Text-chap9

_______________________________________________9 PTC MATERIALS

9.1 MECHANISM OF PTC PHENOMENON (1)

PTC Phenomenon

When barium titanate (BaTiO3) is doped with lanthanum at levels less than 0.3 atm%, the ceramic becomes semiconducting with a resistivity in the range of 10 103 Ω .cm. Moreover, the resistivity is drastically increased, by 3 - 5 orders of magnitude, with increasing temperature around the Curie point. This phenomenon was discovered in 1954, and is referred to as the PTC or PTCR (positive temperature coefficient of resistivity) effect. Since then it has been investigated intensively by many researchers.1,2) Figure 9.1 shows the impact of various dopants on the resistivity of the BaTiO 3 PTC ceramic as a function of temperature.

Fig. 9.1 Resistivity as a function of temperature for several doped BaTiO 3 PTCR ceramics. Dopant concentrations are indicated near each curve. 243

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Chapter 9

Fig. 9.2 Resistivity vs. temperature curves for BaTiO3 PTCR thermistors containing isovalent substitution of Sr or Pb for Ba.

The PTC dopants typically have a higher ionic valence than either the Ba (replaced by ions such as La, Sm, Ce or Gd) or the Ti (replaced by ions such as Nb, Ta, Bi) of the host structure. Since the temperature at which the resistivity anomaly occurs is closely related with the Curie point, the temperature coefficient can be easily modified by forming an appropriate solid solution with BaTiO3. Figure 9.2 shows various PTCR curves for two such solid solution series. The solid line represents BaTiO 3 and the dashed lines show the effect of Sr (resistivity curve shifted to left) and Pb (resistivity curve shifted to right) substitution in the proportions indicated. (2)

Mechanism of the PTC Phenomenon

The theory for the PTC effect has not been established completely. Let us consider the effect in terms of two mechanisms: the semiconducting properties of the doped barium titanate and the grain boundary barrier effect. When sintered at high temperature, lanthanum-doped BaTiO 3 is expected to become an n-type semiconductor through the following reaction:3) Ba1-xLa xTiO3 ---> Ba 2+ 1-x La 3+ xTi4+ 1-xTi3+ xO 2- 3.

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The conduction takes place via transfer of electrons between titanium ions according to Ti4+ + e - ↔ Ti3+ Thus, the BaTiO 3 grains in the ceramic are semiconducting and remain semiconducting even on cooling down to room temperature. However, the grain boundary region changes during cooling. Oxygen is absorbed on the surface of the ceramic and diffuses to grain boundary sites, altering the defect structure along the grain boundaries. The added oxygen ions attract electrons from nearby Ti3+ ions, thereby creating an insulating barrier between grains. If excess oxygen ions are added per formula unit, the composition of the grain boundary region can be described as follows: (Ba 2+ 1-xLa 3+ x)(Ti4+ 1-x+2y Ti3+ x-2y )O 2- 3+y . This situation is illustrated in Fig. 9.3.

Fig. 9.3 Schematic illustration of the Ba 1-xLa xTiO 3 structure near the surface of a grain boundary. Atmospheric oxygen dissociates and diffuses along a grain boundary where the atoms attract electrons and form insulating layers.3)

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Chapter 9

-

-

-

+

-eφ + +

+

+

+

Conduction band - - -

L Ns Grain boundary

Fermi level

Fig. 9.4 Energy-level diagram near a grain boundary of the PTCR BaTiO 3. In order to explain the PTC or PTCR phenomenon, the most acceptable model is illustrated in Fig. 9.4, which was initially proposed by Heywang at al.1) When the two semiconductive (n-type) ceramic particles are in contact at a grain boundary, an electron energy barrier (Schottky barrier) is generated and the barrier height is given by the following equation: φ = eNs 2/2ε0 εNd ,

(9.1)

where Nd is the concentration of donor atoms and Ns is the surface density of negatively charged acceptors (here assumed to be confined to the surface due to Ba vacancies). Note that the permittivity ε obeys the Curie-Weiss law ε = C / (T – T0 ) ,

(9.2)

above TC, and that the low resistance at TC is thus accounted for by the lowering of the potential barrier due to the increase in permittivity as the temperature falls to TC. Below TC the permittivity falls, but the spontaneous polarization appears and controls the electron concentration to reduce the barrier height. This keeps the resistivity in a rather low range. Example Problem 9.1_________________________________________________ Electronic properties in ceramics are strongly affected by the surface layer or by the grain boundary. Suppose that a grain boundary between n-type semiconductive grains possesses acceptor impurities, and that electrons flow into the acceptor levels and an energy barrier is generated as shown in Fig. 9.4. Using the simple charge distribution model represented in Fig. 9.5: ρ(x) = eND (0 < |x| < L) ; ρ(x) = 0 (|x| > L) , answer the following questions:

(P9.1.1)

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ρ(x)

Charge density +

+

+

+

+

+

-L

-

eNd

+

+

+

+

+

+ L

x

Ns

Fig. 9.5 Charge density distribution near the grain boundary between n-type semiconductive grains. (a) Describe the potential φ(x) by using the donor density ND, the barrier thickness L, the permittivity ε0 ε and electronic charge e. Suppose that the change in φ occurs within a region 0 < |x| < L. (b) Describe the barrier thickness L generated by the donor density ND and the surface acceptor density Ns . (c) In semiconductive BaTiO3, the permittivity is decreased significantly above the Curie temperature (= 130o C). Explain the resistivity change by considering the barrier height - e φ0 . Solution (a) Poisson's equation is given by ∂2 φ/ ∂x2 = - eN D/ ε0ε .

(0 < |x| < L)

(P9.1.2)

Taking into account the boundary conditions: φ(L) = φ(- L) = φ(∞) , - φ'(L) = E = 0

(P9.1.3)

with a general solution φ(x) = - (eND/ 2ε0ε) x2 + A x + B, we obtain the particular solution: φ(x) = φ(∞) - (eND/ 2ε0 ε) (|x| - L)2 .

(P9.1.4)

The potential depth at x = 0 is thus obtained as φ0 = - (eND/ 2ε0 ε) L2 .

(P9.1.5)

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(b) Considering charge neutralization, we obtain 2 eND L = eNs .

(P9.1.6)

L = Ns / 2ND .

(P9.1.7)

Then,

(c) The energy barrier height - e φ0 is represented as - e φ0 = e2 N D L2/ 2ε0 ε = e2 Ns 2/ 8ε0 ε N D . Considering the Curie-Wess law; ε = C/ (T - T 0),

(P9.1.8)

(P9.1.9)

we obtain - e φ0 = (e 2 Ns 2/ 8ε0 C ND )(T - T0 ).

(P9.1.10)

The barrier height increases in proportion to temperature. Since the resistivity is proportional to exp(- e φ0 / kT), it increases drastically with temperature (∝ exp(1 T0 / T)) for T > T C. When we consider the situation below TC, the permittivity falls, but the spontaneous polarization appears and controls the electron concentration to reduce the barrier height. This keeps the res istivity in a rather low range. For a temperature region much higher than TC, the resistivity falls because of the very high thermal energy (kT) of electrons which tunnel through the energy barrier. ___________________________________________________________________

9.2 PTC THERMISTORS PTC thermistors are applicable not only for temperature-change detection but also for active current controllers. The thermistor, when self-heated, exhibits a decrease in the current owing to a large increase in resistivity. Practical applications for these devices are found in over-current/voltage protectors, starting switches for motors, and automatic demagnetization circuits for color TVs.4) "Ceramic heaters" have also been widely commercialized in panel heaters, electronic thermos bottles and hair dryers. Figure 9.6 shows a PTC honeycomb air heater for hair dryers and automotive chokes manufactured by NGK.

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Fig. 9.6 PTC honeycomb air heater for a hair dryer (photo courtesy of NGK).

Example Problem 9.2_________________________________________________ The resistivity vs. temperature characteristic of a barium titanate PTC ceramic is shown in Fig. 9.7. Taking into account heat generation through Joule heating, discuss the current vs. voltage relationship under a room-temperature ambient condition qualitatively.

Fig. 9.7 ceramic.

Resistivity vs. temperature characteristic of a barium titanate PTC

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Chapter 9

Fig. 9.8 Current vs. voltage relationship for a barium titanate PTC ceramic.

Solution At the initial stage, the current-voltage relation obeys Ohm's law (that is, ρ is almost constant), and power is dissipated via the Joule heating (V2/R). Around the point A (where a dramatic ni crease in ρ is observed), the current becomes maximized, beyond which it decreases with increasing applied voltage (see Fig. 9.8). Between the points B and C, the temperature of the device is almost stabilized, leading to the relation V x I = constant. Much above the point C, a dramatic increase in current is anticipated, because the saturation of the resistivity and the subsequent NTC (negative temperature coefficient) effect occur in this temperature range. Thus, to realize a stable temperature in the PTC thermistor, the applied voltage must be adjusted between B and C. ___________________________________________________________________

9.3 GRAIN BOUNDARY LAYER CAPACITORS When a semiconductive BaTiO3 ceramic is oxidized to make a resistive surface layer, it can be used as a high capacitance condenser. The capacitance is adjustable in the range of 0.4 - 0.5 µF/cm2 . A new type of grain boundary layer (GBL) capacitor has been developed using electrically resistive grain boundaries. The model for this structure is illustrated in Fig. 9.9. In practice, CeO2 or Bi2 O3 is coated on a semiconductive ceramic and diffused into the grain boundaries by thermal treatment so as to make the boundary layer highly resistive. The resistive grain boundary layers of 1 µm thickness are fully connected in the ceramic with grain size of 10 µm. This type of capacitor exhibits excellent frequency characteristics and can be used as a wide bandpass capacitor up to several GHz.

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Fig. 9.9 Model of the grain boundary layer capacitor.

Example Problem 9.3_________________________________________________ When a GBL capacitor is composed of many cubic core -shell units of a grain size D with a resistive skin of dielectric constant εs (δ: skin thickness, half of the grain boundary thickness), calculate the apparent dielectric constant εapp of this composite material. Assume the sample has an electrode area S and an electrode gap d, and zero resistivity inside the grains. Solution As shown in Fig. 9.10, let us divide the sample into two regions: C 1 and C2. (a) C1: Since the area and the thickness are provided by [S - (D - 2δ) 2 (S/D2)] and d, respectively, C1 = ε0 εs (S/d) [1 - (1 - 2δ/D) 2] = ε0 εs (S/d) (4δ/D) .

(δ /D << 1)

(P9.3.1)

(b) C2 : Since this is a series connection (number d/D) of a capacitor with an area (D 2δ)2 (S/D2 ) and thickness 2δ, C2 = (D/d) ε0εs [S(1 - 2δ/D) 2]/2δ = ε0 εs (S/d) (D /2δ) . (δ /D << 1)

(P9.3.2)

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Area S δ d

C1 (Conductor included)

D

C2 (εs )

Fig. 9.10 Core-shell model of a GBL capacitor.

Ctotal = C1 + C 2 = ε0 εs (S/d) (D /2δ) .

(P9.3.3)

Thus the apparent dielectric constant is provided by εs (D /2δ). ___________________________________________________________________

CHAPTER ESSENTIALS_________________________________ 1.

When barium titanate (BaTiO3 ) is doped with lanthanum at levels less than 0.3 atm%, the ceramic becomes semiconducting with a resistivity in the range of 10 - 10 3 Ω .cm.

2.

PTC effect: the resistivity is drastically increased, by 3 - 5 orders of magnitude, with increasing temperature around the Curie point.

3.

Applications of PTC ceramics: (1) thermistors: over-current/voltage protectors, starting switches for motors, automatic demagnetization circuits for color TVs (2) "Ceramic heaters": panel heaters, electronic thermos bottles, hair dryers, automotive chokes

4.

GBL capacitors: capacitors made of semiconductive BaTiO3 ceramics with highly resistive grain boundaries. ___________________________________________________________________

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CHAPTER PROBLEMS 9.1

Explain the current vs. voltage relationship for ZnO varistors, and describe their applications in comparison with the PTC material.

9.2

Electric properties in ceramics are strongly dependent on the characteristics of surfaces and/or grain boundaries. Let us consider here an n-type semiconductor. When acceptor dopants are localized on a semiconductor surface, and their surface levels exist lower than the Fermi level of the semiconductor, the electrons in the semiconductor flow into the acceptor levels, making a potential barrier. The barrier height Vd (potential) can be expressed as Vd = eND L2/ 2ε0 ε, using the ionized donor density ND in the semiconductor, barrier thickness L, semiconductor permittivity ε0ε, and the electron unit charge e. Since the electron density is very small in this barrier, and the electron needs to be highly excited to overcome this barrier height, the crystal surface can be considered to be highly resistive. Answer the following questions: (a) The density of the surface acceptor levels NS is related with the donor density ND as 2eND L = eNS . Derive an expression of Vd in terms of ND and NS . (b) On the surface of an n-type semiconductor such as SnO2 and ZnO, negative oxygen charges (O- or O 2- ) are adsorbed, generating a potential barrier. When this surface is contacted with flammable gas, the amount of the adsorbed oxygen is decreased through oxidation reaction, leading to an decrease in electrical resistance. This phenomenon is an operating principle of a gas sensor. Supposing that the adsorbed oxygen is decreased by half due to a flammable gas, calculate the change in the potential barrier height. Also discuss the change in resistance due to the flammable gas with the donor density of the semiconductor, in consideration of the change in the electron density. (c) The energy band structure at the grain boundary can be considered in a similar fashion to the above; that is, an interface with surface levels caused by impurities. In a semiconductive barium titanate ceramic,

254

Chapter 9 the permittivity is decreased dramatically above the Curie temperature (around 120o C). Discuss the resistance change (i.e., PTCR effect) with temperature.

REFERENCES 1) 2) 3) 4)

W. Heywang: J. Amer. Ceram. Soc. 47, 484 (1964). E. Andrich: Electr. Appl. 26, 123 (1965-66). R. E. Newnham: "Structure-Property Relations in Electronic Ceramics," J. Materials Education, Vol.6-5. Murata Mfg. Comp. Catalog, "Misterious Stones."