SURFACE RECOMBINATION VIA INTERFACE DEFECTS IN FIELD EFFECT TRANSISTORS

Recombination current at the oxide-semiconductor interface of metal-oxide-semiconductor devices has been analyzed and compared with the experimental result. The activity of interface traps is dependent on the energy level and on the operating conditions. A model is shown to be powerful to describe the effect of energy level of bulk recombination centers on the values of reverse recombination current.


INTRODUCTION
The growing interest in the electronic properties of defects in silicon dioxide and at Si-SiO2 interface appears with the observed radiation damages in metal-oxide-semiconductor (MOS) devices used in space applications. The high electric field sustained by oxide layers of the very large scale integration MOS devices leads to carrier injection into SiO2 layers used as gate insulators. This can generate states at the *Corresponding author.
Si-SiO2 interface, and trapping sites in the oxide layer (considered as process induced defects). Similar defects have been seen after device irradiations (radiation induced defects). The density of defects grows with the number of recombination events. The analysis of the induced degradation of electrical properties of MOS devices requires information to be determined experimentally.
MOS gate-controlled p-n junctions have been extensively used to investigate surface recombination current in planar diffused devices and a theoretical relation between the junction current and the gate voltage, V6, has been derived by many workers [1,2]. The importance of energy level of bulk recombination centers Et compared to the intrinsic Fermi level Ei on variations of surface recombination current of MOS is not discussed in detail, particularly, no analytical approach is made. For detailed discussion of steady recombination current of MOS structure, impurities at a single energy level are usually considered [3][4][5]. Reduced forms [6][7][8][9] of surface recombination rate, Us, of electrons or holes have been considered when taking into account operating conditions and carrier or trap density approximations in order to make manageable calculations. In order to obtain a complete theoretical relation between the current and the energy level of bulk recombination centers Et, it is necessary to consider the whole expression of the steady-state recombination rate.
In the present paper we discuss the effect of energy level of bulk recombination centers on surface recombination current. The method is based on the analysis of forward current-voltage characteristics of the body-drain junction of metal-oxide-semiconductor field-effect transistor (MOSFET) considered as a gate controlled diode. We found that impurities can considerably change the values of the reverse recombination current.

MODELLING
In order to investigate non-ideal processes, the model considers the body-drain n-p junction of a MOSFET. The junction is said to be gate controlled since an applied gate bias makes it possible to modify the carrier concentration. The conduction band at the surface may be brought close to the Fermi level, producing a depleted layer at the surface under the gate. A surface recombination current appears, increasing with the gate voltage. Generation and recombination of electrons and holes take place at crystal lattice dislocations, impurity located atoms, surface defects and interface states. The analysis is based on the description of the current-diode characteristics of diode devices.

Diode Characteristics
The current-voltage I(V) characteristics of the forward biased n-p junctions is conveniently described [10,11] by the implicit equation )-11 (1) where Rs and Rsh are the series and shunt resistances, I01 and I02 are known as the reverse currents. The 101 component is obtained by modelling diffusion and radiative recombination of minority carrier across the diode neutral layer. The I02 component is a result of recombination and this contribution is dominant at low bias.
Theoretical works [12] have shown that this contribution appears when minority carrier concentrations are of the order of the majority carrier concentrations. Surface recombination has been suspected [3] as a major source of I02 type current. There are two main assumptions that lead to a 2KT dependence for surface recombination current. First, the ratio of the electron to hole concentration at the surface is close to unity. Second, the quasi-Fermi levels are flat between the bulk and the surface. The surface recombination current depends on both the applied voltage and the energy level of bulk recombination centres as it will be shown below.

Recombination Reverse Current
The schematic diagram of the body-drain junction of a MOSFET is shown in Figure 1, where the field induced and junction depleted regions are shaded. This study is performed with a positive gate potential V (below the threshold level, 0 to 3 ), a negative drain potential VD (forward body-drain junction bias, typically 0.2 V) with zero source and body potentials. The rate of surface recombination [13] for electron or hole, for steady-state conditions, may be written: where Nt is the number of single-level bulk surface recombination centers by unit area, ns and Ps are the electron and hole densities at the surface, ors. and Crsp are the capture cross-sections for electrons and holes, respectively, Et is energy level of bulk surface recombination centers, E is the semiconductor intrinsic Fermi level, Vt is the thermal velocity, n; is the intrinsic carrier density, T the temperature and K the Boltzmann constant.
The expression of recombination current density may be obtained by integration of the recombination rate Us over the surface layer. U reaches maximum values where the denominator is a minimum [4,14], which corresponds to the case when Et E. Several approximation methods [3][4][5] make it possible to calculate the recombination current, they consider Et E. In order to obtain a complete theoretical relation between the current and the energy level Est of recombination centers, it is necessary to consider the whole expression of the steady-state recombination rate of the carriers given by Eq. (2).
Furthermore, the study of a gate control diode needs a new approach to these calculations since the gate applied voltage creates a particular potential distribution in the depleted region. Carrier concentrations ns and Ps in the layer along the interface under the gate are dependent on the surface potential bs and on the drain forward bias VD [15], they are obtained in the form: where Z and L are respectively the width and the length of the channel.
lo2 dependent on energy level of bulk recombination centers, Est, and related to the surface potential s. The surface potential, bs, is related to the applied gate bias and its variation has been determined (see Appendix I) 3. RESULTS AND DISCUSSION .,. For all centers level positions the reverse surface recombination current 102 increases as soon as the gate applied bias Vo is raised. A maximum value is reached with subthreshold operating conditions (threshold voltage V: is close to 3.1 V for this structure) and the reverse current decreases gradually for V values close to and then above VT. Such variations have been previously obtained experimentally [16,17] from direct measurements of leakage currents and these theoretical results enable us to discuss their physical origin.
The interface recombination center densities (Nst) which have been used in this modelling study correspond to the values of interface trap density in a Si-SiO2 system with respective energy levels (Est) described by Sze [15]. The increase in the reverse recombination current 102 together with the decrease of Est-Ei reflect that recombination centers located near the center of the energy gap are most active and correspond to a maximum value of the recombination rate Us given in Eq. (2). As the gate bias increases, a surface potential appears and the large increase of 102 may be attributed to the extension of the junction space charge region within the induced depleted layer under the gate. For gate bias less than, but close to the threshold voltage value a tangential electrical field along the interface appears and drifts the carriers along the interface leading to the observed maximum 102 step; for large Va values the channel is operating, the reverse surface recombination current decreases rapidly and reaches almost a zero value. The electrical field modulates the resistance of the layer under the gate and allows a current to flow in response to the applied drain voltage. This electrical field effect on the surface recombination current is obviously drain bias dependent as shown in is forward biased, i.e., the body and source potentials are made positive with respect to the drain. A specifically conceived software [11], PARADI, extracts the physical parameters 101, 102, Rs and Rsh from the experimental I(V) diode measurements, providing an excellent fit of the characteristic: sets of parameter values are determined for different bias values, using Newton-Raphson method; The selection of the best-descriptive set related to this specific conduction mechanism model (Eq. (1)) is made via the calculation of the qualification factor Q, that is the root-mean-square of the distances separating the experimental points from the calculated curve.
They may be charges generated in the oxide and trapped at the interface, or free charges generated in the depletion region.
Coulomb's law for equilibrium states: Qs -es dx x=O (2) where es is the semiconductor permittivity and b(x) is the potential at the position x (Fig. 1). Integrating Poisson's equation, for potential b(x), we assume that the surface potential bs is independent of y. The boundary conditions b(x) bs at x 0 gives: The surface potential bs is related to the bias V6 and to the potential Vox across the oxide (bs V6-Vox). Then Eq. (2) gives: Qs -(2. q.es. NA) 1/2 'dl/2 (4) The oxide capacitance, Cox, is obtained from measurements of the drain potential, VDS in the saturation region: Cox [2.es .q. NA (VDs + 2.B)] 1/2 (r% r'os . ,) (5) were bB is the potential difference between the Fermi level and the intrinsic level of the bulk semiconductor.
From Eqs. (1), (4) and (5) we obtain an implicit equation which makes it possible to compute the surface potential bs as a function of the gate voltage.