Investigation of Photoconductivity in n-type Galium Doped PbTe

Persistent photoconductivity at low temperature in PbTe + 0.4 at.% Ga has been investigated using kinetic equations which describe the transport process on DX-like impurity centers. Measured and calculated photoconductivity as a function of illumination and temperature is presented. Experimental results are interpreted assuming the mixed valence of Ga in lead telluride and the formation of centers with negative correlation energy. Numeric values of the mathematical model constant at steady state are calculated by comparing the measured and calculated temperature dependence of the resistivity and carrier concentrations for illuminated and unilluminated n-type samples. Thus, the positions and concentrations of different impurity states are determined.


Introduction
Doping of lead telluride-based alloys with some impurities of group III such as In, Ga results under certain conditions results in the appearance of some unusual effects like stabilization of the Fermi level and occurrence of long-term relaxation processes when the system is disturbed from the equilibrium state at low temperature.In PbTe(Ga) the Fermi level becomes pinned in the upper half of the band gap, ~70meV bellow the conduction-band bottom [1], and the long-term effects (especially photoconductivity [2]) are observed at temperatures bellow 80K.The mechanism suggested to describe this effect is connected with some deep centers, known as DX-like centers.
The solubility of Ga in PbTe is low.If the concentration of Ga is less than one atomic percent then Ga enters in the Pb sublattice.The Fermi level becomes pinned only in some Ga content region.When the concentration of Ga increases in PbTe p-type samples the hole concentration linearly decreases which drives the crystal to an uncompensated state at N Ga ~0.1 at.%.Further doping up to N Ga =0.3 at.% leaves the samples in a semiconducting state [3].The pining position inside the gap results in a semi-insulating semiconductor state.Just above this region, there is a p-n inversion and the conduction of electrons in the n-region quickly rises.If there are no circumstances for Fermi level stabilization, the donor action of Ga becomes unstable with respect to the external factors, such as hydrostatic pressure or temperature [4].

Model of DX-Like Centers in PbTe(Ga)
A great number of experimental results [Ref.5 and the literature cited there] pointed that the electronic spectrum of gallium in PbTe is composed of two-electron ground states, a metastable one-electron state and a conduction band (E c ).Also, it is well known [1,5] that Ga mainly replaces the metal atoms in PbTe.However, the 2+ charge state of impurity atoms, neutral relative to the lattice, is metastable and decays to donor-acceptor pairs according to the reaction: 2Ga 2+ →Ga + +Ga 3+ , i.e., the effective interaction energy of the electrons at the impurity center is negative (negative -U centers).A "configuration" diagram [6,7], such as that shown in Fig. 1, is useful in describing the donor-acceptor states in PbTe(Ga).In Fig. 1 the total energy is given as a function of the configuration parameter Q which describes displacement of the substitutional donor.The three given curves correspond to an ionized donor at the bottom of the conduction band (Ga 3+ ) the neutral donor (Ga 2+ ) and the negatively charged Ga + state, respectively.This model is described in much more detail in Refs.[5,8].
Also, some experimental results [9,10] evidence that the Ga + and Ga 3+ impurity states, which correspond to two electrons localized at the impurity and to the empty center, respectively, correspond to a centrally symmetric position of the impurity atom, whereas, for the metastable state Ga 2+ , which corresponds to one localized electron, the impurity atom is displaced from the inversion center.Consequently, ionization of each of the electrons from the two-electron impurity ground state results in displacement of the impurity atom first to an interstitial position, and then back into a substitution center.As a result, barriers are formed in a configuration space between all the states of the system with different numbers of localized electrons.

Electronic + elastic energy
Lattice distortion, Q Fig. 1 Schematic total energy diagram as a function of the local displacement (Q) of a substitution donor for the ionized Ga 3+ state, the neutral donor Ga 2+ state and a negative, according to the lattice, two-electron donor state Ga + .
We used kinetic equations [11] to describe the electron transitions between three energetic states of impurity and ignoring the band -to band recombination term of heavy and light holes, we obtained the temperature dependence and illumination influence on photoconductivity.

∆
. We consider one-photon processes only.
The charge-balance equation is the third equation, where for T=0K all stages E 1 (DX state in which the donor state is negatively charged) are occupied, but E 2 and E 3 are empty, To separate the illumination influence, → From Eqs. (3) -( 5) numerical values of , and can be calculated and with certain approximations, an analytical solution can be given.If we assume that electronphonon interactions between and states are dominant in equation ( 5), then ) The analytical conductivity expression is , ) , ( ) , ( In equation ( 8), A is the Hall factor that is usually near unity depending on the degeneracy degree and the dominating scattering mechanism [12].For a non-degenerate carrier gas and acoustic phonons, the lattice scattering =1.18, for ionized impurity scattering =1.93, and for neutral impurity scattering =1.Since the high magnetic fields required to set to unity are not found in most laboratories, is frequently not known and is assumed to be unity, as was done in this research.

Experiment and Disscussion
The sample studied was an Ga-doped PbTe single crystal grown by the Czockhralski method.The gallium impurity was introduced into the liquid zone.From Hall effect measurements with a van der Pauw contact geometry the galvanomagnetic coefficients were determined.The sample size was about 5mm in diameter, with a thickness of about 0.75mm.The current through the sample and the magnetic field was 10 mA and 0.45 T, respectively.The sample was installed in a special low-temperature chamber, cooled with liquid helium.In such a way the sample was completely screened from external radiation.Controlled illumination was performed using a photodiode (λ~ 1µm) at an energy greater than the forbidden gap width.The Hall coefficient and the electrical resistivity were measured in the temperature range of 20-290K, under conditions of "darkness" and controlled illumination.
The Ga 2+ , Ga + and Ga 3+ states correspond to s 1 p 2 , s 2 p 1 and s 0 p 3 electronic configurations.The lead atom, which substitutes for gallium, has the s 2 p 2 configuration.The relevant bands in lead halcogenides are almost completely built from atomic p orbitals; for various Ga atom charge states, the electron occupying the deep s shell is localized and p are delocalized.
The principal idea of this model is that the one-electron impurity state with only one electron in the s shell lies, energetically much higher, within the one-electron approximation, than the two-electron ground state and higher than the bottom of the conduction band (Fig. 1).
In PbTe(Ga) Fermi level pinning differs from a similar effect observed in PbTe doped with other Group III elements, such as, indium and thallium [13].In PbTe(Ga), Fermi level pinning occurs only in a narrow range of concentrations of introduced Ga, whereas beyond this range, up to the solubility limit, Ga acts as a donor.In PbTe(Tl) and PbTe(In) Fermi level pinning occurs for any dopant concentration exceeding the concentrations of other electrically active impurities and defects.
Fig. 3 represents a temperature dependence of n 1 , n 2 and n 3 electron concentrations on E 1 , E 2 and E 3 energy levels, respectively.Points represent the calculated values for an illuminated sample, while a full line -a non-illuminated sample of PbTe(Ga).Only for T ‹80K a significant difference in the electron concentration of illuminated and non-illuminated samples is observed in the n 2 and n 3 temperature dependence.The registered difference in electron concentration on these levels is of fundamental importance.Namely, in classic DX centers the metastable one-electron state is shallow and is not separated by a barrier from the completely ionized impurity state.

Conclusion
In this paper we have performed a study of photoconductivity as a function of temperature and illumination on DX-like centers in PbTe with 0.4 at.%Ga.From the measured values for the conductivity and Hall coefficient using a theoretical model connected with DX-like centers, we were able to estimate some parameters of the material.
to the absorbed flux, and the following equations are derived: coefficients of the equation:

and 3 µ
are electron mobilities on levels 2 and 3.The Hall constant for two types of carriers (electrons) is:

Fig. 3
Fig.3Temperature dependence of the carrier concentration of different energy levels for an illuminated (point) and non-illuminated (full line) PbTe + 0.4 at.% Ga sample.