RU2028697C1 - Method of determination of parameters of semiconductor materials and heterostructures - Google Patents

Abstract

FIELD: checking of electrophysical parameters. SUBSTANCE: essence of invention consists in application of sequence of voltage pulses to sample which amplitude changes by linear law with specified duration, in measurement of electric parameter of applied voltage and in determination of parameters of structures with the help of obtained dependence. Charge running off from investigated sample after disconnection of applied voltage is measured as electric parameter. After ending of each voltage pulse to time moment t dependence of charge of charge on charge of amplitude of pulses is measured by which concentration of dopant and value of potential barrier over separation boundary can be determined, for instance. Duration of pulses and time t of measurement of change running off p⁺-i-n⁺ s can be changed to take into account contribution of traps. EFFECT: expanded class of investigated structures due to use of MIS and 10^-6- 10² structures which capacitance depends on bias voltage and state of charge of traps, increased sensitivity and simplified circuit for realization of method. 3 cl, 3 dwg

Description

 The invention relates to the control of the electrophysical parameters of materials and can be used to study and control the parameters of semiconductor materials and heterostructures (MIS, MDM).

A known method for determining the parameters of semiconductor materials and heterostructures (in particular, determining the doping profile of the height of the potential barrier at the interface, etc.), which consists in measuring the dependence of the differential capacitance of the structure C _D on the external bias voltage applied to the sample. In the most common variant of the method in practice, the bias voltage V applied to the sample slowly changes in a given range of values, and the capacitance C _{D is} measured using an alternating sinusoidal voltage U of constant amplitude supplied to the sample simultaneously [V].

 The disadvantage of this method is the inability to determine the parameters (potential barriers at the insulator - semiconductor interface, doping profile of semiconductor materials) in heterostructures with a high density of states (traps), the capture of carriers on which leads to screening of the bias voltage applied to the structure.

 A known method to eliminate this drawback [2]. This is achieved by applying a bias voltage to the sample in the form of a sequence of rectangular pulses with different amplitudes that vary in a given range. The duration of the pulses of the bias voltage V and the frequency of the alternating sinusoidal voltage U, simultaneously with V supplied to the sample, can be chosen so that there is no time to recharge the states in the structure under study, and accordingly, the screening of V. In addition, the pulse mode of application V allows you to exclude or significantly reduce the screening of the bias voltage by free minority charge carriers.

The disadvantage of this method is its unsuitability for determining parameters in a large class of structures whose differential high-frequency capacitance C _D does not depend on both slowly varying and impulse bias voltage, and also does not depend on the charge state of traps, for example, in heterostructures with semiconductor layers , the thickness of which is much less than the expected width of the space-charge region, in metal-dielectric-metal structures or in pin structures.

 The aim of the invention is to expand the class of structures under study (due to MDM and p-i-n structures, that is, structures having an almost constant capacity), as well as improving accuracy and simplifying the circuitry for measuring.

= Q_i+1(V_i+1)-Q_i(V_i) где V_i - амплитуда импульса напряжения смещения, i = 1,2...n-номер импульса.This goal is achieved by the fact that according to the known method, including applying to the sample a sequence of pulses of bias voltage with an amplitude that varies linearly, measuring the dependence of the electric parameter on the applied bias voltage and determining the parameters of the structures using the obtained dependencies, select the charge as the measured electric parameter flowing down from the test sample after disconnecting the applied bias voltage (i.e., unlike the prototype at the same time, the sinusoidal voltage U necessary for measuring the differential capacitance is not supplied to the sample at the same time as the bias voltage V), the flowing charge Q is measured at a given time t ₁ from the beginning of the discharge and the dependencies are found
ΔQ (V _i )

= Q _{i + 1} (V _{i + 1} ) -Q _i (V _i ) where V _i is the amplitude of the bias voltage pulse, i = 1,2 ... n is the pulse number.

 The method allows you to change the filling of the reloading centers, changing the duration τ of voltage pulses, or by illuminating the sample with light absorbed in the studied structure, which allows you to get additional information, in particular, about the capture cross section of the rechargeable centers.

 The proposed method is implemented using the device shown in FIG. 1.

 The device consists of a charging voltage source 1, an integrator on an operational amplifier 2, analog memory cells 3, 4 of an automation unit 5, which includes a charge-discharge driving cycle generator, a charging duration generator, a key management logic. General management is carried out using a microcomputer 6, the results are displayed and / or plotter 7.

 The proposed method is characterized by the following sequence of operations.

1. A voltage pulse of duration τ and amplitude V _{i is} applied to the sample.

 2. The sample is switched from the voltage source to the measuring circuit (at the moment the pulse ends).

3. Measure the amount of charge Q _i (V _i ), drained from the sample to a given point in time t ₁ after switching.

 4. Switch the sample from the measuring circuit to the voltage source.

5. A voltage pulse of duration τ and amplitude V _{i + 1} = V _i + Δ V is applied to the sample (at the time of connecting the sample).

6. Repeat the operation in p.p. 2, 3, 4, while determining Q _{i + 1} (V _{i + 1} ).

7. Determine Δ Q = V _{i + 1} (V _{i + 1} ) - Q _i (V _i ).

 8. Repeat the operation in p.p. 1-7, changing each time the amplitude of the pulse by Δ V.

 9. Using the measured and known values, structural parameters are calculated (for example, the concentration of charge carriers is determined by numerical differentiation).

 Distinctive features of the proposed method in comparison with the prototype are the following.

 Since, unlike the prototype, the measured parameter is not the capacitance, but the charge, it becomes possible to carry out measurements on structures whose high-frequency capacitance does not depend on the charge bias voltage and on the state of levels, for example, p + -i-n + structures (including structures with quantum wells).

 The proposed method is more informative compared to the prototype and in relation to those structures whose study is possible using the prototype, as it allows you to change the filling of rechargeable centers, changing the duration τ of voltage pulses, or illuminating the sample with light absorbed in the studied structure, which makes it possible to take into account contribution of traps with different recharge time constants for a large set of structures of practical interest.

 Charge measurements in comparison with capacitive measurements in many cases give a significant gain in accuracy. For example, for MIS structures, the magnitude of the measured charge can be represented as.

q A k T ln(t₂/t₁)N_ss(E_o) где С_о - емкость диэлектрика,
C_sc(t₁) - емкость области пространственного заряда (ОПЗ) полупроводника в момент времени t₁,
q - заряд электрона,
А - площадь электродов,
k - постоянная Больцмана,
Т - температура,
N_ss - плотность поверхностных состояний,
E_o = E_c - kTln [σ_nU_nN_c (t₂-t₁)]/ln(t₂/t₁),
σ_n - cечение захвата для электронов,
V_n - их тепловая скорость,
N_c - эффективная плотность состояний в зоне проводимости,
Е_с - энергетическое положение дна зоны проводимости.ΔQ _i (V _i ) = -

q A k T ln (t ₂ / t ₁ ) N _ss (E _o ) where С _о is the dielectric capacity,
C _sc (t ₁ ) is the capacity of the space charge region (SCR) of the semiconductor at time t ₁ ,
q is the electron charge,
A is the area of the electrodes,
k is the Boltzmann constant,
T is the temperature
N _ss is the density of surface states,
E _o = E _c - kTln [σ _n U _n N _c (t ₂ -t ₁ )] / ln (t ₂ / t ₁ ),
σ _n is the capture cross section for electrons,
V _n is their thermal velocity,
N _c is the effective density of states in the conduction band,
E _with - the energy position of the bottom of the conduction band.

q A k T ln(t₂/t₁)N_ss(E_o) где ε_s - диэлектрическая проницаемость полупроводника,
w - ширина ОПЗ,
С(t₁) = C_oC_sc(t₁)/(C_o+C_sc(t₁))
На фиг. 2 приведены полученные при анализе выражений для Δ Q_i и C_i расчетные зависимости минимально определяемой концентрации поверхностных состояний N_ss для емкостного (2) и зарядового (1) способов измерений от отношения емкостей диэлектрика С_о и области пространственного заряда C_sc(t). Видно, что эти способы имеют примерно равную чувствительность при малых величинах отношения С_о/C_sc(t₁), а по мере увеличения этого отношения чувствительность, а соответственно и точность зарядовых измерений становится выше, чем у емкостных. Таким образом, использование зарядовых измерений может дать существенные преимущества, например, при исследовании МДП-структур с тонким диэлектриком, для которых С_о/C_sc(t₁) > 10.The value of the measured change in capacitance can be written as
ΔC _i = -

q A k T ln (t ₂ / t ₁ ) N _ss (E _o ) where ε _s is the dielectric constant of the semiconductor,
w is the width of the SCR,
C (t ₁ ) = C _o C _sc (t ₁ ) / (C _o + C _sc (t ₁ ))
In FIG. Figure 2 shows the calculated dependences of the minimum determined concentration of surface states N _ss for the capacitive (2) and charge (1) measurement methods obtained from the analysis of the expressions for Δ Q _i and C _i on the ratio of the capacitances of the dielectric С _о and the space charge region C _sc (t). It can be seen that these methods have approximately equal sensitivity at small values of the C _o / C _sc ratio (t ₁ ), and as this ratio increases, the sensitivity and, accordingly, the accuracy of charge measurements becomes higher than that of capacitive ones. Thus, the use of charge measurements can provide significant advantages, for example, in the study of MIS structures with a thin dielectric for which С _о / C _sc (t ₁ )> 10.

 4. In the proposed method, the measurements are carried out with the separation of the charge and discharge circuits, for example, using electronic keys that switch the test sample from the voltage source to the measuring circuit. This eliminates the errors that occur when using the prototype and associated with the influence of through current (current from the applied voltage) on the measurement results. Accordingly, the accuracy of determining the parameters increases.

 5. The circuit implementation of the proposed method is simpler than the prototype, since it does not use a high-frequency signal generator and a relatively complex system of its registration to find the differential capacitance.

 The authors do not know the technical solution, characterized by a combination of features of the proposed method, which ensure the achievement of new qualities that are absent in the known solutions.

 PRI me R. To implement the method, a device was developed and manufactured, the circuit of which is shown in FIG. 1.

As an integrator 2 (charge meter), an operational amplifier chip (KR544UD2A) with capacitive feedback (capacitance C _os ) was used, and key assemblies KR590KN2 were chosen for key production.

When charging the sample with voltage V _{i, the} key K ₁ closed, and K ₂ opened. The sample was connected to voltage source 1. After a period of time equal to the sample charging time τ, the key K _{1 was} opened, and K ₂ (synchronously with K ₁ ) was closed - the sample was connected to the input of the integrator 2. During the discharge of the sample to the integrator, the keys K ₃ and K _{5 was} maintained in the open state, and K ₄ was closed, and a charge flowing down from the sample was accumulated on the capacitance C _{1 of the} first memory cell. At the time from the beginning of the discharge, the key K _{4 was} opened, and the voltage from the capacitor C ₁ , proportional to the highest charge Q _i / V _i , through the emitter follower U ₁ remained supplied to the first input of the differential amplifier U ₃ .

Then the key K ₂ opened, and K ₁ closed - the voltage V _{i + 1} was applied to the sample. At the same time, when charging the sample, the key K _{3 was} closed and opened, bringing the measuring circuit to its initial state (zero voltage at the input of the integrator 2). After charging the sample with voltage V _{i + 1, the} key K ₁ opened, and K ₂ closed. During the discharge of the sample, the keys K ₃ and K _{4 were} maintained in the open state, and K ₅ was closed and a charge flowing down from the sample was accumulated on the capacitance C _{1 of the} second memory cell. At time t ₁ from the beginning of the discharge, the key K ₅ opened, and the voltage from the capacitance C ₁ proportional to the highest charge Q _{i + 1} (V _{i + 1} ) through the emitter follower U ₂ remained supplied to the second input of the differentiating amplifier U ₃ . At the output of U ₃ (input of the automation unit 5), we have a signal proportional to the desired value Δ Q = Q _{i + 1} (V _{i + 1} ) - Q _i (V _i ).

Repeating the measurement cycle controlled by the microcomputer 6, we find the dependence Δ Q (V _i ).

50

. Большая плотность поверхностных состояний на границе раздела а-C: H/Si исключала возможность использования для определения изгиба зон в Si на границе с а-С: H прототипа, так как измеренная с его помощью дифференциальная емкость не менялась от напряжения. На фиг. 3 показана зависимость СD(V), измеренная с помощью прототипа, а также найденная с помощью предлагаемого способа зависимость Δ Q_i(V_i). Строя зависимость ( Δ V/Δ Q_i)² и экстраполируя линейный участок, по величине отсечки на оси напряжений определяем величину потенциального барьера на границе раздела а-С:H/Si (в данном случае эта величина составляет ≈ 0,4 В, что совпадает с независимо определенной по кинетике фотоотклика величиной). Кроме того, дифференцируя полученную зависимость, можно определить профиль концентрации свободных носителей. Для исследованного образца зависимость

в интервале напряжений 0-1 В представляет собой прямую линию, а

= const , что свидетельствует о равномерном (однородном) легировании образца. Используя выражение
N_Д(x) =

получаем N_D = 4˙10¹⁵ см^-3.The proposed method and the fabricated installation were used to study the structure of Ni / a - C: H / Si with an amorphous carbon layer thickness of ≈ 50

fifty

. The high density of surface states at the a-C: H / Si interface excluded the possibility of using a prototype for determining the zone bending in Si at the a-C: H interface, since the differential capacitance measured with it did not change with voltage. In FIG. 3 shows the dependence CD (V), measured using the prototype, and also found using the proposed method, the dependence Δ Q _i (V _i ). Building the dependence (Δ V / Δ Q _i ) ² and extrapolating the linear section, we determine the potential barrier at the a-C: H / Si interface by the cutoff value on the stress axis (in this case, this value is ≈ 0.4 V, which coincides with the value independently determined by the kinetics of the photoresponse). In addition, by differentiating the obtained dependence, it is possible to determine the concentration profile of free carriers. For the studied sample, the dependence

in the voltage range 0-1 V is a straight line, and

= const, which indicates uniform (uniform) doping of the sample. Using expression
N _D (x) =

we get N _D = 4˙10 ¹⁵ cm ^-3 .

Claims (3)

1. METHOD FOR DETERMINING THE PARAMETERS OF SEMICONDUCTOR MATERIALS AND HETEROSTRUCTURES, including applying to the sample a sequence of pulses of bias voltage with an amplitude that varies linearly and with a given duration, measuring the dependence of the electric parameter on the applied voltage and determining the parameters of the structures using the obtained dependence, characterized in that, to expand the class of structures under study due to MDM and p ⁺ - i - n ^{+-structures,} improving the accuracy and sensitivity, and that the simplification of the circuit implementing the method, as the electrical parameter is measured charge Q, flowing from the sample to the moment of time t when the voltage is turned off after the passage of each pulse of amplitude V and a duration τ, and the parameters of the sample is determined using the dependence of the charge changes from changing pulse amplitude.  2. The method according to claim 1, characterized in that, in order to increase information content, change the duration t of voltage pulses and repeat the measurements of the flowing charge. 3. The method according to claim 1, characterized in that, in order to increase the information content, the time t of measuring charge runoff is selected from 10 ^{- 6} to 10 ² s.

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