The problem associated with the conventional resistance-type oxygen sensors using oxide semiconductors was that the resistance of oxide semiconductor that is a gas detection unit shows strong dependence not only on the oxygen partial pressure, but also on temperature, which resulted in a very strong dependence of the sensor output on temperature. 
The following four measures are known for realizing an oxygen-insensitive characteristic of the resistance, that is, a resistance characteristic that does not depend on oxygen partial pressure and is necessary for a temperature compensation unit of the sensor.  Those measures are listed hereinbelow. 
The first one was reported by M. J. Esper et al. ( SAE Technical paper, 1979), 790140) who used a high-density titanium oxide as a temperature compensation unit insensitive to oxygen gas.  In this case the problem is that the resistance is insensitive to oxygen within a short interval, but shows the dependence on oxygen partial pressure in a long interval. 
Secondly, a gas sensor was reported (European Patent Applications Nos.  0464243 and 0464244) in which part of the gas detection unit was covered with a gas-impermeable layer, thereby making the temperature compensation unit insensitive to oxygen gas.  In this case the problem is that hair cracking occurs in the gas-impermeable layer covering part of the gas detection unit under the effect of degradation with time of thermal shocks, and gas permeates through the layer. 
Thirdly, a method was described (German Patents No.  4210397 and 4210398) by which a gas-insensitive unit was obtained by doping metal atoms, for example, gold to the degree ensuring the loss of gas dependence.  The drawback of this method is that the unit doped with metal atoms lacks stability. 
Fourthly, in the initial report a mixture of p-type and n-type oxygen semiconductors was used as the temperature compensation unit (Japanese Patent Application Laid-open No.  H6-222026) and a system was used in which thin films of p-type and n-type oxide semiconductors were used (Japanese Tokuhyo No.  H10-505164).  However, the problem associated with such temperature compensation units was that the p-type and n-type oxide semiconductors reacted in the operation temperature range of the sensor and long-term stability could not be obtained and that cracks appeared due to the difference in a thermal expansion coefficient between those materials. 
Furthermore, when p-type and n-type oxide semiconductors are stacked in the gas-insensitive unit, the thin film formation conditions have to be accurately controlled to stack the films with good matching.  On the other hand, when a mixture of p-type and n-type oxide semiconductors was produced, the problem was that the mixing process had to be controlled so as to obtain the desirable dispersion of the two oxide semiconductors.  As a result, the process for producing the gas-insensitive unit was complex. 
Furthermore, none of the aforementioned documents indicated that the temperature compensation unit does not depend on the oxygen partial pressure, or when such as indication was provided, the range of oxygen partial pressure was of two orders of magnitude.  Within the framework of the above-described conventional technology, it is possible to suppose that in principle the range in which the resistance of the temperature compensation unit does not depend on oxygen partial pressure is small.  More specially, in p-type semiconductors, the resistance, r, is proportional to −1/n power of oxygen partial pressure P, and in n-type semiconductors, r is proportional to 1/n power of P. Here, n is from 4 to 6.  If an equivalent circuit is considered, then in the case of a parallel circuit, the changes have to be as shown in FIG.  1, and in the case of a serial circuit, the changes have to be as shown in FIG.  2.  Therefore, yet another problem is that if the range without dependence on oxygen partial pressure is small and the oxygen partial pressure shifts from this range, then the dependence of sensor output on oxygen partial pressure becomes extremely small.  Furthermore, none of the aforementioned documents indicates that the output of the oxygen sensor does not depend on temperature or that temperature dependence is small. 
On the other hand, for example solid-electrolyte sensors have been mainly used as oxygen sensors for automobiles (Japanese Patent Application Laid-open No.  S55-137334).  In the sensors of this type, the difference in oxygen partial pressure between a standard electrode and measurement electrode was measured as an electromotive force and it was necessary to use the standard electrode.  The resultant problem was that the structure was complex and difficult to miniaturize.  In order to resolve this problem, for example, a resistance-type oxygen sensor, which required no standard electrode, was disclosed (Japanese Patent Application Laid-open No.  S62-174644).  Explaining the measurement principle of the resistance-type oxygen sensor, first, the concentration of oxygen vacancies in an oxide semiconductor changes when the oxygen partial pressure of the atmosphere changes.  There is a one-to-one correspondence between the resistivity or electron conductivity of oxide semiconductors and the concentration of oxygen vacancies, and the resistivity of the oxide semiconductor changes with changes in the concentration of oxygen vacancies.  The oxygen partial pressure of the atmosphere can be determined by measuring the resistivity. 
The problem associated with the resistance-type oxygen sensor was that the output had poor response when the oxygen partial pressure changed (Japanese Patent Application Laid-open No.  H07-63719).  Another problem was that titanium oxide was used as the oxide semiconductor of the resistance-type oxygen sensor, but this material had poor endurance and stability.  In order to resolve the above-described problems, the inventors have conducted research and development of a resistance-type oxygen sensor using cerium oxide as the oxide semiconductor.  Cerium oxide is known to have good endurance in corrosive gas atmosphere (E. B. Varhegyi et al.,  Sensors and Actuator, B, 18–19 (1994) 569).  The response characteristic was improved by reducing the particle size of cerium oxide to 200 nm in the resistance-type oxygen sensor using cerium oxide (Japanese Patent Application No.  2002-240360). 
However, even in this sensor, the response rate was not sufficiently high and had to be further improved.  Other problems were that in this sensor, the electric conductivity of cerium oxide serving as the oxide semiconductor was low, that is, the resistivity was high and the dependence of electric conductivity (output) on the oxygen partial pressure decreased with the decrease in the operation temperature of the sensor.  Those problems also had to be resolved. 
Further, a sensor was also reported which used an oxide containing cerium ions and zirconium ions at a ratio of the amount of zirconium ions to the total amount of cerium ions and zirconium ions (referred to hereinbelow as “zirconium ion concentration”) of 80 mol % or higher (Guo-Long Tan et al.  Thin Solid Films 330 (1998) 59–61).  However, the detection principle of those sensors was based on using an oxygen concentration increase/decrease cell which measures the difference between the oxygen partial pressure of the reference electrode and measurement electrode as an electromotive force.