1. Introduction

Thermistors are widely used in various industrial and domestic applications, such as, the suppression of in-rush current, temperature measurements and controls, compensation and other circuit elements^{[1, 2, 3, 4]}. During the last decade, with the continuous expansion of thermistors in various applications, the requirement for the accuracy of temperature measurements, sensing, and control have also been increasing, which requires the development of higher thermal-sensitivity thermistors. The experimental results suggest that single-crystal silicon material doped by transition metal elements has a negative temperature coefficient thermal-sensitive characteristic. Doped silicon material can always produce high material sensitivity coefficient ($B$-value) and low electrical resistivity by selecting appropriate deep level impurities. Research on transition metal doped silicon has been previously reported^{[5, 6, 7, 8, 9, 10]}. The energy level structure of impurities directly affects the $B$-value; therefore, the choice of appropriate impurities has a decisive influence on the performance of silicon material. The material's electrical resistivity is lower than that of oxide ceramic thermally-sensitive material for the same $B$-value. By selecting appropriate deep level impurities, it is possible to make a kind of NTC silicon material that has a high $B$-value and low electrical resistivity.

Copper is a common tarnish of single-crystal silicon material^[11], so it is necessary to study the effect of the copper doping on material properties. In this work, the preparations of n-type single-crystal silicon doped by copper have been studied using a high temperature diffusion method. The electrical and sensitivity characteristic of silicon material doped by copper at various diffusion conditions have also been studied.

2. Experimental details

The initial materials for this work were 10 $\Omega \cdot$cm, 350 $\mu$m thick n-type silicon wafers. They were diced into squares of 1~$\times$ 1 cm$^2$ for further use. These silicon wafers were cleaned with organic solvents in an ultrasonic cleaner. Followed by an ammonia/peroxide mixture (APM) cleaning for 15 min at 75 $\pm$ 5 C in a glass container on a hot plate.

For copper diffusion, a CuCl$_{2}$$\cdot$2H$_{2}$O ethanol solution was deposited on the sample surface. After the solution was dried using infrared light, the samples were put into a high temperature furnace at a certain temperature for an appropriate time, which allowed the copper impurities to pass into the silicon. Thereafter, the sample was subjected to the physical grinding to remove the copper residual and oxide from the surface by remove the near-surface layer several tens micrometers in thickness. After being nickel-plated, diced, electrodes welded, and packaged, the silicon wafers were used as a prepared thermistor. The electrical resistance of the materials was measured in an oil bath by an Agilent 34970 digital multimeter.

3. Results and discussion

3.1 Effect of diffusion temperature on material properties

The materials are diffused at 800, 900, 1000, 1100, 1200~C for 2 h with the surface concentration of the copper atoms being 1.10 $\times$ 10$^{-4}$ mol/cm$^{2}$. As Figure 1 shows, when the diffusion temperature is lower than 1100 C, the changes of sample resistivity is limited. However, when the diffusion temperature is beyond 1200 C, the resistivity of sample is found to rise steeply. Copper can form precipitates with electrical activity in silicon when the diffusion temperature is above 800~C, which can then affect the macro resistivity of silicon material^[12]. The copper atoms' diffusion into the silicon material can produce a trapped energy level in the band gap. The trap levels can capture electrons in the n-type silicon material, which play a compensating effect on the material. So the resistivity of the sample rises with the diffusion of the copper. As the diffusion temperature increases, the concentration of the copper atoms diffuse into the silicon increases, and the change of the silicon resistivity becomes more apparent, which is consistent with the experimental results.

3.2 Effect of surface concentration of copper atoms on material properties

Figure 2 shows the effect of silicon resistivity and the $B$-value on the surface concentration of copper atoms. The resistivity and $B$-value of the silicon decreases with an increase of the surface concentration. It is evident that a high concentration of copper is able to much more easily cause a solid phase reaction with silicon on the surface to form a copper-rich silicide layer^{[13, 14]}, as shown in Figure 3. The layer of silicide plays an important role in preventing the further inward diffusion of copper atoms^[17]. Although the surface concentration of the copper atoms increases, the concentration of copper atoms diffused into the silicon is becoming low. So the resistivity and $B$-value of the silicon decreases with an increase of the surface concentration. Since the formation of silicide, the concentration of copper atoms diffuse into the copper can not be calculated using the diffusion method, so Figure 2 only shows the surface concentration of the copper atoms. Future experiments should avoid excessive concentration of copper. If they really need a larger concentration of copper, then they should consider using an ion implantation method.

3.3 Effect of diffusion time on material properties

Figure 4 shows relationship of the silicon resistivity and diffusion time. As diffusion time increases, the resistivity of copper doped silicon first increases and it then decreases. The resistivity of the sample is found to have a maximum (46.2~$\Omega$$\cdot$cm) when the sample is treated at 1200 C for 2~h while the surface density of the copper stays at 1.83 $\times$ 10$^{-7}$ mol/cm$^{2}$. It is believed that the compensation of the copper might play a contribution to the change. At the beginning of the experiment, the compensation of the copper increases as the diffusion time increases, so the resistivity increases. As the diffusion time further increases, the diffusion source is wiped out. The copper that is diffused into the silicon constantly separates out, which leads to a decrease of the resistivity.

3.4 NTC thermistor characteristic

Figure 5 shows the copper-doped silicon resistance-temperature curve. It can be seen that copper doped n-type silicon material has a negative temperature-sensitive characteristic, and the $B$-value is about 4000 K. Figure 6 shows the relationship between ln$R$ and the reciprocal of the absolute temperature. It reveals the linear dependence of temperature and ln$R$ over a wide temperature range.

The energy band configuration of the copper doped silicon is shown in Figure 7^{[16, 17]}. The top-level band $E_{\rm C}$ is the conduction band energy level, the Fermi level band is between the center line $E_{\rm i}$ and the conduction band $E_{\rm c}$, and the lowest band $E_{\rm V}$ is the valence band energy level. The copper atoms introduce two acceptor levels of $E_{\rm c}$ - 0.16 eV and $E_{\rm v}$ $+$ 0.45~eV in n-type single crystal silicon, which is marked as $E_{\rm Cu1}$(AA) and $E_{\rm Cu2}$(AA) in Figure 7. $E_{\rm Cu}$(D) is donor level of $E_{\rm v}$ $+$ 0.23~eV. In n-type silicon material, the material sensitivity coefficient ($B$-value) is^{[18, 19]}:

$B=\left(\Delta E-\frac{3}{2}kT \ln T\right)/k,$

(1)

where $\Delta E$ is interval of acceptor level above the valence band edge or that below the conduction band edge. The Boltzmann constant is $k$ $=$ 8.66 $\times$ 10$^{-5}$ eV/K.

Since copper doped silicon is an n-type silicon, the $B$-value is decided by acceptor level ($E_{\rm Cu1}$(AA) and $E_{\rm Cu2}$(AA)). According to Equation (1), the theoretical $B$-value should be between 5196 and 1848 K. Because the impact of silicide the concentration of copper in the silicon cannot reach the design value, the experimental $B$-value is 3010-4130 K. The range of experimental values is less then the theoretical results. Consequently, we can use the samples prepared by ion implantation to verify the theoretical value.

4. Conclusions

In summary, the copper doped n-type single-crystal silicon materials have been acquired using the high temperature diffusion method. The electrical properties have been investigated in detail. The copper doped samples' resistivity decreases as the surface concentration of the copper increases. The resistivity of the sample shows a maximum value of 46.2 $\Omega\cdot$cm when the doping process is carried out at 1200 C for 2 h, with the surface density of the copper dopant source being 1.83 $\times$ 10$^{-7}$~mol/cm$^{2}$. The silicon has a negative temperature sensitive characteristic and the $B$ value is 3010-4130 K. The $B$-value calculated by the theory of the semiconductor deep level energy is consistent with the experimental $B$-value.