A Theoretical Study of Charge Transport y at Au/ ZnSe and Au/ZnS Interfaces Devices Hadi J. M. Al-Agealy Mohsin A.H. Hassoni Mudhar Sh. Ahmad Rafah I. Noori Sarab S. Jheil Dept. of Physics /College of Education Seience Pure ( Ibn-Al Haitham) /University of Baghdad Received in: 24 November 2013, Accepted in: 2 February 2014 Abstract A quantum mechanical description of the dynamics of non-adiabatic electron transfer in metal/semiconductor interfaces can be achieved using simplified models of the system. For this system we can suppose two localized quantum states donor state |D› and acceptor state |A› respectively. Expression of rate constant of electron transfer for metal/semiconductor system derived upon quantum mechanical model and perturbation theory for transition between |𝐷〉 and |𝐴〉 state when the coupling matrix element coefficient is smaller than 0.025 eV. The rate of electron transfer for Au/ ZnSe and Au/ZnS interface systems is evaluated with orientation free energy using a Matlap program. The results of the electron transfer rate constant are calculated for our modeas well as with experimental results . Key Word :Charge Transport Theory, Metal/ Semiconductor Interfaces 176 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (1) 2014 Introduction Electron transfer is an integral part of many biophysics[1], physical chemistry[2] processes and technology[3], which occurs in a large variety of molecules ranging from small ion pairs up to large system [4].The theory of electron transfer reaction is the subject of persistent interest in physics [5] , over the past several decades, researchers have investigated the transfer of electron through molecule and solid state structure [6] , molecule metal interfaces [7], and metal semiconductors interfaces [8].Metal semiconductor contact from interfaces that give basic features of many metal /semiconductor devices .To construct the diagram of an metal/ semiconductor contact ,we consider the energy band diagram of metal /semiconductor , and align .These ET systems seen important from technological and biological ? where a metal is placed in intimate contact with a semiconductor , the electrons from the conduction band in one material ,which have higher energy ,flow into the other material until the Fermi level on the two sides are brought into coincidence [9]. The energy level in the two material are rearranged relatively to the new common Fermi level. However, the Fermi energy of the metal and semiconductor do not change right away [10].. Fundamental studies, as performed in this paper are expected to provide guidelines for design of such practically useful ET system In this paper, Our main theoretical model to study of electron transfer is at metal/semiconductor interface system .There orientation energy and the rate of electron transfer constant are calculated according to this model. Theoretical Model The fundamental starting point is the derived formula for the transition probability given by first order perturbation theory for a transition from a discrete state to continuum state the state a quantum system which is described by a wave function [11]. Ψ(𝑟, 𝑡) = ∑ 𝐴𝑛n e −𝑖𝐸𝑛𝑡 ħ Ψ𝑛(𝑟)……………………(1) Where Ψ(r, t) is the time dependent state vector in Hilbert space at quantum system state, 𝐴𝑛 is the coefficient of wave founction , 𝐸𝑛 is the energy ,and 𝑡is time .Model Hamiltonians operator used to describe the electron transfer in donor /acceptor system can be written as [12]. 𝐻 = 𝐻𝑜𝑝 + V ………………….(2) Where 𝐻𝑜𝑝is the Hamiltonian before perturbation ,and V refers to the potential where the electron is either on the donor|D> or acceptor |A> , respectively ,it is given [13]. 𝐻𝑜𝑝 = |𝐷 > 𝐻𝐷 < 𝐷| + |𝐴 > 𝐻𝐴 < 𝐴|………….(3) The Hamiltonian operator obeys the Schrödinger equation 𝐻𝛹ᴪ(𝑟, 𝑡) = 𝐸𝑛𝛹(𝑟, 𝑡) .Substituting Eq.(3) and Eq. (2) into Eq.(1)the results �𝐻𝑜𝑝 + 𝑉��𝐴𝑛(𝑡)|ɸ(t) >= 𝑛 𝑖ħ 𝑑 𝑑𝑡 �𝐴𝑛(𝑡) 𝑛 |ɸ(𝑡) > … … . . . . (4) The first term on each side in Eq.(4) is concelled that because |φ(t)>is a solusion to time dependent schrodinger eqution with Hop Eq. (3) becomes . 𝑖ħ∑ 𝑑 𝑑𝑡 𝐴𝑛(𝑡)𝑛 �𝛷(𝑡) > 𝑒 −𝑖𝐸𝑛𝑡 ħ = ∑ 𝐴𝑛(𝑡)𝑛 𝑉�𝛷𝑛(𝑡) > 𝑒 −𝑖𝐸𝑛𝑡 ħ …..(5) 177 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (1) 2014 Multiply both sides of the Eq.(5) by <𝛷𝑚 (t)|for the final state and integral over space , we get :- 𝑖ħ� 𝑑 𝑑𝑡 𝐴𝑛(𝑡) 𝑛 < 𝛷𝑚(𝑡)|𝛷𝑛(𝑡) > 𝑒 −𝑖𝐸𝑛𝑡 ħ = � 𝐴𝑛 𝑛 (𝑡) < 𝛷𝑚(𝑡)|𝑉|𝛷𝑛(𝑡) … . (6) By normalizing the left hand side of Eq. (6) all terms vanish except n=m then. 𝑑 𝑑𝑡 𝐴𝑛(𝑡) = 1 𝑖ħ ∑ 𝐴𝑛(𝑡)𝑛 𝑉𝐷𝐴𝑒 𝑖(𝐸𝑚−𝐸𝑛)𝑡 ħ ……………….(7) Here𝑉𝐷𝐴is the coupling coefficient of donor and acceptor state,and 𝐸𝑚 − 𝐸𝑛 is the difference in the energy between the state m and n respectively with direct integration for Eq. (7),and mathematical treatment,results. 𝐴𝑛(𝑡) = −𝑖𝑉𝐷𝐴𝑒 𝑖(𝐸𝑚−𝐸𝑛)𝑡 2ħ 𝑠𝑖𝑛 (𝐸𝑚−𝐸𝑛)𝑡 2ħ (𝐸𝑚−𝐸𝑛) 2ħ 𝑡 ħ …………………(8) The total probability of finding the particles at time (t) in the final state |m> is given by. 𝑃𝑛(𝑡) = |𝑉𝐷𝐴|2 𝑡2 ħ2 𝑠𝑖𝑛2 (𝐸𝑚−𝐸𝑛)𝑡 2ħ (𝐸𝑚−𝐸𝑛)𝑡 2ħ ……………………….(9) The term 𝑠𝑖𝑛2 (𝐸𝑚−𝐸𝑛)𝑡 2ħ (𝐸𝑚−𝐸𝑛)𝑡 2ħ = 𝜋𝛿 (𝐸𝑚−𝐸𝑛)𝑡 2ħ [14]. Where 𝛿 is delta function 𝛿(𝑎𝑥) = 1 |𝑎| 𝛿(𝑥)𝑎 ≠ 0[14] 𝛿 (𝐸𝑚−𝐸𝑛)𝑡 2ħ = 𝛿 𝑡 2ħ (𝐸𝑚 − 𝐸𝑛) = 2ħ 𝑡 𝛿(𝐸𝑚 − 𝐸𝑛)………(10) So that Eq. (9) becomes : 𝑃𝑛(𝑡) = � 2𝜋𝑡 ħ �𝑉𝐷𝐴|2𝛿(𝐸𝑚 − 𝐸𝑛)………………..(11) The rate of the probability transition per unit time is the rate constant 𝐾𝑒𝑡 of electron transfer that means [15]. 𝐾𝑒𝑡 = 𝑑 𝑑𝑡 𝑃𝑛(𝑡) = 2𝜋 ħ | 𝑉𝐷𝐴|2𝜌𝜌(𝐸)…………………..(12) Such that [16]. ∫ 𝜌𝜌(𝐸)𝛿(𝐸)𝑑𝐸 = 𝜌𝜌(𝐸) ∞ −∞ …………….(13) In plase of the wave function , one in traduces the density operator [17]. 𝜌𝜌 = ∑ 𝜌𝜌𝑛𝑛 |𝛹ᴪ𝑛 >< 𝛹ᴪ𝑛| ,∑ |𝜌𝜌𝑛|2𝑛 = 1 …..(14) According to Eq.(14) and mathematically the corresponding density operator becomes. 𝜌𝜌 = 𝑁 ∑ 𝑒 −�𝐸𝑑−𝐸𝑎� 𝐾𝛽𝑇 𝑛 |𝛷𝑛 >< 𝛷𝑛|𝛹 >…………(15) 178 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (1) 2014 Eq.(15) indicates that the probability is proportional to the Boltzmann's factor 𝑒 −�𝐸𝑑−𝐸𝑎� 𝐾𝛽𝑇 . In non-adiabatic metal/semiconductor interface system the energy difference ∆𝐸 = 𝐸𝑑 − 𝐸𝑎 and equals the activation free energy ∆𝐺+,and can be written Eq.(15) in expression. 𝜌𝜌(∆𝐺) = 𝑁𝑒𝑥𝑝 −∆𝐺 𝑘𝐵𝑇 = 𝑁𝑒𝑥𝑝 −∆𝐺 ++ 𝑘𝐵𝑇 …………..(16) The activation energy according Marcus theory is given by [18]. ∆G++ = (λ+∆G°) 2 4λ ………………….(17) Inserting Eq.(17) in Eq.(16) results. 𝜌𝜌(∆𝐺) = 𝑁𝑒𝑥𝑝 −(𝜆+∆𝐺° ) 2 4𝜆𝑘𝐵𝑇 …………..(18) To Find N we note that using definition of Gamma integral [19]. ∫ 𝑒𝛼(𝜆+∆𝐺°) 2 𝑑∆𝐺° = ( 𝜋 𝛼 ) 1 2 ∞ 0 ……………(19) And for complete set │Φn> we found ∑𝛷𝑛∗𝛷𝑚 = ∑|𝛷𝑛| = 1 𝑁 = ( 1 4𝜋𝜆𝑘𝐵𝑇 ) 1 2…………….(20) Inserting value of N inEq.(18 ) we can get the influence of temperature on the electron transfer rate with Boltzmann distribution to give the common classical expression for the Franck-Condon factor. 𝐹𝐶 = (4𝜋𝜆𝐾𝑇) −1 2 𝑒𝑥𝑝 −(𝜆+∆𝐺°) 2 4𝜆𝑘𝐵𝑇 ……………….(21) Inserting Eq(21) in Eq.(12) we get e the Landau-Zener formula to described the rate of a non- adiabatic electron tunneling from one electronic state to another [20]. 𝐾ET = 2π ћ |VDA(E)|2 FC …………………………(22) where 𝑉𝐷𝐴( E ) is the electronic coupling matrix element of the donor and acceptor. The total electron transfer rate from semiconductor (donor state) ot the metal (acceptor state) can be expressed as the sum of electron transfer rates to all possible accepting states in the metal that are given by [21]. 𝐾ET = 2π ћ ∫ ƒ(E, EF)|VE|2(4πλ𝑘𝐵𝑇) −1 2 exp −(λ+∆G) 2 4π𝑘𝐵𝑇 ∞ −∞ ……(23) Where ƒ(𝐸, 𝐸𝐹)is the Fermi- Dirac function can be related to electron by [22]. ƒ(E, EF) = 1 1+exp �ECB−EF� 𝑘𝐵𝑇 ………………..(24) Here 𝐸𝐶𝐵 is the conduction band energy and 𝐸𝐹 is the Fermi level energy. Inserting Eq.(24) in the Eq.(23) we get 𝐾ET = 2π ћ ∫ 1 1+exp �ECB−EF� 𝑘𝐵𝑇 |V(k,r)|2(4πλKT) −1 2 exp −(λ+∆G) 2 4π𝑘𝐵𝑇 dE ∞ −∞ ..(25) 179 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (1) 2014 The free energy ∆𝐺 is related to occupy energy 𝐸 by [23]. ∆𝐺 = ∆𝐺° − 𝐸………………………….(26) Where ∆𝐺° is the standard free energy of reaction.Substituting Eq.(26) in Eq.(25) results. 𝐾ET = 2π ћ � 1 1 + exp (ECB−EF) 𝑘𝐵𝑇 |V(k,r)|2(4πλKT) −1 2 exp −(λ + ∆G° − E)2 4π𝑘𝐵𝑇 dE … … … … … … … … . . (27) ∞ −∞ The exponent exp (λ+∆G°−E) 2 4π𝑘𝐵𝑇 = exp �(λ+∆G° ) 2 4λ𝑘𝐵𝑇 − (λ+∆G° )E 2λ𝑘𝐵𝑇 + E 2 4λ𝑘𝐵𝑇 � in the integral . The activation energy ∆𝐺++is the height of the barrier of ideal potential contact between metal and semiconductor in the absence of surface state is equal the difference between the metal work function 𝛷𝑚 and the electron affinity𝜒𝜒 of the semiconductor and formulated by ∆𝐺++ = ΦB = �eΦm−e𝜒𝜒� 2 4λ𝑘𝐵𝑇 [24]. Ket = 2π ћ (4πλ𝑘𝐵𝑇) −1 2 e −�eΦm−e𝜒𝜒� 2 4λ𝑘𝐵𝑇 ∫ [1 + ∞ 0 exp �ECB−eVapp−EF ° � 𝑘𝐵𝑇 ]−1|V(k, r)|2e −E 2 4λ𝑘𝐵𝑇 dE ……(28) WhereECB , Vapp, and EF ° are the conduction energy,applied voltage ,and Fermi energy The Fermi-Dirac function in Eq.(28) reduced to the Boltzmann equation when 𝐸𝐶𝐵 − 𝐸𝐹 >> 𝑘𝐵𝑇 ƒ(𝐸, 𝐸𝐹)(𝐸𝐶𝐵 − 𝐸𝐹 ≫ 𝑘𝐵𝑇) ≈ 𝑒𝑥𝑝 −(𝐸𝐶𝐵−𝐸𝐹) 𝑘𝐵𝑇 ………………..(29) The square of the electronic coupling matrix element integrated over the distribution of the electronic state at the given 𝐸 is [25]. 𝐻𝐷𝐴(𝑘, 𝑟)2 = |V(k,r)|2 2𝜋𝛿(𝐸𝐾−𝐸) ……………..(30) Where 𝐻𝐷𝐴(𝑘, 𝑟) denotes < 𝜓𝑘│𝐻│𝜓𝐴 > and describes the electronic coupling matrix element between the metal end semiconductor state , and 𝑘 as the electronic state. The metal density of state 𝜌𝜌(𝐸) can be defined as [17]. 𝜌𝜌(𝐸) = � 2𝜋𝛿(𝐸𝐾 − 𝐸) … … … … … … … … … (31) By substituting Eq.(31) and Eq.(30) in Eq.(28) ,we get. Ket = 2π ћ (4πλ𝑘𝐵𝑇) −1 2 e −�eΦm−e𝜒𝜒� 2 4λ𝑘𝐵𝑇 ∫ ∑ exp −�ECB−eVapp−EF ° � 𝑘𝐵𝑇 ∞ 0 2π|HDA(k, r)| 2𝛿(𝐸𝐾 − 𝐸)𝑒 −𝐸 2 4𝜆𝑘𝐵𝑇 𝑑𝐸………………………………..(32) With recall formulated the above equation. Ket = 2π ћ (4πλ𝑘𝐵𝑇) −1 2 exp eVapp 𝑘𝐵𝑇 e −�eΦm−e𝜒𝜒� 𝑘𝐵𝑇 ∫ ƒ(E)e −(ECB−EF) 𝑘𝐵𝑇 |H(k,r)|2e −E2 4λ𝑘𝐵𝑇 ∞ 0 dE…33) Then the rate constant at semiconductor /metal contact . 180 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (1) 2014 𝐾et(contact) = 2π ћ (4πλ𝑘𝐵𝑇) −1 2 neq Nc exp −eVbi 𝑘𝐵𝑇 �𝜌𝜌(𝐸)ƒ0(E)|HDA(k, r)| 2e −E2 𝑘𝐵𝑇 dE … … … … … . . (34) ThenNc exp −ev𝑏𝑖 𝑘𝐵𝑇 = ∫ 𝜌(𝐸)ƒ0(E) V dE ∞ 0 is readily evaluated being equal to[11]. where 𝑉 is the volume of the until cell of semiconductor . Then Eq.(34) becomes. 𝐾et(contact) = 2π ћ (4πλ𝑘𝐵𝑇) −1 2 neq V ∫ 𝜌𝜌(𝐸)ƒ0(E)dE ∞ 0 exp −�eΦm − e𝜒𝜒� 2 4λ𝑘𝐵𝑇 � 𝜌𝜌(𝐸)ƒ0(E)|HDA(k, r)| 2e −E2 𝑘𝐵𝑇 dE ∞ o …………………………………..(35) The𝐾𝑒𝑡 depend exponentially on distance with a decay constant β,the𝐾𝑒𝑡 becomes [26] 𝐾et = 1 β Ket(contact)………………………..(36) The ratio of the term 𝑒 −𝐸 2 4𝜆𝑘𝐵𝑇 in Eq.(3-86) to 𝐸 𝑘𝐵 is 𝐸 4𝜆 , which is very small since 𝐸 ≈ 𝐾𝐵𝑇 ,i.e,0.025 eV and λ typically is 1 eV that the term 𝑒 −𝐸 2 4𝜆𝑘𝐵𝑇 can then be ignored [18]yielding 𝐾et = 2π ћ (4πλ𝑘𝐵𝑇) −1 2 exp −�eΦm − e𝜒𝜒� 2 4λ𝑘𝐵𝑇 𝑉 β ∫ 𝜌𝜌(𝐸)ƒ0(E)|HDA(k, r)| 2dE ∞ 0 ∫ 𝜌𝜌(𝐸)ƒ0(E)dE ∞ 0 … … … … … … (37) The averaged coupling electronic coefficient of matrix element square is given by |Η(𝐸, 𝑟)|2 = ∫ 𝜌(𝐸)ƒ0(E)|HDA(k,r)| 2dE∞0 ∫𝜌(𝐸)ƒ0(E)𝑑𝐸 [18].Then the rate constant of electron at metal/semiconductor interface is given by. 𝐾et = 2𝜋 ћ (4πλkBT) −1 2 exp −�eΦm − e𝜒𝜒� 2 4λ𝑘𝐵𝑇 𝑉 β |Η(𝐸, 𝑟)|2 … … (38) Whereλ Is the reorientation energy,ћ ,is Planck constant,Φmis the work founction of metal , 𝜒𝜒 is the work founcton of semiconductor ,and β is the attenuation parameter. The reorganization energy is given by[27]. λ° = (∆e)2 4πε0 � 1 2as � 1 ns2 – 1 εs � + 1 2am � 1 nm2 – 1 εm � − 1 4ds � nm2 − ns3 nm2 + ns2 1 ns2 − εm − εs εm + εs 1 εs � − 1 4dm � ns−nm2 2 ns2 + nm2 1 nm2 − εs − εm εs + εm 1 εm � − 2 Rms � 1 ns2 + nm2 – 1 εs + εm �� ………………………………………(39) Where 𝑛𝑚2 𝜀𝑚, 𝑛𝑠2,𝑅𝑚𝑠, 𝑎𝑠, 𝑎𝑚, 𝑑𝑠,and, 𝑑𝑚 are the dielectric constant for semiconductor and metal, refrective index for semiconductor and metal ,distance between metal semiconductor, radii of semiconductor and metal and the distance for semiconductor and metal to electroderespectivel. 181 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (1) 2014 Results Theoretical studies for electron transfer at Au/ ZnSe and Au/ZnS interface system are treated using quantum mechanical theory .We have applied a quantum model results under the weak coupling assumption for the matrix element coupling coefficient to the calculated rate constant of electron transfer at metal/semiconductor interface system using Eq.(38). The evaluate of the rate constant of electron transfer for this system depending on calculation of many parameters, such that: the reorganization free energyλthe exponent for the decay of the square of the matrix element with distance constantβ , the radius 𝑎𝑠, 𝑎𝑚, are the effective radii of both donor and acceptor . The reorganization energy is one of the most important parameters that is calculated using Eq.(39). Substituting in Eq.(39) the values of the static dielectric constant𝜀𝑚,and 𝜖𝑆 for metal , semiconductor and optical dielectric constant , 𝑛𝑚 ,and ,𝑛𝑆 from tables(1-2). Initially of the calculate of rate constant of charge transfer in metal/semiconductor interface system is the reorganization free energy that calculated depending on Marcus– Hush semi classical theory Eq.(39).Inserting the values of𝑎𝑠,𝑎𝑛𝑑𝑎𝑚, are the radii of semiconductor ,and metal, and the distance 𝑑𝑠 = 𝑎𝑠 + 1 ,𝑑𝑚 = 𝑎𝑚 +1,and 𝑅𝑚𝑠 = 𝑎𝑠 +𝑎𝑚 with values of refractive index and static dielectric constant for semiconductor and metal 𝑛𝑠 ,𝑛𝑚,𝜀𝑠, 𝑎𝑛𝑑𝜀𝑚respectively.The results are 0.71502218 , 0.670556312, and 0.673663776, there is on agreement with the experimental result[31]. Substituting these values with work function of metal4.080 [28],and affinity of semiconductor𝜒𝜒𝑠𝑒and value of coupling matrix element from table (4) in a Matlab designed program to evaluate the rate constant of charge transfer Eq.(38),results are summarized in table (3-5)for system Au/ ZnSe andAu/ZnS interface systems. Discussion A theory of charge transport across metal/semiconductor interface has been derived depending on quantum theory .In our theoretical model, we have been assuming the wave function for transfer of charge from donor to acceptor state describe in Hilbert space, and quantum well. When the metal bring to contact with semiconductor, the Fermi level for two material much be coincident at equilibrium state. The charges upon excitation has to be rapidly transfered into the metal before it can fall back to its ground state .The rate constant of charge transfer have been evaluated for ZnSe and ZnS semiconductors contact with gold Au metal system depending on calculation of many parameters, such that: the reorganization free energy work function of metal, affinity of semiconductor, and the coupling matrix element coefficient in table(3) .The rate constant of charge transfer in tables (3) to (5) for two systems Au/ ZnSe and Au/ZnS interface systems indicate the rate constant dependent on the reorganization energy 𝜆°(𝑒𝑉) ,and work founction Φm(𝑒𝑉) ,of metal and affinity of semiconductor 𝜒𝜒𝑠𝑒(𝑒𝑉). Consequently the rate of charge transport across metal/semiconductor system has large according with large reorganization energy and vice versa.This indicates the reorganization free energy is large for large dielectric constant for semiconductor .On the other hand the shift in the reorganization free energy is≈0.1.The ratio of rate indicated the system Au/ZnSe is active media for applied in devices technology according with Au/ZnS system. Conclusion A theoretical model for charge transport across metal/semiconductor interface has been derived depending on quantum theory provided a good model that describe the foundmental charge transfer processes. Also the rate constant of charge transfer at two systems Au/ Zn,Se 182 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (1) 2014 and Au/ZnSdepending on the reorganization free energy that is necessary to alignment and oriented of the configuration system .This energy is limited the ability of transfer . The rate constant is proportional exponentially with height barrier in exp −�eΦm−e𝜒𝜒� 2 4λ𝑘𝐵𝑇 ,for more high ,the rate is small.In summary ,it can be concluded from the results the Au/ZnSe system are in a good matching as compare with the other system. References 1. Daizadeh,I.;Medvedev,E.,S.;and stuchebrukhov,A.,A.(1999) ,Effectof protein dynamics on biological electron transfer. 2. Anderson,M. (2000) Tunning Electron Transfer reaction by selective excitation in prophyrin-acceptor Assemblies,Ph.D.thesisuppsala university. 3. Wang,Y.H.,Zhou,H.,Liu,T,and Guo,x.;(2003) The ET reaction between p-Nitrobenzoates and Dimethylaminonaphthaleue"Chines , Chem.Lett. 14 (2):159-162. 4. Hassooni,M.,A. (2009) A Quantum Mechanical Model for electr transfer at semiconductor/Dye Interface at solvent" Msc thesis. 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Gosavi S.,GaoY.,andRoudolf M.,(2001) Temperature dependent of the electronic factor of non adiabatic electron transfer ,J. of Elect.Chem.,500, 71-77 Table No.(1) Properties of semiconductors[29-30] ZnSe ZnS Semiconductor Properties Zinc blend Zinc blend] Crystal structure o.566 0.541 Lattice constant(nm) 5.42 4.08] Density(g/cm3) 9.2 8.3 Dielectric constant 2.62408 2.52226 Refractive index 2.6 3.6 Energy gap(eV) 4.09 3.9 Electron affinity(ev) Table No.(2) The reorganization energy for Gold metal/semiconductor interface system Reorganization energy λ(ev) System =a+1.0(A0) d=a+1.2(A0) d=a+1.4(A0) d=a+1.6(A0) Au-ZnS o.670556312 o.682074705 o.69202476 0.700700169 Au-ZnSe o.673663776 O.685728201 o.696178713 o.705299904 Table No. (3) The Coupling matrix element�|𝐇𝐃𝐀(𝐤, 𝐫)|𝟐� 2 for gold (Au) E(ev) ||HDA(E, r)|2| 2x1016 (𝑒𝑣)2 𝑚3 ||HDA(k, r)|2| 2x10-11 -1.35 5.889514591 0.4 -0.90 6.625703913 0.45 -0.25 7.361893239 0.5 0 8.098082563 0.55 0.15 8.834271886 0.6 0.3 9.57046121 0.65 0.5 10.30665053 0.7 0.75 11.04283986 0.75 1 11.77902918 0.8 184 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (1) 2014 Table No.(4) Rate of electron transfer between Au-ZnS interface H(k,𝐸)│2 *1016│ (𝑒𝑉 2 𝑚3 ) 11 .7 79 02 91 8 11 .0 42 83 98 6 10 .3 06 65 05 3 9. 57 04 61 21 8. 83 42 71 88 6 8. 09 80 82 56 3 7. 36 18 93 23 9 6. 62 57 03 91 5 5. 88 95 14 59 1 Rate of electron transfer Ket (m 4/Sec) (β A0)-1 2. 28 41 64 43 6E -1 4 2. 14 14 04 15 9E -1 4 1. 99 86 43 88 1E -1 4 1. 85 58 83 60 4E -1 4 1. 71 31 23 32 7E -1 4 1. 57 03 63 05 E- 14 1. 42 76 02 77 3E -` 14 1. 28 48 42 49 5E -1 4 1. 14 20 82 21 8E -1 4 0. 8 2. 03 03 68 38 8E -1 4 1. 90 34 70 36 4E -1 4 1. 77 65 72 33 9E -1 4 1. 64 96 74 31 5E -1 4 1. 52 27 76 29 1E -1 4 1. 39 58 78 26 7E -1 4 1. 26 89 80 24 2E -1 4 1. 14 20 82 21 8E -1 4 1. 01 51 84 19 4E -1 4 0. 9 1. 82 73 31 54 9E -1 4 1. 71 31 23 32 8E -1 4 1. 59 89 15 10 5E -1 4 1. 48 47 06 88 4E -1 4 1. 37 04 98 66 2E -1 4 1. 25 62 90 43 9E -1 4 1. 14 20 82 21 8E -1 4 1. 02 78 73 99 6E -1 4 9. 13 66 57 74 5E -1 5 1 1. 66 12 10 49 9E -1 4 1. 55 73 84 84 3E -1 4 1. 45 35 59 18 6E -1 4 1. 34 97 33 53 1E -1 4 1. 24 59 07 87 4E -1 4 1. 14 20 82 21 8E -1 4 1. 03 82 56 56 2E -1 4 9. 34 43 09 05 8E -1 5 8. 30 60 52 49 6E -1 4 1. 1 1. 52 27 76 29 1E -1 4 1. 42 76 02 77 3E -1 4 1. 33 24 29 25 4E -1 4 1. 23 72 55 73 6E -1 4 1. 14 20 82 21 8E -1 4 1. 04 69 08 7E -1 4 9. 51 73 51 81 8E -1 5 8. 56 56 16 63 6E -1 5 7. 61 38 81 45 4E -1 4 1. 2 185 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. 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Vol. 27 (1) 2014 Table No.(5) Rate of electron transfer between Au-ZnSe interface Reorganization energy λ (eV)=0.673663776 eV H(k,𝐸𝜖)│2 *1016│ (𝑒𝑉2 m3 ) 11 .7 79 02 91 8 11 .0 42 83 98 6 10 .3 06 65 05 3 9. 57 04 61 21 8. 83 42 71 88 6 8. 09 80 82 56 3 7. 36 18 93 23 9 6. 62 57 03 91 5 5. 88 95 14 59 1 Rate of electron transfer (β A0)-1 1. 46 75 51 69 9E -1 1 1. 37 58 29 71 8E -1 1 1. 28 41 07 73 6E -1 1 1. 19 23 85 75 5E -1 1 1. 10 06 63 77 4E -1 1 1. 00 89 41 79 3E -1 1 9. 17 21 98 12 E -1 2 8. 25 49 78 30 8E -1 2 7. 33 77 58 49 6E -1 2 0. 8 1. 30 44 90 39 9E -1 1 1. 22 29 59 74 9E -1 1 1. 14 14 29 09 9E -1 1 1. 05 98 98 44 9E -1 1 9. 78 36 77 99 4E -1 2 8. 96 83 71 49 5E -1 2 8. 15 30 64 99 5E -1 2 7. 33 77 58 49 6E -1 2 6. 52 24 51 99 6E -1 2 0. 9 1. 17 40 41 35 9E -1 1 1. 10 06 63 77 5E -1 1 1. 02 72 86 18 9E -1 1 9. 53 90 86 04 4E -1 2 8. 80 53 10 19 4E -1 2 8. 07 15 34 34 6E -1 2 7. 33 77 58 49 6E -1 2 6. 60 39 82 64 6E -1 2 5. 87 02 06 79 7E -1 2 1 1. 06 73 10 32 6E -1 1 1. 00 06 03 43 1E -1 1 9. 33 89 65 35 4E -1 2 8. 67 18 96 40 4E -1 2 8. 00 48 27 44 9E -1 2 7. 33 77 58 49 6E -1 2 6. 67 06 89 54 2E -1 2 6. 00 36 20 58 7E -1 2 5. 33 65 51 63 3E -1 2 1. 1 9. 78 36 77 99 3E -1 2 9. 17 21 98 12 1E -1 2 8. 56 07 18 24 1E -1 2 7. 94 92 38 37 E -1 2 7. 33 77 58 49 5E -1 2 6. 72 62 78 62 1E -1 2 6. 11 47 98 74 7E -1 2 5. 50 33 18 87 2E -1 2 4. 89 18 38 99 7E -1 2 1. 2 186 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I1@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (1) 2014 نتقال الشحنة لنظام سطح معدن/ شبھ موصلأل دراسة نظریة ھادي جبار مجبل العكیلي محسن عنید حسوني ظھر شھاب احمدم نوريرفاه اسماعیل لسراب سعدي جحی جامعة بغداد بن الھیثم/للعلوم الصرفة اكلیة التربیة قسم الفیزیاء/ 2014شباط 2قبل البحث في : ، 2013تشرین الثاني 24البحث في : استلم لخالصةا شبھ موصل أعتمد باستعمال أنموذج -لوصف الكمي لحركیة االنتقال االلكتروني غیر الكظیم عند سطحي نظام معدنا على التتابع.