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probability evaluation termostimulirovannoj tunnel ionisation an U-minus of centres

Many unique properties halkogenidnyh glasses speak presence in these materials of high concentration of centres with the subzero correlation energy, or an U-minus of centres. Such centres in the basic state appear infected, half of centres is charged plusly, and other half - is subzeroly.

Levels of the first and second ionisation of centres are located near to the forbidden region middle, therefore the Fermi level appears anchored between levels of centres Existence of the considerable concentration (a///-minus of centres (order IO18см ' 3) in many halkogenidah proves to be true lack of paramagnetism (lack of not paired electrons), and also the close values of an activation energy of conductivity in the materials gained in different laboratories by means of various methods.

Well-known, that (a///-minus centres are spotted by electrical properties halkogenidnyh glasses in feeble electric fields. Therefore the guess has been come out, that unique properties HSP in the strong fields, in particular nonlinearity BAX and switching in spending state, are related C by behaviour of centres in the stronger sex. It is obvious, that the probability of ionisation of centre increases in the stronger sex, concentration of the free carriers and conductivity of a material is as a result incremented. Therefore more low we will in detail view processes of ionisation of centres in the stronger sex.

In viewed model the fact of existence (a///-minus of centres and their behaviour in the strong electric field is important. The nature of such states is not concretised and can be related to flaws, the soft potentials, or any other mechanism. Therefore just as in [70], we will designate corresponding states of centres as/?. D0, D ~, however, not meaning the torn off communications as it became in [70].

Let's view film HSP to which the electric field is enclosed. In the stronger sex there will be stimulirovannaja an ionisation an U-minus of centres, therefore we

We consider, that non-linear conductivity HSP in the strong electric fields can be related to processes of ionisation and entrapment of carriers:

For presentation we will feature ionisation and entrapment processes in language of the electrons, similar expressions can be written for a case of ionisation and entrapment of electron defects.

Processes of ionisation and entrapment of carriers elektricheski have been viewed by the active centres in operations of group Perelja [71-76], the detailed enunciating of effects of these operations can be found in the monography [77] and the review [78]. Viewing of processes of ionisation of centres will be grounded on these operations.

Let's view / a-minus centres in models Huanga and Rice according to which the adiabatic terms of various states of centres represent the identical shifted parabolas. Model Huanga and Rice is often used at theoretical calculations thanks to the simplicity and possibility of reception of analytical effects. In the beginning we will view neutral centre D0, such centre can donate one electron and transfer in plusly charged state D +. At an equilibrium configuration of a lattice for an electron on centre there is a potential well.

Lattice oscillations lead to change of potential of centre therefore the electron binding energy varies. We will consider, that the basic contribution to change of levels of energy of centre is imported by one mode of local oscillations. Therefore level of energy of centre is featured by one configurational co-ordinate which we will designate through h.

As balance in a subsystem of electrons is reached much more promptly the characteristic time of change of a kernel configuration, it is possible to use the adiabatic approach according to which the electronic system is considered at any moment as equilibrium. In models Huanga and Rice the electron binding energy on centre is featured in the linear approach [78]

Where εo - a binding energy at an equilibrium configuration of a lattice without an electron, a v - some constant. The total of electronic energies and electrostatic energies with other kerns, formativing potential in which the centre kern moves, term as the adiabatic term. In the elementary approach the adiabatic termionizovannogo centre D+вблизи of a point of balance is set by expression

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In this expression energy and co-ordinate are digitized from an equilibrium level, M - kern mass, ω - an oscillation frequency.

Then it is possible to present the adiabatic term D0центра in the form of the energy total ionizovannogo centre U2и of energy of an electron on centre - ε⅛.

The adiabatic term U ι (x) has the parabolic shape, and the energy minimum is reached at the shifted standing of balance

Therefore model Huanga and Rice often term as model of the identical shifted parabolas. The adiabatic terms of centres in models Huanga and Rice are figured in a Fig. 3.1

Fig. 3.1. The plan of the adiabatic terms in models Huanga and Rice

Through Е2 the distance from a term minimum (7 is designated? To an intersection point of terms, Et - the distance on energy between minimums of terms, is meaningful to energy of thermal ionisation of centre. More low we will use standard labels. Energy of thermal ionisation D+центра we will designate ε∣, and energy of thermal ionisation Do of centre &2.

In halkogenidah energy of the CORE the STATE (the///-minus of centres makes a little the tenth elektronvolta, that several times exceeds the characteristic energy of phonons.

Hence, processes of thermoionization and entrapment of carriers on such centres are multiphonon.

Fig. 3.2. Tunnel ionisation of centre.

In the beginning we will view neutral centre Do.Ядро of such centre the electron binding energy on centre makes thermal oscillations in the potential of U ι (x).pri it changes depending on a kern standing according to (3.2). In an intersection point of terms hs the binding energy is converted in a zero. Uproshchenno it is possible to consider, that ionisation occurs each time when the centre in the course of thermal oscillations reaches points hs. Then the probability of thermal ionisation of an electron is in unit of time equal to oscillation frequency product on probability to a kern to have energy, major, than Ec + E?

However expression (3.5) is valid only at very heats In usual requirements kern transition between terms occurs not in point Xc, and at a smaller diversion from a balance standing thanks to quantum tunneling of a kern. Thus transition from term Uiна a term ⅛ becomes possible at energy of kern E, smaller Eg (a Fig. 3.2). Probability of tunneling from some level of energy Eможно to calculate, using a method of complex classical trajectories Landau [80]:

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The probability of such tunnel transition is small, however this is a little cancelled by magnification of probability of thermal activation to energy of tunneling to that E.Blagodarja, that in models Huanga and Rice the adiabatic terms have the parabolic shape, integrals in expression (3.6) can be calculated analytically.

For evaluation of probability of tunneling we will view an indefinite integral

The gained expression it is used for evaluation of the particular integrals entering into expression (3.6):

It is convenient to enter labels:

Then expression (3.8) can be written down in a view:

It is possible to express probability of ionisation of centre as integral on all possible levels of energy Eот of product of probability of tunneling P (E) C corresponding level of energy and probability of that the centre in the course of thermal oscillations will have energy Et ÷ E:

The integrand consists of product of growing and impinging exponential curves. Such integral can be calculated on a pass method. The integrand has a maximum at energy Eiihкоторая is spotted from a requirement:

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For convenience we will enter a label:

t, it is possible to give to quantity sense of time of tunneling of centre under potential U, from a point and, to an intersection point of terms hs:

For the adiabatic terms featured by the equations (3.13,3.14) value t, can be calculated in an explicit form:

C the account of labels (3.15) most probable energy of tunneling can be spotted from a requirement:

Where quantity G * which as it will be shown more low, makes sense effective temperature of electrons is entered.

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A source: Baturkin Sergey Aleksandrovich. EXAMINATION of CURRENT PERFORMANCES HALKOGENIDNYH STEKLOOBRAZNYH of SEMICONDUCTORS of COMPOSITION GST-225 ALLOYED by NITROGEN And BOHR. The dissertation on competition of a scientific degree of the candidate of physical and mathematical sciences. Tver - 2015. 2015

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