ON THE LUX–VOLTAGE CHARACTERISTIC OF CAPACITOR PHOTO-EMF IN THE Si—SiO₂ SYSTEM

S. A. ZAIDMAN, N. K. KURYNDINA, D. I. SVIRYAKIN

(Presented by the scientific seminar of the Scientific Research Institute of Electrical Measurements)

One of the possible uses of the capacitor photo-EMF method in the study of surface characteristics is the determination of the surface potential from the saturation of lux–voltage characteristics [1, 2, 3]. At the same time, the absence of current contacts, which are necessary in surface studies by the field-effect method, the absence of a metallic electrode on the dielectric surface, which is necessary in the method of \(C\)—\(V\) characteristics, and the possibility of using samples with a wide range of variation of resistivity testify to the prospects of the method in studying the surface of semiconductors in a semiconductor—dielectric system.

The aim of the present work was to evaluate the effectiveness of the method for determining the surface potential \(Y_{s0}\) from the saturation of lux–voltage characteristics in the study of the semiconductor—dielectric system Si—SiO₂, where the SiO₂ film was obtained by thermal oxidation in a dry—wet—dry oxygen cycle.

For this system we observed saturation of the lux–voltage characteristic of the capacitor photo-EMF \(\Delta V_{\phi}\), which made it possible to determine \(Y_{s0}\). In addition, by determining \(Y_{s0}\) by the field-effect method, we were able to compare the results obtained.

The injection level

\[ \left(\delta = \frac{\delta_p}{n_i}\right) \]

was determined from measurement of the photoconductivity; moreover, we could disregard the variation \(\delta = (Y_{s0})\), since under the conditions of our experiment the photoconductivity changed only very weakly as a function of \(Y_{s0}\), whereas appreciable changes in the magnitude of the photo-EMF require significant changes in \(\delta\) (Fig. 1, \(a\)).

Experimental studies of \(\Delta V_{\phi}\) were carried out over a wide range of values of \(\delta\). For comparison with experiment, calculated dependences \(\Delta V_{\phi} = \Delta V_{\phi}(\delta)\) were obtained. They were found by graphical solution of the equation:

\[ 2 q n_i L_i F(y, \lambda, \delta) + q N_d (1 - f_i) - q N_{a i} f_i = \]

\[ = 2 q n_i L_i F_0 (Y_0, \lambda) + q N_d (1 - f_{i0}) - q N_{a i} f_{i0}, \tag{1} \]

which is obtained from the condition of constancy of the total surface charge. In equation (1) the notation of [1] is used. The lux–voltage characteristics calculated by this method for \(Y_{s0} = 22 \dfrac{kT}{q}\), in the case of absence and in the presence of surface states, are shown in Fig. 2. As can be seen from the figure, in the absence of surface states—

Fig. 1. Dependence of the capacitor photo-EMF on the surface potential:
a — calculated dependences for various \(\delta\) without taking into account the trapping of nonequilibrium carriers by surface states (for \(\lambda=\dfrac{p_0}{n_i}=10^3\));
b — experimental dependences for \(\delta_1>\delta_2\).

Fig. 2. Calculated dependences of the capacitor photo-EMF on the injection level \(\delta\) for \(Y_{s0}=22\,kT/q\):
\(1\) — \(N_t=0\);
\(2\) — \(N_t=10^{12}\ \text{states}/\text{cm}^2,\ c_p/c_n=10^{-7},\ v=+4\,kT\);
\(3\) — \(N_t=10^{12}\ \text{states}/\text{cm}^2,\ c_p/c_n=10^3,\ v=4\,kT\).

some tendency toward saturation is observed at very high injection levels \((\delta > 3 \cdot 10^6)\), and the limiting value of \(\Delta U_\phi\) is equal to the value of the equilibrium surface potential. Capture of nonequilibrium charge carriers by surface states leads to a reduced value of \(\Delta U_\phi\) and to an increase in the injection level at which saturation of \(\Delta U_\phi\) is reached.

In an experimental study of the Si—SiO\(_2\) system by the field-effect method, the equilibrium surface potential \(U_{s0}\) was determined; for various samples its values varied within the range

\[ 19—22 \frac{kT}{q}. \]

Figure 3 gives experimental lux-voltage characteristics at different surface potentials corresponding to inversion and accumulation. It is seen from the figure that the values of the surface potential determined from saturation of the experimental curves are considerably lower than its values obtained from the field effect. Thus, for the case of the equilibrium potential \(U_{s0} = 22 \frac{kT}{q}\), saturation corresponds to the value \(8 \frac{kT}{q}\) (for other samples it did not exceed \(11 \frac{kT}{q}\)).

In [4], in studying the dependence of the capacitor photo-emf on the surface potential at various injection levels, it was established that in the formation of the photo-emf signal there is an excess positive signal of diffusion type. This signal begins to prevail in the region of potentials \(U_{s0} < 18 \frac{kT}{q}\) (Fig. 1, b), and in this same range of potentials a more sharply expressed saturation of the lux-voltage characteristics is observed, including the accumulation region (Fig. 3). Comparison of the experimental dependence with the calculated one (Fig. 2) makes it possible to conclude that the substantial underestimation of \(\Delta U_\phi\) is caused by the contribution of the positive excess signal and by the presence of capture of nonequilibrium carriers into surface states.

Fig. 3. Experimental lux-voltage dependences at different \(U_{s0}\). The values of \(U_{s0}\) obtained from the field effect are indicated.

On the basis of the foregoing it may be said that, apparently, the method of determining the surface potential from saturation of the lux-voltage characteristic of the capacitor photo-emf is not a sufficiently reliable and universal method, since capture of nonequilibrium

charge carriers to surface states and the contribution of the excess photo-EMF exert a very substantial influence on the form of this characteristic.

REFERENCES

1. E. O. Jonson. Phys. Rev. 111, 153, 1958.
2. I. Flinn. Surface Science 10, 32, 1968.
3. Y. W. Lam, I. Phus. D. Appl. Phys. 4, 1370, 1971.
4. S. A. Zaidman, N. K. Kuryndina, D. I. Sviryakin. Some features of the dependence of the capacitor photo-EMF on the electric field in the Si—SiO₂ system. (This collection).