Some Specific Features of the Dependence of Capacitor Photo-EMF on the Electric Field in the Si-SiO2 System
Abstract Generated abstract
This study examines how capacitor photo-emf in the Si-SiO2 system depends on surface potential and electric field, with attention to using the method to probe surface-state spectra without depositing a metal electrode directly on the oxide. The authors calculate photo-emf versus surface potential for p-type silicon under low injection, considering different densities, energy positions, and carrier capture cross sections of surface states, and compare these results with measurements at varying injection levels, illumination conditions, and temperature. The calculations indicate that curve shape and sign changes are highly sensitive to surface-state parameters, while experiments show features qualitatively consistent with electron capture by surface states but also reveal an excess positive signal not accounted for by existing photo-emf theory. The paper suggests that this unexplained component may be related to near-surface diffusion processes or effects at dielectric-metal contacts.
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ON SOME FEATURES OF THE DEPENDENCE OF CAPACITOR PHOTO-EMF ON THE ELECTRIC FIELD IN THE Si—SiO₂ SYSTEM
S. A. Zaidman, N. K. Kuryndina, D. I. Sviryakin
(Presented by the scientific seminar of the Research Institute of Electrical Insulation)
The capacitor photo-emf method is often used to determine both bulk parameters of semiconductors [1, 2] and surface characteristics [3, 4]. We were interested in the capabilities of the method in studying the energy spectrum and determining the density of surface states in a semiconductor—dielectric system under conditions of working with systems without depositing a metal electrode directly onto the dielectric film. This provided, in principle, the possibility of studying films of arbitrary thickness.
As the object of study we selected the Si—SiO₂ system, for which, owing to the low concentration of trapping centers, we could determine the surface potential \(Y_{so}\) by the field-effect method and for which modulation of the photo-emf signal by an external electric field was observed. The work used p-type Si with a resistivity of \(700\ \Omega\cdot\text{cm}\). Oxidation was carried out in a dry—wet—dry oxygen cycle at a temperature of \(1200^\circ\text{C}\), followed by etching of the film in an acid etchant. To measure the capacitor photo-emf and the field effect, the techniques described in [3, 5] were used. The sign of the photo-emf was determined under asymmetric pulsed modulation of the light by means of a calibration signal from a standard pulse generator. The signal was considered positive when holes moved toward the surface. The modulation frequency of the light flux ensured that a stationary value of the photo-emf was obtained.
To assess the capabilities of the method, we carried out calculations of the dependence of the capacitor photo-emf \(\Delta V_\phi\) on \(Y_{so}\) for the parameters of the Si—SiO₂ system used in the work. The calculations were performed under the assumption that the quasi-Fermi levels in the near-surface region of the space charge remain constant, both for the case of absence of surface states and taking into account the influence of surface states of one or several types. To calculate the dependences \(\Delta V_\phi = \Delta V_\phi(Y_{so})\) at low injection levels, we used the formula obtained by Frankl and Almer [6].
The calculations were carried out using a “Mir-1” computer. Some results are presented in Fig. 1; they have a quite clear physical meaning. Shown here are calculated dependences of the capacitor photo-emf on the surface potential for various parameters of surface centers:
Fig. 1. Calculated dependences of the capacitor photo-emf on the surface potential for various parameters of surface centers
a) \(\lambda = \dfrac{p_0}{n_i} = 10^3\). \(\nu = \dfrac{E_t - E_i}{kT} = -kT\). Capture cross-section ratio
\[ \frac{C_p}{C_n}=0. \]
\[ N_t\ \frac{\text{states}}{\text{cm}^2} = 0,\ 10^6,\ 10^8,\ 10^9,\ 10^{10},\ 10^{12},\ 10^{14} \]
for curves \(1—7\), respectively.
b) \(\lambda = 10^3\). \(\dfrac{C_p}{C_n}=0\). \(N_t = 10^{12}\ \dfrac{\text{states}}{\text{cm}^2}\). \(\nu[kT] = 0,\ -5,\ -10,\ -15,\ -20,\ +20\) for curves \(1—6\), respectively;
c) \(\lambda = 10^3\). \(\nu = -20 kT\). \(N_t = 10^{12}\ \dfrac{\text{states}}{\text{cm}^2}\). \(\dfrac{C_p}{C_n}=\infty,\ 10^5,\ 10^3,\ 0\) for curves \(1—4\), respectively;
d) \(\nu = 0\). \(N_t = 10^{12}\ \dfrac{\text{states}}{\text{cm}^2}\). \(\dfrac{C_p}{C_n}=0\), \(\lambda = 10,\ 10^2,\ 10^3\) for curves \(1—3\), respectively.
For any values of the parameters of surface states, the photo-emf varies between the limiting saturation values [3], but the overall shape of the curve and the features caused by the presence of capture centers are very sensitive to the parameters of the surface states; this makes it possible, having a set of dependences \(\Delta y_\phi = \Delta y_\phi(y_{s0})\) taking into account the influence of capture on surface centers, to estimate the values of their parameters.
As can be seen from Fig. 1,a, in the region of flat bands, where in the absence of surface states the value of the photo-emf is zero (the Dember potential is small), capture of nonequilibrium electrons leads to an additional “band bending” upward, which corresponds to a negative sign of the photo-emf.
The onset of the capture process depends on the concentration of surface states (1,a) and their energy position (Fig. 1,b). Upon reaching
some enrichment, capture of minority carriers cannot lead to a substantial additional bending of the bands. In this connection, for some \(Y_{s0}\) (the value of \(Y_{s0}\) in this case depends on \(N_t\) and on the energy position of the surface states) the photo-emf signal begins to decrease. Capture of majority carriers (holes) leads to the appearance of a photo-emf of the opposite sign (in comparison with the case \(N_t=0\)); in this case the magnitude of the total photo-emf decreases. If \(N_t\) is large and hole capture is efficient, this even leads to a change of sign in the inversion region (Fig. 1, \(v\)). In the case where the capture cross sections for electrons and holes are equal, the main influence on the course of the dependence \(\Delta Y_{\phi}=\Delta Y_{\phi}(Y_{s0})\) is exerted by capture of the majority carriers. A decrease in \(\lambda\) leads to a decrease in the barrier photo-emf in the inversion region; for \(\lambda<10^3\), capture of nonequilibrium electrons by surface states makes the main contribution to the photo-emf in the range of potentials
\[ -8\,\frac{kT}{q}<Y_{s0}<22\,\frac{kT}{q} \]
(Fig. 1, \(g\)).
Experimental dependences \(\Delta Y_{\phi}=\Delta Y_{\phi}(Y_{s0})\) at different levels of injection of nonequilibrium carriers
\[ \delta=\frac{\delta p}{n_i} \]
are presented in Fig. 2 (the injection level is determined from the photoconductivity). Here curve 1 is given for small injection levels; 2—the same under constant illumination; 3—for high injection levels (\(\delta=50\)) with volume generation; 4—the calculated dependence for \(\delta=50\), \(N_t=0\); 5—the experimental dependence under short-wavelength surface generation (\(\delta<50\)).
Fig. 2. Dependence of the capacitor photo-emf on the surface potential.
The figure shows that the dependence \(\Delta Y_{\phi}=\Delta Y_{\phi}(Y_{s0})\) at small \(\delta\) has two features: the presence of an excess positive signal in the depletion and inversion regions, and the appearance of a maximum in the region
\[ +17\,\frac{kT}{q}. \]
The action of constant illumination smooths out the maximum and leads to a decrease in the positive signal. The maximum is especially pronounced when the temperature is lowered to \(T=227^\circ\mathrm{K}\) (Fig. 3).
Comparison of the calculated dependences \(\Delta Y_{\phi}=\Delta Y_{\phi}(Y_{s0})\) with the experimental dependence shows that the observed behavior of the experimental curve can, at least qualitatively, be explained by capture of nonequilibrium electrons by surface states (Fig. 1, \(a\) and 2) and by the presence of an excess positive signal. One of the features of the excess signal is the increase in its magnitude with
Fig. 3. Dependence of capacitor photo-emf on the voltage at the field electrode at \(T = 227^\circ\text{K}\).
during the transition from bulk generation of nonequilibrium carriers to surface generation (compare curves 3 and 5 in Fig. 2), which argues in favor of a diffusion mechanism for the appearance of the excess positive signal. In [7] it was shown that the capacitor photo-emf is a superposition of barrier and diffusion emf’s. However, the Dember emf calculated by the usual formula [8] under the conditions of our experiment did not exceed 10 µV, which is substantially lower than the experimentally observed excess positive signal. Taking into account the influence of recombination of nonequilibrium carriers in the near-surface region according to [9] also does not lead to the appearance of an excess signal. Thus, the presence of this signal is not explained within the framework of the existing theory of photo-emf; its origin can presumably be associated with diffusion processes in the near-surface region under a certain surface treatment or with processes in the near-contact region at the dielectric–metal boundary.
Additional experiments showed that in a metal–dielectric–metal system, if the metals have different work functions, a potential difference arises, apparently caused by a chemical reaction in the solid with defects [4]. In our case the system is rather complex and represents an \(M,\ \text{SD},\ D_2M_2\) structure. Apparently, the potential arising at the electrodes in the presence of different metals is initially, for small values of \(V_{\text{so}}\), added to the photo-emf, and then, as \(V_{\text{so}}\) increases, is subtracted from the photo-emf.
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