LOCAL ENERGY LEVELS RESULTING FROM THE THERMIC OPERATION OF p-TYPE Ge-Si SOLID SOLUTION MONOCRYSTALS

ФИЗИКО-МАТЕМАТИЧЕСКИЕ НАУКИ

LOCAL ENERGY LEVELS RESULTING FROM THE THERMIC OPERATION OF p-TYPE Ge-Si SOLID SOLUTION MONOCRYSTALS Gahramanov N.F.1, Garayev E.S.2, Gashimova A.I.3, Sadraddinov S.A.4 Email: Gahramanov1171@scientifictext.ru

SUMGAIT STATE UNIVERSITY, SUMGAIT; 4Sadraddinov Sadraddin Alekper oglu - Candidate of Physical and Mathematical Sciences,

Associate Professor,

DEPARTMENT OF GENERAL PHYSICS AND METHODS OF TEACHING PHYSICS, BAKU STATE UNIVERSITY, BAKU, REPUBLIC OF AZERBAIJAN

Abstract: as a result of thermal processing, the local energy levels of the Ge-Si solid monocrystals were determined. The samples first were heated at 8500 Celcius 0.5 to 1 hour and then sharply cooled. The temperature dependence of the Holl coefficient was determined before and after the thermal operation of the samples in the temperature range 77^300 K and accordingly, s0 = 0.085 eV and s02 = 0.30 eV were obtained. The value we get here is in line with the value we received before within the scope of the practice error. This confirms the accuracy of the assumption that the first and second thermal local acceptor levels are created from the same center. Keywords: solid solution, monocrystalline (single-crystal), supercooling (extreme cooling), alloy, priming, concentration.

ЛОКАЛЬНЫЕ УРОВНИ ЭНЕРГИИ В РЕЗУЛЬТАТЕ ТЕРМИЧЕСКОЙ РАБОТЫ МОНОКРИСТАЛЛОВ ТВЕРДОГО РАСТВОРА

Ge-Si p-ТИПА

Гахраманов Н.Ф.1, Гараев Э.С.2, Гашимова А.И.3, Садраддинов С.А.4

Аннотация: в результате термической обработки определены локальные энергетические уровни твердых монокристаллов Ge-Si. Образцы сначала нагревали при 8500 C от 0,5 до 1 часа, а затем загружали охлажденными. Температурная зависимость коэффициента Холла определялась до и после тепловой операции образцов в интервале температур 77^300 Кельвин и, соответственно, были получены значения е0 = 0,085 эВ и s02 = 0,30 эВ.

Значение, которое мы получали здесь, соответствует значению, которое мы получили ранее в рамках экспериментальной ошибки. Это подтверждает точность предположения о том, что первый и второй термические локальные акцепторные уровни создаются из одного и того же центра.

UDC 621.315.592

Р-type crystals, usually concentrated 1014+1015, are obtained when producing of solid solutions Ge-Si. This is the concentration of free holes created by extensible shallow acceptortype doping agent centers at room temperature. The p-type crystals, which have a larger concentration, are obtained by adding more Ga doping agenton them.

Figure 1 shows the dependence of the Holl coefficient on the temperature (77^300K) before the thermal operation (curve 1) and after it (curves 2 and 3) of the samples cut off from the p-type Ge-Si solid solution monocrystalline containing 18 at.% of Si. As it is known from the curve 1, the Holl coefficient of the sample remains unchanged at all intervals before the thermal operation from the liquid nitrogen boiling point (77 K) to room temperature. This means that in the whole region there exists a doping agent, and all the doping centers are full. Completely full doping agent centers in Ge (and also in Ge-Si solid solutions) at the boiling point of liquid nitrogen generates extremely low energy levels [1].

Following this formula R = — =--- (1)

concentration of free holes is P = 3,7 • 1015 sm3. Let&s name the concentration of the shallow acceptor centers, which existed before the thermaloperation, as N^3^. It is obvious that N^3^

equals to this value (for each acceptor centered in a freehole): Nf) = 3,7 • 1015 sm3. At (1) RHoll&s coefficient is a constant that depends on the e - electron load, the p-hole concentration, and the dependence of the A - scattering mechanism (Holl - factor). At acoustic scattering mechanism _ 3л

of phonon A =-. We have used this value of A in formula (1).

In fig.1, the curves 2 and 3 of the sample were created after heating it 0.5 and 1 hours at 8500C and cooling it sharply. As you can see, after the thermal operation, the temperature dependence of the Holl coefficient has changed dramatically. As the temperature drops above the boiling point of the nitrogen, Holl&s coefficient decreases in a half-logarithmic scale, remains stable in a certain region, then decreases linearly and eventually this decrease is even more acute. The change in the different temperature regions is related to the change in the degree of activation of two different additive centers. The sharp decline in the above level value of temperature depends on the conductivity to the specific region from the additive region.

Note that, since the electrons in Ge (as well as in Ge-Si solids) are larger than the hole (approximately twice) of the holes, the concentration of the holes becomes equal to electrons when it passes through the additive region to the specific region by increasing the temperature in the p-type material. That&s why the type of conductivity goes from p to n. This is accompanied by the change of the sign of the Holl coefficient R from the zero in the p type material.

Fig. 1. Temperature dependence of the Holl coefficient beforethermal operation (curve 1) and after it (curves 2, 3) in the Ge-Sisolid solution (18 at% Si) monocrystalline

Fig. 1 shows that additive centers in the low temperature region in 2nd and 3rd curves (which we call the first and second thermal acceptor centers) are finished when the temperature rises. Then, the Holl&s coefficient (R) reaches the saturation value. This value of the Holl coefficient

determines the total concentration of the concentration of the first thermicacceptor ( N0a) and

theconcentration of the initial shallowacceptorcenters ( N0a) inthesample. Let&s find this sum for the curve 2 :

N0a)+ N{a) =

= 7,3-1015sm3.

Let&s find the value for A/n

Nfi") =(7,3-3,7)-1015 sm3 = 3,6-1015 sm"3. (3) Thus we have found the concentration of the first thermic acceptor centers. Let&s find its activation energy. For this, we can use the electric neutrality equation of the crystal.

According to the neutrality conditions of the crystal, the sum of the negative charges in the sample should be equal to the sum of positive charges [2];

e • P =

F-Esl kT

e+N0a)- e.

Here, the left side of equality is the amount of positive charge per unit volume of crystal, and

the right side is the amount of negative charge that volume. P - showsthe concentration of the free holes in the valence zone, e - the charge of the electron (its absolute value), F - Fermi level, Ea1 -the energy of the first thermic acceptor level, the k - Boltzmann constant, the T - absolute temperature, y1 - the degree of degeneration of the level.

At (4) considering that Ea1 = —Eal + eal (AE gis the width of banned time, sa1 - is ionization energy of the first thermic acceptor center), we also need to make certain simplifications:

P=(N0a)+Nia )N

F+AE„

We can determine F considering the dependence of the hole concentration on the Fermi level using the equation (5):

P = Nv exp

F + AE^

Then sa1 will be associated with F. We can use this connection and find sa1. However, if this method is used to determine sa1, its error will be greater, as it is seen from figure 1, the temperature range in which the level is active and the hole concentration change region are relatively small. However, by applying the method proposed in [3], we can determine sa1 with high precision. Let&s include such substitution:

pi = yx Nv exp

We can determine £01with high accuracy by adding this equation and puting [3] here. On the other hand, as seen from (7), the temperature dependence of p[ helps us to find sal:

Igfer&& 2)= IgC - (8)

k• 103 T

Here is the output of C - fixed parameters. We have pointed it out:

ijlrnm; )&2 C = --—.

(8) is the linear equation. From its angle coefficient:

—-a- = tgv and ea=0,198 tga (eV). (9)

k •io3

Temperature dependence calculated by formula (8) in the curve 1 of fig. 1 is given in half -logarithmic scale in fig.3. According to the angular coefficient of this linear dependence (9), the activation energy of the acceptor center is equal to sa1 = 0.085 eV.

The curve 3 in fig. 1 were taken from the sample that was heated for a longer period and were sharply cooled and, as is obvious from the picture, the concentration of thermic receptors is slightly

higher. The temperature dependence of p[ for that crystal (8) is shown in fig.2 in fig.3. Because the curves 2 and 3 are parallel to each other (fig.2), the calculated activation energy for the expression (9) is the same.

As a result of the thermal treatment, the second acceptor center exhibits a higher temperature. Their activation energy is larger than the first thermic acceptor centers. Let us point out the general

concentration of the second thermic acceptor centers as N2a) and the activation energy as ea2. It is possible to assume that the first and second local levels generated in the zone of the prohibited by thermal treatment are created by the same centers with different ionization degree.

As can be seen from fig.1, it is impossible to observe the second thermal centers in the upper temperature zone due to the specific conductivity. However, we can easily define sa2 by using the upper temperature range, accepting the assumption that both levels are created by the same center. The parameter of the second acceptor level (7) is as follows:

p2 =/2 Nv exp

It can be stated that in this case p&2 is expressed in the practice determined by the parameters:

p2- p(/V0a)+Nf) (n)

tJ2 T77t7\\ 7770 «,ta\\ \\ (11)

Fig. 2. Dependency of the statements

lg(r-3/2 )dl q(t-3&2 )

In fig.2 the dependence of

on -that was calculatedin (11) for the curves 2

and 3 is demonstrated in fig.2 for the curves 2& and 3&. The activation energy specified here is the same as that of an experiment 0.30 eV (sa2 = 0,30eV ). Although the value of sa2 for two different examples here is the same, we calculated it based on the assumption that both types of impurity centers are the same. However, we have no direct evidence of the fact that both levels are created by the same centers. That&s why it is of great interest to set the price of sa2 in a more reliable way.

Fig. 3. Energy levels corresponding to local centers in the prohibited zone

For this purpose, it is necessary to use an example of a «-type conductivity that would completely compensate for the shallow acceptor centers. In order to clarify this, the scheme of these levels is shown in fig.3 of the crystal prohibited zone. In the figure, the bottom of the Ec -conductivity zone shows the maximum of the Ev - valent zone. Acceptor centers are located near the valent zone in the prohibited zone, donor centers created by Sb are located near the conductivity zone. In the picture, the concentration of stibium has been shown to be equal to the sum of the

concentration of shallowacceptorcenters [N0a) and first termic acceptorcenters [Na)). Thus,

electrons can pass only to the second thermic acceptor centers from the valent zone in the investigated temperature region. One of these passages is shown in fig.3. Each passage creates a

free hole in the valence zone. Let&s point out the concentration of them as p . In this case, we find

from the crystal&s electric neutrality equation:

(w0(a) + N1a) )+

y2 e KT +1J

= p + N

Here, the left side is the concentration of negative charges and the right side is the concentration of positive charges (each side is divided by one particle charge).

The equation is simplified because of N^ = + N(a):

p = N2a) - N2

F - Ea2 KT

Let&s note, that we do not use the condition where N| and N2a are the same, they can be

different. On the other hand Ea2 = —AEg + sa2 , we can put eq. (6) in eq.(13). Then eq. (8) will be like:

, ^ ea2 • 0,434 1000 = igCj —- a2 &

Finding sa2 from the angular coefficient of this line arequation:

^ = ^^T & tQa = 0At9a[eV) .

In (14), C1 is a constant and is defined as follows:

C =(y2 N2a) )12 • 2

r2xm*p k ^ /4

Fig. 4. Temperature dependence of the Holl coefficient after thermal operation in compensated n-type

Ge-Si monocrystal (18% at. Si)

Fig. 4 shows the temperature dependence of the Holl coefficient of the sample made of monocrystalline n-type Ge-Si solution containing 18 at.% Si.

Fig. 5. The dependence of lg^// ^ j on 1000 that was calculated from the curve 2 in fig. 4

Sb impurity was added to cyristal in the process of changing its color to blue. Before the thermal operation, the sample had n-type conductivity (curve 1) and the concentration of Sb was NSb=7,2-1015cm3. The sample was heated to 850OC for 1 hour and then turned into p-type after sharp cooling. The temperature dependence of the Holl coefficient (curve 2) was practically fully compensated for the first thermic acceptor centers. However, although in a very small amounts, the first thermic acceptor centers remain unaffected. Exceeding the linear dependence at low temperatures indicates this. However, the concentration of holes varies a quarter in the linear part depending on the temperature dependence. This allows you to set sa2 with great accuracy.

lg(FT-34)- 1000

For the linear part of the 2 curves in fig.4, the graph of dependence of IgRT j- on —-— is

given in fig. 5. The calculated value of sa2 is sa2=0,31 eV, using the formula (15) of the angular coefficient of the obtained linear dependence. The study of other crystalline samples also gave the same result. The value we get here is in line with the value we received before within the scope of the practice error. This confirms the accuracy of the assumption that the first and second thermal local acceptor levels are created from the same center.

References / Список литературы