Interface recombination feature in metal–semiconductor junction at high photo-excitation

A theory of the photo-induced electromotive force in a p-type semiconductor accounting for the energy band bending and interface recombination dependence on excitation level is developed. It is shown that at high photo-excitation the effective interface recombination velocity in the metal-semiconductor junction is negligible compared with the volume one, when the surface potential is less than its critical value. The photo-induced electromotive force value is maximal at this condition.


Introduction
The recombination of the nonequilibrium (NE) carriers in the bulk and in the surfaces/interfaces of the semiconductor structure plays an important role in transport phenomena. There are many effects, the values of which depend considerably on the interface recombination: photoconductivity [1], photo-induced electromotive force (EMF), magnetoconcentration effect [2] and so on. Typically used expression of the surface recombination velocity (the Stevenson-Keyes theory) is obtained in quasi-neutrality approximation and assumption of small carrier concentrations' deviation from those of the equilibrium. According to this theory the surface recombination velocity significantly depends on the band bending [1,3]. Though measurements of the interface recombination velocity [5][6][7] are based on the quasineutrality model [3], the criterion of low excitation as a rule is not fulfilled. As it is shown in [4] the expression of the surface recombination velocity of the Stevenson-Keyes theory is invalid at high excitation levels. In general, the surface recombination rate has the form [4] δ δ = + R S n S p s n s p s , where S n , S p are the interface recombination parameters and δn s (δp s ) is the NE electron (hole) concentration in the interface. This expression of the surface recombination rate allows us to eliminate contradiction of the classical Hall electric field generation model related to the NE surface charge layer, which does not depend on the interface recombination value [4]. The expressions of the interface recombination parameters S n and S p at any NE carrier value are derived in [4], and use the Shockley-Read model for the interface recombination. The experimental data corroborates the interface recombination theory [4]. The interface recombination rate is equal to δ = R S p s p s [8,9] in the metal-semiconductor junction (MSJ), because there are no NE electrons in the MSJ ( δ = n 0 s owing to the constancy of metal chemical potential and continuity of electrical potential). As follows from the results of [4], the interface recombination parameter S p decreases, thus increasing the excitation level. This effect is strongly expressed in the junction of a metal and p-type semiconductor at high photo-excitation. In this case the interface recombination can become less than the bulk recombination in a certain region of the surface potential (SP) [3] value. The influence of the interface recombination on the photo-induced EMF can be negligible in this SP region. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. This paper is aimed at the study of the surface potential influence on the interface recombination in the MSJ at high photo-excitation levels.

Theory
In order to study the interface recombination feature let us consider the photo-induced EMF generation. Let us consider a p-type non-degenerate semiconductor plate ⩽ ⩽ x a 0 with the surface at = x 0 illuminated by strongly absorbed light. The thickness of the sample a essentially exceeds the diffusion length. A semitransparent thin metallic film is placed on the surface = x 0. The grounded metallic contact is placed on the surface = x a. Interface recombination is extremely large on the surface = x a. The NE densities of electrons δn and holes δp, as well as the NE electric potential δφ, are obtained from solution of the continuity equations [10,11] and the Poisson equation where −e is the electron charge, j j , n p are the electron and hole current densities, τ n (τ p ) is the parameter characterizing electron (hole) bulk recombination velocity, δρ is the NE charge density, ε is the semiconductor electrical permittivity, and ε 0 is the vacuum permittivity.
The expressions for x-component of partial currents are [3]: where μ μ ( ) n p is the electron (hole) mobility, n x ( ), p x ( ) are the densities of electron and hole accordingly, φ is the electric potential, k is the Boltzmann constant, and T is the temperature of the semiconductor.
The boundary conditions in the MSJ are obtained in [8,9]: m where S p is the interface recombination parameter, δφ m is the NE electric potential of the metallic contact, and G is the electron-hole pair (EHP) surface generation rate. It follows from equation (5) and the results of [4] that parameter S p is not the surface recombination velocity of the holes. The validity of boundary condition (6) is proved in [12], which studies the role of the NE charge in the thermopower generation.
In the most of semiconductors the diffusion length λ significantly exceeds the Debye length r D [8]. Under this condition the solution of equations (1) where λ τ = D n n is the diffusion length of the EHP, τ n is the lifetime of the EHP in the bulk of a p-type semiconductor sample [2,11] and μ = D kT e n n is the diffusion coefficient of the electrons. As follows from [2,8] in a p-type semiconductor the diffusion coefficient of the EHP coincides with the one of the electrons. The density of holes δp r satisfies equation (8) too since in the quasineutrality region the equality δ δ = p n r r is valid. Note that the lifetime of the EHP in the bulk of the sample τ n is constant at δ ≪ n p r 0 [3,11]. We obtain for the R mode:  (4), (10) we obtain the relations between the carrier densities and the electric potential of the D mode [12]:  where α ns (α ps ) is the capture coefficient of electrons (holes), N ts is the total density of interface impurity states, δp s is the NE hole concentration in the interface, the n s 1 (p s 1 ) is the electron (hole) concentration in the surface when the Fermi level matches the activation energy of the interface trapping level [4], We derive from equations (13) and (14): and The developed model is valid under condition α λ ≫ −1 and λ ≫ r D , where α is the light absorption coefficient.

Discussion of results
It follows from equations (14) and (15)  This effect is caused by strong growth of the NE holes' concentration in the interface, which significantly diminishes the effective IRV value at φ φ ⩽ .   semiconductor surface. The equilibrium SP exceeds V 0.45 in the typically used Al/p-Si junction. However it is known [1] that the SP of the semiconductor very largely depends on the surface level density. If we create the sufficient density of the acceptor-type surface levels, we can make the SP value less than 0.37 V.

Conclusions
The effective IRV dependence on the surface potential in the contact of a metal and p-type semiconductor at high photoexcitation level is studied. It is shown that the effective IRV in the MSJ is negligible compared with the volume one in a certain band bending region. The photo-induced EMF is maximal in the same SP region. The experimental verification of the theory is discussed.