S Misyuk - Influence of ge isovalent impurity on anisotropic parameters of n-si single crystals - страница 1


Місюк С. Вплив ізовалентної домішки Ge на анізотропні параметри кристалів n-Si І Місюк С. II Вісник ТНТУ. — 2012. — Том 65. — № 1. — С.53-58. — (механіка та матеріалознавство).

УДК 620; 538.9

S. Misyuk

Lutsk National Technical University


The summary. The paper presents results of influence Ge Isovalent Impurity on anisotropic parameters of n-Si single crystals. The experimental results for investigated single crystals are shown that introduction Ge Isovalent Impurity into n-Si significantly reduce relaxation time <tj> and electron mobility/uj brings to a reduction piezoresistance effect. Increasing of Ge Isovalent Impurity is changing the corresponding anisotropy parameters. Electron collision with Isovalent Impurity is close to isotropy scattering. Zone characteristic of single crystals n-Si with Ge Isovalent Impurity doesn 't change up to NGe< 201019 cm'3.

Key words: isovalent impurity, piezoresistance, single crystal, relaxation time, electron mobility parameter of relaxation times anisotropy.

С. Місюк


Резюме. Представлено результати досліджень впливу ізовалентної домішки Ge на анізотропні параметри кристалів n-Si. Експериментальні результати для досліджених кристалів показали, що введеня ізовалентної домішки Ge в кристали n-Si суттєво зменшує час релаксації <т1>, рухливість електронів та призводить до зменшення п 'єзопору. Розсіювання електронів ізовалентними домішками германію є близьким до ізотропного. Зонні характеристики кристалів n-Si з умістом ізовалентної дмішки Ge з концентрацією NGe<201019 cm-3не змінюються.

Ключові слова: ізовалентна домішка, п 'єзоопір, кристал, час релаксації, рухливість електронів, параметр анізотропії часів релаксації.

Introduction. Modern engineering development demands the new materials investigations. That's why n-Si single crystals with Ge Isovalent Impurity (Gell) investigations are very actual [1]. Inner local stresses arise during doping silicon crystals by germanium atoms as a result of difference between the covalent radius of Si (1.17 A) and Ge isovalent impurity, deforming the crystal lattice, changing its constant and, thus, influencing upon electrophysical and anisotropic properties of the crystal [2].

Objective. This paper presents results of piezo-resistanse effects and anisotropic parameters investigations of in n-Si single crystals with GeII with concentrations of Germanium NGe=2-1019^20-1019cm-3. The investigated crystals were grown by Chokhralsky

17 3

method with oxygen content ~10 cm- . The control samples without Gell were performed for comparison.

Results and discussion. Crystals of n-Si manifest maximal piezosensitivity in case when current J and stress P are directed along [100], that is P||J||[100]. Figure 1 presents the dependencies of longitudinal piezoresistance on pressure P||J||[100] at temperatures T=77K and T=300K. The common feature of plots pP/p0=f(P) is the decrease of piezoresistance coupled with the increase of Gell concentration. As tensoeffect is caused by anisotropy of the crystal, the presented results testify to the fact that doping the crystal with isovalent impurity changes the corresponding anisotropy parameters.

01        23456799       10      11 12

Р 1С"3 Ваг

Figure 1. Longitudinal piezoresistance of n-Si crystals and n-Si with different content of Gell for the case P || J|| [100] at T=77K [3]: 1 - n-Si without GeII, 2 - n-Si with 7VGe=2-1019crn3. 3 - n-Si with NGe=4-1019cm-3, 4 - n-Si with NGe=7-1019cm-3, 5 - n-Si with NGe=20-1019cm-3 and T=300K: 1' - n-Si without GeII, 3' - n-Si with NGe=4- 1019cm-3, 5' - n-Si with NGe=20- 1019cm-3

For crystals of n-Si piezoresistance pP/p0=f(P), which is brought about at P||J||[100] is determined as [4]:

P     0     3(1 + 2C)

C = ^ = e kT , (2) n1

where nj is the concentration of current carriers in lowering ellipsoids, n2 is the concentration of current carriers in rising ellipsoids, K is the parameter of mobility anisotropy [4]:

3 p [100] 1 K = - p--- (3)

Thus, the dependence pP=f(P) can be determined by expression (1) and experimental


data of po and p£00].

For deformations which afford the complete migration of the carriers into energy minima, we may write:


en^|, (4)


where n is a carriers concentration, ju\\ is a current carriers mobility along the main axis of ellipsoid.

As it is known, the parameter of mobility anisotropy is [4]:

K =     , (5)

where /j_L is the current carriers mobility in perpendicular to the main axis of ellipsoid direction.

The parameter of mobility anisotropy K can be defined from experimental data (Figure 1). In accordance to (3) and usage the expression (5) let's plot a dependence /i±=/Noe)- It is shown on Figure 2.

Magnitude /u\\ characterizes the mobility along the main axis of isoenergetic ellipsoid. For / :


where m\\ is a longitudinal component of effective masses tensor, <Ц\> is a relaxation time along the main axis of ellipsoid.

The analysis of the obtained results shows that / practically does not depend (accurate up to 4%) on the concentration of isovalent impurity. So, <Ц\> also practically does not change.

Let us consider the expression for //__:

Ml=— (O, (7)

where m_i_ is a transversal component of effective masses tensor, <rj_> is relaxation time transversal to the leading axis of ellipsoid.

As can be seen from Figure 2 ju± sufficiently depends on the GeII content in n-Si. There are grounds to consider that such behavior of //, ju__ and, hence, times of relaxation <т>, <т__> is provoked by corresponding effective masses тц, m__. It was determined by method of cyclotron resonance that m||=0.9163m0 and m_L=0.1905m0 [4]. So, we may affirm that mass тц is more "inert" to various changes in the crystal and, therefore, <t> practically does not change. As to m_, it is about one fifth as large as m|| and, therefore, its perpendicular component is more "sensitive" to various influences. So, time <г__>, describing pulse relaxation for m_, will change more substantially than <T>, which has been confirmed by the experiment.

Figure 2. ju1=/(NGe), /\=/(NGe) dependences for n-Si crystals with different content of GeII

Plots 1-5 on Fig. 1 furnish to determine the parameter of relaxation times anisotropy as:



where KT




\т±/ "4

Values of K and KT for n-Si crystals without GeII agree with paper data [4]. Figure 3 shows KT dependence on GeII concentration. The graph of parameter KT tends to 1 with the increase of NGe. The obtained result shows that scattering on GeII in silicon crystals is rather close to isotropic one.

15       N. , см"'


1 1 1 1 1

1    1   1 1 1 1II

1    1   1 1 1 1 II1




<    ^ 2







Figure 3. Dependence KT=f(NGe) for n-Si crystals with different content of GeII. 1 - theoretical curve by taking into account of anisotropy scattering on ionized donors [4], - experimental data from [4,5]; 2 - (▲) experimental data for investigated crystals

Usage experimental data (Figure 1) we may determine the constant of deformation potential S„ for n-Si crystals with different concentration of GeII. For temperature T=77K we have [6]:

= , = 1.63.10'!^. (9) where C is determined from (2), P is expressed in Bar.















































































0      1      2      3      4      5      6      7      8 P-10-i Bar

Figure 4. Dependences lg(C104)=f(P) for determination of Su - constants of deformation potential: 1

19       3 19 3

- n-Si with NGe=20-10 cm- ; 2 - for crystals - n-Si without GeII, and with NGe<7-10 cm-

Thus, in the case of the dominating contribution of the electrons inter-valley redistribution mechanism to the piezoresistance we obtain a linear dependence lg(C104)=f(P) (Figure 4). We find the constant of deformation potential Eu=9.3eV from the slopes of

19 3

dependences for pure n-Si and for crystals with GeII up to NGe=7-10 cm- . The decrease of deformation  potential   constant  down  to  Su=9.0eV  is  observed  for concentration

19 -3

NGe=20 1019cm-3. The obtained data testify to the fact that band and elastic characteristics of

19 -3

n-Si with GeII do not practically change at concentrations NGe<20-10 cm- .

Conclusions. Summarizing our investigations of inisotropic parameters and uniaxial piezoresistanse for n-Si with GeII we can make the following conclusions:

- introduction GeII into n-Si crystals actually don't influence on the values of <т> and /иц, but significantly reduce <rj_> and ju±. This reduction can be justified because the increasing of Ge concentration reduces quantity of the scattering centres and therefore increases the probability of impulse scattering. Herewith electron moves faster in equilibrium, and therefore the corresponding relaxation time decreases.

- introduction GeII into n-Si crystals brings to a reduction piezoresistance effect;

- increasing of GeII is changing the corresponding anisotropy parameters;

- electron collision with isovalent impurity is close to isotropy scattering;

19 -3

- zone characteristic of investigated crystals doesn't change up to GeII NGe<20-10 cm- .


1. Баженов, В.К. Изоэлектронные примеси в полупроводниках. Состояние проблемы [Текст] / В.К. Баженов, В.И. Фистуль // ФТП. - 1984. - T. 18, № 8. - С. 1345-1362.

2. Семенюк, А.К. Радіаційні ефекти в багатодолинних напівпровідниках [Текст] / А.К. Семенюк. -Луцьк: Надстир'я, 2001. - 323 c.

3. Semenyuk A., Korovytsky A. Study of electrophysical parameters and tensoeffects in n-type Si<Ge> crystals / A. Semenyuk, A. Korovytsky // Functional materials. - 2001. - Vol. 8, №3. - Р. 493-497.

4. Электрические и гальваномагнитные явления в анизотропных полупроводниках [Текст] / П.И. Баранский, И.С. Буда, И.В. Даховский, В.В. Коломоец. - К.: Наукова думка, 1977. - 269с.

5. Розсіювання електронів у n-Si [Текст] / М. Аше, В.М. Васецький, О.Г. Максимчук, О.Г. Сарбей // УФЖ.- 1970.- Т. 15, № 10.- С.1691-1698.

6. Hensel J.C. Resonance in Uniaxially Stressed Silicon Cyclotron / J.C. Hensel, H. Hasegawa, M. Nakajama // Phys. Rev. - 1965. - Vol. 138, № 1A. - Р. 1552-1560.

7. Баранський П.І. Неоднорідності напівпровідників і актуальні задачі міждефектної взаємодії в радіаційній фізиці і нанотехнології [Текст] / П.І. Баранський, А.В. Федосов, Г.П. Гайдар. - Київ, 2006. - 316с.

Отримано 06.02.2012


Похожие статьи

S Misyuk - Influence of ge isovalent impurity on anisotropic parameters of n-si single crystals