Measurement Techniques, VoL 39, No. 11, 1996

MEASUREMENT DEPENDENCE

OF THE DISTRIBUTION OF THE EFFECTIVE

DENSITY IN THE BASE REGION

AND TEMPERATURE

CHARGE-CENTER

OF DIODE STRUCTURES

F. I. Manyakhin

UDC 621.382.2

A method of measuring the distribution of the effective charge-center density in the base of p-n-junctions and the temperature spectrum of the effective charge-center density is presented. Experimental results obtained using the method are discussed.

The form of the distribution of recombination centers and charge-carrier scattering in the active region of p - n-junctions or MOS-structures has a considerable effect on the parameters and characteristics of semiconductor devices. These centers can be electrically active or neutral depending on the energy position of the level of these centers in the forbidden-energy gap, the temperature, and the electric field in the space-charge region of the active layer. This fact, first, may be the reason for the change in the parameters and characteristics of semiconductor devices and, second, can be used to analyze the parameters of these centers. Below we consider a method of measuring the distribution of the effective charge-center density, i.e., the density of the overall charge of donor and acceptor centers in the weakly doped region of a p-n-junction or in the region of variation of the space charge of MOS-structures, and also a method of determining the parameters of the energy levels of the charge centers from the temperature-frequency spectrum of the effective charge-center density. The distribution of the effective charge-center density over the depth of the active region of emitters was measured by a capacitive method in [1, 2]. In this method a constant bias voltage, for which the barrier capacitance predominates, and a small variable signal, which is the product of two harmonic signals with frequencies of 601 and co2 where ~1 > > ~ are simultaneously applied to the p-n-junction being investigated, connected in the feedback circuit of an operational amplifier. At the output of the operational amplifier two harmonic signals at frequencies ~ 1 and 2~ 2 are detected by selective voltmeters. By changing the constant bias on the p-n-junction smoothly one can very the width of the space-charge region of the p-n-junction, in the region of which the effective charge-center density is measured. The barrier capacitance of the diode, connected in the feedback circuit of the operational amplifier, can be represented in the form of the barrier capacitance of the p-n-junction C b, determined by the constant bias, and an additional capacitance C e, which occurs due to the change in the width of the p-n-junction due to the action of the alternating signal, connected in series. The transfer constant of the alternating signal by the operational amplifier in this case will be

K=(c;' + c-;)q, where C O is the calibrated capacitance at the inverting input of the operational amplifier. The amplitude of the alternating voltage at the output of the operational amplifier is proportional to the input-signal amplitude' uout = Uin(C~/ C b + C0 / Ce),

(1)

where C b = eeoS/w; C e = 2eeoS[dw [ , S is the area of the p-n-junction, w is the width of the space-charge region for a specified constant bias, and dw is the change in the width of the space-charge region when a small alternating signal is applied. Translated from Izmeritel'naya Tekhnika, No. 11, pp. 49-52, November, 1996.

0543-1972/96/3911-1147515.00 9

Plenum Publishing Corporation

1147

Na - ND, 1017 cm-3

T = 300 K

W, /~m i

1

I

I

I

I

0,10

I

I

I

I

0,15

0,20

Fig. 1. Distribution of the effective charge-center density in the active region of ALl56 light-emitting diodes (gallium arsenide, doped with germanium) for two temperatures at a frequency ft = 176 kHz.

-ND, 1017 cm-3

f~ = 176 kH " 196 kI-Iz b T,K I

80

I

I

I

100

I

I

I

200

I

I

I

300

Fig. 2. Temperature dependence of the effective chargecenter density in the active region of an ALl56 IR-diode at two frequencies. The width of the space-charge region w and the effective charge-center density N w can be found, using relation (1), from the expressions W = (s~oS/C~)

U., / Uin ,

N = (CoUin / S) 2 / (2r~oSqUN)

(2)

Here U w and U N are the amplitudes of the harmonic signals at the output of the operational amplifier at the frequencies ~oI and 2~o2, respectively. When Uin = const we obtain w and N w from (2) by direct measurement of the electric signal U N across the additional capacitance at frequencies ~1 and 2o~2, respectively. In the traditional capacitance-voltage methods, the charge-

I148

center density, for example, in the weakly doped region of an abrupt asymmetrical p-n-junction, can be obtained from the relation [2] N., - C t , -

where AC is the change in the barrier capacitance when the bias voltage is changed by AU. When the bias voltage in actual p-n-structures is increased the change in the barrier capacitance is retarded, leading to an increase in the error of the measured effective charge-center density, particularly in strongly doped base regions of p - n junctions. This drawback does not occur in the method described here, and when it is used one can obtain a resolving power with respect to the depth of the distribution of the effective charge-center distribution of up to 10 -7 cm (dw), while the density sensitivity, with an appropriate choice of the parameters occurring in (2), can be up to 1019 cm -3, which is unattainable in practice using traditional methods. The most complete information on the parameters of the charge centers is obtained by analyzing the frequencytemperature curves of the distribution of the effective charge-center density. We will consider the possibilities of this method for which we will use the results obtained in [2]. Suppose that there are fixed acceptor-type centers in the base of an abrupt asymmetrical n + -p-structure, the charged state of which depends on the mutual position of their levels in the forbidden energy gap and the Fermi level. For sirr-,licity, we will confine ourselves to the presence of a single shallow and a single deep acceptor level with densities N s and N d, respectively, uniformly distributed over the volume. It was shown in [2] that the changes in the space-region for shallow and deep centers dw s and dw d, acted upon by a small alternating signal, are the same: dws = dw d = dw. The phase shifts ~ of the change of the charges of the shallow and deep centers with respect to the variable component of the bias voltage are also the same. Taking the above into account, the variable charge in the space-charge region can be expressed by the formula

Q = q S d w ( N s + N a ) I (1 + ttox)) exp [i (at *

~)],

where r is the time constant of the recharging of a deep center. The phase shift is related to the parameters of the charge centers in the space-charge region by the relation [2] ~o= aretg [(NaWdOrtI {Nsw [1 + (oT)21 + Nawd } We will write the relation for the additional capacitance as C = (2qS2seo)[N s + Ndl (1 + io~x)] I (CoUin)

and the amplitude of the voltage at the output of the operational amplifier at the frequency 2oJ2 in the form Us = (C~UIa / S) 2 / {2qczo (N s + Ndl (1 + (a)x)) ~}

(3)

An analysis of (3) shows that U y depends on the product o:r, i.e. on the inertia of the recharging of a deep center -the frequency of the measuring signal and the time taken for the deep center to recharge, which in turn depends on the temperature of the semiconductor. In this method the measured charge-center density is equal to the sum of the densities of the shallow centers at the edge of the space-charge region and of the deep centers in the region where the Fermi energy is the same as the energy of a deep level. Hence, the recharging time constant of a center with a deep level is = [~,.v~

+ p~) + %V,o (n~ + p~)]-~.

(4)

where a n, trp are the trapping cross sections of the charge carriers by a center, Van, Vdp are the thermal v.elocities of the electrons and holes, n 1 = Ncexp(-AEdc/kT), Pl = Nvexp(-AEdv/kT); AEdc, and AEdv are the position of a deep level of a charge center with respect to the edge of the corresponding band. 1149

N

ND, 1015 cm - 3

5-

o

T---I 0,10

I 0,20

I 0,40 w, p.m

0,30

Fig. 3. Distribution of the effective charge-center density in the surface region of a p-type silicon crystal doped with boron. N a - ND, 10 is ctn -3

T,K I

80

100

1

I

I

1

I

I

200

I

1

I

300

Fig. 4. Temperature dependence of the effective charge-center density in the surface layer of a silicon crystal doped with boron in the cross sections shown in Fig. 3.

As a consequence of the fact that n 1 and Pl depend practically exponentially on the temperature of the semiconductor, the center recharging time has a similar temperature dependence. Taking into account the fact that, as a rule, the level is not situated exactly in the middle of the forbidden-energy gap, while the recharging time is determined by the exponential function with the exponent due to the position of the deep level with respect to the nearest band, we will denote it by AEd/kT. We can then write z = A T - 2 e x p ( ~ E d I kT),

(5)

where A is a constant. Hence, when the temperature of the semiconductor changes, the inertia of the recharging of deep centers changes, which in turn affects the additional capacitance Ce when Uin = const. From the temperature dependence of the additional capacitance one can judge the parameters of the deep and shallow centers within the range of variation if the space-charge region, while the experimental data of the temperature scanning of the additional capacitance within the range of variation of the space-charge region enables one to determine the spatial distribution of the centers with deep and shallow levels. Extending this discussion to semiconductors with several types of centers of both the donor type N D and the acceptor type Na, we can write the following expression for the frequency-temperature dependence of the output signal at the frequency 2co2, which contains information on these levels: 1150

U,~ = (CoUi / S) 2 / l[2qc~: (N s + SNd, I (1 +(e'~,)~))][

(6)

Here j is the index of the level, N d is the density of deep centers of the j-th level, and rj is the time taken to recharge the j-th level. In (6) algebraic summation of the charges is carried out taking their signs into account. It follows from (6) that the frequency-temperature dependence of the effective charge-center density, determined by the signal voltage U N at the frequency 2o~2, is charge-center density, determined by the signal voltage U N at the frequency 2~ 2, is N(T, o~) = I{N~ + --,Na, / (1 + (co'~)2)11= (CoUin/S) z t (2qec~U,v) If the parameters of the deep centers are unknown, they can be determined by measuring the temperature dependence of the density at different frequencies. Taking into account the fact that half the drop in the equivalent charge-center density when there is inertia in recharging some level in the Nw(T, oJ) spectrum occurs when ~z = I, for the same center the following equality will hold: ~ r~ 2 exp ( & E l / k ~ ) =

o~'T-2 :t e x p ( ~ / / k

T2).

whence the position of the energy level is

The trapping cross section of charge carriers by this center, if we assume it to be independent of the temperature, can be found from the parameters, obtained from the spectrum at the temperature of the falling part when o~- = 1, taking relations (4) and (5) into account. Figure 1 shows the distribution of the effective charge-center density in the active p-region of commercial ALl56 IRdiodes based on n = GaAIAs(Te)/p = GaAs(Ge) heterostructures. When making the measurements two sinusoidal signals of amplitude up to 40 mV and frequencies of fl = 176-196 kHz and f2 = I0 kHz were applied to the input of an operational amplifier through a calibrated capacitance C O = 100 pF. The constant bias voltage used to measure the width of the spacecharge region was varied for a forward bias of up to 0.5 V (with a contact potential of 1.3 V) and for a reverse bias of up to the breakdown voltage of the p-n-junction. When measuring the frequency- temperature dependence of the effective charge-center density, the barrier capacitance C b was automatically ~ept constant over the whole range 300-77 K of the temperature variation to maintain a constant value of w. Under these conditions the depth resolving power of the layer in the ALl56 diodes amounted to dw = 5.10 -7 cm in the region where the charge-center density was about 1017 cm -3, with a change in the width of the space-charge region in a range of the order of 10 -5 cm, It is noteworthy that there is an increase in the acceptor-type effective charge-center density at T = 77 K to the left of the drop in the effective charge-center density distribution at 300 K, whereas in the remaining part of the active region, to the right of the distribution at T = 300 K, the effective charge-center density falls by almost two orders of magnitude. Obviously the increase in the effective charge-center density is connected with the fact that the compensation in the boundary region of the p-n-junction is due to the presence in it of a high density of donor centers, which become "detached" at 77 K at these measuring frequencies, It can be assumed that these donor centers can be either atoms of germanium, situated at the lattice points of the gallium sublattice, or arsenic vacancies, which occur during the process of reverse diffusion of arsenic in the epitaxial growth of the emitter layer. The second suggestion is the more likely one. In fact, the fall in the effective chargecenter density in the depth of the active layer indicates that the part played by donor centers in it is small and that an overall reduction in the acceptor-type effective charge-center density will be observed when the temperature falls. In Fig. 2 we show the temperature dependence of the effective charge-center density in the active layer of an ALl56 light-emitting diode for a fixed cross section (the initial DC bias voltage is zero) and at frequencies of ft = 176 kHz and 196 kHz. In the spectrum concerned one can clearly distinguish characteristic falling sections in the temperature ranges 300-180 K, 140-110 K and 95-77 K, and also a section where there is a small increase in the acceptor-type effective charge-center density in the 105-95 K temperature range. Taking into account the fact that at 300 V in the region investigated acceptor-type 1151

charge centers predominate, by interpreting the spectra obtained, making use of relation (3), it can be seen that in the active layer of p-GaAs doped with germanium there are at least four types of charge centers: three acceptor and one donor center, which exhibit their own inertial properties in the 77-300 K temperature range at these measuring frequencies. Processing of the spectra shown in Fig. 2 gave the following results. The drops a and b are characteristic for germanium acceptor centers, which, in the forbidden-energy gap, produce the levels E v = 0.07 eV and 0.04 with trapping cross-sections at, = 7.10 -19 cm 2 and 2. I0-18 cm 2. The sections c and d of the spectrum are obviously due to a donor center which is "disconnected" in the 10577 K temperature range, and this manifests itself in an increase in the acceptor-type effective charge-center density, and to an acceptor center the inertia of which manifests itself when there is a further reduction in temperature. An estimate of their energy position gives E c -- 0.18 eV for the donor center and E v + 0.17 eV for the acceptor center, and the calculated values of the trapping cross sections of the charge carriers by these centers is found to be anomalously high: 2-10- lo cm 2 and 3-10-9 cm 2, respectively. We can suggest, however, that the levels of donor and acceptor type centers are arranged spatially close to one another in the space-charge region where a high strength of the imbedded field is observed, and charge-carrier exchange occurs directly between centers when they are recharged. We also obtained the distribution (Fig. 3) and frequency-temperature spectrum (Fig. 4) of the effective charge-center density at fl = 176 kHz for the surface region of p-type silicon crystals grown by the Czochralski method, doped with boron, on the surface of which a Schottk'y barrier was formed in order to make measurements. A measurement of the effective charge-center density distribution showed that at a depth of about 0.2-0.3/~m from the surface there is a compensated layer whose properties are determined by donor-type centers with an energy position of E v + 0.3 eV and a trapping cross section a n = 5-10-14 cm 2. These parameters correspond to so-called donor-type K-centers, which are vacancy-oxygen-interstitial silicon atom complexes. As can be seen from Figs. 3 and 4, at a depth greater than 0.3/zm from the surface, where the effective-center density is determined by the doping impurity, the frequency-temperature spectrum of the effective charge-center density remains practically constant, which indicates that these donor-type centers are of considerably lower density. Hence, we have shown the possibilities of the method of measuring the effective charge-center density and its temperature dependence, based on a measurement of the parameters of the additional barrier capacitance which occurs when an alternating harmonic signal acts on it.

REFERENCES 1.

2.

1152

E. A. Ladygin, A. N. Kovalev, and F. 1. Manyakhin, Elektron. Tekh. Ser. 7, No. 1 (98), 81 (1984). L. S. Berman and A. A. Lebedev, Capacitance Spectroscopy of Deep Centers in Semiconductors [in Russian], Nauka, Leningrad (1981).