conduction band AEC and the valence band AEy as shown in Fig. 1.8. These values can be determined graphically to be

AЈc = q(z{ ~X2) O-19)

AEV= (Eg2-Eg{)-AEC. (1.20)

The static characteristic described by Eqs. (1.1)-(1.7) have to be modified by the two dielectric constants Ki and K2 in the two materials. Specifically,

RELATED DEVICES

(a) (b)

FIGURE 1.8

(a) Energy-band diagram of two isolated different semiconductor materials with opposite types, (b) Example of an anisotype heterojunction between «-type Ge and />-type GaAs. (After Ref. 8)

= K2S2 has to be satisfied at the interface. The potential variation across the «-type and p-type materials are given by

k2na

Vt ^^D +

kxnd

YT knd + K2Na (1.21)

According to Fig. 1.8(b), equilibrium is the difference between the two work functions, q<f>sl-q<l>sy

The current conduction, however, can be either diffusion limited or thermionic-emission limited. In the example shown in Fig. 1.8, the barrier for holes is similar to a standard p-n junction, and hole transport from GaAs to Ge is diffusion limited. Under forward bias, this component is similar to a homojunction

(iVt

qn, D

• r,

J =

p

exp

L Nn

P D

RELATED DEVICES

(1.22)

 

The barrier for electrons is increased by AEc and the current is greatly reduced. Unlike a homostructure p-n junction in which current is dominated by diffusion current in the lightly doped side, an anisotype heterojunction usually favors injection of carriers from the material of larger energy gap. Other current

components are due to tunneling and recombination arising from a non-ideal interface. The suppression of one type of carriers improves the injection efficiency, which makes it beneficial for the emitter-base junction of a bipolar transistor.9 Other applications include photodetectors in which a local absorption coefficient can be optimized.

Varactor

The word varactor comes from variable reactor. A varactor, also called a varactor diode or varicap (variable capacitance) diode, is in principle any two-terminal device whose capacitance varies with the DC bias. In practice, a p-n junction is the most common structure. A Schottky-barrier diode can also perform the same function, and is used especially in ultra-high-speed operations.

When a p-n junction is under a reverse bias, the depletion layer widens, and its capacitance changes according to Eq. (1.17). Forward bias is to be avoided from excessive current which is undesirable for any capacitor. The dependence of capacitance on the DC reverse bias is determined by the doping profile near the junction. It can be described by the form

C = C, (Ybi+vr)~S • (1.23)

For a one-sided junction, if the profile of the lighter doping is approximated by

N(x) = C2xm, (1.24)

it can be shown that6

1

(1.25)

m + 2

For a one-sided step profile, m = 0 and s = 1/2. For a linearly graded junction, m = 1 and s = 1/3. If m < 0, the junction is said to be hyper-abrupt. Specific cases of interest are m = -1, -3/2, -5/3 and s = 1, 2, 3, respectively.

The applications of a varactor are in filters, oscillators, tuning circuits of radio and TV receivers, parametric amplifiers, and automatic frequency control circuits.