CHANGE IN THE RESISTANCE OF THE SEMICONDUCTOR IN THE VARIABLE DEFORMATION FIELD

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1 CHANGE IN THE RESISTANCE OF THE SEMICONDUCTOR IN THE VARIABLE DEFORMATION FIELD M. AHMETOGLU (AFRAILOV) 1, G. GULYAMOV 2, S. H. SHAMIRZAEV 2, A. G. GULYAMOV 2, M. G. DADAMIRZAEV 2, N. APRAILOV 2, F. KOÇAK 1 1 Deparmen of Physics, Uludag Universiy, 16059, Görukle, Bursa, Turkey, afrailov@uludag.edu.r 2 Deparmen of Physics, Namangan Sae Engineering and Technology Insiue, Namangan, Uzbekisan Received Sepember 12, 2006 In his work he influence of variable deformaion on concenraion of nonequilibrium carriers and resisance chances of he semiconducor have been invesigaed. The phase shif define by frequency of deformaion and life ime of nonequilibrium carriers, have been shown beween variable deformaion and semiconducor resisance change. I is esablished ha, in a plane resisance-deformaion he phase rajecory forms hyseresis loop. When conduciviy varies only due o elecronic processes hen he hyseresis loop remains smooh. A he consan frequency and ampliude, he form of he flucuaion does no change. I is shown ha, he srucural changes in he sample leads he hyseresis loop movemen in phase space. Key words: semiconducor, deformaion, hyseresis loop. A influence of deformaion changing of he energy band srucures leads o change of concenraion of carriers and redisribuion of carriers beween he energy valleys [1]. These changes in urn leads o change of resisance of he sample [2]. If exernal deformaion is variable, change of he resisance of he sample on ime occurs o some backlog from he enclosed mechanical influence. Le's consider he response of excess concenraion of elecrons n e on variable deformaion. Deformaion can induce generaion of he elecrons wih a speed g e besides, excess elecrons can ac from oher area of he sample [3]. Concenraion can be deermined by he equaion of a coninuiy n e ne = g + 1 e Jn (1) τ e Where J n densiy of a curren of elecrons, τ is a lifeime of elecrons. For he homogeneous sample he equaion of a coninuiy is Paper presened a he 7 h Inernaional Balkan Workshop on Applied Physics, 5 7 July 2006, Consanþa, Romania. Rom. Journ. Phys., Vol. 52, Nos. 3 4, P , Buchares, 2007

2 344 M. Ahmeoglu (Afrailov) e al. 2 ne ne = ge (2) τ Thus, he reasons of change of resisance can be he diversified. Generaions speed g e, caused by changing of widh of a band or heighs of a barrier, raher quickly adaps o exernal pressure, i.e. pracically repeas dependence of pressure on ime. However, concenraion of nonequilibrium carriers is defined no by insan value of he generaions speed, and all previous values g e. If during he ime = T 1 speed of generaion of excess carriers is zero, his ime he consan deformaion ε 1 is applied (g(ε 1 ) also will be a consan). The decision of Eq. (2) for boundary condiions n e = 0 a = T 1 is T1 ( ) ne = ge () ε τ 1 exp ( > T 1) (3) τ If deformaion is sopped a momen T 2, ha n e is reduce as T2 T1 ( ) ( ) ( ) ne = ge () ε τ exp exp exp ( > T 2 ) (4) τ τ τ The decision of he Eq. (2) for a case when he deformaion is any funcion of ime as [3] 0 ne() = ge( 0)exp( τ ) d 0 (5) Expression (5) can be used o define how he value of nonequilibrium concenraion reacs on varying deformaion. We shall assume, ha deformaion is varies as ε=ε sin( ω ) (6) 0 0 Then he widh of he forbidden zone changes under he same law Δ E =Δε (7) g Where Δε is he deformaion poenial [2]. Speed of hermal generaion has exponenial dependence on widh of he forbidden zone and emperaure of a laice [4]. In his case from he general hermodynamic reasons, generaion speed of nonequilibrium carriers can be presened as Δε( 0 ) ( kt ) g () = g e 1 (8) Then from expression (5) and (8) we have e 0

3 3 Resisance of he semiconducor in variable deformaion field 345 Δε( ) ( ) ( kt ) 0 0 τ 0 τ 0 n () = g exp e 1e d (9) e Seing an obvious kind of ime dependence of deformaion ε(), i is possible o receive he ime dependence of he concenraion n e (). Then having excluded ime from hese equaions, i is possible o ge a phase rajecory of process on a plane n e ε or he equaions connecing n e and ε: f ( n, ε ) = 0. The equaion (9) in enough wide area of deformaions for funcion ε( 0 ) allows o describe change of concenraion of carriers. To show a mehod of recepion n e ε dependences we shall consider, Δε << 1 (weak deformaion) kt Then expression (9) can be presened in he form of ( ) 0 Δε 0 0 kt τ n () = g exp e d τ (10) e Le he deformaion enclosed o he sample is ε=ε sin( ω ) (0 < 0 < π/ω) 0 0 And oher momens of deformaion are no presen. Then from (10) i is had ( ) 0 = Δε ω τ 0 = τ 0 0 kt 0 Δε ωτ2 sin( ω) g0 2 2 n () g exp sin e d e ( ) = ω + cos exp +ω τ ωτ τ, kt 1 (0 < 0 < π/ω) (11) Afer he erminaion of deformaion in he Eq. 10 op limi of inegral should be π/ω Δε ωτ2 n π e() = g0 1+ exp( ) exp( π kt 2 2 ) ( 1 ) 1+ω τ ωτ τ > (12) ω The response of concenraion excess elecrons on deformaion in case ωτ = 1 is shown in Fig. 1. I is possible o show ha, he densiy of he nonequilibrium elecrons, arising a sinus wave deformaion, conains consan and variable componens. Thus, he variable componen of concenraion lags behind from he sinus wave deformaion on a phase on a θ = arcg(ωτ). Hence, beween variable deformaion and change of resisance of he semiconducor here is some always shif of a phase.

4 346 M. Ahmeoglu (Afrailov) e al. 4 Fig. 1 a) Dependence of concenraion on ime (coninuous curves), dependence of deformaion on ime (dashed lines); b) The phase rajecory of process of deformaion forms he hyseresis loop. Fig. 2 a) Dependence of ε on ime for recangular impulses; b) he phase rajecory of dependence he concenraion n e versus deformaion ε for a recangular impulse. Any periodic deformaion can be decomposed in he Fourier series, which are phase displacemen beween he componens of Fourier series for each frequency, and he deformaion and he concenraion. The form of he dependence of deformaion on he ime srongly influences he phase porrai of he flucuaing moion of a change in he resisance of model from he deformaion. We analyze he qualiaive dependence of he form of he phase rajecories of he concenraion of he excess carriers n e on he ampliude ε 0 and he periods T of he square pulses of deformaion. The square pulse of deformaions has an ampliude ε 0 and a period T moreover T = T i + T 0, here T i is he period of he pulse of deformaion and T 0 is he period of he pause beween he pulses. If we increase pulse frequency, and he ampliude o leave of consan he area of loop decreases under he influence of he square pulse of he deformaions.

5 5 Resisance of he semiconducor in variable deformaion field 347 Wih he ampliude reducion he hyseresis loop decreases as along he heigh, hus he widh, moreover simulaneously i displaces o he origin of coordinaes (Fig. 3a, b, c). If he ampliude of deformaion decreases he concenraions of minoriy carriers also decreases. The area of hyseresis loop increases in he lower frequencies. This increase in he area of loop relaes only wih he recangular volage pulse. If he shape of pulse is smooher, ha wih an increase in he oscillaory period he area of loop can again will decrease. Fig. 3 A phase porrai of dependence of concenraion from duraion of deformaion (a) for various recangular impulses of deformaion (b, c). Thus, he phase rajecories n e ε srongly depend on he frequency of he deformaion of ha applied o he model. Therefore i will convenienly presen phase rajecories for differen frequencies in he phase space, moreover as he hird of axis i is convenien o ake pulse frequency ν or is period T = 1/ν. As he example o phase rajecory in phase space n e ε ν (n e concenraion, ε 0 deformaion, ν frequency) le us examine a change in he concenraion of minoriy carriers under he acion of he square pulses of deformaion (Fig. 4). In he hree-dimensional space (n e ε ν) he phase rajecories for differen frequencies will be deermined by he secions of he curved surface of prism. (Fig. 5). If deformaion no recangular and smooher wih he specific period T, in his case phase he rajecory of he flucuaing moion of he concenraion of excess carriers will draw he curvilinear conical surface (Fig. 6). Wih a change in he parameers of projecion sysem of phase rajecory on he phase plane n e forms spiral (Fig. 7). Wih an increase in he ime he concenraion of equilibrium carriers, i also slowly changes. This change in carrier concenraion affecs he resisance of film and he period of he life of nonequilibrium elecrons. This indicaes, ha

6 348 M. Ahmeoglu (Afrailov) e al. 6 Fig. 4 A phase porrai changes of concenraion n a consan ampliude ε 0 (a) and for hree various on duraion of recangular impulses T 1 > T 2 > T 3 (b, c, d). Fig. 5 The phase rajecory (n e ε ν). Fig. 6 The phase rajecory of excess carriers in (ε n ν) space, lies on he conical surface.

7 7 Resisance of he semiconducor in variable deformaion field 349 Fig. 7 Wih an increase in he oscillaory period he helix increases is ampliude. he parameers of he sysem slowly changes and herefore hyseresis loop sails in phase he space of ΔR ε and rajecory in he experimens is no locked by phase. Evidenly, floaing hyseresis loop ino ΔR ε o plane i is possible o explain wih a change in he parameers of film wih repeaed he applicaion of cyclic deformaion. From oher side here is a phase shif beween he sress and he srain which i is deermined by Debye's losses. In his case, i is necessary o use Debye's formulas for he pliabiliy, which mus be conneced wih he processes of relaxaion [5]. Evidenly, he hermodynamic heory of ordering [5] can explain he shifs of hyseresis loop in he phase plane of ΔR ε resisancedeformaion. Possibly, change and shif of hyseresis loop wih an increase in he number of cyclic deformaions i is conneced wih he srucural changes in he film may be conneced wih he faigue of maerial. However, his is no sill accuraely esablished. One should separaely emphasize ha, he form of hyseresis loop srongly depends on he emporary dependence of he deformaion of ε(). For example, wih a very slow change in he pressure he resisance of model compleely manages afer changes in he pressure and phase displacemen beween he deformaion and he resisance is absen. In his case, he area of hyseresis loop is urned ino nul. If here are no changes in he laice a slow change in he deformaion hyseresis is no observed. Wih an increase in he rae of change in he deformaion line of he dependence of resisance on he pressure phase rajecory is convered ino he hyseresis loop or he helix (Fig. 8). Wih he high frequencies of a change in he pressure again he area of loop approaches zero. Evidenly, when he ime of a change in he deformaion of he order of he characerisic of he relaxaion ime of resisance τ, ha he area of hyseresis loop is maximum. A change in he hyseresis loop wih he frequency i mus conain imporan informaion abou he relaxaion processes in he films. If hyseresis loop

8 350 M. Ahmeoglu (Afrailov) e al. 8 Fig. 8 Wih an increase in he frequency firs he area of hyseresis loop grows wih he high frequencies he hyseresis loop i will become he horizonal secion (ν 1 0 < ν 2 < ν 3 < ν 4 ). was formed only due o he elecronic processes and he srucural changes in he film, his does no occur, hen he hyseresis loop should be closed and i in due course in ΔR ε plane should no moves. Really due o mechanical pressure here are irreversible changes in a crysal laice subsequenly i he characerisics of a sample wih ime are slowly vary. As a rule elecronic processes in he model, i flows considerably more rapid, han change in he crysal srucure. For he analysis of experimenal resuls and heoreical sudies convenienly inroduces wo characerisic ime τ e he ime of elecronic processes and τ i ime caused wih he change in he laice. Moreover τ e << τ i. Thus, rapid processes are caused elecronic by processes, and slow wih he changes in crysal laice. Changes in crysal laice mus give disrupion in he hyseresis line and wih he periodic repeiion hyseresis loop i mus i will become he helix (Fig. 9).

9 9 Resisance of he semiconducor in variable deformaion field 351 Fig. 9 a) for he locked rajecories relaxaion is only elecronic; b) he disrupion of loop is caused by srucural changes in he model. On he basis of he lead (carried ou) researches, i is possible o draw he following conclusions: Exisence hyseresis loops of a phase rajecory in a plane resisance deformaion (R ε) i is caused relaxaion by processes in a sample; Closed relaxaion he loop is caused only by elecronic processes and change in a crysal laice do no occur. Open screw rajecory on (R ε) planes i is caused by irreversible srucural changes in a crysal laice. REFERENCES 1. G. L. Bar, G. E. Pikus, Symmery and deformaion effecs in semiconducors, Nauka, 1972, P. S. Kireev, Physics of semiconducors, VSH, 1975, J. Blekmor, The heory of he recombinaion speed in semiconducors. 4. Problems in hermodynamics and he saic physics, Edied by Lansberg, MIR, Moscow, 1974, B. Ridli, Quanum processes in semiconducors, MIR, Moscow, 1986, A. Nowick, W. Heller, Adv. Phys. 12, 251 (1963).